Multi criteria controller design for uncertain MIMO systems using global non-convex optimization

A controller design procedure for MIMO systems with explicit plant uncertainties is suggested. In the proposed method, the closed loop analysis is integrated in the controller synthesis by an outer optimization loop that optimizes the low frequency performance of the closed loop system subject to additional performance and robustness criteria constrained by specifications. Modifications of the specifications then clearly shows the trade off between performance and robustness in different frequency regions. The controller synthesis is based on PID weighted H_∞ loop shaping where the structured singular value (μ) is used in the optimization to guarantee that the performance specifications are met in spite of the uncertainties. The optimization problems are costly, non-convex and ill-conditioned and we use a combination of new global and standard local optimization algorithms available in the TOMLAB optimization environment to solve the problem. The method, which does not rely on a good initial guess and converges robustly in finite time, is applied to a 2×2 model of a distillation column and the example shows how a slight modification of specifications on the sensitivity function and control activity may give large improvements in the load disturbance rejection