Multilevel control-structure design using LQG design sensitivity analysis techniques

Michael Glenn Gilbert, Purdue University

Abstract

Numerous papers outlining integrated control-structure design methods have appeared in recent years. These methods either simultaneously or sequentially determine the structural and control law parameters to reduce the final structural weight and a mean-square control or response measure. Time and frequency dependent criteria critical to specifications on controller bandwidth, tracking performance, stability robustness, and the like have not been considered in these approaches. In this thesis, a new control-structure design method is developed which obtains the structure and control law parameters in a hierarchical algorithm, achieving integration through an upper-level design coordination process. It can include time and/or frequency dependent design criteria. The new method is developed in a general framework for multidisciplinary design which is based on formal design problem decomposition and multilevel optimization techniques, and requires the use of design sensitivity information. A formulation of the design problem decomposition for integrated control-structure design of dynamic aerospace vehicles is presented. A Linear Quadratic Gaussian (LQG) approach is used for control law design. Analytical expressions for calculating LQG gain matrix sensitivity information are derived from the necessary conditions of optimality. Existing analytical expressions are used for the sensitivity of the integrated design criteria. Results for two case studies are presented. The first is a two-bar truss control-structure design problem used to validate the sensitivity developments and illustrate the design algorithm. Three integrated designs of the two-bar truss are presented. The first was formulated to improve stability robustness of the system through changes in both the structure and the control law. The second and third designs were formulated to have conflicting integrated design requirements to investigate the design tradeoff capability of the method. The second case study is of an aeroservoelastic aircraft sensitivity analysis where numerical calculations were performed to evaluate computational burdens in a realistic design problem. The results show that the analytical LQG sensitivity method is more accurate and less computationally intensive than equivalent finite difference methods. The multilevel approach to control-structure design is also shown to achieve integration while maintaining independent structural and control law design steps.

Degree

Ph.D.

Advisors

Weisshaar, Purdue University.

Subject Area

Aerospace materials

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