Active Uncertainty Compensation Based Control With ...web.ecs.baylor.edu/faculty/lee/LEE_AUCBC_presentation.pdf · Active Uncertainty Compensation Based Control With Applications

Active Uncertainty Compensation Based Control

With Applications to Energy Systems

Kwang Y. Lee

Professor and Chair

Department of Electrical & Computer Engineering

May 2019

Content

2

Background

Theoretical development

Experimental Applications

Conclusions

Motion Control

Problem Formulation

Process control

Target Tracking

Accurate model

Strong Nonlinearity

Stable Operation

Modelling Error

Time-delay

Energy Control

Objectives

Frequent Load Tracking

Disturbance Rejection

Difficulties

Dynamic Nonlinearity

Modelling Uncertainty

Various Disturbances

Intractable Dynamics

Time-delay

Non-minimum phase

Multivariable couplings

4

Background

?

4

Insights on Uncertainty

“If there is no uncertainty in the system, the control or the environment,

feedback control is largely unnecessary.”

BROCKETT, R. New issues in the mathematics. Berlin: Springer, 2001: 189 – 220.

H. S. Tsien. Engineering Cybernetics. New York: McGraw-Hill,1954.

Åström K J, Kumar P R. Control: A perspective[J]. Automatica, 2014, 50(1): 3-43.

Background

Tsien questions the basic assumption of the modern control theory

that ‘the properties and characteristics of the system to be controlled

were always assumed to be known’ and points out that, in reality,

‘large unpredictable variations of the system properties may occur.’

“In fact, robustness to model uncertainty was broadly one of

the major shortcomings of early model-based state-space theories.

That this was true even in adaptive control.”

5

State-of-the-art of the uncertainty compensation methods

Method Time Author Model Used Limitation

2DOF-PID 1985 M. Araki, et al

First Order

Plus Dead

time model

Any

Process

Disturbance

Observer1987

K. Ohnishi, et

al.

Transfer

Function

Model

Single-loop

Process

Active

Disturbance

Rejection

Control

1998 Han, J.QCascaded

Integrators

Minimum-

phase

Uncertainty

and

disturbance

Estimator

2004Zhong, QC

and Rees

State Space

model

Stable

processes

Background

Active

Passive

Active Uncertainty Compensation Based Control (AUCBC)

Energy Uncertainties

Multi-Source Disturbances

Modelling Inaccuracy

Nonlinearity

Uncertainty: the dynamics beyond the nominal linear model

Set-point Tracking

7

Background

Renewable Intermittency Frequent load changes Parameter perturbation Uncertain dynamics Fuel variation Heat transfer deterioration ……………………

Uncertainty

Estimation

Uncertainty Compensation

Basic idea

Content

7

Background



Conclusions


8

Two-degrees-of-freedom (2DOF) PI control

Extension of AUCBC to time-delay

Extension of AUCBC to unstable system

Extension of AUCBC to non-minimum phase

Extension of AUCBC to multivariable processes

9

Disturbance RejectionSet-point tracking

u(s) y(s)( )PG s( )cG s

d(s)

r(s) e(s)

0 5 10 15 20 25 30-0.2

0

0.2

0.4

0.6

0.8

1

1.2Step Response

Time (seconds)

Am

plit

ude

0 100 200 300 400 500 600 700 8000

0.01

0.02

0.03

0.04

0.05

0.06Step Response

Time (seconds)

Am

plit

ude

Single-degrees-of-freedom (1DOF) PI control

• A passive compensation structure

Very sluggish!!

A passive compensation structure

14


First-order-plus-time-delay, FOPTD Model

( )1

Ls

P

KG s e

Ts

，

0

1( ) [( ) ( ) ] 0 1

t

p

i

u t k br y r y dt bT

，


d(s)

( )F s

r(s) e(s)

( ) ic p

kG s k

s + ，

1( )

1

i

i

bT sF s

T s

Optimization of PI parameters for disturbance rejection

16

Performance

Objective:


d(s)

( )F s

r(s) e(s)

1

max ( ) max 1.61

S

P c

M S iG i G i

0( ) ( )IAE r t y t dt

，

Robustness

Constraints:

In the presence of step input of disturbance d:


Conventional graphical method

17

Åström K J, Panagopoulos H, Hägglund T. Design of PI controllers based on non-

convex optimization. Automatica, 1998, 34(5): 585-601.

