Multiple Input Multiple Output Systems

MIMO system control requires the simultaneous control of multiple internally interacting variables with their specific performance requirements. In view of an increased complexity of the control problem in comparison to SISO systems, a question is if and under what conditions a MIMO system can be considered as a system with multiple control loops that are weakly coupled or even decoupled and with a SISO controller for each loop. One approach is to compensate internal system interactions by means of a decoupling block so that a block-diagonal centralised controller can be used. The Relative Gain Array (RGA) method and singular value decomposition (SVD) consider the degree of interactions and aim at a pairing of input and output variables. If a MIMO system is approximated by a multi-loop system, the question is whether the block-diagonal controller with SISO controllers for each feedback loop can guarantee stability of the MIMO system. SISO systems can be described by a transfer function, from which the input-output gain, poles and zeros can be easily obtained. In the case of MIMO systems, vectors of inputs and outputs are related by a transfer function matrix. In contrast to SISO systems, the gain of MIMO system depends on the direction of the input vector, and multivariable system zeros are, in general, different from the zeros of the transfer functions which are elements of the transfer function matrix. As a multivariable system may have uncontrollable and/or unobservable subspaces, the question is how to determine the system poles.