Research ArticleActive Disturbance Rejection Control of Valve-ControlledCylinder Servo Systems Based onMATLAB-AMESim Cosimulation

Wenxiao Guo1 Yanbin Zhao2 Ruiqin Li 1 Haigang Ding 2 and Jianwei Zhang3

1College of Mechatronics Engineering North University of China Taiyuan Shanxi China2School of Mechatronic Engineering China University of Mining and Technology Xuzhou Jiangsu China3Department of Informatics University of Hamburg Hamburg Germany

Correspondence should be addressed to Ruiqin Li liruiqinnuceducn and Haigang Ding haierdhg126com

Received 13 July 2020 Revised 27 July 2020 Accepted 31 August 2020 Published 11 September 2020

Academic Editor Jing Na

Copyright copy 2020Wenxiao Guo et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e valve-controlled cylinder position servo system has the advantages of large output force and large power As characteristics ofnonlinearity and uncertainty exist in the hydraulic servo system it is difficult for the traditional PID control to meet the re-quirements of high precision and controle active disturbance rejection control (ADRC) considers the uncertainty of the systemand external disturbances as the total disturbance In this paper the valve-controlled cylinder servo system is designed based onADRC its working principle is described and its mathematical model and cosimulation model based on MATLAB-AMESim areestablished In the case of constant load variable load and long pipeline the comparative simulation of ADRC and PID is carriedout e simulation results show that the ADRC can effectively suppress the disturbance of the internal parameter changes andexternal load changes of the hydraulic system and has strong robustness and high control accuracyis study provides a referencefor the application of ADRC in electrohydraulic servo systems

1 Introduction

e valve-controlled cylinder position servo system is acommon hydraulic power execution system with the ad-vantages of large output force large unit power volume ratioand so on It has been widely used in various fields Howeverthe electrohydraulic position servo control system is time-varying and nonlinear such as nonlinearity of pressure flowand frictional force of the servo valve It presents variousfeatures of time-varying parameters such as leakage coeffi-cient change of load and change of damping ratio Tra-ditional PID control strategy is simple but compared tosome nonlinear time-varying parameters of the system itcannot achieve precise positioning control In order toenhance the antijamming ability of electrohydraulic positionservo control system while improving the precision controlof the system experts and scholars have researched anumber of control strategies including adaptive control

sliding mode control and fuzzy control Considering thatthe electrohydraulic servo system is nonlinear Fang andGuan et al [1ndash5] proposed an adaptive back-stepping slidingmode controller e advantages of adaptive back-steppingcontrol strategy and sliding mode controller strategy can becombined to strengthen the systemrsquos tracking performanceZhang et al [6] proposed a multimodel robust adaptivecontrol theory According to the range of parametric un-certainties multiple identification models are designed andnonlinear robust items are added to the models to suppressthe influence of uncertain nonlinearities and improve therobustness and the transient response performance of thesystem Na et al [7 8] proposed a new control methodwithout using the back-stepping scheme and any functionapproximators ey also propose an alternative and simpleyet efficient estimation method to handle unknown dy-namics and external disturbances for motion control ofrobotic systems

HindawiComplexityVolume 2020 Article ID 9163675 10 pageshttpsdoiorg10115520209163675

In 1999 Han [9ndash11] proposed the active disturbancerejection control (ADRC) In view of the fact that theparameter turning of the original nonlinear ADRC iscomplicated and not convenient for practical industrialapplication Gao et al [12ndash17] simplified the nonlinearpart of the ADRC proposed LADRC that is convenient toset parameters and introduced the basic idea and prin-ciple of ADRC in detail ADRC control strategy does notdepend on the accurate mathematical model of controlledsystems and considers the uncertainty of the system andexternal disturbance as the total disturbance e ex-tended state observer is used for observing internal pa-rameter uncertainties and external disturbances so thatthe disturbances of the system are suppressed effectivelyFor systems with larger amount of uncertainties both indynamics and external disturbances the precise control isrealized with an ADRC controller It has been successfullyapplied in industrial process servo system control au-tomobile engine control aerospace and other fields andhas a good prospect of engineering application Howeverthere are few reports about ADRC used in hydraulic servosystems [18 19]

In this paper an active disturbance rejection controlstrategy is developed to address those electrohydraulicposition servo control systems with inherent nonlinearbehaviors and modeling uncertainties e simulationmodel of ADRC is established by using the MATLAB-AMESim cosimulation method in Simulink module li-brary e physical model of the valve-controlled cylinderposition servo system was established on AMESimsoftware According to the simulation results the ef-fectiveness of the control method is verified and theinfluence of controller parameters on the control effect isanalyzed

2 Mathematical Modeling

e valve-controlled cylinder position servo system studiedin this paper is shown in Figure 1 In this control system theservo valve is the control component and the cylinder is thedrive component e cylinder displacement is detectedusing a displacement sensor and fed back to the ADRCcontroller to control the opening of the servo valve so thatthe cylinder displacement is in the closed-loop control eload (mass block) on the right is driven by the hydrauliccylinder e main goal of this paper is to design thecontroller so that the hydraulic cylinder displacementcontrolled by the controller can track any given displace-ment as quickly as possible

e flow equation of the servo valve is

qL Cdωxv

PS minus PLsgn xv( 1113857

ρ

1113971

(1)

Here Cd is the valversquos port flow coefficient ω is the servovalversquos area gradient xv is the servo valversquos spool dis-placement PS is the servo valversquos inlet pressure PL is theload pressure and ρ is the oil density

sgn(xv) is the symbolic function as follows

sgn xv( 1113857 1 xv ge 0

minus1 xv lt 01113896 (2)

Because the response speed of the servo amplifier is fasterthan that of the hydraulic system the servo amplifier istreated as a proportional link to obtain the relationshipbetween spool displacement (xv) and control input (u) and

xv KvKsvu (3)

where Kv is the gain of controller Ksv is the gain of the servovalve and u is the input signal of controller

e flow continuity equation of the hydraulic cylinder is

qL AP

dxP

dt+ CtppL +

Vt

4βe

dpL

dt (4)

Here AP is the effective area of the piston in the hy-draulic cylinder xP is the piston displacement Ctp is thetotal leakage coefficient of the hydraulic cylinderCtp Cip + 05Cep and Vt is the total volume of the hy-draulic cylinder cavity

e force balance equation of the hydraulic cylinder andthe load is

APpL mt

d2xP

dt2 + Bp

dxP

dt+ KxP + FL (5)