( ) ic p

kG s k

s + ，

Procedures: Sweep w from 0 to infinity; Draw MS contour lines under each w; Find the peak of the envelope;

𝑘𝑝

𝑘𝑖


Deficiency: Difficult to use and understand; Time-consuming

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Re

Im

m

Cgc

New Solution

18

I. Propose new robustness index: Relative delay margin

II. Coordinate Transformation

III. Analyze and optimization under the new coordinate system

=m mdm

gc

RL a

2

sin cos

sin cos

p m m

i m m

Tk K a a a

L

Tk KL a a a a

L


20

(𝜑𝑚 , 𝑎)

0 0.5 1 1.5 2 2.5 3 3.5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

m

a

0m

1.63dmR

0a

arctan( ) m

aTa

L

mapping

Performance

Objective: 0( ) ( )IAE r t y t dt

，

Robustness

Constraints:


= 1.6mdmR

a


Optimization under the new constraint and coordinates:

𝑘𝑝

𝑘𝑖

21

2sin ( 1) cos ( 1) 0dm dm

d Ta r a a r a

da L

Analytical solution: Lagrange multiplier method

(𝜑𝑚 , 𝑎)

Performance

Objective: 0( ) ( )IAE r t y t dt

，

Robustness

Constraints:


= 1.6mdmR

a


Optimization under the new constraint and coordinates:

Li Sun, Donghai Li, and Kwang Y. Lee. Optimal Disturbance Rejection for PI

controller with Constraints on Relative Delay Margin. ISA Transactions, 2016, 63:

103-111.


16


Extension of Active UCBC to time-delay

Modify

Time-delay modification

pk01/ b

y

ESO

e 0u

1nz h

u

r

d

PG

Lse

1 LsEP e

sG

24

Input synchronization

( )1

Ls

P

KG s e

Ts

𝑂𝑟𝑖𝑔𝑛𝑎𝑙 𝑝𝑙𝑎𝑛𝑡

Uncertainty compensation in time-delay process

𝐼𝑑𝑒𝑎𝑙 𝑝𝑙𝑎𝑛𝑡

Extended State Observer, ESO

T

x Ax Bu Eh

y c x

1

2

n

x

x

z

x

h

ˆ

ˆ

e e

T

e

z A z B u H y y

y c z

① ② ③

ℎ 𝑖𝑠 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦

Estimation error feedback

Control design based on the ideal plant

1 Ls

EPe

sG

0; ;

1

1p

e

ok

k

kKb

T LT

；

25

1 1 1/

1p p

p

Ls Ls Ls

CL

pp

Ls

y sG s

r s s s

k ke e e

k e Ls k L sk

pk01/ b

y

ESO

e 0u

1nz h

u

r

d

PG

Lse

𝐹𝑜𝑟 𝑡ℎ𝑒 𝑖𝑑𝑒𝑎𝑙 𝑝𝑙𝑎𝑛𝑡

p Ls

OPG

ke

ss

1

1d Ls

CLeG s

Ls


𝑇𝑢𝑛𝑖𝑛𝑔 𝑓𝑜𝑟𝑚𝑢𝑙𝑎

Simulation verification0.9611.895

( )3.201 1

s

PG s es

Frequency response comparison between the compensated plant and ideal plant

Performance comparison

26

理想对象

2DOF-PI


reference

AUCBC


20



Extension of AUCBC to unstable system

Modify

Modified Uncertainty and Disturbance Estimator

28

Uncertainty compensationstate feedback feedback stablization

U( ) ( ) UDEm ms eB A X B C AX B EK

( + ) ( ) ( )u t L d t x A F x BSystem model

Control law

Uncertainty compensation in unstable process

: ( , ) A B : ( , ) A + F B

( ) ( )+B A I fs G s( )+

B B fG s

UDEtd

c B+Bm

xvVirtual Plant

B+Ke

-yv

uSF

uFB

u x

External disturbance

Controlled Process

d

m

B A A

se

se

Artificial

Delay

Artificial Delay

Lse

Stability analysis

29

Modified Uncertainty and Disturbance Estimator


Theorem： the closed-loop MUDE control system is stable if and only if

si1

n cos1 1

eKT T

(1)

where, is the solution of the equation,

tanT

(2)

in the interval (0, ).

The proof detail is referred to

Li Sun, Donghai Li, Qing-Chang Zhong and Kwang Y. Lee. Control of a Class of Industrial

Processes with Time Delay Based on a Modified Uncertainty and Disturbance Estimator.

IEEE Transactions on Industrial Electronics, 63(1): 7018-7028, 2016.

