Robust Loop Shaping Controller Design for Spectral Models by Quadratic Programming

A quadratic programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants represented by spectral models. The method is based on the shaping of the open-loop or closed-loop frequency functions in the Nyquist diagram. The quadratic error between a desired open loop transfer function and the actual open loop frequency function is minimized in the frequency domain subject to linear constraints guaranteeing stability and robustness margins by quadratic programming. Moreover, it is shown that the H infinity mixed sensitivity robust performance problem can be approximated by linear constraints and be integrated in the control design method. The method can directly consider multi-model as well as frequency-domain uncertainties. An application to a difficult benchmark problem illustrates the effectiveness of the proposed approach.