Here mt is the total mass of the piston and the load Bp isthe viscous damping coefficient of the piston and the load K

is the spring stiffness and FL is the accidental load forceacting on the piston

Take the state variables x1 xp x2 _xp and x3 euroxpand they are displacement velocity and accelerationrespectively

e state space expression of the servo system is

_x1 x2

_x2 x3

_x3 a0x1 + a1x2 + a2x3 + bu + d

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)

where a0 minus4βeCtpmtvt

a1 minusK

mt

minus4βe

mtVt

A2p minus CtpBp1113872 1113873

a2 minusBp

mt

minus4βeCt

Vt

b 4ApβeCdωmtVt

ρ

radic

PS minus PLsgn xv( 1113857

1113969

d(t) minus_FL

mt

minus4βeCtpFL

mtVt

(7)

and y is the output for system position

2 Complexity

3 Design of ADRC

e core design of ADRC is to define an extended state takethe simple cascade integral form as the standard type treatthe parts of the system dynamic that are different from thestandard type (including the uncertainty and disturbance ofthe system) as the total disturbance (including internaldisturbance and external disturbance) and define the totaldisturbance into the extended state en by means of theextended state observer the total disturbance is estimatedand eliminated in real time so as to restore the controlledobject free of disturbance uncertainty and nonlinearity tothe standard integral series type and realize the control of thesystem ADRC makes the control system design fromcomplex to simple from abstract to intuitive

e linear ADRC consists of three parts tracking dif-ferentiator linear extended state observer and linear stateerror feedback control law as shown in Figure 2

e design of ADRC does not need to rely on the specificmathematical model of a controlled object It only needs toknow the relative order of the system For the design ofLADRC based on generalized controlled object formula (6)the following steps are arranged

31 Transition Process In this article ldquoArrange transitionrdquoand ldquoTrack-Differentiatorrdquo are combined to simplify thecontroller structure As shown in Figure 3 the valve-con-trolled cylinder position servo system is a third-order sys-tem so two tracking differentiators are used in series in thesimulation process

Arrange the transition process according to the set valuex0 as follows

fh fhan x1 minus x0 x2 r h( 1113857

x1 x1 + hx2

x2 x2 + hfh

⎧⎪⎪⎨

⎪⎪⎩(8)

Define the fast-optimal control synthesis function ofequation (9) as

fh fhan x1 minus x0 x2 r h0( 1113857 (9)

e realization of fh is shown in the following equation

d rh0

d0 h0d

y x1 minus x0 + h0x2

a0

d2

+ 8r|y|

1113969

a

x2 +a0 + d( 1113857

2sign(y) |y|gtd0

x2 +y

h0 |y|led0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

fhan minus

rsign(a) |a|gtd

ra

d |a|led

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)

Here h0 is the filter factor h is the simulation step lengthand is related to the sampling frequency of the system x0 isthe expected displacement signal and r is the velocity factorwhich determines the speed of tracking expected displace-ment signal

32 Extended State Observer e extended state observer ofthe system is established by tracking and estimating systemstate and disturbance with system output and input

_x3 a0x1 + a1x2 + a2x3 + bu + d (11)

A B

Load

Servo valve

Cylinder

P T

Flp2p1

m

Figure 1 Model of valve-controlled cylinder position servo systems

Complexity 3

Here it is denoted that _x3 f(x1 x2 x3 d) + bu toobtain the generalized controlled plant model

_x1 x2

_x2 x3

_x3 f x1 x2 x3 d( 1113857 + bu

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)

e real-time action of f(x1 x2 x3 d) on the system isexpanded to a new state variable x4 denoted asx4 f(x1 x2 x3 d) and denoted as _x4 w(t) en thesystem (12) can be expanded into a new system as follows

_x1 x2

_x2 x3

_x3 x4 + bu

_x4 w(t)

y x1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)

A linear state observer is established for the extendedsystem

e z1 minus y

z1 z1 + h z2 minus β01e( 1113857

z2 z2 + h z3 minus β02e( 1113857

z3 z3 + h z4 minus β03e + bu( 1113857

z4 z4 + h minusβ04e( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)

where e is the output error State observer (14) is called theextended state observer (ESO) of system (10) the variable x4is called the extended state and the parameter of the ESO is

β01 1h

β02 13h

2

β04 5

133h4

β03 2

82h3

(15)

is set of parameters is ldquoinheritedrdquo for objects of thefourth order and below and is not limited by the estimateddisturbance amplitude c [11]

33 Feedback Law of State Error Linear state error feedback(LSEF) compensates the system disturbance through stateerror feedback In this system LSEF is designed as follows

e1 x1 minus z1

e2 x2 minus z2

e3 x3 minus z3

u0 α11e1 + α12e2 + α13e3

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(16)

where xi(i 1 2 3) is the output value of the track differ-entiator zi(i 1 2 3 4) is the output value of the ESOei(i 1 2 3) is the state error α1i(i 1 2 3) is the gaincoefficient of the controller and u0 is the linear errorfeedback control quantity Considering the disturbanceerror of the system the final output of linear ADRC isobtained by compensating u0

u u0 minusz4(t)

b0 (17)

Controller Controlled system

Extended stateobserver

Control signal Output

Disturbanceestimation

State estimation

ReferenceExternal

disturbance

Figure 2 Structure of ADRC

Step signal

Sine wave signal

Switch S-functionScope

TDTD

Figure 3 Schematic of the tracking differentiator

4 Complexity

34 Parameter Tuning e ADRC controller has manyparameters to be tuned According to the functions of thetracking differentiator the ESO and the feedback controllaw the parameters can be set independently according tothe ldquoseparation principlerdquo

(1) e parameter r mainly affects the performance ofthe tracking differentiator When r becomes largerthe response of the system becomes faster and thetracking accuracy becomes higher but the overshootof the system becomes larger as well When r is smallthe tracking speed of the system will become veryslow even unable to track the reference input signal

(2) e increase of β01 and β02 in a certain range has nogreat influence on the control effect of the systembut when β01 is large the system is prone to divergentoscillation and when β01 is small the tracking effectof the system will become worse so β01 1h isgenerally adopted Larger β03 will produce high-frequency noise signals resulting in poor systemcontrol but smaller β03 will increase the number ofoscillations and increase the amplitude so generallyβ03 282h3 when β04 decreases the tracking speedof the system slows down the transition processtends to be stable but it is easy to cause a large phaselag so β04 5133h4

(3) b0 is the only variable related to the controlled systemin the whole controller e choice of different b0values is equivalent to the change of the total dis-turbance value in different ranges that is thecompensation component will also produce corre-sponding changes e gain α11 of the controlleraffect the corresponding rapidity of the system butovershoot occurs when α11 is too large An appro-priate controller gain α12 will reduce overshoot

