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Chapter 4 Controller Synthesis
MATRIXx Xmath Robust Control Module 4-18 ni.com
-0.500025 + 0.866011 j
-0.500025 - 0.866011 j
5. Try the LQG compensator with the full-order system:
[Syscl_fo]=feedback(Sys,Sysc);
poles(Syscl_fo)
ans (a column vector) =
-0.401519 + 0.864869 j
-0.401519 - 0.864869 j
-0.638796 + 0.855861 j
-0.638796 - 0.855861 j
0.0152647 + 4.90994 j
0.0152647 - 4.90994 j
6. Find a stabilizing reduced order controller using frequency shaping.
To stabilize this system, try a frequency-shaped control-law, where the
weighting on the control signal will be 1 + (ω)
4
.
First, form an augmented system, defining two additional states,
μ and
The augmented system will be:
(4-3)
(4-4)
Note The augmented system has two extra states implementing the frequency shaping on
the control system.
aa=[ar,br,[0;0];0,0,0,1;0,0,0,0];
bb=[0,0,0,1]';cc=[0,0,1,0];dd=0;
Sysa=system(aa,bb,cc,dd)
Sysa (a state space system) =
A
0 1 0 0
-1 -0.01 1 0
u
·
.
d
dt
-----
x
r
u
u
·
A
r
B
r
0
0
0001
0000
x
r
u
u
·
0
0
0
1
v+ A
a
x
A
B
a
v+==
u
0010
x
r
u
u
·
0()v+ C
a
x
A
D
a
v+==