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21. Exploiting SISO Techniques in MIMO Control
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
- 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.