Multivariable Robust Control Design of a Turbofan Engine for Full Flight Envelope Operation

8/12/2019 Multivariable Robust Control Design of a Turbofan Engine for Full Flight Envelope Operation

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Multivariable Robust Control Design of a Turbofan

Engine for Full Flight Envelope Operation

Haiquan Wang, Ling Ouyang, Dongyun Wang Lei Liu

School of Electric and Information Engineering Department of Computer Science and Applications

Zhongyuan University of Technology Zhengzhou Institute of Aeronautical Industry Management

Zhengzhou, Henan Province, China Zhengzhou, Henan Province, [email protected] [email protected]

Abstract In order to fulfill the full flight envelope aero-engine control, as one of the most effective solutions, gain

scheduling control system was designed in this paper which could

weaken the influence of the limited robust of traditional

controller. Based on the previous works such as the engine

modeling and the two degrees-of-freedom (2DOF) H loop-

shaping controller design, the full flight envelope was divided up

into eight regions and the control system which was constituted

by eight 2DOF controllers for each sub-regions was constructed

in which the eight controllers of different sub-regions could be

switched based on the engine altitude and Mach number. In

order to decrease the disturbance in the process of switchoverbetween the controllers of different sub-regions, as an innovation,

the bumpless switch logic based on the technology called inertia

delayed to soften the switch was adopted in the control system.

For the purpose of checking the effect of full envelope control

system, the hardware in-the-loop simulations have been done on

the real-time simulation platformbased on rapid prototype.The

excellent performance of the full envelope robust control system

for the turbofan engine was shown, as well as the validity of flight

envelope dividing method and the bumpless switch logic was

verified.

Index Terms Turbofan engine. Full flight envelope.

Bumpless switch logic.Rapid prototype.

NOMENCLATURE

H Altitude

Ma Mach number

WFM Fuel flow rateA8 Nozzle areaXNHC High pressure compressor speedXNLC Low pressure compressor speedP36 Turbine pressure ratioPLA Power lever angle

I. INTRODUCTION

With the increasing demand to enhance the reliability and

durability of turbofan engine, the demand for multivariablerobust control with excellent performance of robust

stabilization, decoupling and reference tracking is becoming

apparent [1]. As a deformation of H robust controller design

method, 2DOF H loop-shaping design procedure whose

feedback controller and pre-filter are designed respectively to

improve tracking performance while maintaining robustness

has been applied to aero-engine controller design successfully

[2]. However, as the turbofan engine performs over the wide

range envelope, it experiences large changes in the ambient

temperature and pressure, and the engine dynamics change in

a significant nonlinear manner. On the other hand, as a linear

control technique, the effect of H control designed for an

operating point inevitably degrades in off-design operating

point. Thus the tactic of flight envelope dividing up and

divisional governing should be adopted for the better

performance of full flight envelope engine control. The

process could be concluded as follow: First of all, dividing up

the flight envelope according to the engine inlet parameters

and selecting nominal points. Then 2DOF H robust

controller could be designed at the nominal pointscorresponding to each envelope sub-regions. Subsequently,

the control system could be constructed by scheduling the

resulted controllers based on the change of H and Ma. What

should be noted is that in order to weaken the disturbances

caused by the switchover among different controllers of

different sub-regions, bumpless switch logics based on the

technology called inertia delayed to soften the switch will

be introduced in this paper creatively, which could be coded

by automatic code generator and download to the simulation

platform[3][4]. The whole simulation platform for evaluating

purpose are developed based on rapid prototyping approach

which could free the engineers from the tedious and error-

prone task of writing code for a given control law.II. THE 2DOF HCONTROLLER DESIGN

In order to improve the tracking performance and the

robustness of aero-engine control system simultaneously

which couldnt realize in traditional H control method,

2DOF H control design technique [6] is introduced and

employed in H loop-shaping control [5] frame.

The 2DOF H loop-shaping method could be illustrated

as Fig.1, where the normalized left coprime factorization of

the shaped plant is 1s

G M N= ,Kfas the feedback controller is

adopted to guarantee the robustness of the system, Tr is the

reference model that represents the desired closed-loop with

ideal response characteristics, pK is the prefilter whichensures matching between the model Tr and the transfer

function from x to y, and is used to adjust the matching

requirement between Trand the closed-loop system response.

