An adaptive controller for a manipulator with one rigid link and one flexible link is presented. The performance and robustness of the controller are demonstrated by numerical simulation results. In the simulations, the manipulator moves in a gravitational field and a finite element model represents the flexible link. Keywords: Adaptive control, Robot, Flexible link.

Various modelling and control of two-link flexible manipulators are presented in this book. The lumped parameter modelling method and the assumed modes method modelling are comprehensively reviewed. The book also reviews the trajectory tracking problem and tip trajectory tracking problem along with the suppression of tip deflection of the links. An exponential time varying signal and a chaotic signal are considered as the desired trajectories. The identical/ non-identical slave manipulator is synchronised with the controlled master manipulator so that the slave manipulator indirectly follows the desired manipulator.

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems.

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems.

The objectives of this research work are to develop direct and indirect adaptive control strategies for discrete-time nonlinear systems and to investigate the applicability of the proposed schemes to adaptive tracking control of a flexible-link manipulator. The first problem considered is indirect adaptive control of a fully as well as a partially input-output feedback linearizable n th order affine SISO nonlinear system represented in the state-space form. The objective is to make the output y (k) track a reference trajectory y m (k) despite the fact that the parameters of the system are unknown. Towards this end, a local diffeomorphism for the change of coordinates and a nonlinear feedback control law are obtained so that the nonlinear system is rendered input to output equivalent into a linear system. The resulting linear system is then used to solve the output tracking control problem using conventional linear control theory. A multi-output recursive-least-square (RLS) algorithm is employed to identify the unknown parameters. Using the Lyapunov technique it is shown that provided the zero dynamics is exponentially stable the adaptively controlled closed-loop system is stable. The second problem addressed is the direct adaptive tracking control problem of a class of SIS 0 discrete-time nonlinear systems represented in the input-output form. To solve the problem, the state-space model is first derived and the appropriate control input is obtained. By employing the projection algorithm as a parameter estimator, the closed-loop stability of the adaptively controlled system is addressed using Lyapunov technique. As an application, the indirect adaptive control strategy is employed to control a single link flexible manipulator. Towards this end, the discrete-time model of the manipulator and its zero dynamics are derived first. By using the output re-definition technique, the adaptive input-output linearization scheme is then applied. The regressor form of the link's dynamic equations is also developed for the multi-output RLS identification algorithm. The performance of the adaptively controlled closed-loop system is investigated through numerical simulations to show the advantages and the main features of the proposed strategy. Finally to evaluate the performance of the proposed controller, an experimental test-bed of a single-link flexible manipulator is used for implementation. The real-time controller and estimator are implemented on a TMS system board which uses a TMS320C30 Digital Signal Processing (DSP) chip. The actual results are then compared with the simulation results to verify and validate the theoretical findings.