Identification of Time-Delayed Second-Order Unstable systems with Two RHP Poles and no zeros

This article presents new methods for identifying the model parameters of a pure unstable second-order system with time delay (two right-hand side poles without zero) using the closed-loop response. Identification of second-order systems with two unstable poles and no zeros is difficult due to the inherent instability, noise sensitivity, limited excitation possibilities, numerical challenges, and model validation issues associated with such systems. Expertise in system identification, control theory, and numerical methods is crucial when working with these complex dynamics. The process parameters of the transfer function are determined using the nonlinear least square optimization technique and particle swarm optimization technique. Analytical expressions are developed using the process responses to obtain the initial guess values for the model parameters. A mathematical procedure brings the initial guess values for parameters. The method is implemented on an unstable second-order with a time delay system, utilizing a feedback control method. The process response of the model identified by the proposed approaches to set point change compared with that of the actual process. Using both the Least Squares (LSQ) and Particle Swarm Optimization (PSO) methods is supported by evaluations against actual system performance criteria, revealing small but acceptable deviations like 0.88% in integral absolute error. The technique is simple to implement and requires a minimal processing time of around 21 seconds—developed methods for identifying the entire second-order unstable scalar system.