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Parameter Estimation for a Class of Dual-rate Sampled Data Systems

Author: TianJun
Tutor: YangHuiZhong
School: Jiangnan University
Course: Control Theory and Control Engineering
Keywords: Dual- rate system Polynomial transformation Super- martingale convergence theorem Model Identification Dual- rate time-varying systems Forgetting factor least squares Estimation error
CLC: TP13
Type: Master's thesis
Year: 2007
Downloads: 42
Quote: 1
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Abstract


The conventional discrete system parameter identification methods are assumed throughout the system input and output is sampled at the same sampling period, However, in the actual industrial process, sometimes the use of the same cycle parameter identification is uneconomical or unfeasible. Thus multi-rate system identification method has been widely used, it can solve the problem of parameter identification and output estimation of the input and output sampling period is not equal to the discrete system, can be used to detect the output variable single-rate model, at the same time through dual-rate data can be used to design multi-rate system inference control programs, therefore, it has important theoretical significance and value in use. In this paper, a special case of the multi-rate system - dual-rate system, the following results were obtained. 1, the application of the polynomial transform technique to establish dual rate to enter the relationship between the output data, the dual rate system model. Equation for the same system in the dual-rate random error model, the ARX model, research output is estimated based on the dual-rate input output data rate forgetting gradient identification algorithm, as well as loss of forgetting factor selection methods. Then use the martingale super convergence theorem and stochastic process theory to analyze the convergence of the algorithm. When strong persistent excitation conditions established, given the algorithm parameter estimation error upper bound expression. The simulation results show that: by selecting the appropriate forgetting factor, dual-rate forgetting gradient algorithm has satisfactory convergence speed and accuracy, while significantly reducing the amount of computation. 2 CAR model for dual-rate system corresponding single-rate system, the CARMA the model and CARARMA model, respectively, proposed the dual-rate forgetting gradient algorithm augmented, dual-rate forgetting gradient algorithm and dual-rate generalized augmented generalized stochastic gradient algorithm . For unknown unmeasurable noise terms in the information vector in the identification model, with their estimated value instead solve the kind of dual-rate system model identification problem. And a simulation study. 3, double sampling rate for a class of stochastic time varying system, the application of polynomial transform technology and random process theory, strong persistent excitation condition, the dual-rate time-varying forgetting factor method of least squares parameter estimation convergence has been Parameter estimation error upper bound expression. The analysis showed that with the increase of the length of data, the parameters of the proposed algorithm to converge to a constant estimated error bound. Subsequent analysis of the uncertainty of the dual-rate time-invariant systems, random time-invariant systems, deterministic time-varying system parameter estimation error upper bound. And simulation examples confirm the paper presents the theoretical results.

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