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The Evolution of the Relative Gain Array Matrix: the Multivariable Structure Fuction

Carlos E. Ugalde Loo, Eduardo Licéaga-Castro, L. Antonio Amézquita-Brooks, Jesús Licéaga-Castro
Typically, the performance of a control design task is specified in terms of an output response to a given input. This is also the case for multivariable plants, where for clarity of performance specification and design it remains desirable to consider the inputs and outputs in pairs. Regardless of the structure and internal coupling of the plant, it is convenient to establish if decentralized control is capable of meeting design specifications: the control structure will be easy to implement, economic (less programming burden upon implementation), and may provide physical insight. In line with this, the analysis and design of decentralized controllers using the relative gain array (RGA) and the multivariable structure function (MSF) are presented for the general multivariable case. It is shown that the RGA matrix can be expressed in terms of the MSF. Theoretical results are drawn for a general n×n plant, with an example from electrical power systems included to illustrate key concepts.
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