Ascc04 334 Comparative Study of Unstable Process Control

A Comparative Study on Control of Unstable Processes with Time-delay

Qing-Guo Wang, Han-Qin Zhou

Department of Electrical & Computer Engineering

National University of Singapore


Introduction

• Unstable processes are inherently more difficult to control

than stable ones.

• This is largely due to the unstable nature of the dynamics and the limitations imposed by RHP poles

• A lot of design tools are no longer applicable in presence of unstable poles, i.e., Bode stability criterion and the pole/zero cancellation schemes.

• Besides, the design value of the controller gain is also limited into a range, beyond which the closed loop system cannot be stabilized.


Introduction

• Despite these difficulties, control system design for

unstable processes has been an increasingly active research area recently.

• In industrial process control, various controller designing methods for unstable time-delayed processes have been reported.

• There are traditional PID design methods, IMC-based PID design methods and modified Smith predictor controller.


Review of Existing MethodsA. Optimal PID Tuning

Visioli (2001) proposed 3 sets of PID auto-tuning formulas for UFOPDT processes to minimize the ISE, ITSE and ISTE specifications, respectively.

The controller settings are computed by genetic algorithms to obtain a global optimal solution.

The control system configuration is of one degree of freedom.

2

0

2

0

2 2

0

( )

( )

( )

ISE e t dt

ITSE te t dt

ISTE t e t dt


Review of Existing MethodsB. PID-P Control

Park et al. (1998) proposed an enhanced PID control strategy for UFOPDT and USOPDT processes

The control system configuration has double loops to reduce the overshoots and yield reasonable settling time.

The unstable process is stabilized by the inner proportional controller for a optimal gain margin. The main PID is then designed for the stabilized inner closed-loop system.


Review of Existing MethodsC. PI-PD Control

Majhi and Atherton (2000a) proposed another double-loop PI-PD scheme for UFOPTD processes, which is similar to Method B.

The inner PD controller is for stabilization and outer PI controller is designed to minimize the ISTE criterion.


Review of Existing MethodsD. Gain and Phase Margin

PID Tuning Wang and Cai (2002) used gain and phase margin specifications for unstable

process control, and consider the same double-loop structure as that of Method B in design.

They implement the double loop configuration into an equivalent single-loop PID feedback system with a setpoint filter. The controller setting is obtained by assigning gain margin of 3 and phase margin of 60 degree.

The second order Taylor series expansion is employed to approximate the time delay.


Review of Existing MethodsE. IMC-Maclaurin PID Tuning

Lee et al. (2000) proposed IMC-based PID auto-tuning formulas for FOPDT and SOPDT unstable processes. The control system is in the same 2DOF structure as in Method D.

11

11

1( )

( 1) ( 1)1 1

( )1

( 1) ( 1)

mi

iiM

n m

c mi

iiM

n m

sP s

q s sG

Gq sP ss s

IMC is not applicable to unstable systems. But an equivalent feedback controller for IMC controller q can be derived as follows:

This controller Gc can be approximated by a PID controller with the first three terms of its Maclaurin series expansion in s ,i.e.,

''' 21 (0)

( ) ( (0) (0) )2!c

fG s f f s s

s


Review of Existing MethodsE. IMC-based Approximate PID Tuning

Yang et al. (2002) developed another IMC-based method to design PID and high order feedback controllers for unstable processes. In this design methodology, model reduction is employed to approximate the equivalent IMC feedback controller Gc by a standard PID controller Gc,PID .

The non-negative least square method is used to obtain the optimal PID settings to minimize the criterion E, on the desired closed-loop bandwidth.

The desired degree of PID approximation to the IMC controller is usually set as 5%. The control system structure is also of 2DOF with the setpoint filter.

,(0, )

( ) ( )max | | ,

( )b

C PID Cw w

C

G jw G jwE

G jw


Review of Existing MethodsF. Modified Smith Predictor Control

0^

01

( )

1 ( )

Lsc

r

c c

G s G eH

G G G

^^ ^

0 00 1^

01 2 0

[1 ( ) ]

[1 ( ) ][1 ]

Ls L sc c c

dLs

c c c

G e G G G G G eH

G G G G G e

Majhi and Atherton (2000b) proposed this modified SP controller for UFOPDT processes, in which the denominator of closed-loop setpoint transfer function is delay-free.

Therefore the design of controller Gc is facilitated for setpoint tracking.

On the inner loops, Gc1 is to stabilize to delay-free part of the unstable process, while Gc2 is for stabilization and disturbance rejection as well.


Simulation & Comparison

1. Small Normalized Dead-time: 0<L/T<0.693

The plant’s normalized dead-time is 0.5. A unity step setpoint is given at t = 0, and a disturbance of -0.1 is injected at t = 75.

2

4( )

4 1

s

eG s

s


Performance Specifications


Summary of Robustness Analysis


Ranking ( Small Normalized Dead-time )

Setpoint Response

Best: Method G

Excellent: Method E and F

Good: Method C and A

Fair: Method B

Poor: Method D

Disturbance Rejection

Excellent: Method E and F

Good: Method C and A

Fair: Method D and G

Poor: Method B



2. Medium Normalized Dead-time: 0.693<L/T<1

The plant’s normalized dead-time is 0.8, Method B is no longer applicable.

Again, the unity step setpoint is given at t = 0, and a disturbance of -0.1 is injected at t = 75.

1.2

( )1.5 1

s

eG s

s




Ranking ( Median Normalized Dead-time )

Setpoint Response

Excellent: Method G

Good: Method E and F

Fair: Method C and A

Poor: Method D


Excellent: Method A

Good: Method E, F and C

Fair: Method D

Poor: Method G



3. Large Normalized Dead-time: 1<L/T<2

The plant’s normalized dead-time is 1.5. Only Method E and F are workable in this scenario.

Again, the unity step setpoint is given at t = 0, and a disturbance of -0.1 is injected at t = 75.

1.5

( )1

s

eG s

s



Ranking ( Large Normalized Dead-time )

Setpoint Response

Method E is slightly better


Method F is slightly better


Conclusion• According to the control effects, applicabilities and

robustness, the overall ranking is given as follows:

(1) Method F, (2) Method E, (3) Method G, (4) Method C, (5) Method A, (6) Method B, (7) Method D.

• The best available control result of existing methods may be further improved by using linear time varying or non-linear control strategy.


Thank you!

Education

Ascc04 334 Comparative Study of Unstable Process Control