National Instruments 370757C-01 Manual De Usuario
Chapter 4
Controller Synthesis
© National Instruments Corporation
4-9
If no error message occurs, then
is guaranteed. However,
this does not preclude the possibility that either
or that
.
For the former case, there are two checks:
•
Use the
linfnorm( )
function to compute
.
•
Compute the graph
versus
ω.
If
by about 6 dB or more, then you can decrease
gamma
and try
again.
When
gamma
is very large, the specification (Equation 4-1) is easily
met. In this case, the
hinfcontr( )
function returns a controller that
approximately minimizes the H
2
norm of H
ew
while satisfying
Equation 4-2.
Gamma
can be interpreted as a “knob” that smoothly
transforms the H
2
optimal (LQG) controller, (with
gamma
large), to a
H
∞
optimal controller (with
).
Similarly, for a large
gamma
, the controller has good RMS performance
with the noise spectra determined by the weights W
dist
and W
noise
. For a
small
gamma
, the controller has good worst-case performance for noise
spectra that lay below the weights W
dist
and W
noise
.
Example 4-1
Example of hinfcontr( )
Referring to Figure 4-2, suppose G has the state space description,
where:
1.
The extended system matrix for G is:
A = 1;
B1 = [1,0]; B2 = 1; B = [B1,B2];
C1 = [1;0]; C2 = 1; C = [C1;C2];
D11 = zeros(2,2); D12 = [0;1]; D21 = [0,1]; D22 = 0;
D = [D11,D12; D21,D22];
G = system(A,B,C,D);
nw = 2; nz = 2;
H
ew ∞
γ
≤
H
ew ∞
γ
«
γ
opt
H
ew
∞
«
H
ew ∞
σ
max
H
ew
j
ω
( )
[
]
H
ew ∞
γ
«
gamma
γ
opt
≈
x·
x d
+
=
u
+
y
x n
+
=
z
x
u
=
v
d
n
n
=