Overshoot Elimination for Control Systems with Parametric Uncertainty via a PID Controller

Abstract

One of the key performance requirements for different control systems is non-overshooting step response, so that the controllable value should not overcome the reference value within a transient process. The problem of providing a non-overshooting step response was examined in this paper. Despite much scientific research being dedicated to the overshoot elimination problem, there are little to no results regarding parametric uncertainty for the discussed problem. Consideration of parametric uncertainty, particularly in the form of interval-given parameters, is essential, since in many physical processes, electronic devices and control systems parameter values can be obtained with acceptable error, and they can vary under different conditions. The main result of our research is the development of a proportional-integral-derivative (PID)-controller tuning approach for systems with interval-given parameters that provides a non-overshooting step response for such classes of control systems. This paper investigates analytical conditions and constraints for linear time invariant (LTI) systems in order to have no overshoot, enhances them with respect to parametric uncertainty, and formulates rules for tuning choices of parameters.