• TITLE: QFT Automatic Loop-Shaping of QFT Controllers via Linear Programming
• AUTHORS: Chait, Y.
• ABSTRACT: An open problem in QFT is the design of a nominal-loop function. The common design approach involves classical frequency-response loop-shaping via manipulation of the gain, poles and zeros of the nominal transfer function. This design process is executed most efficiently using computer-aided design software such as the QFT Control Design MATLAB Toolbox. It is generally agreed that such a design process is efficient for "simple" problems such as those that do not require complex, high-order controllers. Novice QFT designers, however, often face difficulties even with "simple" problems for lack of loop-shaping experience. Recent automatic loop-shaping techniques have been formulated in terms of open-loop bounds which can never be made convex. Hence, they inherently involve approximations which severely limit the techniques’ utility. In this paper we focus on the following automatic loop-shaping problem: given a nominal plant, a finite set of QFT bounds and a fixed controller order, synthesize a controller that achieves internally stability, satisfies its bounds and has a minimum high-frequency gain. We show that if one translates the open-loop bounds into appropriate closed-loop bounds, the above automatic loop-shaping problem can be formulated as a linear program. We discuss the nature of these closed-loop bounds and certain approximation that may be required with typically negligible consequences in terms of design conservatism, and illustrate our results using a numerical example.
• STATUS: Procs. Symp on Quantitative Feedback Theory and other Frequency Domain Methods and Applications, Glasgow, Scotland, September, 1997, pp. 13-28. Also, submitted to ASME J. Dynamic Systems, Measurement, and Control.
• DATE OF ENTRY: October 15, 1997
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