Ratio algorithm

Process Control A Practical Approach Myke King 2011 John Wiley Sons Ltd. ISBN 978-0-470-97587-9 

The ratio algorithm is found in most DCS as a standard feature. Strictly, since it does not have feedback, it is not a controller - although it is often described as such. It is however more than just a simple multiplier. It incorporates the equivalent of PV tracking. When in manual mode the ratio SP tracks the actual ratio. If is the ratio SP, / the input measurement and M the algorithm s output then the algorithm performs the calculation 

When switched to automatic the ratio SP is fixed at the current value and the calculation changes to 

Once initialised in this way the operator may change the ratio SP, or may cascade a controller to adjust it as necessary. This means that we do not need to measure the stream 

In this particular case, which is an example of blending, abetter approach is to manipulate the ratio between the controlled flow and the total flow. If and are the flows of the two streams then, if the specific heats of the two streams are the same. 

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With the ratio in place the range of the ratio algorithm replaces that of the flow controller and the change in ratio target is converted to change in water flow by multiplying it by the measured steam flow Fsteand, i-C-... 

The ratio algorithm provides a means by which two strategies can manipulate the same variable. In our example both the feedforward and feedback parts of the scheme can change the flow of stream B as necessary without flghting each other. 

Rather than multiply them together, an alternative means of combining two signals is to add them. In addition to the ratio algorithm, the DCS is likely to include a bias algorithm. This performs in a similar way to the ratio. When in manual mode the bias (B) is determined by... 

In this example it would be incorrect to apply a ratio algorithm. We do not wish to keep the two fuel flows in proportion. However there are situations were either algorithm may be used. For example, in Chapter 4, we described how the three-element level control scheme for a steam drum may be adapted to either approach. 

Another difficulty may be in the determination of the feedforward gain (K) that should be used. Unlike feed rate feedforward, feed composition feedforward requires a bias not a ratio algorithm and so K is not 1 (see Chapter 6 for explanation). Figure 12.114 shows how each of the possible MVs should be adjusted as feed composition changes. The shape of these lines was explained earlier in the chapter (see Figure 12.68). K is the gradient of the line. 

Various partitions, resulted from the different combinations of clustering parameters. The estimation of the number of classes and the selection of optimum clustering is based on separability criteria such as the one defined by the ratio of the minimum between clusters distance to the maximum of the average within-class distances. In that case the higher the criterion value the more separable the clustering. By plotting the criterion value vs. the number of classes and/or the algorithm parameters, the partitions which maximise the criterion value is identified and the number of classes is estimated. 

The successful appHcation of pattern recognition methods depends on a number of assumptions (14). Obviously, there must be multiple samples from a system with multiple measurements consistendy made on each sample. For many techniques the system should be overdeterrnined the ratio of number of samples to number of measurements should be at least three. These techniques assume that the nearness of points in hyperspace faithfully redects the similarity of the properties of the samples. The data should be arranged in a data matrix with one row per sample, and the entries of each row should be the measurements made on the sample, as shown in Figure 1. The information needed to answer the questions must be implicitly contained in that data matrix, and the data representation must be conformable with the pattern recognition algorithms used. 

Foxboro developed a self-tuning PID controller that is based on a so-called expert system approach for adjustment of the controller parameters. The on-line tuning of K, Xi, and Xo is based on the closed-loop transient response to a step change in set point. By evaluating the salient characteristics of the response (e.g., the decay ratio, overshoot, and closed-loop period), the controller parameters can be updated without actually finding a new process model. The details of the algorithm, however, are proprietary... 

The gas turbine eontrol loop eontrols the Inlet Guide Vanes (IGV) and the Gas Turbine Inlet Temperature (TIT). The TIT is defined as the temperature at the inlet of the first stage turbine nozzle. Presently, in 99% of the units, the inlet temperature is eontrolled by an algorithm, whieh relates the turbine exhaust temperature, or the turbine temperature after the gasifier turbine, the eompressor pressure ratio, the eompressor exit temperature, and the air mass flow to the turbine inlet temperature. New teehnologies are being developed to measure the TIT direetly by the use of pyrometers and other speeialized probes, whieh eould last in these harsh environments. The TIT is eontrolled by the fuel flow and the IGV, whieh eontrols the total air mass... 

Equation 13-39 is a cubic equation in terms of the larger aspect ratio R2. It can be solved by a numerical method, using the Newton-Raphson method (Appendix D) with a suitable guess value for R2. Alternatively, a trigonometric solution may be used. The algorithm for computing R2 with the trigonometric solution is as follows ... 

A number of workers at Pennsylvania State University examined the push-pull system and found good agreement between their numerical and experimental work. The computational algorithm SIMPLER was used to solve the flow in the two-dimensional push-pull system and it was concluded that for a tank 1.8 m long, the push jet must have an initial velocity of 3.8 m s, that the exhaust flow rate per unit width should be 0.495 m s", and that the ratio of the pull to push flow rates, q /qj, must be between 8.8 and 17.8. 

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