Solution of the benchmark control problem by constrained H∞ optimization

Constrained H_∞ Optimization [2] allow the design of control laws which minimize the infinity norm of a (weighted) closed loop transfer function (Matrix) under the requirements of closed loop stability and constraints on several closed loop time responses to test signals (steps, impulses, etc.) over a finite horizon. This formulation provides a systematic tool to trade-off frequency and time domain specifications exactly and is ideally suited for the Benchmark Control. Problem which calls for frequency domain (robustness, noise attenuation) and time domain (settling times, limited control action) specifications. A sixth order controller is Produced, which achieves robustness with respect to the three uncertain parameters, achieves disturbance rejection with a settling time of l5secs while the control action remains within ±1, and achieves attenuation of high-frequency measurement noise at the plant input.