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MPC Tutorial I: Dynamic Matrix Control



07 Apr 2008 (Updated )

A tutorial for beginners to learn dynamic matrix control

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This is the first part of the planned series for Model Predictive Control (MPC) tutorials.

Dynamic Matrix Control is the first MPC algorithm developed in early 1980s. It is probably also the most widely used MPC algorithm in industry due to the fact that its internal model, the step response model is easy to obtain in an industrial process.

The package provides a dmc function to perform dynamic matrix control and to show the principal of DMC. An example file is included to show how the dmc function can be used to solve a control problem. It only uses basic MATLAB commands. No any other toolboxe is required.


This file inspired Mpc: Multivariable Constrained State Space Example, Mpc Tutorial Iv: Dmc Simulink Block And Example, and Mpc Tutorial Ii: Multivariable And State Space Mpc V2.0.

MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (13)
16 Sep 2014 Abhishek

I keep getting an error Maximum Recursion Limit 0f 500 Reached.
I changed it but to 750 Matlab shuts itself down.
How to fix this problem?

13 Feb 2014 Hassan  
17 Nov 2012 Sarav


Can anyone tell how to calculate the step response co-efficients from step test data?
how can i fix the prediction and control horizons?

thx in advance.

01 Oct 2012 Sarav

thx matija, i got it
thank you very much Mr.Yi Cao
for this nice tutorial

01 Oct 2012 matija

Function "filter" is digital filter which takes coefficients of discrete transfer function polynomial. To get digital filter approximation of continuous filter with transfer function "1/(1+T*s)" and sampling period Ts use coefficients p.a=exp(-Ts/T) ,b=[0,p.a], a=[1,-p.a].

30 Sep 2012 Sarav

thx, matija
actually i dont have any idea on how filter works, i tried to understand the help file in matlab, but i coudnt. Is there any other alternate for filter to this particular application.

29 Sep 2012 matija

Reference trajectory is generated with first order filter. The initial condition of filter is initialized to p.y and then the set point is filtered so you get "smooth" transition of reference trajectory from current PV to desired SP.

28 Sep 2012 Sarav

hi can anyone pls explain the following line
w=filter([0 (1-p.a)],[1 -p.a],ref,p.y)

24 Jan 2012 Mr Smart  
06 Oct 2011 matija

I got it. The plant has 3 samples of delay, but you only used 2 for generating p.sr. So p.sr=[g1,g2...]'.

Thanks for this nice tutorial.

05 Oct 2011 matija


I noticed that in Camacho's Model Predictive Control G is built like:

however it seems like here in dmc.m it is built like:

Is that a flaw or am I missing something?

The filter function produces y=[y0,y1, ...]', right?
And since input is X=[1,1,1, ...]' we could say that y=g=[g0,g1, ...]' and according to Camacho we would use g(2:P+1) for building G but in mpc.m it is used p.sp=(1:P) which would be g(1:P) in books notation.

05 Apr 2009 V. Poor  
28 Apr 2008 Haryanto Ade

This is a good tutorial and best. It make clear understanding of MPC.

Let continue the tutorial, please!! Thanks alot.

07 Apr 2008

Update the html file.

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