getrom

This example shows how to obtain a reduced-order model for a linear time-invariant (LTI) model using the modal truncation method. In this example, you reduce a high-order model with a focus on the dynamics in a particular frequency range and damping.

Load a model and examine its frequency response.

load('highOrderModel.mat','G')
bodeplot(G)

G is a 48th-order model with several large peak regions around 5.2 rad/s, 13.5 rad/s, and 24.5 rad/s, and smaller peaks scattered across many frequencies.

Create a model order reduction task.

R = reducespec(G,"modal");
view(R,"damp")

Suppose that for your application you are only interested in the dynamics between 10 rad/s and 40 rad/s with damping less than 0.04. Focus the model reduction on the region of interest to obtain a good match with a low-order approximation.

rsys = getrom(R,Frequency=[10,40],Damping=[0.022 0.04]);
opt = bodeoptions;
opt.PhaseMatching = "on";
bodeplot(G,rsys,"r--",opt)
legend("Full order","Reduced order")

The reduced-order model provides a good approximation for the specified targets.

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.