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.

中文翻译：

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使用 Moore-Penrose 伪逆评估非平方系统的 RGA

已经提出了一种最近派生的用于计算奇异和/或非平方系统的相对增益阵列 (RGA) 的替代方法，该方法可证明可保证单位不变性。使用摩尔-彭罗斯 (MP) 伪逆的传统方法不提供此属性。在本文中，我们注意到传统 MP-RGA 缺乏尺度不变性并不一定意味着在实际应用中存在实际缺陷。换句话说，虽然控制器的性能确实不应该依赖于其输入和输出变量的单位选择，但这并不{\em一定}意味着由此产生的组件交互的 MP-RGA 测量会导致不同的控制器设计输入输出配对。在本文中，我们考虑将 MP-RGA 应用于实际系统（Sakai 分馏系统），以评估在这种情况下与温度相关的单元选择是否影响确定的输入-输出配对的选择通过得到的 RGA 矩阵。我们的结果表明确实如此，从而证实了 MP-RGA 的单元敏感性削弱了其在 MIMO 控制器设计中的严格使用。