Multi-variable systems and multi-loop control

In the feedback control section of this course we only considered systems with a single active controlled variable (although selective control had several controlled variables, only one was active at a time). Most real systems require the simultaneous control of many controlled variables (sometimes several hundred). This wouldn't be too much a problem if the individual loops acted independently, but unfortunately this isn't usually the case. The reason for this is that each manipulated variable can simultaneously affect several controlled variables leading to problems with interacting loops. In some cases this interaction can cause controllers which are well-tuned when operating in single-loop mode to go completely unstable when the other loops are switch on.

Problems with interaction can be reduced, or even eliminated, by making the correct choice of loop pairings (i.e. deciding which manipulation to use to control which controlled variable). Unfortunately there is no easy way to make this choice! Luyben and Marlin both provide  good discussions on the problems on making good choices of loop pairings.

In the absence of good scientific tools, the old fallback is to use rules of thumb (or heuristics, if you want to pretend they're scientific!). Here are some I've gathered:

• Choose loop pairings where the manipulations have strong, direct effects on the controlled variables: it is possible to control the level in a flash drum by varying the vapour flowrate, but its probably best to use the liquid flow!
• Choose loop pairings with the minimum amount of dead-time. Dead-time always reduces control performance, if it can be minimised by changing pairings then better control should result.
• Choose loop pairings where the manipulation has sufficient range to move the controlled variable as required. This was covered in the discussion on operating envelopes.