This example shows how to obtain a reduced-order model of a structural beam using the zero-pole truncation method. For this example, consider a SISO sparse state-space model of a cantilever beam. This example uses the linearized model from the Linear Analysis of Cantilever Beam example.
Load the beam model.
Sparse second-order model with 1 outputs, 1 inputs, and 3303 degrees of freedom.
Analyze the frequency response of the model.
To perform sparse zero-pole truncation, first create a model order reduction task using reducespec
with the "zpk"
method.
For this task, set the frequency range of focus to compute modes up to 3e5
rad/s. Doing so prevents the algorithm from computing all the poles and zeros of the sparse model, which can take a long time in some cases.
Run the model reduction algorithm. This computes the derived information, which are the poles, zeros, and gains of model, stored in the object R
.
You can visualize the map of computed poles and zeros using the view
function.
Obtain the reduced zero-pole-gain approximation based on the specified frequency of focus.
Compare the response of the original and reduced models.
The reduced-order model provides a good approximation for the original sparse model in the specified range of interest.