Optimizing system using Simulink Design Optimization 

• T= torque applied to the motor
• Kt= torque gain
• Td=time delay
• U=current input applied to the motor

This model contains the butterfly valve dynamics

 where:

• J= valve inertia
• C=valve viscous friction
• K= valve spring constant
• : angular position and velocity.

Also there is a term which block the valve angular position between 15-90 degrees:

Sometimes our data is noisy and contains unexpected values (also called outliers. Despite this, It could be improved. Actually, with Simulink design optimization, it is possible to remove noise and, in general, do preprocessing of data (scale, offset removal, filters, replacing outliers, etc.). Let's see how real and simulated data looks!

Let's imagine that real measured data is given, let's plot the measured data, for this, you have to run the model in Simulink and see how the workspace in MATLAB is updated.

For this, write spe_engine_throttle1 on MATLAB command windows

If that does not work, write: load('spe_engine_throttle1.mat') on MATLAB command windows

For simulated output data it is nothing but to see the graph in your scope block in Simulink:

As you see, Real Output measured is, actually, noisy. This response is established about in 0.15 seconds, while the Simulated Output does it in about 0.33 seconds. So maybe the parameters of your model may not be the same as the real model. So, you could think about it is time to use the Parameter estimator app to do model parameters fit the real response. However, notice that because of Real Output measured remains noisy, it could be so difficult to obtain real values. Don't worry; using the Parameter estimator app is also possible to remove noise in signals and, in general, do preprocessing data.

I want you to first notice that simulated data is going until 0.5 seconds while measured data is until 0.7 seconds, so, let's cut the data, go to Simulink, and then select the app menu, finally find and choose Parameter estimator.

Now click on the Experiments menu and select New Experiment:

1. Write: [time1,position1]
2. Write: [time1,input1]

Then select Save As, now you will see how Exp_1 data is created in the Experiments window. Now select Exp_1 data and select plot measured experiment data.

You will notice now that there are some outliers values in the data. They are not expected, so it is time to remove them. Go again to the Experiment plot menu but now choose to replace data. Doing this will be useful for the estimation algorithm!

1. Select the last 7 outlier values
2. Choose replace with constant value option and select 90

Then do the same for the other outlier values, replace them by 15, 15, and 86. Then apply the changes and see the new data. Choosing these values will provide the data which is more flatter!

This is an optional step, maybe you could be interested in applying some filter to smoothen the signal. Go again to the experiment plot menu and select a low-pass filter. Choose 0.4 as the value for normalized cutoff frequency and then choose your filter as a first-order one.

Then apply the changes, and finally, your signal will be ready to be used for estimating your real model values.

This is the easiest part of the app. The next step is to choose what parameters you want to find, let's say we are interested in estimating J, c, input delay, and k values. So, go to parameters window => Edit => Select Parameters.

Now select the mentioned previously:

Now, save your session, and then feel free to click on the Estimate option!

Note: Please ensure that your data has been selected for estimating as is shown below, in fact, remember we are using two different kinds of data, one for estimating and the other for validation, the second one will be used later to compare if our estimated parameters are correct.

Next, click again in the estimate, and you should wait while MATLAB computes the parameter values when the algorithm finishes you could see the graphs. This one shows you the number of iterations and function cost values as well.

This other one shows the final real and simulated signals so that you can compare the results of parameter estimation, you will notice how the cost function values are decreasing, which is good! This means our parameters are being estimated correctly.

Now that our parameters have been updated, It would be a good idea to validate if we change the input, the real data will be similar to simulated data to identify if there was or not some kind of overfitting in the estimated parameters. Go now to Experiments window and add next real data measures:

• Validation1: for output signal use [time2,position2] while for input [time2,input2]
• Validation2: for output signal use [time3,position3] while for input [time3,input3]

Next, do right click on validation1 and select it as use experiment for validation, then do click on validate option, then, do the same for Validation2 experiment. You will see something like this:

So, the result is not as expected since, in both cases, graphs Measured and Simulated should be similar; this is because the estimation is overfitted. We have to recompute the estimated parameters, go to parameter windows, and do them be only positive. Then do the estimation again:

So, ensure your minimum data value is zero for all your parameters!

Then, re-estimate the parameter values again and do the validation again, if the parameters are well estimated, the validation graphs should be like:

With response optimization, you could improve your time-domain requirements as shown previously, but also you could try to track some reference signal

Let's say we are interested in tracking a reference r(t) = 1-exp(-t) but first we are using another model (previous does not work since we have already designed a PI controller)

So let's consider the next model:

Initialize the controller parameters in the value that you want, create the variables in the model workspace.

Remember update your PID block as shown below:

Now, go to new requirements and select Signal tracking.

Also, remember to select and add the system output signal because this signal is the one that should track the reference.

Then plot the actual model response :