A New Design Method for PI‐PD Control of Unstable Fractional‐Order System with Time Delay

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.

Modified Cascade Controller Design for Unstable Processes With Large Dead Time

“…The maximum sensitivities of the inner and outer loops are assumed as 2 and 1.6 respectively (The sensitivity Ms and α are obtained by curve fitting toolbox using MATLAB and n this article it is recommended). The chosen fractional order parameters = = 0.2 (As suggested in [27] the values are taken), for the PI-PD primary controller is further used to obtain the PD and PI centroid controller parameters. The parameters of the centroid PD controller and PI controller are obtained as per the steps 1,2 and 3 of the parameter calculation.…”

“…The internal feedback loop characteristic equation can be further written as Eq (27), 28into the real and imaginary part and equate to 0 then we can obtain the unknown parameters of and . ∇ 2 = 2 + 2 = 0 (29) The 2 , 2 are the real and Imaginary part of the decomposed PD controller Eq (29) which is a function of the unknown parameters and and frequency variable.…”

“…The concept of PI-PD combined with the cascade structure for the stable and unstable process with the larger dead-time will provide the expected closed-loop response when the proper tuning methods are used. However, with the tuning methods of PI-PD controllers, there some severe problems pointed out in the chemical process due to uncertainties and larger delay time [26][27][28][29][30][31][32][33]. superior performance is reported recently with fractional controller design over the integer design.…”

Derivative Proportional – Integral Controller Using Nelder-Mead Optimization for Glycerine Purification Heating Process

“…In recent year, the Proportional Integral-Proportional Derivative (PI-PD) [19][20][21] control structure has been used in unstable system with time delay. The control structure was modified in which the PI action is on the error and the PD action is on the process variable.…”

Generic Noninteger Order Controller for Time-Delay Systems

“…Delays are involved in challenging areas of robotics and real-time systems [3], which are generally sources of instability. To eliminate this instability, researchers introduced several approaches of control among the conventional PID controller [4,5]. ese controllers are the most used in industrial purposes due to their simplicity, easy designing method, and their setting methods [6].…”