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 its fundamental limitations. A nonlinear controller, such as Reset Control (RC), is needed to overcome these. RC is promising since, unlike other nonlinear methods, it easily integrates into the PID design framework preferred by industry. Thus far, closed-loop behaviour of RC has been analysed in the frequency domain either through Describing Function analysis or by direct closed-loop numerical computation. The former method computes a simplified closed-loop RC response by ignoring all harmonics, an approach which literature has found to inflict significant modelling errors. The latter method gives an accurate solution but does not provide understanding of how open-loop RC design affects closed-loop performance. No methods link these aspects, which impairs RC design and tuning. The main contribution of this work is aimed at providing this link, while achieving an accurate closed-loop RC model. A novel approach for modelling RC is considered, which uses state-dependent impulse inputs. This approach is shown to permit an accurate computation of closed-loop RC behaviour starting from an open-loop model, thus linking both aspects, enhancing system understanding. A frequency-domain description for closed-loop RC is obtained, as needed for the PID design framework, which is solved for analytically by inserting several well-defined assumptions. This 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.