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IDCON Example - Car Velocity Model

Lets consider we want to determine a car velocity model based upon Input throttle, (or "Gas Pedal") position.  We have measured both the input and output data from a small test, and now we want to determine a transfer function model for this system.

1. Collect the Data

In this example, the input and output data is being generated via a Simulink model.  We have developed a system for the "Gas Pedal" input and also one for the vehicle's speed.  To make it a little more "interesting" and "real-life", we have added noise to the Gas Pedal input , ( not just to the measured input), and also to the measured output speed  The output from the Simulink model is shown below:





As you can see, the data we have obtained, ( 90 seconds of data @ sample rate of 10 Hz), is modestly noisy, and is not just a simple "step" test.  The other thing you notice, is this data is not from a model of a F1 car, more like a small city car, ( 0-60 MPH in 25 seconds, pretty slow!)

2. Identify the system

Now lets use the functions with in the IDCON Classic Toolbox, to take our input and output data and identify a transfer function model of the system.  One of the ways to do this is via the supplied GUI, IDCMENU, (alternatively you could call the individual toolbox functions via m-files).

Once the data is loaded we can go and define the parameters of the desired system we are trying to identify and also options used in the identification process.  The following Menu appears and we can specify information about the order of the numerator and denominator, whether the system has pure integrating components, and if any of the states initial conditions were non-zero.

In this system, we are not sure what the order the numerator or denominator should be, so we choose 1 and 3 respectively, ( more on this later).  The system has no pure integrating part that we know of, and the data was collected from zero initial conditions.



Now we can run the identification algorithm by pushing the "Start Ident." pushbutton, and after a few iterations, the following information is shown on the IDCON Main Menu. 

This is a good time to briefly explain the IDCON Main Menu.  The GUI consists of four windows, the left side shows information about the measured data, and the right side shows information about the identified system.  The top half gives textural information, such as data lengths and identified transfer function, while the bottom half shows graphical output, like input and output data and comparison to identified system.  Data ranges can be selected graphically or via text menus, system information can be obtained, as well system responses, can be plotted.  On the right hand side we have two sets of pushbuttons, the top drive the identification process, from loading data and defining the parameters and options, to the identification, order reduction and display of results.  The bottom set of pushbuttons, are really for the GUI functionality, allowing you to save and load projects, print results, and configure the GUI format.  The bottom pushbutton allows you to go directly into the Automatic Controller Design ACD Toolbox ,(more about that later).



So, in the identification output section, you can see we have a model that seems to fit the data well.  Lets look at this output a little closer.  We can easily zoom out to the full GUI size to see the output in more detail, as shown below:



As you can see we have a very good fit with the noisy data.  We could also look at the step response or Bode Plot of the identified system at this point.  Lets move on to looking at the identified model in a little more detail.

Once again we can zoom out and look at the model information in more detail.  Here we are looking at the poles and zeros of the identified model.



3. Order Reduction

As you can see, this model has what seems to be a pole / zero cancellation, so we could look at reducing the order of the model.  We simply press the "Order Reduction" pushbutton, and the following menu appears asking for the order of the numerator and denominator of the reduced model.



Now the output below is the bode plot of the original and reduced identified models.  As you can see, there is virtually no difference between the two systems, and so we would conclude that we had initially used too high an order model for the identification.



4. Results

The reduced model is shown in detail below, along with quality of fit information.



From the system response and fit with the original data, you must say we have a very good fit, and with a very low order system. 

Oh by the way, the transfer function used in the "Car Model" in the Simulink model, is as shown below,



As you can see, IDCON Classic Toolbox did very well, even with all that noise!

5. Controller Design

We can transfer this model into a state space system, or use the transfer function directly in a Simulink model.  We could alternatively continue on the process and design say a cruise controller for this vehicle.  We can do this very easily with another Toolbox that is part of the ExpertControl range, the Automatic Controller Design, ACD Toolbox.  By simply clicking on the "Contr. Design" pushbutton, located at the bottom right hand side of the GUI, the following menu appears, asking which model we would like to use in the ACD Toolbox.  Since the reduced model was such a good fit, we have chosen to use the simpler model in the control design process.



Now go to the Automatic Controller Design Example, to continue the process of defining a cruise control.

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