2121978-1-4244-5704-5/10/$26.00 2010 IEEE

Proceedings of the 2010 IEEEInternational Conference on Information and Automation

June 20 - 23, Harbin, China


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Fig.1Two degrees-of-freedom H loop-shaping design frameAfter a series of derivation, the 2DOF H loop-shapingcontrol design problem could be expressed as synthesizing thecontroller [ ]

p fK K K= by the standard H algorithms based

on the general plant Pwhich could be realized by:1/ 2

1/ 2

2 2 1/ 2

1/ 2

0 0 ( )

0 0 0

0 0 0 0

0 0

0 0 0 0

0 0

T T

r r

r r

A BD ZC R B

A B

I

C R D

C C D R D

I

C R D

+

Wheres

A BG

C D

=

, r rr

r r

A BT

C D

=

, R=I+DDT and Z is the

solution to the following RICCATI equation:1 1 1 1( ) ( ) 0T T T T T A BS D C Z Z A BS D C ZC R CZ BS B + + =

The details and the simulation results of 2DOF H loop-

shaping engine controller design could be seen in [2], the

results show H loop-shaping method possesses more

robustness than any other linear design method,

IV.FULLFLIGHT ENVELOPE DIVIDING

A. The engine system

The system used to demonstrate the full envelope control

system design technique is a twin spool, mixed ow, afterburning military-type gas turbofan engine wherein the low-

pressure rotor system is mechanically independent of the high-

pressure rotor system.

The nonlinear engine model mentioned in this paper is adynamic computer component level model capable of

simulating the engine operating envelope based on C++ andthe linear model at different operating point could begenerated withthe modelling method called fitting as shownin [7]. The modelling results are listed in [4].

B. Full envelope division

As a typical linear multivariable design method, the resultsin [2] show that only a H controller for an operating pointcant fulfil the full envelope flight control task, envelopedividing and controller scheduling scheme should be used.

The procedure of envelope dividing adopted in this paper

could be defined as roughly dividing and subdivision based on

the engine inlet parameters as discussed in [4]. With thismethod the full envelope could be divided into eight sub-regions as shown in Fig.2 and the nominal points representingsub-regions are (1.85, 0.3), (2.5,1), (6, 1), (6.5, 1.5), (11, 1.5),

(12.3, 2), (17.5, 1.6), (16, 2) respectively.

0 0.5 1 1.5 2 2.50

5

10

15

20

Ma

H

Fig.2 Divided full flight envelope

Obviously, the eight divided sub-regions could fully coverthe whole flight envelope, and there are almost no gaps

between any two of the sub-regions.

.FULLENVELOPECONTROLSYSTEMDESIGN

A. Control system structure

Based on the linear models corresponding to the eight

nominal points, 2DOF H loop-shaping controllers could be

designed for eight sub-regions, and the controller-schedulecontrol system for full flight envelope could be constructed

with the change of engine altitude and Mach number:The whole control system is built up by the SISO control

system for acceleration process, deceleration process as well

as steady-state control and the MIMO control system designed

for augmented transient condition. During the full flight

envelope control operating process, for every control cycle of25 milliseconds, the form of the controller should be

ascertained firstly based on the current state of engine, then

one of the eight controllers for different sub-regions could be

selected and aroused based on the engine altitude and Mach

number. Meanwhile, the other seven controllers are standingby and waiting for the switching signal thus the computational

burden of the digital electronic engine control (DEEC) could

be reduced effectively.

The whole structure has been constructed inMATLAB/Simulink which could be automatic coded by RTW

and downloaded to DEEC in the simulation platform

mentioned in [3][4].

B. Bumpless switch logic

Obviously, during the full envelope engine control, the

controllers for different sub-regions always switch back and

forth, and the perturbations of the control variables occur

inevitably during the switchover between any two of thecontrollers. In order to achieve smooth transition during the

switchover between any two of the controllers for differentsub-regions, the inertia delayed to soften the switch

technology has been introduced in this paper:

Take SISO controller as example, suppose at a certain timet1, the change of the region where the engine locates has taken

place, and the corresponding controller has been switched

from A to B. Then the output U of the control system could be

defined by

( )at

b a bU U e U U = + (1)

Where Ua represents the output of controller A at the

switching time t1, it is unchanged during the controller Bs

working process until the next switch, and Ubis the output of

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controller B in the current time t2. tis the total working hoursof B, from the switch time t1 to the current time t2, whichcould be deduced from the duty cycles of the controller. t

should be re-assigned to zero at the moment of next switch

time, and re-start timing,

As we can see from (1), at the controller switching time t1,tis equal to zero, and the output of the full envelope control

system is equal to Uawhich represents the output of controller

A in the previous control cycle. With the increasing of thetime t, the influence of Ua which has been switched offgradually weakens, meanwhile the controller output Ubgradually increases its influence. What should be noted is that

the value of a was validated as 1 in this system throughrepeated debugging, which directly affects the fading out

speed of Uaand the fading in speed ofUb, as well as affects

the stability of the control system. With the help of the

equation, its clear that the control variables disturbancesoccurred before and after switching could be restrained, and

the smooth transition could be realized.

