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 <ul><li>Unstable processes are inherently more difficult to control than stable ones. </li></ul><ul><li>This is largely due to the unstable nature of the dynamics and the limitations imposed by RHP poles </li></ul><ul><li>A lot of design tools are no longer applicable in presence of unstable poles, i.e., Bode stability criterion and the pole/zero cancellation schemes. </li></ul><ul><li>Besides, the design value of the controller gain is also limited into a range, beyond which the closed loop system cannot be stabilized. </li></ul>
Introduction <ul><li>Despite these difficulties, control system design for unstable processes has been an increasingly active research area recently. </li></ul><ul><li>In industrial process control, various controller designing methods for unstable time-delayed processes have been reported. </li></ul><ul><li>There are traditional PID design methods , IMC-based PID design methods and modified Smith predictor controller . </li></ul>
Review of Existing Methods <ul><li>A. Optimal PID Tuning </li></ul>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.
Review of Existing Methods <ul><li>B. PID-P Control </li></ul>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 Methods <ul><li>C. PI-PD Control </li></ul>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 Methods <ul><li>D. Gain and Phase Margin PID Tuning </li></ul>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 Methods <ul><li>E. IMC-Maclaurin PID Tuning </li></ul><ul><li>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. </li></ul>IMC is not applicable to unstable systems. But an equivalent feedback controller for IMC controller q can be derived as follows: This controller G c can be approximated by a PID controller with the first three terms of its Maclaurin series expansion in s ,i.e.,
Review of Existing Methods <ul><li>E. IMC-based Approximate PID Tuning </li></ul>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 G c by a standard PID controller G c,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.
Review of Existing Methods <ul><li>F. Modified Smith Predictor Control </li></ul>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 G c is facilitated for setpoint tracking. On the inner loops, G c1 is to stabilize to delay-free part of the unstable process, while G c2 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.
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
Simulation & Comparison 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.
Ranking ( Median Normalized Dead-time ) Setpoint Response Excellent: Method G Good: Method E and F Fair: Method C and A Poor: Method D Disturbance Rejection Excellent: Method A Good: Method E, F and C Fair: Method D Poor: Method G
Simulation & Comparison 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.
Performance Specifications Ranking ( Large Normalized Dead-time ) Setpoint Response Method E is slightly better Disturbance Rejection Method F is slightly better
Conclusion <ul><li>According to the control effects, applicabilities and robustness, the overall ranking is given as follows: </li></ul><ul><li>( 1 ) Method F, ( 2 ) Method E, ( 3 ) Method G, ( 4 ) Method C, ( 5 ) Method A, ( 6 ) Method B, ( 7 ) Method D. </li></ul><ul><li>The best available control result of existing methods may be further improved by using linear time varying or non-linear control strategy. </li></ul>