Calculation of PID Controller Parameters for Unstable First Order Time Delay Systems

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Author(s) 
Hamideh Hamidian, Ali Akbar Jalali 

KEYWORDS 
Fractional order PID controller, numerical approach, time delay.


ABSTRACT 
In this paper, a numerical approach for the fractional order proportionalintegralderivative controller (FOPID) design for the unstable first order time delay system is proposed. The controller design is based on the system time delay. In order to obtain the relation between the controller parameters and the time delay, for several amounts of the plant time delay and the fractional derivative and integral orders, the ranges of stabilizing controller parameters are determined. First, for a typical time delay plant and the fractional order controller, the Ddecomposition technique is used to plot the stability region(s). The controller derivative gain has been considered as one. By changing the fractional derivative and integral orders, a small amount in each stage, some ranges of proportional and integral gains are achieved which stabilize the system, independent of the fractional l , μ orders. Therefore a set of different controllers for any specified time delay system is obtained. This trend for several various systems with different values of time delay has been done and the proportional and integral gains of the stabilizing controller have been calculated.


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