Chapter 4 ControllerSynthesis
© National Instruments Corporation 4-9 MATRIXx Xmath Robust Control Module
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 (Equation4-1) is easily
met. In this case, the hinfcontr( ) function returns a controller that
approximately minimizes the H2 norm of Hew while satisfying
Equation 4-2. Gamma can be interpreted as a “knob” that smoothly
transforms the H2 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 Wdist and Wnoise. For a
small gamma, the controller has good worst-case performance for noise
spectra that lay below the weights Wdist and Wnoise.
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;
Hew ∞γ≤
Hew ∞γ«
γopt Hew ∞«
Hew ∞
σmax Hew jω()[]
Hew ∞γ«
gamma γopt
≈
x
·xd+= u+
yxn+=
zx
u
=vd
n
=