Optimal Design of Low Order Controllers Satisfying Sensitivity and Robustness Constraints

The set of all stabilizing controllers of a given low order structure that guarantee specifications on the gain margin, phase margin and a bound on the sensitivity corresponds to a region in n-dimensional space defined by the coefficients of the controllers. For several practical criteria defined in the paper it is shown that the optimal controller lies on the surface of that region. Moreover, it is shown how to reduce that region to avoid actuator saturation during operation.