- 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
- full paper (postscript, 980KB)
Zip file (135KB)
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