PID Tuning Using Extremum Seeking Page: 4 of 29
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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 , . 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 .
Unfalsified control for an infinite set of PID controllers has been developed in ; this approach
requires a carefully chosen input signal .
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 . This method
is based on the performance of the closed-loop system during a step response experiment ,
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 ,
, 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,
Here’s what’s next.
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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/m1/4/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.