Chapter 2 RobustnessAnalysis
MATRIXx Xmath Robust Control Module 2-2 ni.com
system, including how the uncertain transfer functions are connected to the
system and the magnitude bound functions li(w).
To do this, extract the uncertain transfer functions and collect them into a
k-input, k-output transfer matrix Δ, where:
(2-2)
The resulting closed-loop system can be viewed as a feedback connection
of the nominal closed-loop system with transfer matrix H(jω) and the
uncertain transfer matrix Δ(jω). You describe your nominal closed-loop
system as a linear system with
input and output .
Note The signals r and q are not really inputs and outputs of the nominal system; r and q
show how the uncertain transfer functions connect to your nominal system. The signals r
and q each have k components.
You will partition H into the four submatrices,
so that Hzw is the nominal transfer matrix from w to z, Hzr is the nominal
transfer matrix from r to z, Hqw is the nominal transfer matrix from w to q,
and Hqr is the nominal transfer matrix from r to q.
The magnitude bound functions li(jω) from Equation 2-1 are described
with the PDM delb:
Thus, a complete description of your system requires the system SysH
torepresent Hjw and the response delb to represent the bounds.
Δjω() diagonal δ1jω(),..., δkjω()()=
w
r
z
q
HHzw Hzr
Hqw Hqr
=
DELB
ω1
:
ωm
l1ω1
()…lkω1
()
::
l1ωm
()…lkωm
()
,
=