MoDMPC Toolbox Demonstration File

A. Stenman,* M. W. Braun,** and D. E. Rivera**

*Division of Automatic Control, Department of Electrical Engineering
Linköping University, SE-581 83 Linköping, Sweden
 
**Department of Chemical and Materials Engineering
Control Systems Engineering Laboratory,
Arizona State University, Tempe, Arizona 85287-6006

1   Introduction

The goal of this file is to provide the user with a hands-on demonstration of how to use the MoD V&V GUI for MATLAB, and the MoDMPC Toolbox for Simulink.  This example will make use of a Non-Adiabatic (or Diabatic) Continuous Stirred Tank Reactor (CSTR) simulation.  The main idea is to identify a model of the interation between the jacket temperature of the reactor, and the concentration of the effluent.  An informative input/output dataset had already been generated using a multi-level pseudo-random sequence excitation signal.

Be sure that you have downloaded the MoDMPC toolbox, unzipped it, and placed the toolbox directory and all of the subfolders in your MATLAB path.

If you need a decompression utility, try WinZip.

Here is a list of the demo Simulink files, and the data used to run them:

Each Simulink file runs a different MoDMPC block from the library, as indicated by the name.

2   Using the Model-on-Demand Visualization and Validation GUI

In this section, we'll load the input/output data and look at the coverage in the time, input/output, and frequency spaces. Then we will try to predict the output of the validation data, using a few iterations of MoD to validate our user decisions. Remember that Model-on-Demand estimation is data driven, so the estimation data must cover the expected operating regions of the process.  The validation data must test the interpolative ability of the MoD estimator using the estimation dataset, so robust user decisions can be made.  This is why it's important to "visualize" both datasets first!

2.1   Loading the Data and NARX Matrix

To start, click the "Load Estimation Data" button, and select "demo1e.mat" from the "demos" directory as shown below.  Press "open" to complete the operation:

In a similar manner, select "demo1v.mat", after pressing the the "Load Validation Data" button, and then press "open".
To load the NARX structure matrix, press "Load NARX Matrix", and select "demo1n.mat".
 

2.2   Visualizing the Data in the Time Domain

First, let's see what the data looks like in the time domain.  To do this we will first specifiy the correct number of inputs (1) and outputs in the data (1), and the sampling time (0.1 hour) at which it was recorded by editing the text boxes shown below.  We would also like to see how the validation data compares, and we can check that option, so both datasets are plotted together.

Having made these selections, press the "Plot Time Domain" button to generate the following figure.

If the data properties have not been specified such that they make sense with the datafile, an error message will appear in the GUI.

2.3   Visualizing the Data in the Input/Output Domain

We can get a sense for how well the data covers the possible input/output combinations within the expected operating regions of the input and output.  To do this simply select the "plot input by output" option, and press "Plot Space Domains".

To get a sense for the second order information in the data, we can look at the differenced input/output spaces.  To plot the differenced versions of the options selected in the Space Domains area, press "Plot Dif. Space Domains". 













2.4   Visualizing the Data in the Frequency Domain


Next, we can observe how

much support the estimation data provides for predicting the validation

data in the frequency domain.  For this, we will select the options

to plot the input power spectra, the output power spectra, and the ETFE. 

We will also disregard the DC component, so we can get a good look at the

rest of the frequencies.





















2.5   Making Decisions about the MoD Estimator


To begin, we would like to see how well MoD predicts the output of the

entire validation set (infinite-step ahead prediction).  So "Inf"

is typed in the prediction horizon text box.  Next, we would like

to specify how little or how much data can be considered by the candidate

bandwidth selection.  kmin

(the lower limit on the number of data to be considered) is set to 10 as

an initial guess and kmax is set

to 200 (since we have a relatively small database, we can consider nearly

all the data).  We will use a local polynomial of order one (the only

specification allowed by the MoDMPC Simulink Library), and we will choose

not to include the 95% confidence intervals for now.  The standard

Akaike's Information Criteria (AIC), will be used to judge the candidate

bandwidths.  A variance penalty of 3 will be used for the AIC. 

Lastly, we will use the global goodness-of-fit option.










Pressing the "Validate" button, we get the wait bar and then see the

following plots:













Note that the MoD Estimator selected an ill-conditioned model just before

time 3.  The number of datapoints used at this time was 36. 

So we know that   kmin


should probably be raised to something above this.  Let's choose

45, and validate again.










At this point,  kmin has

been set high enough to provide well-conditioned local models for prediction

through the regressor spaces of the validation data.  Note that this

value may still need to be raised if "bursts" are evident during control

experiments of Simulink models.  By inspection of the plot, we see

that the MoD estimator does not predict the last 4 to 5 hours as well as

the first 10 hours.  This is partly due to the way the input signal

was designed (to emphasize high frequency).  We can look at a 15 step

ahead prediction to see how the initial time prediction of MoD performs

with this data.










Now that we are satisfied with the validation, we will use the "Save

Parameters" button to save ALL the parameters under one structure. 

Then we can load this structure back into the workspace, so we can run

a MoDMPC block.  As an example, we have saved the variable "demoparms".


 




3   Running the "cstr.mdl" demo


Now that we have made our user decisions (and they work), we can try out

MoDMPC Block #1 in "cstr1.mdl".  Open "cstr1.mdl" via Simulink.










First, 2x click on the button "2x Click to Initialize".  Next,

bring up the "MoDMPC 1" parameters by double clicking on the MoDMPC 1 block.


Type in the name of the parameters structure you specified in 2.5,

we'll use "demoparms".  Be sure to load the parameter set into the

workspace (i.e. type "load demoparms").  The rest of the controller

options have been prespecified, such that the controller will run with

good performance.










The Simulink window is now started.  Note that there are scopes

on the control and manipulated variables, so you may watch the results

as they are generated.  Once the simulation is done, the button "2x

click to plot data" may be pressed to generate a figure of the results,

along with RMS control error calculations.










In a similar manner, the other demos included with the toolbox can be

used to understand the specifics of each type of controller block, along

with the help file.