Frequency-Domain Modelling of Reset Control Systems using an Impulsive Description

Abstract: The ever-increasing industry desire for improved performance makes linear controller design run into fundamental limitations. Nonlinear control methods such as Reset Control (RC) are needed to overcome these. RC is a promising candidate since, unlike other nonlinear methods, it easily integrates into the industry-preferred PID design framework. Thus far, RC has been analysed in the frequency domain either through describing function analysis or by direct closed-loop numerical computation. The former computes a simplified closed-loop RC response by assuming a sufficient low-pass behaviour. In doing so it ignores all harmonics, which literature has found to cause significant modelling prediction errors. The latter gives a precise solution, but by its direct closed-loop computation does not clearly show how open-loop RC design translates to closed-loop performance. The main contribution of this work is aimed at overcoming these limitations by considering an alternative approach for modelling RC using state-dependent impulse inputs. This permits accurately computing closed-loop RC behaviour starting from the underlying linear system, improving system understanding. A frequency-domain description for closed-loop RC is obtained, which is solved analytically by using several well-defined assumptions. This analytical solution is verified using a simulated high-precision stage, critically examining sources of modelling errors. The accuracy of the proposed method is further substantiated using controllers designed for various specifications.