Pairing of Controlled and Manipulated Variables

The most popular and widely used technique for determining the best controller pairing is the relative gain array (RGA) method (Bristol, On a New Measure of Process Interaction, IEEE Trans. Auto. Control, AC-11 133, 1966). The RGA method provides two important items of information  

A measure of the degree of process interactions between the manipulated and controlled variables 

An important advantage of the RGA method is that it requires minimal process information, namely, steady-state gains. Another advantage is that the results are independent of both the physical units used and the scaling of the process variables. The chief disadvantage of the RGA method is that it neglects process dynamics, which can be an important factor in the pairing decision. Thus, the RGA analysis 

RGA Method for 2x2 Control Problems To illustrate the use of the RGA method, consider a control problem with two inputs and two outputs. The more general case of NxN control problems is considered elsewhere (McAvoy, Interaction Analysis, ISA, Research Triangle Park, N.C., 1983). As a starting point, it is assumed that a linear, steady-state process model in Eqs. (8-54) and (8-55) is available, where Ui and U2 are steady-state values of the manipulated inputs l7 and Y2 are steady-state values of the controlled outputs and the K values are steady-state gains. The Y and U variables are deviation variables from nominal steady-state values. This process model could be obtained in a variety of ways, such as by linearizing a theoretical model or by calculating steady-state gains from experimental data or a steady-state simulation. 

By definition, the relative gain between the ith manipulated variable and thej th controlled variable is defined as 

The RGA has the important normalization property that the sum of the elements in each row and each column is exactly 1. Consequently, the RGA in Eq. (8-57) can be written as 

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Strong process interacHons can cause serious problems if a conventional multiloop feedback control scheme (e g., PI or PID controllers) is employed. The process interacHons canproduce undesirable control loop interac tions where the controllers fight each other. Also, it may be difficult to determine the best pairing of controlled and manipulated variables. For example, in the in-hne blending process in Fig. 8-40(<7), should w be controlled with and x with tt>g, or vice versa ... 

Pairing of Controlled and Manipulated Variables A key decision in multiloop-control-system design is the pairing of manipu-... 

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... 

Next, we consider a systematic approach for determining the best pairing of controlled and manipulated variables, the relative gain array method. An alternative approach based on singular value analysis is described later in this chapter. 

A recommendation concerning the most effective pairing of controlled and manipulated variables. 

Using the following information, propose a pairing of controlled and manipulated variables for a conventional multiloop control configuration based on physical arguments. It is not necessary to calculate a RGA. 

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