16.7 Summary

MPC is the most widely applied advanced control technique in industry. Our presentation focused on DMC, which has achieved a great deal of success in the petroleum refining and petrochemicals industries. Most MPC techniques have been based on step or impulse response models, but there has been a recent trend toward state space models. New mathematical techniques are making it easier to develop state space models from plant data. Regardless of the model type, the same basic ideas are used. At the current time step, future process output predictions are based on two contributions: the free or unforced response (how the outputs will change if no further control moves are made) and the forced response (the effect of current and future control moves on the predicted outputs). In DMC, the free response is the effect of the past control moves and the additive correction term, while the forced response is the effect of the current and future (to be calculated) control moves.

We studied two simple examples to develop a basic understanding of how to tune SISO model predictive controllers. When using step or impulse models, it is important to make certain that the model length (N) is long enough to capture the steady-state change; although not discussed, it is important to "filter," or smooth, the step response data. We found that it is also important to make certain that the prediction horizon (P) is long enough to avoid stability problems, particularly for systems with inverse response behavior. Generally, control horizons (M) are much shorter than are prediction horizons, yielding more robust performance. A disadvantage of MPC is that there are many parameters (model length, prediction horizon, control horizon, manipulated input weighting, and even sample time) that affect the closed-loop performance.

The variables used in this chapter are as follows:

M	control horizon (N P M)
P	prediction horizon (P M)
N	model length (N P)
Sf	dynamic matrix
S	vector of step response coefficients
Spast	matrix, used for effect of past control moves
si	step response coefficient
Dt	sample time
u	manipulated input
Du	change in manipulated input (control move)
w	weight applied to manipulated in the objective function (often 0 if P >> M)

The following nomenclature is common

DMC	dynamic matrix control
FIR	finite impulse response
FSR	finite step response
MPC	model predictive control