By P.P. Kanjilal

ISBN-10: 0863411932

ISBN-13: 9780863411939

This publication is set prediction and keep an eye on of procedures which are expressed through discrete-time types (i.e. the features differ indirectly with time). the purpose of the e-book is to supply a unified and accomplished insurance of the rules, views and techniques of adaptive prediction, that's utilized by scientists and researchers in a large choice of disciplines

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**Extra info for Adaptive prediction and predictive control**

**Sample text**

The objective is to represent f(t) in terms of functions of constituent frequency components. An obvious choice is to use sinusoidal functions. e. wo = 2ir/T. Since coswt = cos(c<>t±2ir) and sinwt = sin(a>t±2n), cosa>ot « cos(wot+2im)f n = ±1, ±2, ... 1 A continuous-time having period length T. • periodic signal f(t) 38 Chapter 2 Process Models Similarly, sina>ot « sinwo(t+nT). 1b) Hence it should be possible to represent f(t) in terms of the sinusoidal functions. The Fourier series Consider the infinite series a0 + (a1coswot+b1sinwot) + (a2cos2wot + b2sin2wot) + ...

1 Some Basic Models Autoregressive (AR) model These models can be expressed as y(k) + a ^ k - 1 ) + ... ,^ are the model parameters; y(k) refers to the measurement of the output at time k. , y(k-l) are measurements of the output at successive 26 Chapter 2 Process Models time instants in the past; for example in the case of monthly data, these are data for successive months, e is referred to as the noise or the disturbance; it accounts for the errors in the measurements, the unaccounted for disturbances acting on the process and the modelling error.

Bmq"m; d is the time delay between the input u and the output y, that is a change in u results in a change in the output y after d time-steps. ARMAX and CARMA or Controlled ARMA models are of the same category. e. Controlled ARIMA) model has the same structure; the use of CARIMA models in process control features in Chapters 12 and 13. Remarks (1) The models discussed here are algebraically similar to the regression model y(k) » a o + a1x1(k) + ... + a ^ d c ) + e(k). Here, each regressor vector is a time series by itself.

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