Sampled-Data LTV Regulation using Reconstruction Observer

Abstract

Sampled-data output feedback regulation for continuous time varying system is discussed in this dissertation. The continuous time varying system is generally referred as plant. The plant output asymptotically tracks a continuous reference signal generated by an exogenous system. It is assumed that only the sampled-output of both plant and reference signals are available for measurement. The problem is to design a continuous-time (non-impulsive) reconstruction observer for both plant and exogenous system states estimation followed by a continuous-time controller to achieve ripple free smooth regulation. The design of reconstruction observer is based on two proposed observer schemes named mainly in accordance of their functionality that is current impulsive observer and prediction impulsive observer. This insight to the problem leads to an innovative idea of continuous (non-impulsive) reconstruction observer with the fusion of two impulsive observer designed under well-defined weighting function. A comprehensive convergence analysis of the proposed observer is presented for stable, unstable and highly unstable continuous-time linear time varying systems. The application of reconstruction (non-impulsive) observer for sampled data regulation without ripple is explored for linear time varying system. Augmented stability analysis is proposed for closed loop system. The overall scheme is iv demonstrated with the help of linear time varying system. Subsequently, single input single output feedback linearizable nonlinear system regulation is investigated in the frame work of suggested theory of non-impulsive observers. The proposed novel observer design not only provides state estimates but also performs feedback linearization for a nonlinear system. This ultimately leads to a non-impulsive continuous-time sampled-data regulation without ripples for a nonlinear system. A stability analysis is carried out while considering the model uncertainties of a nonlinear system as a non-vanishing perturbation. An example of a third order nonlinear system illustrates the efficacy of proposed design methodology.