IEEE Electrification Magazine - December 2017 - 68

1

δ Pin

0.5

Unstable
A

0

Robustly
Stable

-0.5
-1
1

Stable
0.5

0

δ Lin -0.5

-1 -1

-0.5

0

0.5

1

δ Cin

Figure 10. The three uncertain parameters system is robustly stable
within the largest cube of coordinate size (1/ n = 0.201), which is
centered about the nominal point (0, 0, 0) and connects the system
stability plane at point A.

two dominant subdistribution systems in the MEA
architecture, i.e., the PMMD system and the buck con-
verter system, are assessed based on the n method in
the ensuing sections.

PMMD System
The stability of a PMMD system, generally employed
for an actuation system in an aircraft EPS, was studied
in the laboratory (Areerak et al. 2011, Areerak et al.
2009). The circuit representation of the analyzed sys-
tem is depicted by Figure 11 (Areerak et al. 2011,
Areerak et al. 2009). An ideal three-phase balanced volt-
age source was used in an experiment to represent the
engine generator with the generator control unit, denot-
ed as G and GCU, respectively, in Figure 11. The trans-
mission line or ac bus from the power supply to the
rectifier was modeled by a resistor-inductor circuit. A
six-pulse uncontrolled rectifier was employed as a typi-
cal multiphase autotransformer-rectifier unit of a real
on-board system. It provided dc power to the surface-
mounted PM machine-based EMA through an LC filter.

The EMA was a standard vector-controlled PM motor
drive (Areerak et al. 2011, Areerak et al. 2009). Sumsur-
ooah et al. present the detailed modeling and robust
stability analysis of the system.
The aim of the study was to identify whether the sys-
tem remains stable when the applied torque is allowed to
vary within the uncertainty set [2 Nm, 38 Nm], (i.e., 20 ±
18 Nm), where 20 Nm is the mean value of the torque on
the given uncertainty set (Sumsurooah et al. 2016). The
system in Figure 11 was analytically modeled to account
for uncertainty in torque and system nonlinearities (Sum-
surooah et al. 2016). n analysis was employed to predict
boundary stability. From n analysis of the system model,
the measure of robust stability n was found to be 2.31.
The robust stability margin, calculated as 1 /n = 0.42, cor-
responds to a critical destabilizing torque of 27.6 Nm. Lab-
oratory tests showed that the PMMD system becomes
unstable when the torque is increased to 26.7 Nm, which
is in close agreement with the n prediction of 27.6 Nm.
The analysis showed that the EMA system under
study is not robustly stable, as indicated by n exceeding
1, i.e., it becomes unstable if operated within the defined
uncertainty set (i.e., within 20 ! 18 Nm). The robust sta-
bility margin of 0.42 represents the value by which the
maximum range of uncertainty in torque must be scaled
to ensure stability robustness, as depicted in Figure 12.
This requires that the operation of the EMA system be
limited within 20 ! 7.6 Nm. Therefore, from the prior
discussion, it can be concluded that n provides a direct
measure of stability robustness of an EPS, as it determines
by how much uncertain parameters can be changed
without causing a system to become unstable.

Buck Converter System

In practice, actual systems are continually subject to per-
turbations. These include, but are not limited to, variations
in load, line resistance, and operating temperature. Fur-
ther, the nominal system model generally contains para-
metric model uncertainties. While uncertainties are a
known occurrence in actual sys-
tems, the question is whether it is
acceptable or even safe to neglect
them during the design process.
dc/ac Converter
ac
wT
To answer this question, a series of
iin
Bus
PM
studies was performed on the
+
Motor
v
LC
widely employed dc/dc buck con-
LC
G
in
wr
Filter
Filter
verter system to gauge the impact
-
of the uncertainties on the stabili-
GCU
is
ty robustness of a system. The block
diagram of the system under study
Generator
ac/dc
w
dc-Link
r
is shown in Figure 2. The experimen-
PWM
with Control
Converter
Voltage
Controller
tal buck converter system that was
Filter
Unit
used in the study consisted of a
CPL (EMA)
wr∗
U3825 PWM controller, a Type III
analogue compensator, and an LC
input filter. The buck converter,
Figure 11. The PM machine-based EMA. PWM: pulsewidth modulation.

68

I E E E E l e c t r i f i cati o n M a gaz ine / DECEMBER 2017



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