Dynamics and Control of Constrained Nonlinear Systems

Abstract

As applications have grown in the fields of robotics and automation, power systems, and electronic circuit systems, there has been an increasing interest in the control of constrained dynamic systems described by differential equations coupled with algebraic constraint relations. Recent developments in the geometric theory of nonlinear control systems have yielded an effective method for the analysis and design of control systems. The need for applying geometric theory to the systematic study of constrained nonlinear systems has become more apparent.<P>This thesis deals with two issues central to extending our understanding of the dynamics and control of constrained nonlinear systems. First, we investigate the dynamics of constrained nonlinear systems. We give precise definitions of the constraint submanifold and constrained dynamics. We discuss how to determine the reduced-order equation for the constrained dynamics. Second, we develop a systematic approach for controller design of constrained nonlinear systems. Our approach is based on nonlinear feedback and exact linearization. We show the advantage of our approach compared to the traditional linear approximation approach in some interesting control problems such as asymptotic stabilization, output tracking, etc. impose the holonomic constraint between the end-effector and the surface in terms of joint torques. We discuss controller design for various constrained tasks such as to control the end-effector to track a given path on the surface while at the same time regulating the contact force, etc. We also show how to use state feedback H control to reduce the effect of uncertainties. Our control scheme is valid globally and a quantitative performance bound is provided.<P>