Advanced Process Identification & Control by Enso Ikonen

By Enso Ikonen

Complicated strategy identity & keep watch over КНИГИ ;НАУКА и УЧЕБА Автор: Kaddour NajimНазвание: complex technique id & ControlИздательство: CRC PressГод: 2001Страниц: 632Формат: PDFISBN-10: 082470648XЯзык: АнглийскийРазмер: 11.64 MBPresents the latest innovations in complex method modeling, identity, prediction, and parameter estimation for the implementation and research of business structures. obtain reflect zero 1 2 three four five

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TLFeBOOK 30 CHAPTER 2. LINEAR REGRESSION Lemma1 (Matrix inversion lemma) Let A, B, C and D be matrices compatible dimensions so that A ÷ BCDexists. 64). 93) l+~T(k)P(k_ 1)~(k) Thusthe inversion of a square matrix of size dim0 is replaced by the inversion of a scalar. 93) for P (k) reorganizing. The recursive algorithm needs someinitial values to be started up. In the absence of prior knowledge,one possibility to obtain initial values is to use the least squares method on the first k0> dim 0 samples.

The algorithm is able to follow the changesin the process. There exists a large numberof other forgetting schemes. Many(if not most) of themare inspired by the robustness of the Kalmanfilter, discussed in the next section. 5 Kalman filter In the Bayesian approach to the parameter estimation problem, the parameter itself is thought of as a randomvariable. Based on the observations of other randomvariables that are correlated with the parameter, we mayinfer information about its value. The Kalmanfilter is developed in such a framework.

Example 14 (Stability) Consider the system in Example 13 with initial condition y (0) = y0 and control input u (k) = 0. Thefuture values of the system for k = 1, 2, ... 27) If ]a I < 1, then y (k) tends to zero and the system is stable. 2BIBO stability: bounded output. 2. 2 Deterministic disturbances In general, a real process is always subjected to disturbances. The effects of the system environmentand approximation errors are modelled as disturbance processes. Modelsof disturbance processes should capture the essential characteristics of the disturbances.

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