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Parametric optimization-based design of PI controllers: application to a DC servomechanism

Mohammad Tabatabaei (Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran)

World Journal of Engineering

ISSN: 1708-5284

Article publication date: 30 May 2019

Issue publication date: 14 June 2019




This paper aims to propose an analytical method for designing parametric optimization-based proportional integral (PI) controllers.


In this method, a performance index containing the weighted summation of the integral square of the error and its derivative is minimized. This performance index is analytically calculated in terms of the controller parameters by solving a Lyapunov equation. Then partial derivatives of the performance index with respect to controller parameters are calculated. Equating these partial derivatives to zero gives explicit relations for the PI controller parameters.


The experimental tests on a DC servomotor system are given to demonstrate the efficiency of the proposed method.


This paper proposes an analytical parametric optimization approach for designing PI controllers for the first time. The application of the proposed method in a laboratory experiment is examined.



Tabatabaei, M. (2019), "Parametric optimization-based design of PI controllers: application to a DC servomechanism", World Journal of Engineering, Vol. 16 No. 3, pp. 351-356.



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