Download e-book for kindle: Dynamic Modeling, Predictive Control and Performance by Biao Huang

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By Biao Huang

ISBN-10: 1848002327

ISBN-13: 9781848002326

ISBN-10: 1848002335

ISBN-13: 9781848002333

ISBN-10: 2008923061

ISBN-13: 9782008923062

A usual layout process for version predictive regulate or regulate functionality tracking contains: 1. identity of a parametric or nonparametric version; 2. derivation of the output predictor from the version; three. layout of the keep an eye on legislation or calculation of functionality indices based on the predictor.

Both layout difficulties want an particular version shape and either require this three-step layout approach. Can this layout strategy be simplified? Can an particular version be shunned? With those questions in brain, the authors put off the 1st and moment step of the above layout technique, a “data-driven” technique within the experience that no conventional parametric types are used; accordingly, the intermediate subspace matrices, that are received from the method facts and another way pointed out as a primary step within the subspace identity equipment, are used without delay for the designs. with no utilizing an particular version, the layout process is simplified and the modelling errors attributable to parameterization is eliminated.

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Extra info for Dynamic Modeling, Predictive Control and Performance Monitoring: A Data-driven Subspace Approach

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10, we can derive yN +2 ⎞ ⎛ ⎞ eN uN ⎟ ⎜ ⎟ ⎜ = CA2 xN + CAB CB D ⎝ uN +1 ⎠ + CAK CK I ⎝ eN +1 ⎠ uN +2 eN +2 ⎛ Continue this procedure until t = 2N − 1. 11, we can derive y2N −1 ⎛ u ⎜ N ⎜ u N +1 = CAN −1 xN + CAN −2 B CAN −3 B · · · D ⎜ ⎜ .. ⎝. u2N −1 + CAN −2 K CAN −3 K · · · I ⎛ ⎞ e ⎟ ⎜ N ⎜ eN +1 ⎟ ⎟ ⎜. ⎟ ⎜. ⎠ ⎝. 2 Subspace Matrices Description 35 Assembling the results, for t = N, N + 1, . . 15 changes to ⎞ ⎛ ⎞ ⎛ C yN +1 ⎟ ⎜ ⎟ ⎜ ⎜ yN +2 ⎟ ⎜ CA ⎟ ⎟ ⎜ ⎟ ⎜ 2 ⎜ yN +3 ⎟ = ⎜ CA ⎟ xN +1 + ⎟ ⎜ ⎟ ⎜ ⎝ ··· ⎠ ⎝ ··· ⎠ y2N CAN −1 ⎛ ⎞ ⎞⎛ uN +1 D 0 0 ··· 0 ⎜ ⎟ ⎟⎜ ⎜ CB D 0 · · · 0 ⎟ ⎜ uN +2 ⎟ ⎜ ⎟ ⎟⎜ + ⎜ CAB CB D · · · 0 ⎟ ⎜ uN +3 ⎟ ⎜ ⎟ ⎟⎜ ⎝ ··· ··· ··· ··· ···⎠⎝ ··· ⎠ CAN −2 B CAN −3 B CAN −4 B · · · D u2N ⎛ ⎞ ⎞⎛ eN +1 I 0 0 ··· 0 ⎜ ⎟ ⎟⎜ ⎜ CK I 0 · · · 0 ⎟ ⎜ eN +2 ⎟ ⎜ ⎟ ⎟⎜ + ⎜ CAK CK I · · · 0 ⎟ ⎜ eN +3 ⎟ ⎜ ⎟ ⎟⎜ ⎝ ··· ··· ··· ··· ···⎠⎝ ··· ⎠ CAN −2 K CAN −3 K CAN −4 K · · · I e2N Continue this procedure by adding the time subscripts of the variables with 2, 3, until j − 1.

Measure of the prediction error. In the stochastic framework, L1 (z −1 ; θ) and L2 (z −1 ; θ) are typically chosen to obtain an optimal predictor, as discussed above. The criterion to measure the prediction error can be chosen in many different ways. 27) Given Gp (0; θ) = 0 and Gl (0; θ) = I, which also implies Gp (0; θ0 ) = 0 and Gl (0; θ0 ) = I , it can be verified that Φu (0; θ, θ0 ) = 0 Φe (0; θ, θ0 ) − I = 0 Namely, both Φu (0; θ, θ0 ) and (Φe (0; θ, θ0 ) − I) have at least one sample time delay.

69) where the process noise wt and measurement noise st are zero-mean white noise, both independent of the input ut . The approach taken by MOESP is through QR factorization and then a procedure similar to statistical correlation analysis, by extensive use of the property of white noise. Owing to the use of QR factorization for solving the problem, the MOESP is expected to be quite robust numerically. Let the input ut be persistent excitation of sufficient order.

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Dynamic Modeling, Predictive Control and Performance Monitoring: A Data-driven Subspace Approach by Biao Huang


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