Chapter 4 ControllerSynthesis
MATRIXx Xmath Robust Control Module 4-2 ni.com
The function hinfcontr( ) can be used to find an optimal H∞ controller
K that is arbitrarily close to solving:
(4-2)
The hinfcontr( ) function description in the hinfcontr( ) section
describes how the optimum can be found manually by decreasing γ until
an error condition occurs, or conversely by increasing γ until the error
condition is fixed.
The particular restrictions, required by the 2-Riccati solutions and
summarized in the Restrictions on the Extended Plant section are
those imposed in [GD88,DGKF89].
Extended Transfer Matrix
Referring to Figure 4-1, plant P specifies two groupings of vector inputs
and outputs. Such systems or transfer matrices are referred to as extended
transfer matrices or systems. To enter these in Xmath requires a
modification of your existing system representation. The standard system
has the form y=G(s)u and can be described either in state-space form:
or as a transfer matrix:
G(s) can be described in Xmath using the state-space system object:
G = system(A,B,C,D)
There is, however, insufficient information in this form to distinguish
the input/output groupings in the extended system P in Figure 4-1.
The state-space form of P is:
K
min Hew ∞γ≤γ
opt
=
x'Ax Bu+=
yAxDu+=
Gs() DCsIA–()
1–B+=
x
·Ax B1wB
2u++=
eC
1xD
11wD
12u++=
yC
2xD
21wD
22u++=