Simulation verification: Unstable with time delay 203.433( )

103.1 1

sG s es

0 100 200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

t/s

y

参考轨迹

MSP

FSP

MUDE控制

32

Li Sun, Donghai Li, Qing-Chang Zhong and Kwang Y. Lee. Control of a Class of Industrial

Processes with Time Delay Based on a Modified Uncertainty and Disturbance Estimator.

IEEE Transactions on Industrial Electronics, 63(1): 7018-7028, 2016.


Theoretic development

24



Extension of AUCBC to unstable

Extension of AUCBC to Non-minimum phase (NMP)

Modify

NMP Process Description

Right-half Plane (RHP) zero in TF. Initial inverse response in step response.

Bed Temperature response in Fluidized bed combustor

34

Bed temperature

11 /

P ni i

s zG s

s p

Uncertainty compensation in NMP process

Combined feed-forward and AUCBC solution

Process

Internal

Uncertainties

External

Disturbance

Modified

ESO

Modified

ESO

Dist. Est.

The Enforced Plant

Rejector

C sSignal

generator

Reference

Feedforward

Controller

0u u1u AUCBC: Enforce the NMP

plant behave like nominal The feed-forward control

produces the optimal set-point tracking.

35

0

0 1

1

1

1 , [ , )

, [ , )

z t t

use ra t t tu t

r t t

1 0

ln 1/ 1usat t

z

ˆ ˆ ˆ

ˆ ˆ

e e

T

e

x A x B u H y y

y c x

1

2

0 1 1

0 1

, , 1 0 00 1

T

o o o

n n

A B c

a a a

, ,0 0

0

o o o

e e

T T

e o

A B B

c c

A B

0

Feed-forward control produces the optimal set-point tracking

Algorithm basics: AUCBC: Enforce the NMP

plant behave like nominal MESO is designed based on

Canonical form


Process

Internal

Uncertainties

External

Disturbance

Modified

ESO

Modified

ESO

Dist. Est.

The Enforced Plant

Rejector

C sSignal

generator

Reference

Feedforward

Controller

0u u1u

36


Convergence analysis:

Theorem 1: Assuming (i) q is bounded, i.e., q t , (ii) A is Hurwitz and (iii)

1

110

n

i i na

, then the estimation error ε is bounded, i.e., there exist a constant

0 i and a finite T1 > 0 such that i it , i = 1, 2, · · · , n+1, ∀t ≥ T1 > 0.

Furthermore,1

1i

n

Ol

.

1 1

2

1

1

0 1 1

1

1

1

0 0 0

0

T

ne e

n

n n n

n

h

hA A Hch

a h a a

h

11

1 1

1

1

1

0n

n

hA

h

Li Sun, Donghai Li, Zhiqiang Gao, Zhao Yang and Shen Zhao. Combined feedforward and

model-assisted active disturbance rejection control for non-minimum phase system. ISA

Transactions, 2016, 64: 24-33.

4

'

2

123.853 10 3.5

6.5 42.25 45 190

sG s

s s s s

2

144.86 3

6.5 42.25

sG s

s s

38

Simulation verification


Actual plant Nominal model

0 1 2 3 4 5 6 7 8 9 10-1

0

1

2

Outp

ut

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

Contr

ol

Time (sec)

Reference

MADRC [G(s)]

MADRC [G'(s)]

DOBC [G'(s)]


29



Extension of AUCBC to unstable

Extension of AUCBC to Non-minimum phase (NMP)

Extension of AUCBC to Multivariable process

Multivariable Control

+

+

-

-

-

PI

11g

12g

22g

21g

1y

2y

1r

2r

PI1u

2u

Uncertainty compensation in Multivariable process

Conventional

Decentralized

Solution

Simple but unsatisfactory

-

-

11g

12g

22g

21g

1c

2c

1y

2y

1r

2r

1u

2u

GGDGC

1cG

2cG

11d

21d

12d

22d

Conventional

Decoupling

Control

Poor Robustness

+

+

-

-

-

PI-

11g

12g

22g

21g

2c

1y

2y

1r

2r

1( )Q s1

1 11( )Q s g

PI1c

2 ( )Q s 1

2 22( )Q s g

1u

2u

-

DOB-I

DOB-II

1d̂

2d̂

41

• Considering the couplings as a kind of uncertain disturbance for each single loop, as well as other uncertainties.

• Design disturbance observer to estimate the lumped uncertainties.• Compensate the estimated term in the inner loop. • The outer-loop controllers are designed individually.


