Synthesis of Insensitive Controllers in Linear Quadratic Control Problems
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概要
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Usually, the design objectives of control systems are not only to achieve specified performances at the nominal operational points but also to guarantee admissible performances over the range of parameter variations which inevitablly exist in the actual systems. In this paper we consider the insensitive controller which guarantees the robustness explicitly in terms of parameter variations while preserving the performance in terms of cost. There have been reported many design methods as to this subject. Some investigated the techniques which augmented the system structures such as the adaptive systems or others. But here we consider the insensitive controller design that keeps its structure as usual regulators from the view point of reliability. For this purpose we evaluate the "Additive Term Design" methods in which the proper additional terms are introduced in the covariance propagation equations or the cost equations in order to assess the deterioration of the performance index (cost). Reviewing the previous works we clarify some properties of these "Additive Term Designs". And devising a few of new approaches we show that these techniques can improve the cost surfaces and the stability and the stability margins and the sensitivity with respect to the equivalent open loop systems. To show the practical applicability, these techniques are applied to three numerical examples. One is the longitudinal autopilot of aircraft and the others are the estimation problem of radar tracking and the attitude control system of a large flexible booster. These reveal that the "Additive Term Design" techniques are very effective to those systems and that particularly the M.C.V. ("Maximum Cost Variation") method improves the cost surfaces satisfactorily. Since this robustness realization requires only a slight cost increase at the nominal operational point, these techniques are expected to be applied to a large number of systems with satisfactory improvement.
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