Parameter estimation of an unstable system with a PID controller in a closed loop configuration

An essential part of the auto-tuning control involves parameter estimation of a suitable low order model. Since a common way to control an unstable system is via a PID controller, there is a growing interest in the application of new PID-based algorithms for the identification task. In this light the relative advantages of two recently published methods are investigated. The first method is based on typical data of the reaction curve and the time delay is measured directly from the initial portion of the curve. The second method utilizes a least-squares algorithm to get an equivalent time delay together with the values of the other parameters. Thus, the obtained time delay approximates not only the true delay but also part of the nonlinear and the higher order dynamics. This is an advantage when a PID auto-tuning is sought. Two examples are provided to demonstrate and compare between the results of the methods.