Adaptive robust control of nonlinear time-varying systems with application to flexible mechanisms

This thesis presents several new control system design techniques for a broad class of nonlinear systems, including many mechanical systems. The main feature of these control designs is their ability to overcome modeling uncertainty and provide both robust stability and high-performance tracking. The class of nonlinear systems considered is referred to as a semi-strict feedback system and includes parametric uncertainty, input gain uncertainty and unknown but bounded nonlinear functions. The approach developed to control this class of nonlinear systems combines several methods, which results in an adaptive robust control law. The key components of the control design are the use of the backstepping design procedure, sliding mode control and Lyapunov-based parameter estimation. The backstepping method is used to recursively design virtual controllers for each step in the procedure. Each virtual controller and the resulting actual controller, are designed using sliding mode control and Lyapunov-based parameter estimation, providing both robustness and adaptation respectively, to compensate for model uncertainty. Two different algorithms which use this approach have been developed: a static controller and a dynamical controller. These two approaches have been tested in simulation on two plant models. The first is a benchmark third-order system for the study of uncertain semi-strict feedback systems and has no physical significance. However, the study of this benchmark system has allowed many insights into the transient characteristics of the closed loop system. The second plant model is that of a cable array robot, which is a novel robotic mechanism which has been described in detail in the thesis including kinematic and dynamic modeling. The cable array robot uses multiple cables in a closed-chain configuration to manipulate objects in three dimensions. The results of computer simulations for the benchmark system and the cable array robot show that both the static and dynamical controller provide excellent tracking results. However, the dynamical controller does not require the analytical derivatives of the virtual controllers at each step. This results in an algorithm which is simpler to implement on hardware. Furthermore, the dynamical controller is less susceptible to errors in the dynamic modeling.