AUCBC Solution Idea:

Equivalent block diagram transformation

+

+

-

-

-

PI

-

11g

12g

22g

21g

2c

1( )y s

2 ( )y s

1r

2r

1( )Q s1

1 11( )Q s g

PI1c

2 ( )Q s 1

2 22( )Q s g

1( )u s

2 ( )u s

-

1

2 22( )Q s g

-

-

-

1

1 11( )Q s g

1( )u s

2 ( )u s

11( )y s

22 ( )y s

12 ( )y s

21( )y s

1ˆ

id

2ˆ

id

1ˆ

od

2ˆ

od

42


PI-

-

-

PI-

11g

12g

22g

21g

1c

2c

1y

2y

121

11

( )g

Q sg

1r

2r21

2

22

( )g

Q sg

1u

2u

GGDGC

43

Sun L, Li D, Lee K Y. Enhanced decentralized PI control for fluidized bed combustor

via advanced disturbance observer. Control Engineering Practice, 2015, 42: 128-

139.

Equivalent block diagram transformation


Conclusion: The proposed AUCBC Solution can be equivalent to the conventional inverted decoupling, but with robustness significantly improved!!!

Laboratory verification

46

Experimental platform

Coupling

Master

ComputerMonitor

SensorsPLC

Measurements

Control Signal

Pump Pump

Li Sun, Junyi Dong, Donghai Li, Kwang Y. Lee. A Practical Multivariable Control Approach

Based on Inverted Decoupling and Decentralized Active Disturbance Rejection Control.

Industrial & Engineering Chemistry Research, 2016, 55(7): 2008-2019. (Citation: 53)


Performance

Content

35

Background



Conclusions

36

AUCBC configuration in various DCS

EmersonABB

GE

Matlab

37

水箱

泵

监视器

DCS机柜

运行人员

阀门

PI 控制PI 控制 ADRC控制ADRC控制

MVMV

PVPV

无扰切换无扰切换SPSP

执行器饱和执行器饱和

执行器饱和执行器饱和

时间/分钟时间/分钟00 33 66 99 1212

Test Platform

Test results

Bumpless Transfer & Anti-saturation


Application Examples

38

Water level control in a 1000MW power plant

Temperature Control in a 300MW power plant

Fuel cell control

39

Application in power plant regenerator


40


0 200 400 600 800 1000 120025

30

35

40

45

50

55

60

65

70

75

Time (s)

PV

(m

m)

SP

Desired tracking

PV

The experimental controlled output agrees well with the theoretic trajectory!

41

Sun L, Li D, Hu K, et al. On tuning and practical implementation of active disturbance

rejection controller: a case study from a regenerative heater in a 1000 MW power plant.

Industrial & Engineering Chemistry Research, 2016, 55(23): 6686-6695.


SP

PV

MVDisturbance (#2 valve)

340s10mm

PVd

10%

MV

SP

PV

MVDisturbance (#2 valve)

310s

24mm

PV MV d

10%

AUCBC

PID

VS

42

Application in superheated steam temperature cascaded control


43

Application in superheated steam temperature cascaded control


1J

2J

A

B

C

D

1J A 1J D

Pareto

2J A

2J D

E

Repository

Start

Initialize

Simulation

& Evaluation

Dominance

Sorting

Non-dominatd

solutions

Update best

ip

Update bestg

Leader

Slection

Update ith

particle

Density

Evaluation

Terminate?

i N

1i i

YES

NO

NO

YES

End

M particles

Search space

i=0

Max Generation

Model

in Section 2

Dominance

Comparison

Based on

Eq. (21)-(22)

Swam Moved

Solutions

MOPSO Algorithm

AUCBC parameter tuning: MOPSO

44

Long-term running data statistics under different controls


Sun L, Hua Q, Shen J, et al. Multi-objective optimization for advanced superheater steam

temperature control in a 300 MW power plant. Applied Energy, 2017, 208: 592-606.

45

Fuel cell control (500W)


Sun, L., Shen, J., Hua, Q., & Lee, K. Y. Data-driven oxygen excess ratio control for proton exchange membrane fuel cell. Applied Energy, 2018, 231: 866-875.

0 100 200 300 400 500 60024.0

24.5

25.0

25.5

26.0

26.5

27.0

27.5

28.0

Tem

per

ature

(℃

)

PI

Time (s)

3 506.5T s2 344.9T s1 149.2T s

max, 26.27ADRCt Cmax, 26.47PIt C

min, 25.25PIt C

ADRC

min, 25.82ADRCt C

Stack temperature control (500W)

Compressor

Movements

Content

46

Background



Conclusions

47

Conclusion

Uncertainty is universal, inevitable and essential for control;

A new computation algorithm is developed for PI optimization.

