A specific example of a multivariable control problem is shown in Figure 13-2. Here, two different streams are blended together. The objective is to manipulate the individual stream flow rates to meet specifications on the output flow rate and the output composition. Let the outputs be represented by y_{2} (total flow) and y_{1} (composition), and the inputs by u_{1} (flow rate of stream 1) and u_{2} (flow rate of stream 2). How should our outputs and inputs be paired? If we assume that the output-input pairings are y_{1}-u_{1} and y_{2}-u_{2}, the instrumentation diagram is shown in Figure 13-3a. If we assume that the output-input pairings are y_{1}-u_{2} and y_{2}-u_{1}, the instrumentation diagram is shown in Figure 13-3b.

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