Multiobjective H2/H∞ guaranteed cost PID design

This article presents a methodology for sub-optimal design of PID compensators for systems subject to disturbance signals and to parametric uncertainties of polytope type. The adopted optimality criteria are the H₂ and H_∞ norms of the transfer matrices from the disturbance inputs and from the reference input to the controlled output error. Time constant constraints are also employed in the optimization procedure. The PID parameter selection combines the different optimization criteria through a multiobjective technique. True guaranteed cost values for optimization criteria are calculated. An example is presented, showing the uncertainty polytope construction from physical parameters tolerances and the PID synthesis procedure. A genetic algorithm and extensive simulations are employed in order to evaluate the proposed algorithm performance