4 Cosimulation Modeling

Because the electrohydraulic position servo control systemshave inherent nonlinear behaviors and modeling uncer-tainties it is difficult to establish an accurate mathematicalmodel so the cosimulation platform using MATLAB andAMESim is applied in this work e mechanical and hy-draulic parts are built in AMESim and the control part ismodeled by MATLAB-Simulink By using AMESimrsquos in-terface technology to Simulink and combining two excellentprofessional simulation tools AMESimrsquos outstanding fluidmechanical simulation performance can be brought intoplay and Simulinkrsquos powerful numerical processing capa-bility can be utilized to achieve more perfect complementaryeffects

e cosimulation principle of the valve-controlled cyl-inder servo system in ADRC based on MATLAB-AMESimplatform is shown in Figure 4 e concrete realizationprocess of cosimulation between AMESim and Simulink isas follows First create an interface through the interfacemenu in the AMESim to connect Simulink Next completethe submodel mode and parameter mode setting Finallyrun the hydraulic system model to generate S-function for

Simulink A cosimulation model built on MATLAB-AMESim platform is shown in Figure 5 nad main pa-rameters of the system are listed in Table 1

ADRC parameters are set as follows r 025 h 0011and T 0011

Observer parameters are

β0i 1h

13h

22

82h35

133h41113890 1113891 (18)

Controller parameters are

b0 50

α1i 400 0062 011113858 1113859(19)

PID control is the most common and effective controlmethod in engineering and its controller is designed asfollows

u Kp e + Ki 1113946t

0edt + Kd

de

dt (20)

where Kp is the proportional gain Ki is the integral gain Kd

is the differential gain and e is the error ose parametersare tuned to the best after many tests In this paper ADRCand PID are compared and analyzed

5 Simulation Results and Analysis

In order to analyze the dynamic performances of the systemin ADRC the following three simulation scenarios aredesigned in this section (1) dynamic responses underconstant load (2) dynamic responses under variable load(3) dynamic responses under long pipeline Comparativeanalyses of the control characteristics of ADRC and PID aremade

51DynamicResponses underConstantLoad When the loadforce is constant step responses of the system in ADRC andPID are shown in Figure 6 where reference displacement ofthe hydraulic cylinder is 200mm Under this condition theparameters of PID are set as follows Kp 200 Ki 105 andKd 25 Figure 6(a) shows that under the ADRC and PIDthe maximum rise time is 05 s and 1 s respectively themaximum adjustment time is 12 s and 5 s respectively andthe maximum overshoot quantity is 1 and 95 respec-tively Figure 6(b) shows that compared to PID the spooldisplacement under the ADRC changes smoothly during theprocess of opening there is no impact and the maximumopening is about 80 larger

Figure 7 indicates sinusoidal response under ADRC andPID It shows that the system in ADRC can accurately trackthe reference signal with smaller phase lag In the initialstage the displacement of the spool in ADRC is large so thatthe hydraulic cylinder can quickly refer to the signal enthe spool displacement is basically the same as the PIDcontrol In the commutation phase the overshoot of thehydraulic cylinder under ADRC control is smaller thanunder PID control

Complexity 5

e step response and sinusoidal response show thatADRC has more advantages than PID and the system inADRC has fast dynamic response and high controlaccuracy

52DynamicResponses underVariable Load In practice theload usually changes so it is necessary to investigate thedynamic characteristics of the control system under variableload In this part the load force is variable in the simulation

Reference ADRC Servo valve Driving cylinder Load

Stroke sensorAMESimMATLAB-Simulink

Figure 4 Schematic diagram of cosimulation principle

Cylinder

Load

X u

Servo valueController

in Simulink

Pump source MOT

A B

P T

MF

X

(a)

AMESimMATLAB

TDTD Control

Z1

Z2

Z3

Z4

ESO

Scope

S-function

u xSimcenter Amesimmodel_

(b)

Figure 5 Cosimulation model (a) Hydraulic system model in AMESim (b) ADRC model in MATLAB

6 Complexity

1 2 3 4 50Time (s)

ADRCPIDRreference

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a)

1 2 3 4 50Time (s)

00

02

06

08

10

Serv

o va

lve s

pool

pos

ition

()

ADRCPID

(b)

Figure 6 Step responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

250

200

150

100

50

0

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

05

04

02

03

01

00

-01

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

ADRCPID

(b)

Figure 7 Sinusoidal responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

Table 1 Main parameters of the system

Parameters ValueCylinder diameter 4563mmLoad mass 100 kgMotor speed 1500 rminPump delivery 100mLrRelief pressure 350 barLoad spring rate 10000Nm

Complexity 7

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

3 Design of ADRC

e core design of ADRC is to define an extended state takethe simple cascade integral form as the standard type treatthe parts of the system dynamic that are different from thestandard type (including the uncertainty and disturbance ofthe system) as the total disturbance (including internaldisturbance and external disturbance) and define the totaldisturbance into the extended state en by means of theextended state observer the total disturbance is estimatedand eliminated in real time so as to restore the controlledobject free of disturbance uncertainty and nonlinearity tothe standard integral series type and realize the control of thesystem ADRC makes the control system design fromcomplex to simple from abstract to intuitive

e linear ADRC consists of three parts tracking dif-ferentiator linear extended state observer and linear stateerror feedback control law as shown in Figure 2

e design of ADRC does not need to rely on the specificmathematical model of a controlled object It only needs toknow the relative order of the system For the design ofLADRC based on generalized controlled object formula (6)the following steps are arranged

31 Transition Process In this article ldquoArrange transitionrdquoand ldquoTrack-Differentiatorrdquo are combined to simplify thecontroller structure As shown in Figure 3 the valve-con-trolled cylinder position servo system is a third-order sys-tem so two tracking differentiators are used in series in thesimulation process

Arrange the transition process according to the set valuex0 as follows

fh fhan x1 minus x0 x2 r h( 1113857

x1 x1 + hx2

x2 x2 + hfh

⎧⎪⎪⎨

⎪⎪⎩(8)

Define the fast-optimal control synthesis function ofequation (9) as

fh fhan x1 minus x0 x2 r h0( 1113857 (9)

e realization of fh is shown in the following equation

d rh0

d0 h0d

y x1 minus x0 + h0x2

a0

d2

+ 8r|y|

1113969

a

x2 +a0 + d( 1113857

2sign(y) |y|gtd0

x2 +y

h0 |y|led0

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

fhan minus

rsign(a) |a|gtd

ra

d |a|led

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(10)

