Abstract

Most engineering systems encountered in practice exhibit significant nonlinear behavior. For control of systems exhibiting nonlinearities, the normal design procedure is to construct a linearized approximation of the process model followed by the application of a linear control methodology. This procedure, however, can yield unsatisfactory performance, especially when the system is highly nonlinear and undergoes large motions, that is, it operates over wide nonlinear dynamical ranges, as is often the case in the problems of attitude control, advanced aircraft control, and the control of robotic manipulators. Furthermore, most systems are seldom completely known and therefore, their mathematical models should include some uncertain parts. The control of an uncertain system is required to be robust with respect to modeling uncertainties. Robust control strives to characterize the uncertainty in the model of the plant and to evaluate the degrees of freedom left to achieve the control task within specified bounds. This dissertation is concerned with the control of a highly complicated and nonlinear system, namely, a flexible-link manipulator. The general procedure taken in this regard is to develop, design and analyze nonlinear H P techniques applied to flexible-link manipulators. For the purpose of robust control of an uncertain model of the flexible-link manipulator two types of modeling are studied. In the first type, uncertainty is due to parameter variations of the manipulator while performing a task or when its configuration is changing. The uncertainties considered in this regard may be L 2 bounded and/or constant. In the second type of modeling, a new look at, the notion of flexibility in robotic manipulators is presented. Based on this interpretation, flexible structures exhibit two kinds of behavior, one of which may be treated as a disturbance acting on the modeled dynamics. For designing the nonlinear H P controller, the approximate polynomial solution of the Hamilton-Jacobi-Isaac (HJI) inequality for a general nonlinear system is derived. Also by exploiting the stability properties of perturbed systems, qualitative behavior of nonlinear H P controllers is considered.