Multi-criteria Optimization of PD Controllers for Plants including Integral Action

A simple design method for robust PD controllers is presented for systems including integral action. The design method is based on a multi-criteria optimal control formulation, which is easily solved by a few lines of MATLAB code. Most criteria are based on H∞measures, but since the focus is on reference signal tracking and not load disturbance compensation, the settling time is also included as a relevant performance measure. Since a PD controller is equivalent to a lead filter, the optimal PD controller is compared with ordinary text book design rules for lead filters. More specifically, it is shown that the common recommendation to place the mid frequency of the lead filter at the desired gain crossover frequency often gives bad servo performance. The suggested optimal solution, still including robustness and control activity adjustments, is on the other hand a simple and flexible design method for arbitrary plants including integral action