Pseudo random binary sequence

As stated in the previous section, the major reactant feed was chosen as the manipulated variable. In the trial this feed was subjected to a pseudo-random binary sequence (PRBS) signal in an open loop operation of the process. The results of the trial, plotted in Fig. 2, show a strong -- but delayed -- cross-correlation between the manipulated feed rate and the reactor temperature. Using techniques described by Box and Jenkins (2), a transfer function relating the manipulated variable to the control variable of interest can be developed. The general form of this transfer function is... 

Now let us take a time period of detector signals large enough to encompass the length of the pseudo random binary sequence Injection code which produced It, and cross-correlate It with this Injection code of -1 and 1. 

A special kind of random noise, pseudo random noise, has the special property of not being really random. After a certain time interval, a sequence, the same pattern is repeated. The most suitable random input function used in CC is the Pseudo Random Binary Sequence (PRBS). The PRBS is a logical function, that has the combined properties of a true binary random signal and those of a reproducible deterministic signal. The PRBS generator is controlled by an internal clock a PRBS is considered with a sequence length N and a clock period t. It is very important to note that the estimation of the ACF, if computed over an integral number of sequences, is exactly equal to the ACF determined over an infinite time. 

A very popular sequence of inputs is the pseudo-random binary sequence (PRBS), which is illustrated in Fig. 16.6. It is easy to generate and has some attractive statistical properties (see System Identification for Self-Adaptive Control, by W. D. T. Davies, 1970, Wiley-Interscience, London). 

PRBS (pseudo random binary sequence) signal is widely used in identifying the unknown parameters of a system because of its good statistic properties, and the possibility of reducing the noise to the least level. 

The structure of MPC is shown in the block diagram of Figure 12.40 [7]. A mathematical model of the process is used to predict the current values of the output (controlled) variables. The model is usually implemented in the form of a multi-variable linear or nonlinear difference equation. It is typically developed from data collected during special plant tests consisting of changing an input variable or a disturbance variable from one value to another using a series of step-changes with different durations, or more advanced protocols such as the pseudo random-binary sequence described in Ref 7. The residuals (that is, the difference between the pre-... 

Often normal process operating data are not fit for dynamic model identification. It just does not contain sufficient information, resulting in a poor model. The process input is therefore usually perturbed, for example by using a Pseudo-Random Binary Sequence (PRBS) or any other form of perturbation. The PRBS signal provides a sequence of upward and downward steps as shown in Fig. 24.1. 

A pseudo-random binary sequence (PRBS), shown in Fig. 24.12, is often used in parametric model identification. 

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