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PID Tuning Using Extremum Seeking

Description: 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 ...
Date: November 15, 2005
Creator: Killingsworth, N & Krstic, M
Partner: UNT Libraries Government Documents Department

Surface topography measurements over the 1 meter to 10 micrometer spatial period bandwidth

Description: A recently-developed long-trace surface profiling instrument (LTP) is now in operation in our laboratory measuring surface profiles on grazing incidence aspheres and also conventional optical surface. The LTP characterizes surface height profiles in a non-contact manner over spatial periods ranging from 1 meter (the maximum scan length) to 2 mm (the Nyquist period for 1 mm sampling period) and complements the range of our WYKO NCP-1000 2.5X surface roughness profiler (5 mm to 9.8 {mu}m). Using these two instruments, we can fully characterize both figure and finish of an optical surface in the same way that we normally characterize surface finish, e.g., by means of the power spectral density function in the spatial frequency domain. A great deal of information about the distribution of figure errors over various spatial frequency ranges is available from this data, which is useful for process control and predicting performance at the desired wavelength and incidence angle. In addition, the LTP is able to measure the absolute radius of curvature on long-radius optics with high precision and accuracy. Angular errors in the optical head are measured in real time by an electronic autocollimator as the head traverses the linear air bearing slide. Measurements of kilometer radius optics can be made very quickly and the data analyzed in a format that is very easy to understand. 17 refs., 10 figs.
Date: September 1, 1989
Creator: Takacs, P.Z.; Furenlid, K.; DeBiasse, R.A.; Church, E.L. (Brookhaven National Lab., Upton, NY (USA) & Army Research and Development Command, Dover, NJ (USA))
Partner: UNT Libraries Government Documents Department