Reset Control Systems in Dynamical Frameworks

Reset control systems represent a class of hybrid regulators that intertwine continuous dynamics with discrete state resets, offering an avenue to transcend the fundamental limits of linear controllers. At their core, reset controllers periodically reset selected internal states to predefined values when specific trigger conditions are met, thereby introducing controlled nonlinearity. This mechanism can significantly reduce phase lag and sharpen transient performance without sacrificing robustness. Within dynamical frameworks, these systems are modelled as impulsive dynamical systems, wherein the continuous evolution is interrupted by instantaneous jumps. Such a representation unifies the analysis of existence and uniqueness of solutions, stability criteria and frequency-domain characteristics. Advances in analytical tools, spanning describing function methods, Lyapunov-based criteria and frequency-domain formulations, have broadened the understanding of stability and performance trade-offs. Applications span high-precision motion platforms, power electronics and automotive systems, where reset strategies can mitigate overshoot, enhance disturbance rejection and circumvent limitations such as the waterbed effect. The global relevance of reset control emerges from its capacity to integrate seamlessly into established proportional–integral–derivative design workflows, offering industry practitioners a practical route to performance improvements without wholesale paradigm shifts.

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Research from all publishers

Recent work in Automatica has developed a frequency-domain stability assessment tailored to first- and second-order reset elements, enabling practitioners to infer uniformly bounded-input bounded-state behaviour directly from measured frequency responses. This approach facilitates the design of high-precision motion controllers without reliance on detailed parametric models. Complementing this, studies in Nonlinear Analysis: Hybrid Systems have introduced an impulsive description for reset control, treating resets as state-dependent impulses and yielding an analytic closed-loop frequency-domain model. This framework clarifies how open-loop design choices propagate into closed-loop performance and offers a more accurate prediction of harmonic content than classical describing functions. Further insights have emerged in the IEEE Transactions on Automatic Control, where a closed-loop frequency-analysis tool has been proposed to characterise both the fundamental and higher-order harmonics of reset systems under periodic excitation. By defining pseudosensitivities, this method streamlines the evaluation of robustness and performance trade-offs, providing a direct software-oriented implementation for control engineers.

Reset Control Systems in Dynamical Frameworks publication trend

The graph below shows the total number of articles in reset control systems in dynamical frameworks across all publications each year (not limited to Nature Index journals).

Technical terms

Reset element: A controller component whose state is instantaneously set to a specified value when a predefined condition is met, introducing controlled nonlinearity.

Describing function: An approximate analysis technique that characterises the fundamental harmonic response of a nonlinear element under sinusoidal excitation.

Uniformly bounded-input bounded-state (UBIBS): A stability property ensuring that any bounded input yields a system state that remains bounded for all time.

Impulsive description: A mathematical representation of a hybrid system in which discrete resets are modelled as instantaneous impulses affecting the continuous state trajectory.

Closed-loop frequency response: The relationship between periodic reference or disturbance signals and the resulting steady-state output of a feedback system, encompassing fundamental and higher-order harmonic content.

References

1. Frequency-domain stability methods for reset control systems. Automatica (2023).
2. Frequency-domain modelling of reset control systems using an impulsive description. Nonlinear Analysis Hybrid Systems (2023).
3. Closed-Loop Frequency Analysis of Reset Control Systems. IEEE Transactions on Automatic Control (2022).
4. Well‐Posedness of Reset Control Systems as State‐Dependent Impulsive Dynamical Systems. Abstract and Applied Analysis (2012).