view

This example shows how to obtain a reduced-order model of a structural beam using the modal 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.

load linBeam.mat
size(sys)

Sparse second-order model with 1 outputs, 1 inputs, and 3303 degrees of freedom.

Plot the Bode response.

bode(sys,w)

Create a model order reduction task.

R = reducespec(sys,"modal");

Set the Focus option to compute the eigenvalues only in the specified frequency range.

R.Options.Focus = [0 5e5];

Analyze the model and compute the derived information.

R = process(R);
size(R.Mode)

ans = 1×2

    26     1

The original model contains 26 modes. View the DC contribution of the modal components using the view function.

view(R,"contrib")

Discard the modes with smaller contributions. For this example, discard all modes with DC contribution smaller than 1e-6. This results in a reduced model with 12 modes.

[rsys,info] = getrom(R,MinDC=1e-6);

Plot the bode responses.

bode(sys,rsys,w)

The reduced-order model provides a good approximation for the original sparse model.

This example shows how customize the plots of modal components obtained using the view function.

For this example, create a model order reduction specification for an LTI model using the modal truncation method. Generate a random discrete-time state-space model with 40 states.

rng(0)
sys = drss(40);

Create a specification object.

R = reducespec(sys,"modal");

Visualize the DC contributions of the modes.

view(R,"contrib")

To customize the plots for the modal truncation method, you can use an Axes object.

figure
ax1 = axes('Position',[0.1 0.1 0.7 0.7]);
ax2 = axes('Position',[0.65 0.45 0.28 0.28]);
h1 = view(R,"contrib",Axes=ax1);
h2 = view(R,"damp",Axes=ax2);

To further customize the plots, use the plot handles to set the options.

h2.YScale = "linear";
h1.FontWeight = "bold";