By Yucai Zhu PhD, Ton Backx PhD (auth.)
Identification of Multivariable business Processes offers a unified method of multivariable business strategy identity. It concentrates on business strategies almost about version functions. The parts coated are scan layout, version constitution choice, parameter estimation in addition to blunders bounds of the move functionality. This ebook is meant to fill the space among smooth structures and keep watch over concept and business program. it really is according to the result of 10 years of analysis and alertness reviews. The theories and types mentioned are absolutely defined and illustrated with case stories. At an early level the reader is brought to genuine applications.
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Additional info for Identification of Multivariable Industrial Processes: for Simulation, Diagnosis and Control
In most of the chapters discrete-time models are treated; in Chapter 10 we study continuous-time model estimation. 1 The Principle of Least-Squares The least-squares technique is a mathematical procedure by which the unknown parameters of a mathematical model are chosen (estimated) such that the sum of the squares of some chosen error is minimized. Suppose a mathematical model is given in the form y(t) = x (t)9 + x (t)9 +... + x (t)9 I I 1 where y(t) is the observed variable. parameters, xl(t).
8) is nonsingular. This is called the parameter identifiability condition which has been discussed in Chapter 3. 5) can be generalized by introducing a weighting matrix to allow each error term to be weighted individually. Let W be the desired weighting matrix which is symmetrical positive definite, then the weighted error criterion becomes Minimization of Vw(9) with respect to 9 follows the same procedure as above, 40 the parameter estimator is given by This is called weighted least-sqUlUes estimator.
1 shows the idea of the solution which can be called two-loop scheme. In doing so, we avoid the problem of closed loop identification which is more complex than the open loop problem. al. (1990). _.............................. ~ ............ ! A) Identification of the closed loop system Diaturbances Outputa B) Design of the second loop controller Fig. 1 The two-loop scheme for combining identification and control CHAPTER 4 IDENTIFICATION BY THE LEAST-SQUARES METHOD In this chapter we will study the least-squares method.