Convenient parameter estimation approaches for process control systems with time-delay via step responses

This paper focuses on the problem of the parameter estimation for the control systems with a time-delay. Many control systems can be expressed by a first-order system with a time-delay, which is used widely in process control for its good characteristic of describing the dynamical systems. In this work, an easy method for estimating the parameters of the first-order system with time-delay is presented based on the observed data from the discrete-time sampling. By picking up some datum points and having some convenient operations, the convenient parameter estimation methods, i.e., the one-point method and the two-point method are developed for the time-delay systems. The numerical simulation is carried out to test the performance of the proposed approaches.

1 Introduction

System identification is the study of the theory and method to establish the mathematical model of dynamic systems [1]–[5]. In terms of the system style, it can be divided into linear systems and nonlinear systems, time invariant systems and time-varying systems. Although the real systems are nonlinear time-varying systems, the analysis and synthesis of nonlinear time-varying systems are extremely complicated. In other hand, the linear system theory is extremely mature and many control strategies are based on the approximated linear systems. The actual system is often approximated as a linear system by linearization at the operating point, so that linear system theory can be used for analysis and controller design [6],[7]. Transfer function is a continuous time model to describe the dynamic characteristics of the system in the analysis and design of classical control systems. Even though many advanced control methods are developed, most of them are based on the transfer function models. In terms of many practical control objects, we cannot obtain the transfer functions to describe their dynamical characteristics from the mechanism. However, the dynamical information of the system can be obtained by applying a certain input signal to the system [8], [9]. These dynamical information reflects the characteristics of the systems, which can be collected and used to construct the system models.