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[SysCC, vEV] = fslqgcomp(SysF, SysC)

The 

fslqgcomp( )

 function combines filter and control law to compute a 

controller from a control law and an estimator. For more information on the 

fslqgcomp( )

 syntax, refer to the Xmath Help.

This extended example uses the previously discussed functions to 
demonstrate frequency-shaped control design techniques. A four-state, 
poorly damped system is studied to demonstrate how robustness can be 
attained using frequency shaping. The control law and filter are designed 
on a reduced second order system with and without frequency shaping. 

1.

Create a full-order system:

a=[0,1,0,0;-1,-.01,0,0;0,0,0,1;0,0,-25,-.05];

b=[0,1,0,1]';

c=[0,1,0,-1]; d=0;

Sys=system(a,b,c,d);

2.

Calculate open-loop eigenvalues:

eig(a)

3.

Create a reduced order system by selecting only the first mode:

ar=a(1:2,1:2);br=b(1:2);cr=c(1:2);

Sysr=system(ar,br,cr,d);

4.

Design an LQG compensator for the reduced-order system, without 
using frequency shaping:

qxx=diagonal([0,1]);quu=1;

kr=regu(Sysr,qxx,quu);     # Linear-Quadratic-Regulator

ke=esti(Sysr,qxx,quu);     # Linear-Quadratic-Estimator

Sysc=lqgcomp(Sysr,kr,ke);  # LQG Compensator

Syscl=feedback(Sysr,Sysc); # Reduced-order closed-loop

poles(Syscl)