modalsum

Sum of modal components

Since R2023b

Syntax

G = modalsum(H,H0)

Description

G = modalsum(H,H0) takes a model array H and a static gain H0 and returns the sum

$$G(s)=H_0+{\displaystyle \sum _{j=1}^N{H}_j(s)}$$

where H_j(s) are the H(:,:,j)) models in the array H.

modalsum is useful to sum up a subset of modal components computed using modalsep.

Examples

Retain Subset of Modal Components

This example shows how to retain only a subset of modal components from a modal decomposition. In this example you perform modal decomposition and retain the modes with a relative DC contribution of more than 10% by summing those components.

Create a random states-space model with order 10.

rng(0)
G = rss(10,2,2);

Obtain the modal decomposition. Also, obtain the info output argument to store the modal information.

[H,H0,info] = modalsep(G);
size(H)

9x1 array of state-space models.
Each model has 2 outputs, 2 inputs, and between 1 and 2 states.

The decomposition returns nine modal components.

To obtain the subset of modal components with a relative DC contribution of more than 10%, use the DCGain property of the info output argument.

Hsub = H(:,:,(info.DCGain>0.1));
size(Hsub);

4x1 array of state-space models.
Each model has 2 outputs, 2 inputs, and 1 states.

The subset contains four modal components. Obtain the sum of modal components using modalsum.

Gr = modalsum(Hsub,H0);
order(Gr)

ans = 
4

Compare the Bode responses of the two models.

bode(G,Gr,"r--")

Input Arguments

H — Modal components

model array

Modal components, specified as an array of models. Typically, you obtain such an array using modalsep.

H0 — Static gain

matrix | ss object

Static gain, specified as a matrix value or a static ss object.

Output Arguments

G — Sum of modal components

ss | tf | zpk

Sum of modal components, returned as model of same type as models in the array H.

Version History

Introduced in R2023b