Approximate Plant Model by Additive Error Methods

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

rng(1234,'twister'); G = rss(30,4,3);% random 30-state model% balanced truncation to models with sizes 12:16[G1,info1] = balancmr(G,12:16);% 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-.') legend('G',G1的,'G2')

The plot compares the original modelGwith the reduced modelsG1andG2.

To determine whether the theoretical error bound is satisfied, calculate the peak difference across frequencies between the gain of the original system and the reduced system. Compare that to the error bound stored in theinfostructure.

norm(G-G1(:,:,1),'inf')

ans = 2.2965

info1.ErrorBound(1)

ans = 9.7120

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(“错误绑定和模型错误”)

See Also

balancmr

Related Topics

• Model Reduction Techniques
• Approximate Plant Model by Multiplicative Error Method