Researches On PID Controllers For First-Order System With Time Delay In Frequency Domain

In industrial processes, there exist time delays in different degrees. It is difficult to control a process with time delay. The larger the percent of time delay in the whole dynamic process, the more difficult to control it. Therefore, stabilizing a time-delay system is important for process control. The open-loop transfer function of an industrial process is often described as a first-order process with time delay.PID controllers have become one of the basic control schemes and are widely used in industry control because of their simple configurations, clear functions and strong robustness. The paper uses PID control scheme to stabilize a first-order linear system with time delay. Because the closed-loop system has the time delay unit in its characteristic equation, it is difficult to analyze the stability with the latent root. The paper uses the bode plot frequency-domain design method of the classical control theory. Some questions of the first-order time-delay systems are analyzed based on the method. The main content in this paper is stated as follows:1) Introducing lots of achievements in the area of stabilizing time-delay systems with the frequency-domain design method of control theory, especially the Smith predictor.2) The problem of stabilizing a first-order time-delay system with PID controller is discussed with two steps. In the first step, it discusses the complete parameter sets of stabilizing PI controllers for both first-order stable and unstable systems with time delays. Using frequency-domain design method, not only the complete parameter set of stabilizing PI controller is achieved, but also the necessary and sufficient condition for the existence of a stabilizing PI controller for an open-loop unstable system is derived. In the second step, it also discusses the problem of first-order time-delay systems with PID controllers. Both the complete set of stabilizing PID parameters and the necessary and sufficient condition for the existence of a stabilizing PID controller for an open-loop unstable system is obtained. The complete set of cut frequency and its turning direction is deduced simultaneously.3) Doing some researches on the stabilization of first-order multivariable time delay systems with PID controllers. Based on the row characteristic transfer function method and the pseudodiagonalisation method, the multivariable stabilizing PID controllers are designed respectively. The controllers which aredesigned with the former method have strong robustness. At last the advantage and disadvantage of two methods are pointed out, and the parts which need to be improved are also illustrated.Finally, a conclusion of the whole paper and some advises for the future researches are presented.