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| R2011b Documentation → System Identification Toolbox | |
Learn more about System Identification Toolbox |
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How to Estimate Linear Models Using Quick Start |
You can use the Quick Start feature in the System Identification Toolbox to estimate linear models. Quick Start might produce the final linear models you decide to use, or provide you with information required to configure the estimation of accurate parametric models, such as time constants, input delays, and resonant frequencies.
You must have already processed the data for estimation, as described in Plotting and Processing Data.
If you have not performed this step, click here to complete it.
To identify linear models:
In the System Identification Tool GUI, select Estimate > Quick start.
This action generates plots of step response, frequency-response, and the output of state-space and polynomial models. For more information about these plots, see Validating the Quick Start Models.
Quick Start estimates the following four types of models and adds the following to the System Identification Tool GUI with default names:
imp — Step response over a period of time using the impulse algorithm.
spad — Frequency response over a range of frequencies using the spa algorithm. The frequency response is the Fourier transform of the impulse response of a linear system.
By default, the model is evaluated at 128 frequency values, ranging from 0 to the Nyquist frequency.
arxqs — Fourth-order autoregressive (ARX) model using the arx algorithm.
This model is parametric and has the following structure:
y(t) represents the
output at time t, u(t) represents
the input at time t, na is
the number of poles, nb is
the number of b parameters (equal to the number
of zeros plus 1), nk is
the number of samples before the input affects output of the system
(called the delay or dead time of
the model), and e(t) is the white-noise disturbance.
The System Identification Toolbox product estimates the parameters
and
using the input and output data
from the estimation data set.
In arxqs, na=nb=4, and nk is estimated from the step response model imp.
n4s3 — State-space model calculated using n4sid. The algorithm automatically selects the model order (in this case, 3).
This model is parametric and has the following structure:
y(t) represents the output at time t, u(t) represents the input at time t, x is the state vector, and e(t) is the white-noise disturbance. The System Identification Toolbox product estimates the state-space matrices A, B, C, D, and K.
Quick Start generates the following plots during model estimation to help you validate the quality of the models:
Step-response plot
Frequency-response plot
Model-output plot
You must have already estimated models using Quick Start to generate these plots, as described in How to Estimate Linear Models Using Quick Start.
If you have not performed this step, click here to complete it.
The following step-response plot shows agreement among the different model structures and the measured data, which means that all of these structures have similar dynamics.
Tip If you closed the plot window, select the Transient resp check box to reopen this window. If the plot is empty, click the model icons in the System Identification Tool window to display the models on the plot. |
Step Response for imp, arxqs, and n4s3
Tip You can use the step-response plot to estimate the dead time of linear systems. For example, the previous step-response plot shows a time delay of about 0.25 s before the system responds to the input. This response delay, or dead time, is approximately equal to about three samples because the sampling interval is 0.08 s for this data set. |
The following frequency-response plot shows agreement among the different model structures and the measured data, which means that all of these structures have similar dynamics.
Tip If you closed this plot window, select the Frequency resp check box to reopen this window. If the plot is empty, click the model icons in the System Identification Tool window to display the models on the plot. |
Frequency Response for Models spad, arxqs, and n4s3
The Model Output window shows agreement among the different model structures and the measured output in the validation data.
Tip If you closed the Model Output window, select the Model output check box to reopen this window. If the plot is empty, click the model icons in the System Identification Tool window to display the models on the plot. |
Measured Output and Model Output for Models imp, arxqs, and n4s3
The model-output plot shows the model response to the input in the validation data. The fit values for each model are summarized in the Best Fits area of the Model Output window. The models in the Best Fits list are ordered from best at the top to worst at the bottom. The fit between the two curves is computed such that 100 means a perfect fit, and 0 indicates a poor fit (that is, the model output has the same fit to the measured output as the mean of the measured output).
In this example, the output of the models matches the validation data output, which indicates that the models seem to capture the main system dynamics and that linear modeling is sufficient.
Tip To compare predicted model output instead of simulated output, select this option from the Options menu in the Model Output window. |
 | Saving the GUI Session | Estimating Accurate Linear Models |  |
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