Design of Stabilizing PI and PID Controllers

Tan, Nusret and Atherton, Derek P (2006) Design of Stabilizing PI and PID Controllers. International Journal of Systems Science, 37 (8). pp. 543-554. ISSN 0020-7721

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Abstract

In this paper, a new method for the calculation of all stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the (kp, ki)-plane and then computing the stabilizing values of the parameters of a PI controller for a given control system. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus, it offers several important advantages over existing results obtained in this direction. The proposed method is also applied for computation of all stabilizing PI controllers for multi-input multi-output (MIMO) control systems with consideration given to two-input two-output (TITO) systems using decoupling technique. Beyond stabilization, the method is used to compute all stabilizing PI controllers which achieve user-specified gain and phase margins. Furthermore, the method is extended to tackle 3-parameters PID controllers. The limiting values of PID controller parameters which stabilize a given system are obtained in the (kp, ki)-plane for fixed values of kd and (kp, kd)-plane for fixed values of ki. However, for the case of PID controller, a grid on the derivative gain or integral gain is needed for computation of all stabilizing PID controllers. Examples are given to show the benefits of the method presented.

Item Type: Article
Additional Information: The paper presents an improved method for calculating all stabilizing PI controllers which does not require either sweeping over all parameters or linear programming to solve a set of inequalities. Results are given for both SISO and TITO systems and the approach is then extended for finding parameter bounds to achieve user specified gain and phase margin conditions. The method is then extended to PID controllers, where it is shown that to compute all stabilizing parameters a grid on the derivative or integral gain is required.
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Derek Atherton
Date Deposited: 06 Feb 2012 18:37
Last Modified: 29 Mar 2012 13:48
URI: http://sro.sussex.ac.uk/id/eprint/17444
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