Regular quantisation with hysteresis: a new sampling strategy for event‐based PID control systems

Abstract

In this study, a new sampling strategy for networked control systems, called regular quantification with hysteresis (RQH), is proposed. This alternative presents some benefits with respect to symmetric-send-on-delta sampling, which is one of the most used strategies in the event-based proportional-integral-derivative (PID) control loops. The behaviour of the RQH is defined by two parameters, the signal quantification and hysteresis, whose effect on the overall system performance is studied and guidelines about its choice are given in terms of noise measurement and steady-state error. The limit cycle oscillations that could be induced by this sampling strategy are studied and new robustness measures to avoid them are proposed based on the describing function approach. The suitability of some tuning rules for continuous PI when applied to control systems with a RQH sampling is evaluated using the proposed measures. The results show that these tuning rules can be applied under certain conditions.

Design and Analysis of an Active Disturbance Rejection Robust Adaptive Control System for Electromechanical Actuator

“…In the task of performing the ADRRAC for EMA position servo control, we take two other comparative control strategies, which are PID (Proportional Integral Derivative) control and ARC (Adaptive Robust Control). In practical use, the former is of high robustness and high reliability [36,37] while the latter is known for its stability and accuracy [38,39]. Specifically, the Ziegler-Nichols tuning method is applied to the PID controller for parameter tuning, based on which to reduce the oscillation and improve the robustness [40].…”

Event-Based PID Controllers with Fixed Threshold Sampling Strategies

“…To select the proper parameters for the RQH sampler a simple procedure was presented in [42]. Firstly, the hysteresis h is selected slightly greater than the peak-to-peak amplitude of the measure noise to prevent it from generating events.…”

“…Graphically, if it exists an intersection between the open-loop transfer function and the inverse negative of the DF, the system will present limit cycle oscillations. The DF for the RQH sampling strategy was presented in [42] and is given by the following equation:…”

“…Taking these effects of the hysteresis into account, in [42] a new sampling strategy called Regular Quantization with Hysteresis (RQH) was presented. This sampling strategy consists of a quantification with fixed thresholds and with variable hysteresis, which can be chosen freely, and depending on these parameters choice the intermediate cases between the RQ and SSOD appear.…”

“…In this chapter, a tuning procedure for PI controllers within a loop in which the error signal is sampled according to the RQH principles is proposed. The procedure takes into account classical robustness measures as gain and phase margin, as well as it includes specific robustness measures, also in terms of gain and phase, to the oscillations induced by the sampler in the loop, which were presented in [42]. The tuning procedure and the obtained margins are tested in simulation for several processes which prove the tuning procedure applicability.…”