Linear design models for robust control synthesis

Abstract

Absttact Two new methods for defining linear design models which directly incorporate known model parameter uncertainty are introduced in this paper. Construction of the two different design model types, called the averaged and worst case design models, is motivated by stability robustness considerations. The averaged design model is given by a reduced-order approximation of a system model defined by summing several transfer function models and dividing by the number of available models. The worst case design model is formed by combining the nominal plant model with parameter uncertainty of the worst anticipated magnitude in the worst direction. The worst magnitude and direction are determined by the structured singular value stability robustness analysis. Two examples are shown to demonstrate the modeling techniques. J. IntroducDon In most cases, aircraft flight control system design models consist of rigid-body airframe dynamics linearized about a given flight condition. No attempt is made to modify the design model dynamics other than changes in the number of inputs or outputs considered. However, it has been shown in the past that some performance gains can be achieved if the designer selects different modes to be included in the design model. As an example, Gilbert, Schmidt, and Weishaar showed that unsatisfactory results can be obtained when elastic modes are ignored, while improved results were obtained when the elastic modes were included in the design model.[l] Therefore, the design model was modified by including additional dynamics (the elastic modes) to improve the design. Lately, most multivariable control system synthesis techniques utilize weighting filters for loop shaping purposes.[2] In fact, these weighting filters are usually connected to the aircraft design model such that a new "augmented plant" is formed. The addition of weighting filters represents another method of modifying the aircraft design model in order to improve control system performance. The objective of the design model techniques developed in this paper is to determine linear design models which directly incorporate some of the information available about the model parameter uncertainty. Two different approaches are considered in this paper. An example is given at the end of each section and conclusions drawn from this work are provided at the end of the paper.