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The ever-increasing industry desire for improved performance makes linearcontroller design run into fundamental limitations. Nonlinear control methodssuch as Reset Control (RC) are needed to overcome these. RC is a promisingcandidate since, unlike other nonlinear methods, it easily integrates into theindustry-preferred PID design framework. Thus far, RC has been analysed in thefrequency domain either through describing function analysis or by directclosed-loop numerical computation. The former computes a simplified closed-loopRC response by assuming a sufficient low-pass behaviour. In doing so it ignoresall harmonics, which literature has found to cause significant modellingprediction errors. The latter gives a precise solution, but by its directclosed-loop computation does not clearly show how open-loop RC designtranslates to closed-loop performance. The main contribution of this work isaimed at overcoming these limitations by considering an alternative approachfor modelling RC using state-dependent impulse inputs. This permits accuratelycomputing closed-loop RC behaviour starting from the underlying linear system,improving system understanding. A frequency-domain description for closed-loopRC is obtained, which is solved analytically by using several well-definedassumptions. This analytical solution is verified using a simulatedhigh-precision stage, critically examining sources of modelling errors. Theaccuracy of the proposed method is further substantiated using controllersdesigned for various specifications.

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