PID Tuning Using Extremum Seeking

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Although proportional-integral-derivative (PID) controllers are widely used in the process industry, their effectiveness is often limited due to poor tuning. Manual tuning of PID controllers, which requires optimization of three parameters, is a time-consuming task. To remedy this difficulty, much effort has been invested in developing systematic tuning methods. Many of these methods rely on knowledge of the plant model or require special experiments to identify a suitable plant model. Reviews of these methods are given in [1] and the survey paper [2]. However, in many situations a plant model is not known, and it is not desirable to open ... continued below

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Killingsworth, N & Krstic, M November 15, 2005.

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Although proportional-integral-derivative (PID) controllers are widely used in the process industry, their effectiveness is often limited due to poor tuning. Manual tuning of PID controllers, which requires optimization of three parameters, is a time-consuming task. To remedy this difficulty, much effort has been invested in developing systematic tuning methods. Many of these methods rely on knowledge of the plant model or require special experiments to identify a suitable plant model. Reviews of these methods are given in [1] and the survey paper [2]. However, in many situations a plant model is not known, and it is not desirable to open the process loop for system identification. Thus a method for tuning PID parameters within a closed-loop setting is advantageous. In relay feedback tuning [3]-[5], the feedback controller is temporarily replaced by a relay. Relay feedback causes most systems to oscillate, thus determining one point on the Nyquist diagram. Based on the location of this point, PID parameters can be chosen to give the closed-loop system a desired phase and gain margin. An alternative tuning method, which does not require either a modification of the system or a system model, is unfalsified control [6], [7]. This method uses input-output data to determine whether a set of PID parameters meets performance specifications. An adaptive algorithm is used to update the PID controller based on whether or not the controller falsifies a given criterion. The method requires a finite set of candidate PID controllers that must be initially specified [6]. Unfalsified control for an infinite set of PID controllers has been developed in [7]; this approach requires a carefully chosen input signal [8]. Yet another model-free PID tuning method that does not require opening of the loop is iterative feedback tuning (IFT). IFT iteratively optimizes the controller parameters with respect to a cost function derived from the output signal of the closed-loop system, see [9]. This method is based on the performance of the closed-loop system during a step response experiment [10], [11]. In this article we present a method for optimizing the step response of a closed-loop system consisting of a PID controller and an unknown plant with a discrete version of extremum seeking (ES). Specifically, ES is used to minimize a cost function similar to that used in [10], [11], which quantifies the performance of the PID controller. ES, a non-model-based method, iteratively modifies the arguments (in this application the PID parameters) of a cost function so that the output of the cost function reaches a local minimum or local maximum. In the next section we apply ES to PID controller tuning. We illustrate this technique through simulations comparing the effectiveness of ES to other PID tuning methods. Next, we address the importance of the choice of cost function and consider the effect of controller saturation. Furthermore, we discuss the choice of ES tuning parameters. Finally, we offer some conclusions.

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PDF-file: 29 pages; size: 0.9 Mbytes

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  • Journal Name: IEEE Control Systems Magazine, vol. 26, no. 1, February 1, 2006, pp. 70-79

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  • Report No.: UCRL-JRNL-217161
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 898587
  • Archival Resource Key: ark:/67531/metadc888465

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  • November 15, 2005

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  • Sept. 22, 2016, 2:13 a.m.

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  • Nov. 30, 2016, 4:46 p.m.

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Killingsworth, N & Krstic, M. PID Tuning Using Extremum Seeking, article, November 15, 2005; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc888465/: accessed June 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.