Frequency-domain optimization of fixed-structure controllers

This paper aims to introduce a new approach to optimize the tunable controller parameters of linear parameterizable controllers. The presented approach is frequency-domain based and can therefore directly be used to tune, among others, proportional integral derivative controllers, low/high-pass filters, and notch filters, using a Frequency Response Function of the plant. The approach taken in this paper is to extract the tunable controller parameters into a diagonal matrix gain and absorb the remainder of the controller in the plant. Then, the generalized Nyquist stability criterion is exploited so as to impose stability and H∞ performance specifications on the closed-loop system. It is shown that the approach results in a convex feasibility problem for certain controller cases and can be reformulated such that it can also be used for grey-box system identification. Simulation and experimental examples demonstrate the efficacy of the approach.