Answer to Question 2

The first stage is to calculate the gain matrix

In runs 1 and 2 S is constant and so

Similarly in runs 4 and 5 R is constant and so

Hence the gain matrix is

Using the formula

the RGA is calculated to be

Compare this with the answer below calculated from

In runs 3 and 4 x_B is constant and so

Hence the RGA is

As can be seen the two different methods give the same answer. From the RGA obtained R should be paired with x_D and S with x_B. Pairing the other way means that the direction of response depends on whether the loop is open or closed.

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