Intelligent controller design based on gain and phase margin specifications Daniel Czarkowski  and Tom O’Mahony* Advanced Control Group, Department of Electronics Engineering, Cork Institute of Technology, s: 

ISSC 2004, Belfast2 Overview Do advanced control structures significantly outperform PID for SISO systems? Compare –PID –2-DOF PID –GPC

ISSC 2004, Belfast3 Contents List Types of controllers Tuning –Gain and phase margin criteria –Non convex problem to be solved –Genetic Algorithms Models used in the evaluation Results Conclusions

ISSC 2004, Belfast4 PID controller Controller structure Control law 3 Variables to tune

ISSC 2004, Belfast5 2-DOF PID controller Controller structure Control law 6 variables to tune

ISSC 2004, Belfast6 GPC controller Introduced by Clarke et al., 1987 Two degree of freedom structure Digital controller was used Unconstrained control algorithm 7 tuning parameters

ISSC 2004, Belfast7 GPC properties Advantages –Two degree of freedom –Optimal controller –Can handle more complex systems –More flexible structure Disadvantages –No well developed tuning rules –More difficult to tune –Very few industrial implementations

ISSC 2004, Belfast8 Design strategy Performance & robustness Performance –IAE servo + regulator Robustness –Gain and phase margin

ISSC 2004, Belfast9 Non-convex problem Inverse unstable system Avoid local minima!

ISSC 2004, Belfast10 Genetic Algorithms Stochatistic optimisation method –Gray Coding –Stochatistic Universal Sampling, SUS –Single point crossover –Maximum number of generations, 300 –Population size, 100 –Constraints on the controller parameters

ISSC 2004, Belfast11 Direct the GA GA optimisation problem Penality factors on gain and phase margins

ISSC 2004, Belfast12 Models Benchmark test –Inverse unstable system –Integrating systems –Underdamped system –Conditionally stable system –3 models with time delay –First order model 12 models were evaluated (K. J. Åström 1998, 2000)

ISSC 2004, Belfast13 Results Comparison of PID, 2-DOF PID and GPC GPC outperforms the other two counterparts

ISSC 2004, Belfast14 Results Design based on minimum Am=6dB –GPC vs PID, average IAE decreased by 43% –GPC vs 2-DOF PID, average IAE decreased by 25% –2-DOF PID vs PID, average IAE decreased by 24% Design based on minimum Am=14dB –GPC vs PID, average IAE decreased by 37% –GPC vs 2-DOF PID, average IAE decreased by 22% –2-DOF PID vs PID, average IAE decreased by 15%

ISSC 2004, Belfast15 Set-point following Model Design Results Better robustness achieved by PID controllers!

ISSC 2004, Belfast16 Model Design Results Set-point following GPC performs 25% better than the PID controllers!

ISSC 2004, Belfast17 Set-point following Model Design Results GPC does not perform better than the PID controllers!

ISSC 2004, Belfast18 Summary of work A GA approach to tuning controllers based on gain and phase margin was applied Novel optimisation function was proposed Twelve models were tuned Three controllers were evaluated The controllers were subsequently employed on a real time system

ISSC 2004, Belfast19 Conclusions GPC performance depends on the sampling period Tuning strategy works well, but... GPC performed better in simulation, but... Do advanced control algorithms perform better?

Questions?