Approximating Plant Models — Additive Error Methods

Given a system in LTI form, the following commands reduce the system to any desired order you specify. The judgment call is based on its Hankel singular values as shown in the previous paragraph.

rand('state',1234); randn('state',5678);
G = rss(30,4,3);
% balanced truncation to models with sizes 12:16
[g1,info1] = balancmr(G,12:16); % or use reduce
% Schur balanced truncation by specifying `MaxError'
[g2,info2] = schurmr(G,'MaxError',[1,0.8,0.5,0.2]);
sigma(G,'b-',g1,'r--',g2,'g-.')

shows a comparison plot of the original model G and reduced models g1 and g2.

To determine whether the theoretical error bound is satisfied,

norm(G-g1(:,:,1),'inf') % 2.0123
info1.ErrorBound(1) % 2.8529

or plot the model error vs. error bound via the following commands:

[sv,w] = sigma(G-g1(:,:,1));
loglog(w,sv,w,info1.ErrorBound(1)*ones(size(w)))
xlabel('rad/sec');ylabel('SV');
title('Error Bound and Model Error')

Overview of Model Reduction Techniques

Approximating Plant Models — Multiplicative Error Method

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