Dynamic matrix control tuning for a distillation column

DMC on a column is tuned with four numbers: a prediction horizon long enough to cover the slowest tray-to-tray response, a shorter control horizon, a move weight that trades speed against valve wear, and per-CV weights that decide which spec gives way when they conflict. Defaults are horizon 20, control horizon 5, move weight 0.1.

mpcdmcdistillationtuninghow-to

Concept

Dynamic matrix control predicts where the column is heading over a horizon, then picks the sequence of moves that minimises predicted error plus a penalty on the moves themselves. On a column that matters more than on most units, because reflux and reboil both move both product compositions — the loops interact, and single-loop PID fights itself.

The math

Show the governing equations

\min_{\Delta u} \; \sum_{j=1}^{P} \|\,\hat y_{k+j} - r_{k+j}\,\|^2_{W_y} \;+\; \lambda \sum_{j=1}^{M} \|\Delta u_{k+j}\|^2

P is the prediction horizon, M the control horizon, lambda the move weight and W_y the per-CV weights. Only the first move of the computed sequence is applied; the whole problem is re-solved next tick.

Execution

The four numbers

Knob	Default	Raise it to	Cost of raising it
Prediction horizon P	20	See the full response of the slowest CV	More computation; sluggish if far past settling
Control horizon M	5	Give the controller freedom on a hard move	More aggressive, less robust to model error
Move weight lambda	0.1	Calm a valve that is working too hard	Slower rejection of disturbances
CV weights W_y	equal	Protect the spec that must not move	The other CV gives way instead

Rule of thumb for a column: set P to cover the slowest tray-to-tray response end to end, M to roughly a quarter of P, and then tune only lambda. Most bad column DMC is a move weight problem, not a horizon problem — the controller is either chattering the reflux valve or too damped to catch a feed disturbance, and both are lambda.

The overhead composition is usually the CV to weight highest: it is the spec that gets sold, and bottoms purity has the reboiler to absorb the correction.

Execution

Getting the model

DMC needs a step-response model. MaximaLabs identifies one from plant data rather than from a step-test campaign: a PRBS dither on the MVs, then a fit against the recorded CV response, so the loop can be commissioned without taking the column off spec for a week. The identified model lands as pending_model for review before it goes live — a model is never swapped underneath a running controller.