Here h0 is the filter factor h is the simulation step lengthand is related to the sampling frequency of the system x0 isthe expected displacement signal and r is the velocity factorwhich determines the speed of tracking expected displace-ment signal

32 Extended State Observer e extended state observer ofthe system is established by tracking and estimating systemstate and disturbance with system output and input

_x3 a0x1 + a1x2 + a2x3 + bu + d (11)

A B

Load

Servo valve

Cylinder

P T

Flp2p1

m

Figure 1 Model of valve-controlled cylinder position servo systems

Complexity 3

Here it is denoted that _x3 f(x1 x2 x3 d) + bu toobtain the generalized controlled plant model

_x1 x2

_x2 x3

_x3 f x1 x2 x3 d( 1113857 + bu

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)

e real-time action of f(x1 x2 x3 d) on the system isexpanded to a new state variable x4 denoted asx4 f(x1 x2 x3 d) and denoted as _x4 w(t) en thesystem (12) can be expanded into a new system as follows

_x1 x2

_x2 x3

_x3 x4 + bu

_x4 w(t)

y x1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)

A linear state observer is established for the extendedsystem

e z1 minus y

z1 z1 + h z2 minus β01e( 1113857

z2 z2 + h z3 minus β02e( 1113857

z3 z3 + h z4 minus β03e + bu( 1113857

z4 z4 + h minusβ04e( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)

where e is the output error State observer (14) is called theextended state observer (ESO) of system (10) the variable x4is called the extended state and the parameter of the ESO is

β01 1h

β02 13h

2

β04 5

133h4

β03 2

82h3

(15)

is set of parameters is ldquoinheritedrdquo for objects of thefourth order and below and is not limited by the estimateddisturbance amplitude c [11]

33 Feedback Law of State Error Linear state error feedback(LSEF) compensates the system disturbance through stateerror feedback In this system LSEF is designed as follows

e1 x1 minus z1

e2 x2 minus z2

e3 x3 minus z3

u0 α11e1 + α12e2 + α13e3

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(16)

where xi(i 1 2 3) is the output value of the track differ-entiator zi(i 1 2 3 4) is the output value of the ESOei(i 1 2 3) is the state error α1i(i 1 2 3) is the gaincoefficient of the controller and u0 is the linear errorfeedback control quantity Considering the disturbanceerror of the system the final output of linear ADRC isobtained by compensating u0

u u0 minusz4(t)

b0 (17)

Controller Controlled system

Extended stateobserver

Control signal Output

Disturbanceestimation

State estimation

ReferenceExternal

disturbance

Figure 2 Structure of ADRC

Step signal

Sine wave signal

Switch S-functionScope

TDTD

Figure 3 Schematic of the tracking differentiator

4 Complexity

34 Parameter Tuning e ADRC controller has manyparameters to be tuned According to the functions of thetracking differentiator the ESO and the feedback controllaw the parameters can be set independently according tothe ldquoseparation principlerdquo

(1) e parameter r mainly affects the performance ofthe tracking differentiator When r becomes largerthe response of the system becomes faster and thetracking accuracy becomes higher but the overshootof the system becomes larger as well When r is smallthe tracking speed of the system will become veryslow even unable to track the reference input signal

(2) e increase of β01 and β02 in a certain range has nogreat influence on the control effect of the systembut when β01 is large the system is prone to divergentoscillation and when β01 is small the tracking effectof the system will become worse so β01 1h isgenerally adopted Larger β03 will produce high-frequency noise signals resulting in poor systemcontrol but smaller β03 will increase the number ofoscillations and increase the amplitude so generallyβ03 282h3 when β04 decreases the tracking speedof the system slows down the transition processtends to be stable but it is easy to cause a large phaselag so β04 5133h4

(3) b0 is the only variable related to the controlled systemin the whole controller e choice of different b0values is equivalent to the change of the total dis-turbance value in different ranges that is thecompensation component will also produce corre-sponding changes e gain α11 of the controlleraffect the corresponding rapidity of the system butovershoot occurs when α11 is too large An appro-priate controller gain α12 will reduce overshoot

4 Cosimulation Modeling

Because the electrohydraulic position servo control systemshave inherent nonlinear behaviors and modeling uncer-tainties it is difficult to establish an accurate mathematicalmodel so the cosimulation platform using MATLAB andAMESim is applied in this work e mechanical and hy-draulic parts are built in AMESim and the control part ismodeled by MATLAB-Simulink By using AMESimrsquos in-terface technology to Simulink and combining two excellentprofessional simulation tools AMESimrsquos outstanding fluidmechanical simulation performance can be brought intoplay and Simulinkrsquos powerful numerical processing capa-bility can be utilized to achieve more perfect complementaryeffects

e cosimulation principle of the valve-controlled cyl-inder servo system in ADRC based on MATLAB-AMESimplatform is shown in Figure 4 e concrete realizationprocess of cosimulation between AMESim and Simulink isas follows First create an interface through the interfacemenu in the AMESim to connect Simulink Next completethe submodel mode and parameter mode setting Finallyrun the hydraulic system model to generate S-function for

Simulink A cosimulation model built on MATLAB-AMESim platform is shown in Figure 5 nad main pa-rameters of the system are listed in Table 1

ADRC parameters are set as follows r 025 h 0011and T 0011

Observer parameters are

β0i 1h

13h

22

82h35

133h41113890 1113891 (18)

Controller parameters are

b0 50

α1i 400 0062 011113858 1113859(19)

PID control is the most common and effective controlmethod in engineering and its controller is designed asfollows

u Kp e + Ki 1113946t

0edt + Kd

de

dt (20)

where Kp is the proportional gain Ki is the integral gain Kd

is the differential gain and e is the error ose parametersare tuned to the best after many tests In this paper ADRCand PID are compared and analyzed

5 Simulation Results and Analysis

In order to analyze the dynamic performances of the systemin ADRC the following three simulation scenarios aredesigned in this section (1) dynamic responses underconstant load (2) dynamic responses under variable load(3) dynamic responses under long pipeline Comparativeanalyses of the control characteristics of ADRC and PID aremade

51DynamicResponses underConstantLoad When the loadforce is constant step responses of the system in ADRC andPID are shown in Figure 6 where reference displacement ofthe hydraulic cylinder is 200mm Under this condition theparameters of PID are set as follows Kp 200 Ki 105 andKd 25 Figure 6(a) shows that under the ADRC and PIDthe maximum rise time is 05 s and 1 s respectively themaximum adjustment time is 12 s and 5 s respectively andthe maximum overshoot quantity is 1 and 95 respec-tively Figure 6(b) shows that compared to PID the spooldisplacement under the ADRC changes smoothly during theprocess of opening there is no impact and the maximumopening is about 80 larger

