Closed-loop identification of a first-order plus time delay model using Lambert W function

Abstract

The paper considers the estimation of all parameters of a first-order plus time delay system model. A new analytic method of parameter identification was introduced. Parameter estimation is based on the data received from the closed-loop step response using proportional controller. With the usage of Lambert W function for the chosen proportional gain as well as the received gain of the first-order plus time delay model, the time constant and the time delay are received by solving the transcendental characteristic system equation. The results were compared to the results of the other methods from literature.