The Use of the Moore-Penrose Pseudoinverse for Evaluating the RGA of Non-Square Systems

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