Continuous-Time System Identification And System Analysis Based On Laguerre Functions

Generally,system identification is a discipline to search for the mathematical model which reflects the natural property of system by measuring system response data excited by outside force and using optimization techniques according to some certain identification criterion and modeling purpose.At present,most system identification methods for discrete-time systems are established,but there will be some problems in continuous-time system identification using methods of discrete-time system identification.Therefore,it is necessary to identify continuous-time system directly in practice.The first issue of direct identification of continuous-time systems is the treatment of differential operator.As is known,the differential operator amplifies the noise signals,while the system mixed with noise is inevitable.Therefore it is necessary to convert the differential operator to other operator which is not sensitive to noise signals.In general,continuous-time system models can be divided into two major categories, non-parametric models and parametric models.For non-parametric models,a set of orthogonal functions can be used to approximate the impulse response of system;for parametric models,a set of orthogonal functions can also be used to pre-processing of input and output signals instead of the differential operation in continuous-time system. In addition,the sequence of orthogonal functions can be used to the analysis of complex systems.In this paper,the Laguerre orthogonal functions are introduced for continuous-time system identification and system analysis after the comparison of discrete-time system models and continuous-time system models.This article mainly studies the following aspects:(1) After analyzing the background of the project,the targets of the study are determined and the major problems are put forward.After a brief overview on discrete-time system identification,the problems of discretization of continuous-time system model are focused on.Then the least square method is discussed in details,a continuous-time least square method and a continuous-time recursive least square method for continuous-time system identification are put forward.(2) The Laguerre orthogonal functions are introduced,and Laguerre functions' orthogonality is proved.Then two broad categories of continuous-time system identification-parametric model identification and non- parametric model identification are studied in details.The state-variable filter and sub-space model identification are introduced for parametric model identification,a new algorithm for continuous-time system identification using Laguerre functions is put forward based on the known algorithms;In the non-parametric model identification,Laguerre functions are used to approximate the impulse response of system.Finally,various algorithms are compared by MATLAB6.5 simulation software.(3) Control system analysis based on Laguerre functions are studied by converting the differential,integral,scaling stretch,time-delay into the matrix operators of Laguerre spectrum coefficients.A system state analysis for multiple-time delay, multi-scale system model is obtained.The algorithm is simulated by MATLAB6.5 simulation software.