The multivariable structure function as an extension of the RGA matrix: relationship and advantages
Amezquita-Brooks, Luis A.
Ugalde Loo, Carlos Ernesto
It is common practice to specify the performance of control design tasks in terms of an output response to a given input. In spite of a greater complexity, this is also the case for multivariable plants, where for clarity of performance specification and design 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 further 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 demonstrated that the RGA\ud matrix can be expressed in terms of the MSF. Moreover, it is shown that the correct interpretation of the MSF offers significative advantages over the RGA matrix analysis. While the RGA offers insight about the adequate pairing of input-output signals in a multivariable system, the MSF, besides providing this information, plays a crucial role in the design of stabilizing controllers (and their requirements) and the subsequent robustness and performance assessment of the closed loop control system. Theoretical results are drawn for a general n×n plant, with examples from electrical power systems and laboratory tank processes included to illustrate key concepts.
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