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.