Given a linear MIMO system with quite a number of internal interactions of different strength between internal variables, it is natural to ask whether the MIMO plant controlled by an MV controller accounting for the internal couplings can be approximated by a multi-loop system consisting of single-input-single-output loops so that SISO controllers and engineering experience can be used. The question has been addressed already a long time ago and given rise to subsequent analysis, e.g. which input variables should be paired with which output variables. Is the internal coupling between them still acceptable? For SISO systems, the gain between an input and an output is clear. In MIMO systems, the gains may have a direction. The chapter briefly recalls three methods, i.e. input-output decoupling, relative gain array (RGA) and singular value decomposition (SVD). Moreover, the entries of a transfer function matrix are transfer functions. All of them may have no zero in their numerator. Nevertheless, the MIMO system may have MV zeros of different kind and may have a direction. Also, all entries of a transfer function matrix do have a denominator. However, what are the MV poles of the MIMO system, and how can they be computed?

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Multiple-Input-Multiple-Output Systems

  • Wolfgang Borutzky

摘要

Given a linear MIMO system with quite a number of internal interactions of different strength between internal variables, it is natural to ask whether the MIMO plant controlled by an MV controller accounting for the internal couplings can be approximated by a multi-loop system consisting of single-input-single-output loops so that SISO controllers and engineering experience can be used. The question has been addressed already a long time ago and given rise to subsequent analysis, e.g. which input variables should be paired with which output variables. Is the internal coupling between them still acceptable? For SISO systems, the gain between an input and an output is clear. In MIMO systems, the gains may have a direction. The chapter briefly recalls three methods, i.e. input-output decoupling, relative gain array (RGA) and singular value decomposition (SVD). Moreover, the entries of a transfer function matrix are transfer functions. All of them may have no zero in their numerator. Nevertheless, the MIMO system may have MV zeros of different kind and may have a direction. Also, all entries of a transfer function matrix do have a denominator. However, what are the MV poles of the MIMO system, and how can they be computed?