A Frequency-Domain Tuning Method for a Class of Reset Control Systems

Stacking Integrators Without Sacrificing the Overshoot in Reset Control Systems

“…It is worth mentioning that the CgLp element has a constant gain and since according to Remark 2, CR architecture will not change the gain and phase behaviour of CgLp, the overall control loop will have a DF gain and phase matching to that of PI n D. Thus the control design in open-loop can be done in frequency domain. According to the guidelines presented in [10], [14], [19] for tuning of CgLp elements, the following values can be proposed for CgLp parameters:…”

“…Describing Function (DF) analysis of this element shows that it can provide broadband phase lead while maintaining a constant gain. Such an element is used in the literature to replace some part of the differentiation action in PID controllers as it will help improve the precision of the system according to loop-shaping concept [10], [13], [14], [19]. In [13], [19], it is suggested that DF analysis for reset control systems can be inaccurate as it neglects the higher-order harmonics created in response of reset control systems.…”

Complex-order Reset Control System

“…DF analysis of this element shows that it can provide broadband phase lead while maintaining a constant gain. Such an element is used in the literature to replace some part of the differentiation action in PID controllers as it will help improve the precision of the system according to the loop-shaping concept [17]- [20]. Despite the fact that the analysis and designs are focused on describing functions without taking higher-order harmonics into account, significant tracking and steady-state precision improvements are reported.…”