طراحی کنترلر ساده مقاوم PI / PID از طریق رویکرد بهینه سازی عددی

This paper presents a simple but effective method for designing robust PI or PID controller. The robust PI/PID controller design problem is solved by the maximization, on a finite interval, of the shortest distance from the Nyquist curve of the open loop transfer function to the critical point-1. Simulation studies are used to demonstrate the effectiveness of the proposed method.

The proportional-integral (PI) and proportional-integral-derivative (PID) controllers are widely used in many industrial control systems for several decades since Ziegler and Nichols proposed their first PID tuning method. This is because the PID controller structure is simple and its principle is easier to understand than most other advanced controllers. On the other hand, the general performance of PID controller is satisfactory in many applications. For these reasons, the majority of the controllers used in industry are of PI/PID type. Most of real plant operate in a wide range of operating conditions, the robustness is then an important feature of the closed loop system. When this is the case, the controller has to be able to stabilize the system for all operating conditions. To this end, it is possible to employ an internal-model-based PID tuning method [12] and [4]. However, this method gives very slow response to load disturbance for lag-dominant processes because of the pole-zero cancellations inherent in the design methodology [2]. Another popular approach with similar emphasis is the tuning of PI or PID controller by the gain and phase margin specifications [9] and [1]. Gain margin and phase margin have always served as important measures of robustness. It is well known that phase margin is related to the damping of the system, and can therefore also serve as a performance measure [6]. In this way, numerous progress has been made to improve the performances of the PI/PID control [8]. In particular, tuning methods based on optimization approach have recently received more attention in the literature, with the aim of ensuring good stability robustness of the controlled system [10] and [7]. However, these new methods are not easy to use for the operating engineer who is the main user of the PI/PID controller. The objective of this paper is to propose a novel robust PI or PID controller which is simple and easy to use. The paper is organized as follows. Section 2 presents the process models used for the synthesis of the PI or PID controller. In Section 3, the robust PI/PID controller design problem is formulated and solved by the maximization, on a finite interval, of the shortest distance from the Nyquist curve of the open loop transfer function to the critical point-1. Simulation studies are conducted in Section 4 and comparison with the works of other authors are given. Section 5 concludes this paper.

n this paper, a simple robust PI/PID controller design method was developed via numerical optimization approach. Various simulation studies have demonstrated the effectiveness of the proposed approach.