The Mathematical Modelling of Liner Movement in a Magnetic Compressor: Elastic, Liquid and Plastic Liner Models Comparison

Галанин, М П; Lototsky, A.P.; Rodin, A S

doi:10.3846/13926292.2012.644406

Cited by 2 publications

(1 citation statement)

References 1 publication

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“…Multivariable system modelling has received much attention in various practical systems, including magnetic compressors and magnetic fluids [9,17], piston engines [8], distillation columns [13,14], fault detection systems [12,18] and travelling waves [11], etc. As a consequence of this wide variety of applications, different identification algorithms for multivariable systems have been vastly reported in the literature, e.g., the gradient based iterative algorithm and the least squares based iterative algorithm for multivariable CARARMA systems [7], the hierarchical gradient-based iterative identification algorithms for multivariable CARAR-like systems [21], the stochastic gradient estimation algorithm for multivariable equation error systems [15], the auxiliary modelbased multi-innovation stochastic gradient algorithm for multiple-input singleoutput systems [16], the bias compensation based identification algorithms for multivariable systems [22,23], and the coupled-least-squares identification for multivariable systems [1].…”

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confidence: 99%

Data Filtering Based Stochastic Gradient Algorithms for Multivariable Carar-Like Systems

Wang

Shan

Ding

2013

Mathematical Modelling and Analysis

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This paper considers identification problems for a multivariable controlled autoregressive system with autoregressive noises. A hierarchical generalized stochastic gradient algorithm and a filtering based hierarchical stochastic gradient algorithm are presented to estimate the parameter vectors and parameter matrix of such multivariable colored noise systems, by using the hierarchical identification principle. The simulation results show that the proposed hierarchical gradient estimation algorithms are effective.Replacing the unknown α and θ in (3.12) with the estimatesα(t − 1) and θ(t − 1), the estimateŵ(t) can be computed bŷUseŵ(t − i) to construct the estimate of ψ n (t):Use the parameter estimateĉ(t) = [ĉ 1 (t),ĉ 2 (t), . . . ,ĉ nc (t)] T to construct the estimates of C(z): C(t, z) := 1 +ĉ 1 (t)z −1 +ĉ 2 (t)z −2 + · · · +ĉ nc (t)z −nc .By filtering u(t) and y(t) withĈ(t; z), one obtains the estimates of u f (t) and y f (t):û f (t) =Ĉ(t, z)u(t),ŷ f (t) =Ĉ(t, z)y(t).Filtering Based Stochastic Gradient Algorithms for CARAR-Like Systems 381Also,û f (t) andŷ f (t) can be recursively computed bŷ u f (t) = u(t) +ĉ 1 (t)u(t − 1) +ĉ 2 (t)u(t − 2) + · · · +ĉ nc (t)u(t − n c ), y f (t) = y(t) +ĉ 1 (t)y(t − 1) +ĉ 2 (t)y(t − 2) + · · · +ĉ nc (t)y(t − n c ).Construct the estimates of ϕ f (t) and ψ f (t) withû f (t−i) andŷ f (t−i) as follows:

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