Linear controller retuning approach based on nonconvex nonsmooth optimization

The purpose of this paper is to describe how the fundamental problem of linear controller design can be solved, for general specifications, by combining a theoretical result with a recent numerical nonconvex nonsmooth optimization technique. Various temporal and/or frequency design criteria and constraints can be considered. The formulated optimization problem is complex; it involves implicit and explicit design parameters and nonsmooth criteria as well. A new algorithm based only on the gradient notion is fully described. This algorithm, mixing with an exact computation of gradients based on parametric sensitivity functions, appears to be well suited for controller design and retuning. As illustration, this method is used to design an optimal PI controller for a benchmark oscillatory model and to tune a PID controller for a motor position control. Computer simulations and experimental bench results are given to demonstrate the effectiveness of the proposed algorithm.