Covariance Matrix Adapted Evolution Strategy Based Design of Mixed H2/H ∞  PID Controller

This paper discusses the application of the covariance matrix adapted evolution strategy (CMAES) technique to the design of the mixed H

2

/H

 ∞ 

PID controller. The optimal robust PID controller is designed by minimizing the weighted sum of integral squared error (ISE) and balanced robust performance criterion involving robust stability and disturbance attenuation performance subjected to robust stability and disturbance attenuation constraints. In CMAES algorithm, these constraints are effectively handled by penalty parameter-less scheme. In order to test the performance of CMAES algorithm, MIMO distillation column model is considered. For the purpose of comparison, reported intelligent genetic algorithm (IGA) method is used. The statistical performances of combined ISE and balanced robust performance criterion in ten independent simulation runs show that a performance of CMAES is better than IGA method. Robustness test conducted on the system also shows that the robust performance of CMAES designed controller is better than IGA based controller under model uncertainty and external disturbances.