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21. Exploiting SISO Techniques in MIMO Control

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In the case of SISO control, we found that one could use a wide variety of synthesis methods. Some of these carry over to the MIMO case. However, there are several complexities which arise in the MIMO case. For this reason, it is often desirable to use synthesis procedures that are automated in some sense. In this chapter we will see how far we can take SISO design into the MIMO case. In particular, we will study:

  • decentralized control as a mechanism for directly exploiting SISO methods in a MIMO setting
  • robustness issues associated with decentralized control

Summary
  • A fundamental decision in MIMO synthesis pertains to the choice of decentralized versus full MIMO control.
     
  • Completely decentralized control:
    • In completely decentralized control the MIMO system is approximated as a set of independent SISO systems.
    • To do so, multivariable interactions are thought of as disturbances; this is an approximation since the interactions involve feedback, whereas disturbance analysis actually presumes disturbances to be independent inputs.
    • When applicable, the advantage of completely decentralized control is that one can apply the simpler SISO theory.
    • Applicability of this approximation depends on the neglected interaction dynamics, which can be viewed as modeling errors; robustness analysis can be applied to determine their impact.
    • Chances of success are increased by judiciously pairing inputs and outputs (for example by using the Relative Gain Array, RGA) and using feedforward.
    • Feedforward is often a very effective tool in MIMO problems.
    • Some MIMO problems can be better treated as SISO problems if a pre-compensater is first used.