LQG-Optimal versus Simple Event-Based PID Controllers

Abstract

In this paper, we study event-based PID control from an optimal stochastic control perspective. The purpose is to better understand what implementation features are critical for achieving good event-based PID performance. For this end, we formulate an LQG control design problem for a double integrator process with an integral disturbance, where the solution is an ideal PID controller. We then consider the tradeoff between LQG cost and average sampling rate and give an interpretation of the optimal sampled-data controller and event- based sampling policy in terms of PID control. Based on insights from the optimal solution, we finally discuss how suboptimal but simple event-based PID controllers can be implemented. The proposed implementation is evaluated in a simulation study and compared to earlier work in event-based PID control. The results highlight the importance of considering both the triggering rule and the transmitted information in order to obtain an event-based PID controller with good performance.