Asian Journal of Control, Vol. 13, No. 2, pp. 328 337, March 2011 Published online 25 November 2010 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/asjc.278 –Brief Paper– INTEGRAL CRITERIA FOR OPTIMAL TUNING OF PI/PID CONTROLLERS FOR INTEGRATING PROCESSES Ahmad Ali and Somanath Majhi ABSTRACT Tuning formulas for PI/PID controllers for integrating processes are presented in this paper. The controller parameters are obtained by minimizing various integral performance index. Bacterial Foraging strategy, a new entrant to the family of evolutionary algorithms is used for minimization to avoid the local minima in the optimization procedure. A setpoint filter is used to reduce the large overshoot, and a significant improvement in control performance is obtained when compared to recently reported methods. Simulation results for an assumed perturbation in the plant delay are also given to illustrate the robustness of the proposed controller design method. Key Words: Optimal, integrating processes, PID controller, robustness. I. INTRODUCTION The ability of proportional-integral (PI) and proportional-integral-derivative (PID) controllers to meet most of the control objectives has led to their widespread acceptance in the control industry. The absence of derivative action makes PI controllers less sensitive to noise and more preferable than PID controllers [1]. A comprehensive summary of PI and PID controller tuning relations proposed in the literature is given in [2]. It can be concluded from [2] that there are many more tuning rules for stable overdamped processes than for unstable and integrating processes. Several PI/PID tuning methods for integrating processes have been proposed in the literature [3–9]. Tyreus and Luyben [3] have shown that the IMC based PI controller can lead to poor control performance if Manuscript received September 1, 2008; revised January 2, 2009; accepted October 2, 2009. A. Ali is with the Department of Electrical Engineering, Indian Institute of Technology Patna, Bihar-800013, India (e-mail: ali@iitp.ac.in). S. Majhi is Professor and Head of the Department of Electronics and Communication Engineering, Indian Insti- tute of Technology Guwahati, Guwahati-781039, Assam, India (e-mail: smajhi@iitg.ernet.in). the closedloop time constant is not chosen properly. Furthermore, the authors have proposed simple tuning rules based on the classical frequency response method to achieve maximum closed loop log modulus of 2 dB. Two methods for obtaining the parameters of the PI controller are proposed in [5]. In the first method (KPGM), the controller parameters are obtained to achieve user defined values of gain and phase margins whereas the controller settings are obtained by mini- mizing weighted ISE in the second method (KWISE). Tuning rules for PI controllers based on the maximum peak resonance specification are proposed in [6]. However, the above methods do not give settings for PID controllers. The method proposed in [3] is extended for designing PID controllers in [4]. The desired control signal trajectory is used as a performance specification to design the PID controller in [8]. Chidambaram and Sree [9] have obtained the parameters of a PI, PID and PD controller by matching the coefficients of corre- sponding powers of s in the numerator to that in the denominator of the closed loop transfer function for a servo problem. The method proposed in [9] is extended using two tuning parameters to improve robustness by Sree and Chidambaram [10]. Skogestad [11] has used the IMC framework to derive tuning rules (SIMC) for PI/PID controllers for various class of process models. As the ISTE criterion results in step responses with 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society