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CALIFORNIA INSTITUTE OF TECHNOLOGY
Control and Dynamical Systems
CDS 140b
R. M. Murray
Winter 2008
Problem Set, Weeks 7–8
Issued:
26 Feb 08
Due:
6 Mar 08
The MooreGreitzer equations model rotating stall and surge in gas turbine engines describe the
dynamics of a compression system, such as those in gas turbine engines. The threestate “MG3”
equations have the form:
dψ
dt
=
1
4
B
2
l
c
(
φ

Φ
T
(
ψ
))
,
dφ
dt
=
1
l
c
p
Φ
c
(
φ
)

ψ
+
J
8
∂
2
Ψ
c
∂φ
2
P
,
dJ
dt
=
2
μ
+
m
p
∂
Φ
c
∂φ
+
J
8
∂
3
Φ
c
∂φ
3
P
J,
where
ψ
represents the pressure rise across the compressor,
φ
represents the mass ±ow through
the compressor and
J
represents the amplitude squared of the ²rst modal ±ow perturbation (cor
responding to a rotating stall disturbance). For the Caltech compressor rig, the parameters and
characteristic curves are given by:
B
= 0
.
2
,
Φ
T
(
ψ
) =
γ
r
ψ,
l
c
= 6
,
Ψ
c
(
φ
) = 1 + 1
.
5
φ

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This note was uploaded on 01/04/2012 for the course CDS 140b taught by Professor List during the Fall '10 term at Caltech.
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