Process Control: Modeling, Design, and Simulation

16.3. Dynamic Matrix Control

DMC was developed by Shell Oil Company in the 1960s and 1970s (see Cutler and Ramaker, 1980). It is based on a step response model, which has the form (see Appendix 16.1 for a derivation)

Equation 16.6

which is written in the form

Equation 16.7

where ŷ_k is the model prediction at time step k, and uk – N is the manipulated input N steps in the past.

Note that the model-predicted output is unlikely to be equal to the actual measured output at time step k. The difference between the measured output (y_k) and the model ...