  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.
