Robustness improvement of actively controlled structures through structural modifications

Abstract

The parameter variations introduced by the analysis model, uncertain material properties, or optimization may adversely influence the stability and performance characteristics of a closed-loop controlled structure. The improvement of robustness of actively controlled structures through structural modifications is considered in this work. The stability and performance robustness indices are defined as measures of robustness of actively controlled structures. The integrated structural/control design problem is considered as a multiobjective optimization problem, in which three objectives—structural weight, stability robustness index, and performance robustness index—are considered for minimization. The utility function, lexicographic, and goal programming methods are applied to solve the multiobjective nonlinear programming problem. Two examples, a two-bar truss and two-bay truss, are considered to demonstrate the procedure. HERE has been a dramatic increase in the past decade in the use of active control systems to improve structural performance.1'2 The major challenge in the field of active control of structures is in the design of control systems for very large space structures. These structures are by nature distributed parameter systems with multiple inputs (controls) and a continuum of outputs (displacements). The finite-ele- ment method is commonly used for the description of these structures. This is a source of parameter errors and truncated (or reduced order) models in the system. In addition, the structural properties of large space structures cannot be tested before they are put into orbit and, hence, sizeable uncertain- ties exist in modal parameters. A great deal of research is currently in progress on develop- ing methods for the simultaneous (integrated) design of the structure and the control system. The weight of the structure was minimized, with constraints on the distribution of the eigenvalues and/or damping ratio of the closed-loop system by Khot et al.3 Miller and Shim4 considered the simultaneous minimization, in structural and control variables, of the sum of structural weight and the infinite horizon linear regulator quadratic control cost. The structure/control system optimiza- tion problem was formulated by Khot et al.,5 with constraints on the closed-loop eigenvalue distribution and the minimum Frobenious norm of the control gains. It can be seen that in all the above works the consideration of robustness of the control system has been ignored. The parameter variations introduced by the analysis model, uncertain material properties, or optimization may adversely influence the stability and performance characteristics of the control system. The robustness is an extremely important feature of a feedback control design. A robust control design is one that satisfactorily meets the system specifications, even in the presence of parameter uncertainties and other modeling errors. Since the system specifications could be in terms of