A continuous analysis of multi-input, multi-output predictive control

A continuous formulation and method of analysis is constructed for multi-input, multi-output (MIMO) predictive control and used to compare Dynamic Matrix Control (DMC) with Simplified Predictive Control (SPC). Approximate characteristic equations are derived for each of DMC and SPC and these are used to determine, and thus compare, the closed-loop control behaviour of these methods at times long compared with the sampling time. The MIMO control problem considered is the general case of control over two coupled zones of a first order, linear process where a single control move is simultaneously input into each zone and a single output or measurement, is made from within each zone. The analytical results are illustrated through MIMO control of the terminal composition of a binary distillation column. A practically important result is an analytic basis to understand previous experimental observations that, for a wide range of processes, SPC appears to be as capable as the more sophisticated DMC. Furthermore, it is also shown here that SPC is well-conditioned over its entire parameter range in contrast to DMC. This well-conditioned behaviour makes it especially suitable for remote applications where unknown, and variable timing of future moves may be a significant issue.