Stability Analysis and Controller Design for Unstable Systems Using Relay Feedback Approach

Abstract

In this paper, a novel approach to identify the parameters of the unstable systems is considered and the stability analysis of the unstable system has been carried out. The relay feedback approach has been chosen to obtain the sustained oscillations, and single-relay feedback approach is considered for different bench examples for the analysis purpose unlike the conventional Z–N methods. The simplest method to generate sustained oscillation is used. An attempt is made to stabilize the oscillations of the unstable process considered, and the stability checking criterion such as Nyquist plot was also used. Simple relay identification with hysteresis is used to identify the unstable system parameters. In this analysis, a few transfer functions are considered with ratio of time delay to time constant less than 0.693 for analysis purpose. A new method of control is proposed for different unstable systems.