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

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.