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Chapter 4 Controller Synthesis
MATRIXx Xmath Robust Control Module 4-8 ni.com
•For all ω ≥ 0,
•
Condition 1 is a standard condition to ensure the existence of a stabilizing
controller. Condition 2 ensures that the control signal u is contained in the
normalized error vector e (refer to Figure 4-3). Conversely, condition 3
ensures that some exogenous input (disturbance or noise) affects the
measured signals (refer to Figure 4-3). Conditions 4 and 5 ensure certain
minimal realizations of subblocks of the extended plant ([GD88]).
hinfcontr( )
[SysC,Syszw]=hinfcontr(SysAug,gamma,nw,nz,{method})
The hinfcontr( ) function designs an H
∞
controller for an augmented
plant. The augmented plant should satisfy the five restrictions in the
Restrictions on the Extended Plant section. The
hinfcontr( ) function
tests for these restrictions and returns an error if they are violated.
Assuming the restrictions are not violated, a controller satisfying
will exist if certain low-level conditions also hold. These
involve conditions for the solution of the underlying Riccati equations
and conditions for some other constraints. The details can be found in
[GD88,DGKF89] and are beyond the scope of this manual. If the low-level
conditions are violated, an error statement is displayed:
hinfcontr –>No stabilizing controller meets the spec!
Adjust gamma and try again!
When this occurs it means that the original gamma is too small and a
larger
gamma (for example, a looser spec) is required to eliminate the
error condition. If
gamma is too small, or any other necessary condition
is not met, the
hinfcontr( ) function returns a zero controller and the
closed-loop system is equal to the open-loop system:
SysC = system( [], [], [], 0 ),
Syszw = system(A, B1, C1, D11)
rank
AjωI– B
2
C
1
D
12
NS NU+=
rank
AjωI– B
1
C
2
D
21
NS NY+=
H
ew
∞
γ≤