Robust syntesis of the proportional integral diferential controller for discret-continuous system

Abstract

This article is aimed to improve the robust synthesis of the discrete proportional-integraldifferential (PID) controller with first and second derivatives in the control law. The PID control tuning and synthesis methods are based, in many cases, on the experimental or online information without mathematical model. Also, the fuzzy PID control is in usage. The synthesis problem of PID control still actual, because of plant uncertainty and perturbations. Then, the enhanced PIDm control with m-order derivatives in the control law is offered in this article. The proposal is based on the modal control with high amplification in the PIDm control channel. That provide the domination of the controller parameters in the system when plant parameters are uncertain. However, in case of the discrete (digital) control, the linear system stability is bounded by the amplification values, so the additional analysis is required. The analysis is accomplished of the system with PID controllers in cases of m = 1 and m = 2. The expressions are established for PID controllers parametrization. The developed PID parametrization can be evaluate for m ≥ 2. The simulation is accomplished of the systems with proposed parametrization of PIDm controllers for m = 1 and m = 2 cases. The results of the simulation show the effectiveness of the proposed technique of synthesis in conditions of plant perturbations.