ROBUST CONTROL DESIGN STRATEGY WITH PARAMETER DOMINATED UNCERTAINTY Moshe Idan* Guy E. Shavivt Department of Aerospace Engineering Technion. Israel Institute of Technology, Haifa, Israel Abstract A robust controller design strategy is introduced for systems, parameters of which are affected d~minant~ly by a few unknown physical quantities. The result- ing procedure has ad~ant~ages over simple frequency bounding or model parameters bounding by using the functional dependence of the model parameters on the physical quantities and thus being less restrictive. This potentially may lead to a better trade-off be- tween performance and robustness. The procedure of the uncertain system modeling relies on the Linear- Fractional-Transformation algebra and reduction of the uncertainty block dimension. The resulting model can be used for control synthesis using any robust con- - trol design technique. I11 this work p synthesis was adopt.ed since it best fit,s the structured uncertainty model obtained. An example is given for a controller design for an unmanned flight vehicle, the model pa- rameters of which depend on t,he unknown mass of it8spayload. The aircraft equations are derived and a ,u controller is synthesized. The controller is com- pared to other control met,hods and its advantages are demonstrated. I. Introduction Dynamic syst,ems are often described by linear models wit.h numerous parameters depending dominantly on a few unknown physical quantities. As an example, parameters of a linear model of an aircraft strongly depend on the location of the vehicle center of gravity (c.g.), the trim angle of attack (a,,,,) and the Mach number (M), as well as other parameters. Each of these parameters changes some or all of the model co- efficients simultaneously in a known fashion1. Some of these dependencies may be modeled analytically in a relatively simple form (e.g., the model coefficient de- pendence on t,he aircraft c.g.) while others may be more difficult to model analytically, but still could 'Annie and Charles Corrin Academic Lecturer, Member AIAA t~raduate Student Copyright 01995 by Moshe Idan and Guy E. Shaviv. Published by the American Instit,uteof Aeronaut.icsand Astronautics, Inc. with pernfission. be expressed empirically (e.g., Mach number around M = 1 or dependence on angles of attack for large In addition, there are model uncertaint.ies that are not related to any common physical quantity, such as uncertaint.ies in the non dimensional aerodynamic stability and control derivatives. However, in this work it is assumed that the overall effect of these un- certainties is small compa.red to those caused by the uncertainties in the above mentioned physical parame- ters. The design goal is to achieve robust performance for the uncertainties in these parameters. A related problem can be formulated ,when design- ing a controller for a dynamic systems at several oper- ating points distinguished by different values of some physical parameters. These parameters can be consid- ered unknown and allowed to perturb within a speci- fied range. The requirement for the controller is then to provide robust stability and performance of the sys- tem while the physical parameters vary in the given range. Several approaches exist for designing robust con- trollers. The multi-model approach2 (and references therein) evaluates the syst,em model at several oper- ating points and attempts to find a controller t,hat meets performance criteria for all of t,he models si- multaneously. Complexity, which increases with the number of controller parameters and t,he number of uncertainty parameters and thus the number of pos- sible models, makes this solution difficult t,o imple- ment beyond very few of these parameters. In addi- tion, there is no guarantee on the performance at op- erating points not considered in the design. Another method is to model the uncertainty as a general bound on the frequency response of the plant and to mini- mize a weighted sensitivit,~ function3! 4. This method is usually applied with an H, controller design. A different met,hod is to specify bounds on each of the model coefficients5~ 6. This method is usually applied with p controller synthesis. The dra.wback of the last two uncertainty modeling approaches is that the ex- act functional dependence (if such exists) of the plant coefficients on the uncertain physical parameters is not incorporated and the bounds which are given en- compass cases which are not physical and so are not, required to be handled by the controller. This over- 164 American Institute of Aeronautics and Astronautics