Controller approximation using semidefinite programming

Controller design, and the resulting control system performance, is frequently limited by the capabilities of the available control system hardware. When the control system hardware provides only a small set of fixed controller structures (e.g., proportional-integral-derivative, PID) or limited programming capabilities, it may be desirable to use the available functional elements in a manner such that the implemented fixed structure controller matches the performance of some reference advanced controller as closely as possible. This paper presents a systematic method for approximating the performance of an advanced controller with simpler fixed structure controllers using semidefinite programming. Tuning of the simple, fixed structure controller is obtained by matching a specific desired behavior of the advanced controller. The proposed method is illustrated using two case studies: the approximation of a linear quadratic regulator for a distillation column by a multiloop PID controller and cross-direction profile control for a paper machine.