Pairing Controlled and Manipulated Variables

In some Instances, the correct pairing of controlled and manipulated variables is obvious. Occasionally it does not matter how they are paired. Cited in Fig. 7.3 are examples of each extreme. In the separa tor, vapor flow does not affect liquid level, nor does liquid flow influence pressure, so the arrangement of loops is obvious, hi the pipeline, how ever, both valves appear to affect pressure and flow equally, so either combination will work. But many times a control en eer will be faced with a situation where a decision must be made that is not obvious, and 

Picture any process as consisting of a block with a number of input (manipulated) variables and an equal number of output (controlled) variables. The object is to control a given process output by manipulating the one input that will have the greatest influence on it. If this is not done, another input will have more influence on the controlled variable than the one which it manipulates through the controller. To assess all the possibilities, the gain of each controlled variable to each manipulated variable must be determined. It is extremely desirable that these gain terms be normalized to eliminate dimensions and to place them all on the same basis. 

It is convenient to arrange a table of these gains in the form of a matrix such as that shown below  

This greatly facilitates comparison of the different combinations. The combinations with the largest positive numbers should be selected for closed loops, for reasons that will soon be explained. 

To see how the matrix is derived, the pressure-flow process of Fig. 7.3 will be exammed, using the following simphfied equations to express the flowing differential h and the controlled pressure 

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RGA is often presented as the method for pairing controlled and manipulated variables. In this respect some comments are useful ... 

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