  A recently-derived alternative method for computing the relative gain array
(RGA) for singular and/or non-square systems has been proposed that provably
guarantees unit invariance. This property is not offered by the conventional
method that uses the Moore-Penrose (MP) pseudoinverse. In this paper we note
that the absence of the scale-invariance property by the conventional MP-RGA
does not necessarily imply a practical disadvantage in real-world applications.
In other words, while it is true that performance of a controller should not
depend on the choice of units on its input and output variables, this does not
{\em necessarily} imply that the resulting MP-RGA measures of component
interaction lead to different controller-design input-output pairings. In this
paper we consider the application of the MP-RGA to a realistic system (a Sakai
fractional distillation system) to assess whether or not the choice of unit,
which in this case relates to temperature, affects the choice of input-output
pairings determined by the resulting RGA matrix. Our results show that it does,
thus confirming that unit-sensitivity of the MP-RGA undermines its rigorous use
for MIMO controller design.
