Code covered by the BSD License  

Highlights from
Feedback Control of Dynamic Systems, 4th Ed., G. F. Franklin, J. D. Powell, A. Emami-Naeini

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Feedback Control of Dynamic Systems, 4th Ed., G. F. Franklin, J. D. Powell, A. Emami-Naeini

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25 Apr 2003 (Updated )

.m and .mdl files for Feedback Control of Dynamic Systems

fig9_23.m
%  Figure 9.23      Feedback Control of Dynamic Systems, 4e
%                        Franklin, Powell, Emami
%
%  fig9_23.m is a script to generate Fig. 9.23,    
%  the rootlocus of the  LQR symmetric rootlocus compensator of the 
%  satellite position control, non-colocated case WITH ESTIMATOR

% Parameter values
m=[1, .1]; k=[0, .091] ; d=[0, .0036]; k1=[0, 0.4];

% call model
[f,g,h,j] = twomass(m,k,d);

% compute feedforward values
s=[f, g;h, 0];
r=[0*g;1]; 
n=s\r;nx=n(1:4);
nu=n(5);

% call model
[f1,g,h,j] = twomass(m,k1,d);

% form G(s)G(-s) in state-space
a=[f, 0*f;
-h'*h, -f'];
b=[g;0*g];
c=[0*h, g'];
d=[0];
hold off; clf
P=eig(a-b*c*0.1621);
pc=P(real(P<0)==1);
K=place(f,g,pc);
nbar=nu+K*nx;
% eig(f-g*K)
P=eig(a-b*c*3.056e7);
pe=P(real(P<0)==1);
L=place(f',h',pe)';
ac=f-g*K-L*h ;bc=L;cc=K;dc=0;
[Aol,Bol,Col,Dol]=series(ac,bc,cc,dc,f,g,h,j);
[acl,bcl,ccl,dcl]=feedback(f,g,h,j,ac,bc,cc,dc);
[acl1,bcl,ccl,dcl]=feedback(f1,g,h,j,ac,bc,cc,dc);
bcl= nbar*[g;g];
rlocus(Aol,Bol,Col,Dol);
grid;
v=[-2, 2, -1.5, 1.5]
axis(v);
title('Fig. 9.23 Rootlocus for D4(s)G(s).')

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