On the Intelligent Proportional Controller Applied to Linear Systems

TL;DR

This paper investigates the stability effects of the intelligent proportional controller on linear systems, deriving conditions for stability and instability, supported by simulations and experimental validation.

Contribution

It provides new stability criteria for the intelligent proportional controller applied to linear systems, including conditions for failure and success.

Findings

Identifies conditions where the controller fails to ensure exponential stability.

Provides criteria for achieving exponential stability with the controller.

Validates results through numerical simulations and an electronic throttle valve experiment.

Abstract

We analyze in this paper the effect of the well known intelligent proportional controller on the stability of linear control systems. Inspired by the literature on neutral time delay systems and advanced type systems, we derive sufficient conditions on the order of the control system, under which, the used controller fails to achieve exponential stability. Furthermore, we obtain conditions, relating the system s and the control parameters, such that the closed-loop system is either unstable or not exponentially stable. After that, we provide cases where the intelligent proportional controller achieves exponential stability. The obtained results are illustrated via numerical simulations, and on an experimental benchmark that consists of an electronic throttle valve.