Figure 7 indicates sinusoidal response under ADRC andPID It shows that the system in ADRC can accurately trackthe reference signal with smaller phase lag In the initialstage the displacement of the spool in ADRC is large so thatthe hydraulic cylinder can quickly refer to the signal enthe spool displacement is basically the same as the PIDcontrol In the commutation phase the overshoot of thehydraulic cylinder under ADRC control is smaller thanunder PID control

Complexity 5

e step response and sinusoidal response show thatADRC has more advantages than PID and the system inADRC has fast dynamic response and high controlaccuracy

52DynamicResponses underVariable Load In practice theload usually changes so it is necessary to investigate thedynamic characteristics of the control system under variableload In this part the load force is variable in the simulation

Reference ADRC Servo valve Driving cylinder Load

Stroke sensorAMESimMATLAB-Simulink

Figure 4 Schematic diagram of cosimulation principle

Cylinder

Load

X u

Servo valueController

in Simulink

Pump source MOT

A B

P T

MF

X

(a)

AMESimMATLAB

TDTD Control

Z1

Z2

Z3

Z4

ESO

Scope

S-function

u xSimcenter Amesimmodel_

(b)

Figure 5 Cosimulation model (a) Hydraulic system model in AMESim (b) ADRC model in MATLAB

6 Complexity

1 2 3 4 50Time (s)

ADRCPIDRreference

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a)

1 2 3 4 50Time (s)

00

02

06

08

10

Serv

o va

lve s

pool

pos

ition

()

ADRCPID

(b)

Figure 6 Step responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

250

200

150

100

50

0

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

05

04

02

03

01

00

-01

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

ADRCPID

(b)

Figure 7 Sinusoidal responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

Table 1 Main parameters of the system

Parameters ValueCylinder diameter 4563mmLoad mass 100 kgMotor speed 1500 rminPump delivery 100mLrRelief pressure 350 barLoad spring rate 10000Nm

Complexity 7

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

Here it is denoted that _x3 f(x1 x2 x3 d) + bu toobtain the generalized controlled plant model

_x1 x2

_x2 x3

_x3 f x1 x2 x3 d( 1113857 + bu

y x1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(12)

e real-time action of f(x1 x2 x3 d) on the system isexpanded to a new state variable x4 denoted asx4 f(x1 x2 x3 d) and denoted as _x4 w(t) en thesystem (12) can be expanded into a new system as follows

_x1 x2

_x2 x3

_x3 x4 + bu

_x4 w(t)

y x1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(13)

A linear state observer is established for the extendedsystem

e z1 minus y

z1 z1 + h z2 minus β01e( 1113857

z2 z2 + h z3 minus β02e( 1113857

z3 z3 + h z4 minus β03e + bu( 1113857

z4 z4 + h minusβ04e( 1113857

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(14)

where e is the output error State observer (14) is called theextended state observer (ESO) of system (10) the variable x4is called the extended state and the parameter of the ESO is

β01 1h

β02 13h

2

β04 5

133h4

β03 2

82h3

(15)

is set of parameters is ldquoinheritedrdquo for objects of thefourth order and below and is not limited by the estimateddisturbance amplitude c [11]

33 Feedback Law of State Error Linear state error feedback(LSEF) compensates the system disturbance through stateerror feedback In this system LSEF is designed as follows

e1 x1 minus z1

e2 x2 minus z2

e3 x3 minus z3

u0 α11e1 + α12e2 + α13e3

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(16)

where xi(i 1 2 3) is the output value of the track differ-entiator zi(i 1 2 3 4) is the output value of the ESOei(i 1 2 3) is the state error α1i(i 1 2 3) is the gaincoefficient of the controller and u0 is the linear errorfeedback control quantity Considering the disturbanceerror of the system the final output of linear ADRC isobtained by compensating u0

u u0 minusz4(t)

b0 (17)

Controller Controlled system

Extended stateobserver

Control signal Output

Disturbanceestimation

State estimation

ReferenceExternal

disturbance

Figure 2 Structure of ADRC

Step signal

Sine wave signal

Switch S-functionScope

TDTD

Figure 3 Schematic of the tracking differentiator

4 Complexity

34 Parameter Tuning e ADRC controller has manyparameters to be tuned According to the functions of thetracking differentiator the ESO and the feedback controllaw the parameters can be set independently according tothe ldquoseparation principlerdquo

(1) e parameter r mainly affects the performance ofthe tracking differentiator When r becomes largerthe response of the system becomes faster and thetracking accuracy becomes higher but the overshootof the system becomes larger as well When r is smallthe tracking speed of the system will become veryslow even unable to track the reference input signal

(2) e increase of β01 and β02 in a certain range has nogreat influence on the control effect of the systembut when β01 is large the system is prone to divergentoscillation and when β01 is small the tracking effectof the system will become worse so β01 1h isgenerally adopted Larger β03 will produce high-frequency noise signals resulting in poor systemcontrol but smaller β03 will increase the number ofoscillations and increase the amplitude so generallyβ03 282h3 when β04 decreases the tracking speedof the system slows down the transition processtends to be stable but it is easy to cause a large phaselag so β04 5133h4

(3) b0 is the only variable related to the controlled systemin the whole controller e choice of different b0values is equivalent to the change of the total dis-turbance value in different ranges that is thecompensation component will also produce corre-sponding changes e gain α11 of the controlleraffect the corresponding rapidity of the system butovershoot occurs when α11 is too large An appro-priate controller gain α12 will reduce overshoot

4 Cosimulation Modeling

Because the electrohydraulic position servo control systemshave inherent nonlinear behaviors and modeling uncer-tainties it is difficult to establish an accurate mathematicalmodel so the cosimulation platform using MATLAB andAMESim is applied in this work e mechanical and hy-draulic parts are built in AMESim and the control part ismodeled by MATLAB-Simulink By using AMESimrsquos in-terface technology to Simulink and combining two excellentprofessional simulation tools AMESimrsquos outstanding fluidmechanical simulation performance can be brought intoplay and Simulinkrsquos powerful numerical processing capa-bility can be utilized to achieve more perfect complementaryeffects

e cosimulation principle of the valve-controlled cyl-inder servo system in ADRC based on MATLAB-AMESimplatform is shown in Figure 4 e concrete realizationprocess of cosimulation between AMESim and Simulink isas follows First create an interface through the interfacemenu in the AMESim to connect Simulink Next completethe submodel mode and parameter mode setting Finallyrun the hydraulic system model to generate S-function for

