SAMPLED-DATA OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS

Abstract

This thesis discusses solution to sampled-data output feedback regulation and tracking problems for cases of known and unknown plant models of nonlinear minimum phase system. For known plant model, Extended Kalman filter (EKF), Unscented Kalman filter (UKF) and Cubature Kalman filter (CKF) are used to estimate state vector (for regulation problem) or error vector (for tracking problem). However, when plant model is unknown, Kalman estimators cannot perform. In such a case, State-Space Recursive Least Squares (SSRLS) with constant velocity model is employed to estimate state or error vector. Emulation Design based discrete controller using eigenvalues placement is designed for regulation problem. Whereas for tracking problem, discrete feedback linearization controller based on Emulation Design is employed. Simulation results show good estimation performance given by EKF, UKF and CKF estimators for Magnetic Levitation system. Moreover, the performance exhibited by SSRLS estimator for unknown model case (of Magnetic Levitation system), is comparable to the performance of Kalman estimators for known model case. Results also demonstrate importance of tuning process and observation noise covariance matrices for EKF, UKF iv and CKF estimators. Whereas, the performance of SSRLS estimator depends on value of forgetting factor. Further the thesis presents an Euler approximate discrete-time Sliding Mode observer (SMO) which simultaneously estimates states and combined effect of unmodeled system dynamics and disturbances. Emulation Design procedure is employed in designing of discrete feedback linearization controller. Computer simulations demonstrate performance of presented novel sampled-data output feedback scheme for tracking applications of Magnetic Levitation and DC motor systems. Results illustrate that increasing sampling period more adversely affects Euler approximate discrete observer performance for faster changing system dynamics than for slower changing dynamics. The proposed scheme also exhibits good performance in presence of disturbances and parameters perturbation. Furthermore, it is demonstrated via simulations that robust tracking control is achived on using estimator (e.g Kalman filter, SMO, SSRLS filter) in sampled-data output feedback configuration, as compared to performing tracking using sampled-data state feedback scheme. Simulation results show that Sliding Mode observer (SMO) based output feedback tracking is most robust, followed by CKF and EKF based output feedback scheme. UKF based output feedback scheme is robust against external disturbance; but for case of system parameter perturbation, UKF tracking error takes longer time to converge. State-Space Recursive Least Squares (SSRLS) based scheme behaves poorly in presence of external disturbance. This is because SSRLS estimation is based on constant velocity model and not on actual nonlinear system model. v Black-box system identification and output prediction for unknown sampled-data nonlinear minimum phase systems have also been achieved using feedforward neural network (multilayer perceptrons) and Unscented Kalman filter (UKF) in open-loop sampled-data configuration. Next neuro-estimator based sampled-data output feedback control configuration is presented. The scheme employs NN-UKF (neural network-aided dual Unscented Kalman filter) estimation algorithm and Emulation Design based discrete feedback linearization controller. Estimated state (signal) vector and estimated error function which represents combined effect of unknown system parameters, model uncertainties, unmodeled system dynamics and disturbances, both are used in discrete controller designing. Computer simulation results of proposed scheme for tracking applications of Magnetic Levitation system in presence of external disturbance are demonstrated. Results exhibit that tracking error using NN-UKF based feedback linearization approach has a peak value which is 10 times smaller as compared to tracking error of sampled-data feedback linearization scheme based on UKF estimator. Also tracking error of NN-UKF scheme converges to a smaller (minimum) value as compared to tracking error of UKF scheme. Finally, sampled-data output feedback control scheme for case of unknown system parameters has been presented. The scheme employs dual UKF estimation algorithm and Emulation Design based discrete feedback linearization controller. Simulation results exhibit that presented output feedback control scheme demonstrates better tracking performance and parameter estimation error when parameter estimate is initialized with a value (in dual estimation algorithm) which is closer to actual system parameter value.