In order to utilize the simulation platform based on rapidprototype, the switch logic should be rearranged and

constructed in MATLAB/Simulink with the assistance of theSimulink blocks such as Embedded MATLAB function, Unit

delay, Goto/From, and so on. The whole structure of one

controller in the SISO control system with switch logic isshown in Fig.3. The controller output---Wfm could be

calculated through the sum of the current controller output Ub

represented by point 1 and the output of swich logicrepresented by point 2 in the structure.

Obviously, from (1), the difficulty of the problem is thedetermination of the operating time tof the current controller

especially in MATLAB/Simulink. A creative solution adopted

in this paper is to number to each controller representing each

eight sub-regions, thus every controller for each sub-regionhas a specifically ID signal.Through the controller ID signals

comparison between the previous control cycle and currentcontrol cycle in the Embedded MATLAB Function, the resultthat if there has been any switchover before the current controlcycle could be concluded, thus with the help of Simulink

block Unit delay, the output Uaof the switch-off controller at

switching time and the number of current controllers duty

cycle can be decided, and the operating time tof the currentcontroller could be calculated consequently.

.SIMULATION

With considerations of real-time, safety and low costs inmind, the real-time simulation has been done based on theopen and developable hardware-in-the-loop simulation

platform [3] as shown in Fig.4.There are three parts in thesimulation platform which are workstation, Simulated PC, andDEEC. The full envelope control system which has been

designed in workstation and the turbofan engine component

level modelcould be automatic coded with the help of Real-

Time Workshopand downloaded to DEEC and simulated PC

respectively through the network.

Fig.3 Sturcture of the SISO controller with switch logic

TCP/IP Network

External hardware IRQ

Real-Time loop

D/A

A/D

Workstation(PC)

MATLAB/Simulink/RTW/S-Function

Tornado/Vxworks Explr/xPC Target

HUB

DEEC(PC104)

Vxworks

PM511PPC104 Bus

Simulated PCxPC Target

PCL-812PG

ISA busCircuits

TCP/IP network

Fig. 4 Architecture of the simulation platform

The simulation for steady-state control has been carried out

firstly, where the PLA was kept at 600, H and MA were

changed according to the timing as shown in Fig.5. Thesimulation results are shown in Fig.6. The results shown that

the condition of the engine kept almost the same under thecommand from power lever, and the fluctuate of the control

variable and the controlled variable whose maximumpercentages reached to 0.25% and 3.9% respectively during the

switch between different controllers was weakened with the

help of switch logic.

Then the transition state control simulation has been donewhile the PLA,Hand Mawere changed as shown in Fig.7 andFig.5 respectively, and the results are shown in Fig.8.

Obviously, as the controlled variable, XNLC varied with the

change of PLA, the variety of the ambient environment hadalmost none effect to the condition of aero-engine which was

under control. Furthermore, the bump during controller

switchover process has been reduced visibly, the values ofXNLC and WFM account for 0.4 and 2.67 percent decrease.

Finally, the augment transient simulation has been executed

where the engine condition was changed according to thetiming as shown in Fig.9. The switch procedure has been done

when the engine was stable at the 1100 position, and thesimulation results are shown in Fig.10. The good tracking

performance has been obtained during the augment transient

process no matter how the operating point change, and the

bumps of the control variablesWFM, A8, as well as the

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controlled variables---XNLC and P36 have been eliminated.From the results, it is clear that no matter what condition the

engine are, maybe the steady-state, transition state or augment

transient process, the control system could fulfill the aero-

engine flight envelope control, the bump during the sub-region

controller switching process could be eliminated effectively.

.CONCLUSION

Several key technologies such as division of flightenvelope and the bumpless switchover during multivariable

robust control system design for turbofan engine full flight

envelope operation have been discussed has been discussed.

The results of the hardware-in-the-loop simulation indicate the

designed full envelope control system is effective for theturbofan engine.

REFERENCES

[1] S. Adibhatla, Propulsion control law design for the NASA STOVLcontrols technology program, AIAA93-4842, CA, Dec. 13, 1993.

[2]Haiquan Wang, Yingqing Guo, Research of aero-engine two degrees-of-freedom robust controller based on LMI approach, Journal of AerospacePower,pp.1413-1419,Vol.24, 2009

[3]Jun Lu, Yingqing Guo, Research on automatic code generationtechnology for control method based on RTWEC, Journal of AerospacePower, Vol.6 2008.

