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### Highlights from MPC Tutorial I: Dynamic Matrix Control

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# MPC Tutorial I: Dynamic Matrix Control

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07 Apr 2008 (Updated )

A tutorial for beginners to learn dynamic matrix control

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Description

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.

Acknowledgements
MATLAB release MATLAB 7.5 (R2007b)
13 Feb 2014
17 Nov 2012

Hi,

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

01 Oct 2012

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

01 Oct 2012

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

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

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

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

24 Jan 2012
06 Oct 2011

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

Hi,

I noticed that in Camacho's Model Predictive Control G is built like:
g1,zeros;
g2,g1,zeros;
...

however it seems like here in dmc.m it is built like:
g0,zeros;
g1,g0,zeros;
...

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
28 Apr 2008

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

Let continue the tutorial, please!! Thanks alot.