Discretization and Stabilization of Energy-Based Controller for Period Switching Control and Flexible Scheduling

TL;DR

This paper presents a novel discretization method for energy-based controllers that can switch between multiple periods, enhancing system flexibility and stability in real-time control applications with variable sampling rates.

Contribution

It introduces the first discretization approach for energy-based controllers capable of arbitrary period switching without destabilization, with a practical digital controller design and stability analysis.

Findings

Effective control of a DC motor with elastic load demonstrated

Controller maintains stability across multiple switching periods

Simulation results confirm robustness and adaptability

Abstract

Emerging advanced control applications, with increased complexity in software but limited computing resources, suggest that real-time controllers should have adaptable designs. These control strategies also should be designed with consideration of the run-time behavior of the system. One of such research attempts is to design the controller along with the task scheduler, known as control-scheduling co-design, for more predictable timing behavior as well as surviving system overloads. Unlike traditional controller designs, which have equal-distance sampling periods, the co-design approach increases the system flexibility and resilience by explicitly considering timing properties, for example using an event-based controller or with multiple sampling times (non-uniform sampling and control). Within this context, we introduce the first work on the discretization of an energy-based controller that can switch arbitrarily between multiple periods and adjust the control parameters accordingly without destabilizing the system. A digital controller design based on this paradigm for a DC motor with an elastic load as an example is introduced and the stability condition is given based on the proposed Lyapunov function. The method is evaluated with various computer-based simulations which demonstrate its effectiveness.