view

This example shows how to obtain a reduced-order model using the balanced truncation of normalized coprime factors method.

Load a 30-state plant model G.

load ncfModel.mat G
size(G)

State-space model with 2 outputs, 3 inputs, and 30 states.

Create a model order reduction task.

R = reducespec(G,"ncf");

To help you select a suitable target reduction order, examine the plot of Hankel singular values and approximation errors.

Create the plot.

view(R)

The function generates a Hankel singular value plot, which shows the relative energy contributions of each state in the coprime factorization of G, arranged in decreasing order by energy. The plot also shows the upper bound on the error between the original and reduced-order models that you obtain by truncating the states at that point. Examine this plot to choose the target order. For instance, for a maximum error of 0.01, you can reduce the model to 13th order.

Examine the singular values of G and of the difference between G and Gred.

Gred = getrom(R,MaxError=0.01);
sigma(G,G-Gred)
legend("G","G-Gred")

The difference is small across all frequencies, showing that the reduced-order model is a good approximation of the full-order model.

This example shows how to customize the state contribution plots obtained using the view function in the model order reduction workflow.

For this example, create a model order reduction specification for an LTI model using the balanced truncation of normalized coprime factors method.

Generate a random discrete-time state-space model with 40 states.

rng(0)
sys = drss(40);

Create a specification object.

R = reducespec(sys,"ncf");

Visualize the Hankel singular values.

view(R)

To customize the plots for balanced truncation methods, you can use hsvoptions properties as input arguments.

h = view(R,"sigma",YScale="linear");

You can further customize this plot by modifying the properties of h.

h.AxesStyle.GridVisible = "off";