[4] Haiquan Wang, H Robust Controller Design for Aero-engine andSimulation, Ph.D.dissertation, Northwestern polytechnical university,

2009[5] Haiquan Wang, Yingqing Guo, et al, Aero-engine Robust H loop-shaping Controller Design Based on Genetic Algorithm, IEEE 2nd IITA,Shanghai, pp.1035-1039, 2008.

[6] Limebeer D., Kasenally E., and Perkins J., On the design of robust twodegree of freedom controllers,Automatica, 1993, 29(I), pp. 157-168.

[7] Zhengping Feng, Jianguo Sun, A new method for establishing a statevariable model of aeroengine, Journal of Aerospace Power, Vol. 13, No.4, pp. 435-438, 1998.

0 20 40 60 80 1000

5

10

15

20

t(s)

H(km

)

0 20 40 60 80 1000

0.5

1

1.5

2

t(s)

Ma

0 20 40 60 80 1004000

5000

6000

7000

8000

9000

t(s)

XNLC(r

/min)

32 32.5 33 33.5 34 34.5

8020

8040

8060

8080

8100

8120

t(s)

XNLC(r

/min)

Fig.5(a) Altitude curve Fig.5(b) Mach number curve Fig.6(a) XNLC with (dashed) andwithout (solid) switch logic

Fig.6(b) Amplification curve w(dashed) and without (solid) switch lo

0 20 40 60 80 100500

1000

1500

2000

2500

3000

3500

4000

t(s)

WFM(kg/h)

32 32.5 33 33.5 34 34.5960

980

1000

1020

1040

1060

t(s)

WFM(kg/h)

0 20 40 60 80 10035

40

45

50

55

60

65

70

t(s)

PLA(o)

0 20 40 60 80 5500

6000

6500

7000

7500

8000

8500

9000

t(s)

X

NLC(r/min)

Fig.6(c) Wfm with (dashed)and without (solid) switch logic

Fig.6(d) Amplification curve with(dashed) and without(solid) switch logic

Fig.7 PLA curve Fig.8(a) XNLC with (dashed) and with(solid) switch logic

78 78.5 79 79.5 80 80.5 81

7420

7440

7460

7480

7500

7520

t(s)

XNLC(r/min)

0 20 40 60 80 100500

1000

1500

2000

2500

3000

3500

4000

4500

5000

t(s)

WFM(kg/h)

78 79 80 81 82 83

2200

2250

2300

2350

2400

2450

t(s)

WFM(kg/h)

0 20 40 60 80 10

5

10

15

20

t(s)

H(km)

Fig.8(b) Amplification curve with(dashed) and without (solid)switch logic

Fig.8(c) Wfm with (dashed) andwithout (solid) switch logic

Fig.8(d) Amplification curve with(dashed) and without(solid) switchlogic

Fig.9(a) Altitude curve

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0 20 40 60 80 1000

0.5

1

1.5

2

t(s)

Ma

0 20 40 60 80 1004000

5000

6000

7000

8000

9000

10000

11000

t(s)

XNLC(r/min)

78 78.5 79 79.5 80 80.5 81

8750

8800

8850

8900

t(s)

XNLC(r/min)

0 20 40 60 80 11000

2000

3000

4000

5000

6000

t(s)

WFM(kg/h)

Fig.9(b) Mach number curve Fig.10(a) XNLC with (dashed) andwithout (solid) switch logic

Fig.10(b) Amplification curve with(dashed) and without (solid)switch logic

Fig.10(c) Wfm with (dashed) andwithout (solid) switch logic

77 78 79 80 81 82 83

3700

3750

3800

3850

3900

3950

t(s)

W

FM(kg/h)

0 20 40 60 80 1006

7

8

9

10

11

12

t(s)

P36

73 73.5 74 74.5 75 75.5

10.56

10.58

10.6

10.62

10.64

10.66

10.68

10.7

10.72

t(s)

P36

0 20 40 60 80 10.2

0.3

0.4

0.5

0.6

0.7

t(s)

A8(m*m)

Fig.10(d) Amplification curve with(dashed) and without (solid) switchlogic

Fig.10(e) P36 with (dashed) andwithout (solid) switch logic

Fig.10(f) Amplification curve with(dashed) and without (solid) switchlogic

Fig.10(g) A8 with (dashed) and witho(solid) switch logic

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Multivariable Robust Control Design of a Turbofan Engine for Full Flight Envelope Operation