By Enso Ikonen
Complex method id & keep watch over КНИГИ ;НАУКА и УЧЕБА Автор: Kaddour NajimНазвание: complicated method id & ControlИздательство: CRC PressГод: 2001Страниц: 632Формат: PDFISBN-10: 082470648XЯзык: АнглийскийРазмер: 11.64 MBPresents the newest suggestions in complex strategy modeling, id, prediction, and parameter estimation for the implementation and research of business platforms. obtain replicate zero 1 2 three four five
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19) n=l where p~ are the nn real poles and z 2 + anZ + ~ contain the nc complex pMrs of pol~ of the system. In a simil~ way, B (z) can be represented B (z) nR = (z nc + + &) n=l where r~ are the na real zeros and z2 + a~z + ~ contain the nc complex pairs of zeros of the system. TLFeBOOK 52 CHAPTER 3. 16) it is simple to derive the followingresult. 22) where K,~ E ~ denotes the steady-state gain of the system. 25) z-a This system has one pole in z = a. 26) 1-a In general, a system is stable2 if all its poles are located inside the unit circle.
Owingto the fact that the measurementsare disturbed, the vector parameter estimation ~ is random. An estimator is said to be unbiased if the mathematical expectation of the parameter estimation is equal to the true parameters O. The least squares estimation is unbiased if the noise E has zero meanand if the noise and the data (I) are statistically independent. Notice, that the statistical independenceof the observations and a zero mean TLFeBOOK 26 CHAPTER 2. G I0 LINEAR REGRESSION 1 2 1 2 0 0 I 00 3 .
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.
Advanced Process Identification & Control by Enso Ikonen