Abstract
In this paper, a practical PI‐PD controller parameter tuning method is proposed, which uses the incenter of the triangle and the Fermat point of the convex polygon to optimize the PI‐PD controller. Combined with the stability boundary locus method, the PI‐PD controller parameters that can ensure stability for the unstable fractional‐order system with time delay are obtained. Firstly, the parameters of the inner‐loop PD controller are determined by the centre coordinates of the CSR in the kd − kf plane. Secondly, a new graphical method is used to calculate the parameters of the PI controller, in which Fermat points in the CSR of (kp − ki) plane are selected. Furthermore, the method is extended to uncertain systems, and the PI‐PD controller parameters are obtained by using the proposed method through common stable region of all stable regions. The proposed graphical method not only ensures the stability of the closed‐loop system but also avoids the complicated optimization calculations. The superior control performance of this method is illustrated by simulation.
Highlights
Proportional-integral-derivative (PID) controller has been widely used in industrial control systems for decades because of its simple structure and convenient implementation [1,2,3,4,5,6]
Embedding PD controller parameters into transfer function, desired stability boundary locus of Pl controller is computed by the same procedure. en, a quadrilateral Fermat point in convex stable region (CSR) of the outer loop is obtained which is the parameter of the PI controller. is method only needs simple geometric calculation to obtain the parameters of the PIPD controller, which is solved in the stable region to ensure the closed-loop stability
In order to ensure that the obtained point is in the stable region, here we propose the concept of the incenter of the CSR, whose coordinate expression is as follows: a
Summary
Proportional-integral-derivative (PID) controller has been widely used in industrial control systems for decades because of its simple structure and convenient implementation [1,2,3,4,5,6]. E integral-order PID (IOPID) controller has limitations in control integration, instability, and delay process, and it often leads to large step response, large overshoot, and large impact, especially for unstable complex systems with time delay, and it is di cult to obtain good closed-loop performance [8,9,10,11,12]. Is method only needs simple geometric calculation to obtain the parameters of the PIPD controller, which is solved in the stable region to ensure the closed-loop stability. It uses several special points of the stable region and fewer points describing the coordinates than the WGC method, ensuring that the calculated points are situated in the stable region and the PI-PD controller has superior robustness.
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