Frequency-domain analysis for reset systems using pulse-based model

In the precision motion industry, the demand for machines with higher speed, accuracy, and stability is rapidly increasing. Traditional linear controllers struggle to meet these requirements due to fundamental limitations such as Bode's gain-phase relationship and waterbed effects. Hence, non-linear controllers that can address these constraints are needed. Reset controllers are potential alternatives with the advantage of phase lead in comparison to their linear counterparts. However, reset controllers are incompatible with the loop-shaping analysis technique, since loop-shaping relies on the simple first-order element, whereas reset controllers include complex higher-order harmonics. Thus, the analysis and design of reset controllers remain bottlenecks in their way of widespread application. In this paper, a new analytical technique for reset controllers is proposed to break the limitations. A novel pulse-based model for analyzing general reset control systems both in open-loop and closed-loop is developed, for the first time enabling loop-shaping implemented into the analysis of reset control systems accurately. Corresponding sensitivity functions are subsequently illustrated. Finally, through intuitive examples, the accuracy of the proposed model is evaluated.