Random binary signal

Nasserzadeh V., Swithenbank J., Lawrence D Garrod N. and Jones. B, (1995) Measuring gas-residence times in large municipal incinerators by means of pseudo-random binary signal tracer technique. Journal of (be Institute of Energy, September 1995, 68, pp. 106-120... 

For tracer experiments periodic sequences of pseudo random binary signals (PRBS) can be used, which show good results after a shorter measuring period (Havlicek and Cermak, 1977 Unbehauen and Funk, 1974). A PRBS sequence consists of a stochastic series of rectangular tracer pulses (concentration c, time interval At). The sequences recur with a period T. Each period is divided into N time intervaUs T = N-At). 

The design of the experiment can be split into two parts preliminary identification using step tests and final identification using a random binary signal. 

Once a basic understanding of the system parameters has been obtained, the input signal can be designed. As mentioned before, the best input signal to consider is the random binary signal. In order to use this signal, three components must be selected levels, sampling time, and bandwidth. 

A random binary signal does not approximate a white noise signal. 

To specify a random binary signal, the physical values for the levels, the sampling time, and bandwidth are required. 

This process has an approximate settling time of 199 sec and is sampled with an interval of 1 sec. Thus the parameter N is chosen to be 199 for both the FSF and FIR models. For the identification experiment, we have used a binary input signal with amplitude equal to unity. The input signal has been taken as a generalized random binary signal (GRBS) with probability... 

The parameter estimation is done by using a PRBS (Pseudo Random Binary Signal) such as excitationinputsignal. Thisguaranteesthe correct excitation of all dynamic sensible modes of the... 

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. 

We adopt the input/output data-based prediction model using the subspace identification technique. To find the correlation between the inputs and outputs, we need to obtain the input and output data. On the basis of the triangle Aeoiy[6], the optimal feed flow rate ratios at steady state are calculated. Then, the pseudo random binary input signal is generated on the basis of this optimal value. Figure 1 compares the output from the identified model (dot) with that from the first principles model (solid curve). Clearly, we observe that the identified model based on the subspace identification method shows an excellent prediction performance. The variance accounted for (VAF) indices for both outputs are higher than 99%. The detailed identification procedure can be founded in the literature [3,5,9,10]. 

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 above analysis shows that, as long as the disturbances are fast relative to the process dynamics, an accurate model can in fact be constructed from step response data. However, many process 2ire affected by slow, drifting disturbances that effectively mask the true process response. For these types of disturbances, the proposed Ls erre approach may produce process models with significant errors. In this case, other types of input signals, such as a random binary input signal or a periodic input signal, should be used to enable the effect of the disturbances on the process output to be separated from the process response due to the input variable. 

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. 

Random Binary Sequence (RBS) forcing involves a series of pulses of fixed height and random duration. At each sampling instant, a random number generator determines whether the input signal is set at its maximum or minimum value. However, it is more convenient to... 

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