MPC Tutorial I: Dynamic Matrix Control

A tutorial for beginners to learn dynamic matrix control

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: This submission has inspired the following:; MPC: Multivariable Constrained State Space example, MPC Tutorial IV: DMC Simulink Block and Example, MPC Tutorial II: Multivariable and State Space MPC V2.0
• MATLAB release: MATLAB 7.5 (R2007b)

[Haryanto Ade]

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

Let continue the tutorial, please!! Thanks alot.

[V. Poor]

 

[matija]

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.

[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.

[Mr Smart]