The data-driven uncertainty compensation method is extended totime-delay, unstable, NMP and multivariable processes.

Several successful applications in power plants and fuel cells

More application examples and theoretic details can be found:

48

References• Li Sun, Junyi Dong, Donghai Li, and Yuqiong Zhang. «Model-Based Water Wall Fault Detection and Diagnosis of FBC Boiler Using Strong

Tracking Filter.” Hindawi Mathematical Problems in Engineering, Volume 2014, Article ID 504086, 8 pages, http://dx.doi.org/10.1155/2014/504086.

• Li Sun, Donghai Li, and Kwang Y. Lee. "Enhanced decentralized PI control for fluidized bed combustor via advanced disturbanceobserver." Control Engineering Practice 42 (2015): 128-139, http://dx.doi.org/10.1016/j.conengprac.2015.05.014.

• Li Sun, Donghai Li, Zhiqiang Gao, ZhaoYang, Shen Zhao. “Combined feedforward and model-assisted active disturbance rejectioncontrol for non-minimum phase system.” ISA Transactions 2016, http://dx.doi.org/10.1016/j.isatra.2016.04.020.

• Li Sun, Donghai Li, and Kwang Y. Lee. "Optimal disturbance rejection for PI controller with constraints on relative delay margin." ISATransactions 63 (2016) 103-111, http://dx.doi.org/10.1016/j.isatra.2016.03.014.

• Li Sun, Donghai Li, Qing-Chang Zhong, and Kwang Y. Lee. "Control of a class of industrial processes with time delay based on amodified uncertainty and disturbance estimator." IEEE Transactions on Industrial Electronics, Vol. 63, No. 11, pp. 7018-7028,November 2016, DOI 10.1109/TIE.2016.2584005.

• Li Sun, Junyi Dong, Donghai Li, and Kwang Y. Lee. "A Practical Multivariable Control Approach Based on Inverted Decoupling andDecentralized Active Disturbance Rejection Control." Industrial & Engineering Chemistry Research, 55(7): 2008-2019, February 2016.DOI: 10.1021/acs.iecr.5b03738.

• Li Sun, Donghai Li, Kwang Y. Lee, and Yali Xue, “Control-oriented modeling and analysis of direct energy balance in coal-fired boiler-turbine unit.” Control Engineering Practice 55 (2016): 38-55.

• Li Sun, Donghai Li, Kangtao Hu, Kwang Y. Lee, and Fengping Pan. "On Tuning and Practical Implementation of Active DisturbanceRejection Controller: A Case Study from a Regenerative Heater in a 1000MW Power Plant." Industrial & Engineering ChemistryResearch, 55(23): 6686-6695. DOI: 10.1021/acs.iecr.6b01249.

• Li Sun, Qingsong Hua, JiongShen, Yali Xue, Donghai Li, and Kwang Y. Lee, “Multi-objective optimization for advanced superheatersteam temperature control in a 300 MW power plant,” Applied Energy 208 (2017) 592-606,http://dx.doi.org/10.1016/j.apenergy.2017.09.095.

• Li Sun, Qingsong Hua, Jiong Shen, Yali Xue, Donghai Li, and Kwang Y. Lee, “A Combined Voltage Control Strategy for FuelCell,” Sustainability 2017, 9, 1517; doi:10.3390/su9091517.

• Li Sun, Qingsong Hua, Donghai Li, Lei Pan, Yali Xue, and Kwang Y. Lee, “Direct energy balance based active disturbance rejectioncontrol for coal-fired power plant,” ISA Transactions 70 (2017) 486-493, http://dx.doi.org/10.1016/j.isatra.2017.06.003.

• Li Sun, Jiong Shen, Qingsong Hua, and Kwang Y. Lee, “Data-driven oxygen excess ratio exchange membrane fuel cell,” Applied Energy231 (2018) 866-875, https://doi.org/10.1016/j.apenergy.2018.09.036.

• Guanru Li, Lei Pan, Qingsong Hua, Li Sun, and Kwang Y. Lee, “Water Pump Control: A Hybrid Data-Driven and Model-Assisted Active Disturbance Rejection Approach,” Water 2019, 11, 1066; doi:10.3390/w11051066.

http://dx.doi.org/10.1155/2014/504086

http://dx.doi.org/10.1016/j.conengprac.2015.05.014

http://dx.doi.org/10.1016/j.isatra.2016.04.020


http://dx.doi.org/10.1016/j.apenergy.2017.09.095


https://doi.org/10.1016/j.apenergy.2018.09.036

Thank you for your attention!

Q&A

49

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