On LQG-Optimal and Heuristic Event-Based PID Controllers

We formulate an LQG design problem where the solution is an ideal PID controller with given parameters. For this design problem, we then consider the trade-off 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 discuss how suboptimal but simpler event-based PID controllers could be implemented. The proposed controllers are 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. (Less)