Simulink A cosimulation model built on MATLAB-AMESim platform is shown in Figure 5 nad main pa-rameters of the system are listed in Table 1

ADRC parameters are set as follows r 025 h 0011and T 0011

Observer parameters are

β0i 1h

13h

22

82h35

133h41113890 1113891 (18)

Controller parameters are

b0 50

α1i 400 0062 011113858 1113859(19)

PID control is the most common and effective controlmethod in engineering and its controller is designed asfollows

u Kp e + Ki 1113946t

0edt + Kd

de

dt (20)

where Kp is the proportional gain Ki is the integral gain Kd

is the differential gain and e is the error ose parametersare tuned to the best after many tests In this paper ADRCand PID are compared and analyzed

5 Simulation Results and Analysis

In order to analyze the dynamic performances of the systemin ADRC the following three simulation scenarios aredesigned in this section (1) dynamic responses underconstant load (2) dynamic responses under variable load(3) dynamic responses under long pipeline Comparativeanalyses of the control characteristics of ADRC and PID aremade

51DynamicResponses underConstantLoad When the loadforce is constant step responses of the system in ADRC andPID are shown in Figure 6 where reference displacement ofthe hydraulic cylinder is 200mm Under this condition theparameters of PID are set as follows Kp 200 Ki 105 andKd 25 Figure 6(a) shows that under the ADRC and PIDthe maximum rise time is 05 s and 1 s respectively themaximum adjustment time is 12 s and 5 s respectively andthe maximum overshoot quantity is 1 and 95 respec-tively Figure 6(b) shows that compared to PID the spooldisplacement under the ADRC changes smoothly during theprocess of opening there is no impact and the maximumopening is about 80 larger

Figure 7 indicates sinusoidal response under ADRC andPID It shows that the system in ADRC can accurately trackthe reference signal with smaller phase lag In the initialstage the displacement of the spool in ADRC is large so thatthe hydraulic cylinder can quickly refer to the signal enthe spool displacement is basically the same as the PIDcontrol In the commutation phase the overshoot of thehydraulic cylinder under ADRC control is smaller thanunder PID control

Complexity 5

e step response and sinusoidal response show thatADRC has more advantages than PID and the system inADRC has fast dynamic response and high controlaccuracy

52DynamicResponses underVariable Load In practice theload usually changes so it is necessary to investigate thedynamic characteristics of the control system under variableload In this part the load force is variable in the simulation

Reference ADRC Servo valve Driving cylinder Load

Stroke sensorAMESimMATLAB-Simulink

Figure 4 Schematic diagram of cosimulation principle

Cylinder

Load

X u

Servo valueController

in Simulink

Pump source MOT

A B

P T

MF

X

(a)

AMESimMATLAB

TDTD Control

Z1

Z2

Z3

Z4

ESO

Scope

S-function

u xSimcenter Amesimmodel_

(b)

Figure 5 Cosimulation model (a) Hydraulic system model in AMESim (b) ADRC model in MATLAB

6 Complexity

1 2 3 4 50Time (s)

ADRCPIDRreference

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a)

1 2 3 4 50Time (s)

00

02

06

08

10

Serv

o va

lve s

pool

pos

ition

()

ADRCPID

(b)

Figure 6 Step responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

250

200

150

100

50

0

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

05

04

02

03

01

00

-01

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

ADRCPID

(b)

Figure 7 Sinusoidal responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

Table 1 Main parameters of the system

Parameters ValueCylinder diameter 4563mmLoad mass 100 kgMotor speed 1500 rminPump delivery 100mLrRelief pressure 350 barLoad spring rate 10000Nm

Complexity 7

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

34 Parameter Tuning e ADRC controller has manyparameters to be tuned According to the functions of thetracking differentiator the ESO and the feedback controllaw the parameters can be set independently according tothe ldquoseparation principlerdquo

(1) e parameter r mainly affects the performance ofthe tracking differentiator When r becomes largerthe response of the system becomes faster and thetracking accuracy becomes higher but the overshootof the system becomes larger as well When r is smallthe tracking speed of the system will become veryslow even unable to track the reference input signal

(2) e increase of β01 and β02 in a certain range has nogreat influence on the control effect of the systembut when β01 is large the system is prone to divergentoscillation and when β01 is small the tracking effectof the system will become worse so β01 1h isgenerally adopted Larger β03 will produce high-frequency noise signals resulting in poor systemcontrol but smaller β03 will increase the number ofoscillations and increase the amplitude so generallyβ03 282h3 when β04 decreases the tracking speedof the system slows down the transition processtends to be stable but it is easy to cause a large phaselag so β04 5133h4

(3) b0 is the only variable related to the controlled systemin the whole controller e choice of different b0values is equivalent to the change of the total dis-turbance value in different ranges that is thecompensation component will also produce corre-sponding changes e gain α11 of the controlleraffect the corresponding rapidity of the system butovershoot occurs when α11 is too large An appro-priate controller gain α12 will reduce overshoot

4 Cosimulation Modeling

Because the electrohydraulic position servo control systemshave inherent nonlinear behaviors and modeling uncer-tainties it is difficult to establish an accurate mathematicalmodel so the cosimulation platform using MATLAB andAMESim is applied in this work e mechanical and hy-draulic parts are built in AMESim and the control part ismodeled by MATLAB-Simulink By using AMESimrsquos in-terface technology to Simulink and combining two excellentprofessional simulation tools AMESimrsquos outstanding fluidmechanical simulation performance can be brought intoplay and Simulinkrsquos powerful numerical processing capa-bility can be utilized to achieve more perfect complementaryeffects

e cosimulation principle of the valve-controlled cyl-inder servo system in ADRC based on MATLAB-AMESimplatform is shown in Figure 4 e concrete realizationprocess of cosimulation between AMESim and Simulink isas follows First create an interface through the interfacemenu in the AMESim to connect Simulink Next completethe submodel mode and parameter mode setting Finallyrun the hydraulic system model to generate S-function for

Simulink A cosimulation model built on MATLAB-AMESim platform is shown in Figure 5 nad main pa-rameters of the system are listed in Table 1

ADRC parameters are set as follows r 025 h 0011and T 0011

Observer parameters are

β0i 1h

13h

22

82h35

133h41113890 1113891 (18)

Controller parameters are

b0 50

α1i 400 0062 011113858 1113859(19)

