A H∞ constrained robust H∞ solution for a benchmark problem

A combined H₂/H_∞ design method is applied to a benchmark problem. The approach is to design robust controllers that minimize an upper bound of a quadratic performance index subject to an H_∞ norm bound on a disturbance transfer function matrix. Real parameter variations are included in the design through the addition of fictitious weighted disturbances. Three design cases, each with different robustness, performance, and disturbance rejection requirements, are considered for the benchmark problem. Uncertain parameters and noncolocation of the sensor and actuator make the problem non-trivial. Compensators are found that meet the requirements with reasonable control effort, controller complexity, and noise rejection.