CONTROL DESIGN FOR PARAMETER SENSITIVITY REDUCTION IN LINEAR REGULATORS: APPLICATION TO LARGE FLEXIBLE SPACE STRUCTURES

RAMAKRISHNA YEDAVALLI, Purdue University

Abstract

This dissertation addresses the problem of control design for linear systems having parameter uncertainty. Two viewpoints are considered in tackling the above problem: (i) to minimize or reduce the trajectory and/or performance cost dispersion from the nominal values in the presence of small variations in the system parameters (labeled the "Parameter Sensitivity Reduction" problem); (ii) to maintain some optimal or satisfactory level of performance in the presence of small variations in the system parameters subject to model/controller truncation (labeled the "Performance Robustness" problem). The first part of the thesis treats the former aspect while the second part deals with the latter. The contribution of the first part is theoretically oriented while the second--a major part of the thesis--is application oriented. The first part of the dissertation begins with a brief survey of the past approaches to parameter sensitivity reduction in linear regulators. As a prelude to the control design methodology based on sensitivity function augmentation, the sensitivity characteristics of the standard linear state feedback regulators (both optimal and non optimal) are briefly examined. It is then shown that the minimization of a modified performance index that includes a quadratic term of trajectory sensitivity (state, output or control) subject to the augmented sensitivity system dynamics causes reduction not only in trajectory sensitivity but also in cost sensitivity. Inclusion of both output (state) sensitivity and control sensitivity terms in the integrand of the original cost functional is shown to improve cost sensitivity reduction and facilitate the unification of the approaches "trajectory sensitivity reduction" and "cost sensitivity reduction". Two control design methods, one based on a linear formulation and the other on a nonlinear formulation, are given for both deterministic and stochastic systems and the improvement of these methods over existing methods is established. In the second part, attention is focused on application oriented control design. The application considered is the control of large flexible space structures--a relatively new frontier in the area of control system design. In this application, where there is large uncertainty associated with the modal data and constraints on the controller order, model reduction is required before one can apply linear multivariable theory to design controllers. The preliminary step taken in this direction is to use the concepts of open loop 'modal cost analysis'--a special version of the 'component cost analysis', originated by Skelton--to derive explicit analytical formulae for 'modal costs' and 'parameter costs' for specific performance objectives by which one can determine the significant modes and parameters for large numbers of modes. This information can be useful in applications such as model reduction, parameter estimation and structure redesign etc. Next the problem of control design is addressed. In the case of large scale systems, a reduced order control design method based on sensitivity cost analysis is proposed, according to which only those states of the standard Linear Quadratic Gaussian (LQG) closed loop controller that make largest contributions to the sensitivity augmented performance index are fed back for control purposes. The proposed approach is applied to a large space structure model. Finally the dissertation offers some concluding remarks and explores avenues for further research.

Degree

Ph.D.

Subject Area

Aerospace materials

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