  Reset controllers have demonstrated their effectiveness in enhancing
performance in precision motion systems. To further exploiting the potential of
reset controllers, this study introduces a parallel-partial reset control
structure. Frequency response analysis is effective for the design and
fine-tuning of controllers in industries. However, conducting frequency
response analysis for reset control systems poses challenges due to their
nonlinearities. We develop frequency response analysis methods for both the
open-loop and closed-loop parallel-partial reset systems. Simulation results
validate the accuracy of the analysis methods, showcasing precision
enhancements exceeding 100% compared to the traditional describing function
method. Furthermore, we design a parallel-partial reset controller within the
Proportional-Integral-Derivative (PID) control structure for a
mass-spring-damper system. The frequency response analysis of the designed
system indicates that, while maintaining the same bandwidth and phase margin of
the first-order harmonics, the new system exhibits lower magnitudes of
higher-order harmonics, compared to the traditional reset system. Moreover,
simulation results demonstrate that the new system achieves lower overshoot and
quicker settling time compared to both the traditional reset and linear
systems.
