Download Advanced Process Identification & Control by Enso Ikonen PDF

By Enso Ikonen

Complex strategy identity & keep an eye on КНИГИ ;НАУКА и УЧЕБА Автор: Kaddour NajimНазвание: complex procedure identity & ControlИздательство: CRC PressГод: 2001Страниц: 632Формат: PDFISBN-10: 082470648XЯзык: АнглийскийРазмер: 11.64 MBPresents the newest innovations in complicated technique modeling, identity, prediction, and parameter estimation for the implementation and research of commercial structures. obtain reflect zero 1 2 three four five

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117). In such a case, the coefficient A is referred to as the forgetting factor. 4 illustrates the weighting obtained using a constant A. The effect of A can be illustrated by computing the equivalent memory 1(a~ = 1 for all i). 99. horizon H = T=X WhenA is close to 1, the time constant for the exponential decay is approximately H. 99 corresponds, roughly, to rememberingthe 20 - 100 most recent data. TLFeBOOK 36 CHAPTER 2. tious. 84). 2 Algorithm Nowthe recursive least squares algorithm with exponential forgetting can be given.

Fiance of a r~dom ~riable x is defined by c~(x) E {[~- E {~}1 [~- E {~}1~}. 2. METHODOF LEAST SQUARES 27 of the estimation error is given by = since E h~ zero mean and v~i~ce a~ (and its components are identicMly distributed), and E and ¢ are statistically independent. It is a me~e of how well we can estimate the u~nown 0. 71) The squ~e root of the diagonal elements of P, ~, repr~ents the standard e~ors of each element ~ of the estimate ~. The v~iance can be ~timated ~ing the sum of squ~ed errors divided by de~ees of freedom where I is the numberof p~ameters go ~timate.

Fig. 3 illustrates the evolution of the parameters a, b and c, as well as the on-line prediction by the model. Remark 2 (Factorization) The covariance matrix must remain positive definite. 3. ). In order to maintain numerical accuracy it is more advisable to update the estimator in a factorized form which guarantees that P (k) remains positive definite and that the roundoff errors, unavoidablein computerapplications, do not affect the solution significantly. Oneof the most popular methodsis the UDfactorization which is based on the decompositionof P (k) P (k) = V (k) D UT (k) where the factors U (k) and D (k) are, respectively, a unitary upper triangulax matrix and a diagonal matrix.

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