PID control is the most common and effective controlmethod in engineering and its controller is designed asfollows

u Kp e + Ki 1113946t

0edt + Kd

de

dt (20)

where Kp is the proportional gain Ki is the integral gain Kd

is the differential gain and e is the error ose parametersare tuned to the best after many tests In this paper ADRCand PID are compared and analyzed

5 Simulation Results and Analysis

In order to analyze the dynamic performances of the systemin ADRC the following three simulation scenarios aredesigned in this section (1) dynamic responses underconstant load (2) dynamic responses under variable load(3) dynamic responses under long pipeline Comparativeanalyses of the control characteristics of ADRC and PID aremade

51DynamicResponses underConstantLoad When the loadforce is constant step responses of the system in ADRC andPID are shown in Figure 6 where reference displacement ofthe hydraulic cylinder is 200mm Under this condition theparameters of PID are set as follows Kp 200 Ki 105 andKd 25 Figure 6(a) shows that under the ADRC and PIDthe maximum rise time is 05 s and 1 s respectively themaximum adjustment time is 12 s and 5 s respectively andthe maximum overshoot quantity is 1 and 95 respec-tively Figure 6(b) shows that compared to PID the spooldisplacement under the ADRC changes smoothly during theprocess of opening there is no impact and the maximumopening is about 80 larger

Figure 7 indicates sinusoidal response under ADRC andPID It shows that the system in ADRC can accurately trackthe reference signal with smaller phase lag In the initialstage the displacement of the spool in ADRC is large so thatthe hydraulic cylinder can quickly refer to the signal enthe spool displacement is basically the same as the PIDcontrol In the commutation phase the overshoot of thehydraulic cylinder under ADRC control is smaller thanunder PID control

Complexity 5

e step response and sinusoidal response show thatADRC has more advantages than PID and the system inADRC has fast dynamic response and high controlaccuracy

52DynamicResponses underVariable Load In practice theload usually changes so it is necessary to investigate thedynamic characteristics of the control system under variableload In this part the load force is variable in the simulation

Reference ADRC Servo valve Driving cylinder Load

Stroke sensorAMESimMATLAB-Simulink

Figure 4 Schematic diagram of cosimulation principle

Cylinder

Load

X u

Servo valueController

in Simulink

Pump source MOT

A B

P T

MF

X

(a)

AMESimMATLAB

TDTD Control

Z1

Z2

Z3

Z4

ESO

Scope

S-function

u xSimcenter Amesimmodel_

(b)

Figure 5 Cosimulation model (a) Hydraulic system model in AMESim (b) ADRC model in MATLAB

6 Complexity

1 2 3 4 50Time (s)

ADRCPIDRreference

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a)

1 2 3 4 50Time (s)

00

02

06

08

10

Serv

o va

lve s

pool

pos

ition

()

ADRCPID

(b)

Figure 6 Step responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

250

200

150

100

50

0

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

05

04

02

03

01

00

-01

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

ADRCPID

(b)

Figure 7 Sinusoidal responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

Table 1 Main parameters of the system

Parameters ValueCylinder diameter 4563mmLoad mass 100 kgMotor speed 1500 rminPump delivery 100mLrRelief pressure 350 barLoad spring rate 10000Nm

Complexity 7

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

e step response and sinusoidal response show thatADRC has more advantages than PID and the system inADRC has fast dynamic response and high controlaccuracy

52DynamicResponses underVariable Load In practice theload usually changes so it is necessary to investigate thedynamic characteristics of the control system under variableload In this part the load force is variable in the simulation

Reference ADRC Servo valve Driving cylinder Load

Stroke sensorAMESimMATLAB-Simulink

Figure 4 Schematic diagram of cosimulation principle

Cylinder

Load

X u

Servo valueController

in Simulink

Pump source MOT

A B

P T

MF

X

(a)

AMESimMATLAB

TDTD Control

Z1

Z2

Z3

Z4

ESO

Scope

S-function

u xSimcenter Amesimmodel_

(b)

Figure 5 Cosimulation model (a) Hydraulic system model in AMESim (b) ADRC model in MATLAB

6 Complexity

1 2 3 4 50Time (s)

ADRCPIDRreference

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a)

1 2 3 4 50Time (s)

00

02

06

08

10

Serv

o va

lve s

pool

pos

ition

()

ADRCPID

(b)

Figure 6 Step responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

250

200

150

100

50

0

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

05

04

02

03

01

00

-01

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

ADRCPID

(b)

Figure 7 Sinusoidal responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

Table 1 Main parameters of the system

Parameters ValueCylinder diameter 4563mmLoad mass 100 kgMotor speed 1500 rminPump delivery 100mLrRelief pressure 350 barLoad spring rate 10000Nm

Complexity 7

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

1 2 3 4 50Time (s)

ADRCPIDRreference

0

50

100

150

200

250

Disp

lace

men

t (m

m)

(a)

1 2 3 4 50Time (s)

00

02

06

08

10

Serv

o va

lve s

pool

pos

ition

()

ADRCPID

(b)

Figure 6 Step responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

250

200

150

100

50

0

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

05

04

02

03

01

00

-01

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

ADRCPID

(b)

Figure 7 Sinusoidal responses in ADRC and PID under constant load (a) Cylinder displacement response (b) Spool position response

Table 1 Main parameters of the system

Parameters ValueCylinder diameter 4563mmLoad mass 100 kgMotor speed 1500 rminPump delivery 100mLrRelief pressure 350 barLoad spring rate 10000Nm

Complexity 7

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

process Under this condition the parameters of PID are setas follows Kp 200 Ki 85 and Kd 2

Figure 8 shows that the actual displacement of the hy-draulic cylinder controlled in ADRC and PIDwill be affectedto different degrees in the process of load change Howeverthe ADRC controller considers the external disturbance astotal disturbance and the disturbance is estimated andeliminated by the extended state observer in real time so asto realize accurate control erefore the system in ADRCcan respond faster and can track the reference displacementIn addition in the early stage of response in ADRC theopening of the servo valve is very large to move the hydrauliccylinder to the set position quickly e cylinder displace-ment controlled by PID not only takes a long time to reach

the set value but also fluctuates greatly by the variable forceresulting in poor stability

53 Dynamic Responses under Long Pipeline e hydraulicpipeline is one of the indispensable components of thehydraulic system and plays the role of connecting thecomponent and the transmission medium e character-istics of the pipeline have a great influence on the dynamicand static characteristics of the hydraulic system When thepipeline is short the pipeline effect can be ignored but whenthe pipeline is long the pipeline effect will cause the responseto lag and the control accuracy will reduce is sectionmainly discusses the dynamic characteristics of systems with

