By P.P. Kanjilal
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
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.
Adaptive prediction and predictive control by P.P. Kanjilal