Design of IMC-Based PID Controllers for FOPTD and SOPTD Models

Abstract

Compared to other controllers, PID controllers have been widely used in most industries since their structure is simple and can be operated relatively easily by field engineers. Generally, if the gain is increased to improve the performance of a PID controller, the overshoot increases, and sometimes the system becomes unstable. Conversely, if the gain is reduced, the response speed slows down and steady state errors exist, which can worsen performance. Therefore, in controller design and tuning, it is necessary to properly compromise this counter-relationship. A basic PID controller has three adjustment parameters: proportional gain, integral time, and derivative time. These must be adjusted harmoniously to improve the response performance of the system and ensure stability. However, it is not easy to properly balance the three parameters. Among the many methods to overcome this, control methods that have been used a lot recently are IMC-based PID control and DS-based PID control. The DS method adjusts the time constant of the desired closed loop transfer function to adjust the 3 parameters of PID control, and the IMC method adjusts the IMC filter time constant. In other words, what these two methods have in common is that they only have one adjustment variable to adjust the three parameters of the PID controller. Therefore, after designing a PID controller, the method of tuning the three parameters is generally easier than the other methods. However, in general, the DS method is often more complicated than the IMC method in the process of developing a formula to obtain the parameters of a controller. Therefore, in this paper, IMC-based PID controller design and tuning technique based on IMC principles is proposed. To verify the validity of the proposed method, it was applied to two FOPTD models and two SOPTD models. The proposed controller is compared to the controller proposed by Lee and Skogestad for FOPTD models, and the controller proposed by Louis Ben and Skogestad for SOPTD models.