Load

(N)

Time (s)

30000

20000

10000

40000

02 4 6 8 100

Load

(a)D

ispla

cem

ent (

mm

)

Time (s)

250

200

150

100

50

00 2 4 6 8 10

ADRCPIDReference

(b)

Serv

o va

lve s

pool

pos

ition

()

0 2 4 6 8 10Time (s)

08

06

04

02

10

00

ADRCPID

(c)

Figure 8 Step responses in ADRC and PID under variable load (a) Sinusoidal load (b) Cylinder displacement response (c) Spool positionresponse

8 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

long pipelines In the simulation the pipeline length is set to50m and diameter is set to 25mm Under this condition theparameters of PID are set as follows Kp 105 Ki 20 andKd 01

e simulation results shown in Figure 9 indicate thatthere is a certain delay in the step response of the longpipeline hydraulic systems but the delay by ADRC isshort e hydraulic cylinder in PID control has a longadjustment time and a large overshoot while that inADRC can reach the set position quickly and there isalmost no overshoot It can be seen that ADRC has ob-vious advantages in the hydraulic system with longpipelines

6 Conclusion

(1) A cosimulation model of the valve-controlledcylinder based on MATLAB-AMESim platform ismore accurate than the mathematical model and iscloser to the real system

(2) e structure and basic principles of active dis-turbance rejection control are introduced theactive disturbance rejection controller is designedand the rule of parameter setting is clarified

(3) e comparative simulation with ADRC and PIDis carried out in cases of constant load variableload and long pipeline e simulation resultsshow that the ADRC can effectively suppress thedisturbance of the internal parameter changes andexternal load changes of the hydraulic system hasstrong robustness and control accuracy and haspotential in electrohydraulic systems for high-performance control

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

is work was supported by the Fundamental ResearchFunds for Central Universities (2019XKQYMS37) the KeyResearch and Development Program of Shanxi Province(International Cooperation) (201903D421051 and201803D421028) and the Youth Fund Project of ShanxiProvince (201901D211210)

References

[1] YM Fang Y C Han L L Zhao andQ Li ldquoAdaptive controlfor electro-hydraulic servo system with uncertain coefficientsin control inputrdquo Control 8eory and Application vol 26no 2 pp 156ndash160 2009

[2] Y M Fang Z X Jiao W B Wang and P Z Shao ldquoAdaptiveback-stepping sliding mode control for rolling mill hydraulicservo position systemrdquo Electric Machines and Control vol 15no 10 pp 95ndash100 2011

[3] S Y Ruan G J Li and X H Jiao ldquoAdaptive control forVSCHVDC systems based on back-stepping methodrdquo ElectricPower Systems Research vol 77 no 5 pp 559ndash569 2011

[4] C Guan and S Pan ldquoAdaptive sliding mode control ofelectro-hydraulic system with nonlinear unknown parame-tersrdquo Control Engineering Practice vol 16 no 11pp 1275ndash1284 2008

0

50

100

150

200

250

Disp

lace

men

t (m

m)

2 4 6 8 100Time (s)

ADRCPIDReference

(a)

00

02

04

06

08

10

Serv

o va

lve s

pool

pos

ition

()

2 4 6 8 100Time (s)

ADRCPID

(b)

Figure 9 Step responses of the hydraulic system with long pipelines (a) Cylinder displacement response (b) Spool position response

Complexity 9

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity

[5] C Guan and S A Zhu ldquoBack-stepping based multiple cascadeadaptive sliding mode control of an electro-hydraulic servosystemrdquo Acta Instrumentation vol 26 no 6 pp 569ndash573 2005

[6] Y Z Zhang Q li W C Zhang and Y Y Yang ldquoSurvey ofmulti-model adaptive control theory and its applicationsrdquoChinese Journal of Engineering vol 429 no 2 pp 135ndash1432020

[7] J Na Y Li Y Huang G Gao and Q Chen ldquoOutput feedbackcontrol of uncertain hydraulic servo systemsrdquo IEEE Trans-actions on Industrial Electronics vol 67 no 1 pp 490ndash5002020

[8] J Na B Jing Y Huang G Gao and C Zhang ldquoUnknownsystem dynamics estimator for motion control of nonlinearrobotic systemsrdquo IEEE Transactions on Industrial Electronicsvol 67 no 5 pp 3850ndash3859 2020

[9] J Q Han ldquoActive disturbance rejection controller and itsapplicationsrdquo Control and Decision vol 13 no 1 pp 19ndash231998

[10] J Q Han ldquoFrom PID technology to active disturbance re-jection control technologyrdquo Control Engineering of Chinavol 9 no 3 pp 13ndash18 2002

[11] J Q Han ldquoParameters of the extended state observer andfibonacci sequencerdquo Control Engineering of China vol 15pp 1ndash3 2008

[12] S Chen W Y Bai Y Hu Y Huang and Z Q Gao ldquoOn theconceptualization of total disturbance and its profound im-plicationsrdquo Science China Information Sciences vol 63 no 2pp 221ndash225 2020

[13] Z Q Gao ldquoOn the foundation of active disturbance rejectioncontrolrdquo Control 8eory and Application vol 30 no 12 2013

[14] Z Q Gao ldquoScaling and bandwidth parameterization-basedcontroller tuningrdquo in Proceedings of 2003 American ControlConference pp 4989ndash4996 Denver CO USA June 2003

[15] Z Q Chen J J Liu and M W Sun ldquoOverview of a novelcontrol method active disturbance rejection control tech-nology and its practical applicationsrdquo CAAI Transactions onIntelligent Systems vol 13 no 6 pp 866ndash877 2018

[16] Y Huang W C Xue and C Z Zhao ldquoActive disturbancerejection control methodology and theoretical analysisrdquoJournal of Systems Science and Mathematical Sciences vol 31no 9 pp 1111ndash1129 2011

[17] Z Gao ldquoEngineering cybernetics 60 years in the makingrdquoControl 8eory and Technology vol 12 no 2 pp 97ndash1092014

[18] B W Gao J P Shao and X D Yang ldquoA compound controlstrategy combining velocity compensation with ADRC ofelectro-hydraulic position servo control systemrdquo ISA Trans-actions vol 53 no 3 pp 1910ndash1918 2014

[19] J TMiao X L Yao J X Zhang and SW Yang ldquoApplicationof ADRC in hydraulic AGC systemrdquo in Proceedings of the 33rdChinese Control Conference Nanjing China July 2014

10 Complexity