Sampled-data implementation of derivative-dependent control using artificial delays

TL;DR

This paper presents a method for implementing derivative-dependent controllers in sampled-data systems using artificial delays, ensuring stability through LMIs and introducing event-triggering to reduce control signal usage.

Contribution

It develops a stability-preserving sampled-data implementation for derivative-dependent controllers using LMIs and introduces an event-triggering mechanism to optimize control signal usage.

Findings

Maximum sampling period derived from LMIs.

Stability preserved under fast sampling.

Event-triggering reduces control signal updates.

Abstract

We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\ge 2$ that can be stabilized using $r-1$ output derivatives. Then, we consider PID control of a second order system. In both cases, the Euler approximation is used for the derivatives giving rise to a delayed sampled-data controller. Given a derivative-dependent controller that stabilizes the system, we show how to choose the parameters of the delayed sampled-data controller that preserves the stability under fast enough sampling. The maximum sampling period is obtained from LMIs that are derived using the Taylor's expansion of the delayed terms with the remainders compensated by appropriate Lyapunov-Krasovskii functionals. Finally, we introduce the event-triggering mechanism that may reduce the amount of sampled control signals used for stabilization.