Adaptive control of nonlinear discrete-time systems and its application to control of a flexible-link manipulator

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 nth order affine SISO nonlinear system represented in the state-space form. The objective is to make the output y( k) track a reference trajectory ym( 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.