Date of Award
Doctor of Philosophy (PhD)
Naresh K. Sinha
This thesis investigates the problem of adaptive control for a class of nonlinear systems which are explicitly linearizable by nonlinear state feedback. A theoretical framework and a systematic design procedure have been established for adaptive control of feedback linearizable systems with parametric and dynamic uncertainties. An error model for adaptive tracking problem is introduced for the first time considering both the parametric and dynamic uncertainties. The significance of the error model lies its explicit physical meanings. It can serve as a basis for the development of adaptive strategies and control algorithms for feedback linearizable systems. Four new adaptive algorithms have been proposed. The stability and parameter convergence of these algorithms are theoretically established by using two different approaches. The robustness of the algorithms for adaptive regulation problem has been analyzed. The tracking ability and effect of initial parameter estimates have been studied also. The restrictive matching conditions and nonlinearity growth conditions are two of the main problems appearing in literature of adaptive control for nonlinear systems. The two problems have been solved here for the first time. A Model Reference Adaptive Control algorithm and an Augmented Error Control algorithm have been presented to remove these restrictive limitations. The class of nonlinear systems for which adaptive control can be applied has been substantially enlarged. A comparison between adaptive control schemes and nonadaptive control schemes has been made. The results of comparison show that the performance of adaptive controllers is superior to that of nonadaptive state feedback controllers. A decentralized adaptive control strategy is introduced for nonlinear systems. It has been shown that a decentralized adaptive control system is much easier to implement than a centralized control system and is more robust to structural disturbance. To demonstrate practical applications, the proposed adaptive control algorithms have been applied to the control problems of a class of robotic manipulators. Three different types of adaptive tracking problems of manipulator systems have been investigated. The results of simulations demonstrate considerable improvements in tracking accuracy over the traditional inverse dynamics control methods in the presence of significant parametric uncertainty.
Han, Yuexin, "Adaptive tracking in feedback linearizable systems" (1992). Open Access Dissertations and Theses. Paper 3784.