Tuning proportional, integral, derivative controllers using error-integral criteria and response surfaces based optimization

A method for tuning a Proportional, Integral, Derivative (PID) controller in order to optimize its response is presented. A state-space realization of the controller and the plant is used. A response surface approximation-based optimization approach is used to minimize the number of detailed controller response analyses. A heuristic algorithm is used to select designs that are close to D-optimal designs to construct the initial linear approximation. The tuning methodology is directly applicable to multi-input, multi-output control systems and is shown to obtain improved results compared to the traditional tuning techniques such as Ziegler–Nichols method. Realistic applications are provided to illustrate the method outlined in this paper.