Identification and Control of Class of Time Varying Systems

Abstract

In this work, adaptive control of linear time invariant (LTI), linear time varying (LTV) as well as a class of nonlinear time varying (NTV) plant are considered. The plant is unknown and the parameters are constant or varies with respect to time. 2-Stage adaptive strategy, under the multiple model category, is proposed for identifying and controlling linear plants. Available literature says that the assumed compact region in which the plant parameters lie in can be large whenever the plant parameters are unknown. In order to make sure that atleast one of the model to be closer to the plant, large number of identification model is needed. The proposed method for linear systems mitigate the above requirement satisfactorily well by identifying the compact set in the first stage itself. newlineTo demonstrate the efficacy of the proposed method, first and higher order systems are considered. Parameter variations can be smooth/ discontinuous, slow/ fast, periodic/ non-periodic. In existing literature, any one or two parameter variations are considered. However, in this work all type of variations are considered for simulation. In case of higher order systems, system matrix and desired system matrix are considered in companion form. For demonstration, combination of constant and time varying parameters are considered in the simulation. Further, though the stability analysis of LTI system is well established with rigorous proof, stability analysis of LTV systems needs to be explored more. Stability analysis of LTI can be extended to LTV systems when the parameters slowly vary with time. In this work, stability analysis of LTV systems of first/higher order with all type of parameter variations are shown. This proves that the tracking error, identification error and parametric error are uniformly bounded. This is examined in simulation via mean square error (MSE), variance accounted for(VAF) and number of models required. newlineAlso, this work considers the identification and control of class of nonlinear systems which is linear