Grey wolf optimization for PID controller design with prescribed robustness margins

The grey wolf optimization algorithm is proposed to design proportional, integrative and derivative controllers using a two degrees of freedom control configuration. The control system is designed in order to achieve good set-point tracking and disturbance rejection performance. The design is accomplished by minimizing an aggregated cost function based on the time-weighted absolute error integral, subjected to robustness constraints. The control system robustness levels are prescribed in terms of the vector margin and maximum complementary sensitivity function values. Simulation results are presented for several common systems dynamics and compared with the ones obtained with a particle swarm optimization algorithm.