Flatness-Based Control of an Induction Machine
Fed via Voltage Source Inverter - Concept, Control
Design and Performance Analysis
Joerg Dannehl and Friedrich W. Fuchs
Power Electronics and Electrical Drives, Christian-Albrechts-University of Kiel
Kaiserstr. 2, 24143 Kiel
Germany
jda@tf.uni-kiel.de, fwf@tf.uni-kiel.de
Abstract— In this paper a rather new nonlinear control method
based on differential flatness is applied to the induction machine
fed by a voltage source converter. The control design is done
by designing a feedforward using the flatness of the system
to lead it to the reference trajectory. Due to nonidealities an
additional stabilizing linear feedback controller is inserted. A
speed and rotor flux control with inner current loops is designed
and tuned for the induction machine. Simulation results are
presented, analyzed and a comparison with the today’s standard
control method for ac electrical drives, the field-oriented control,
is carried out. Thereby the flatness-based control shows a good
performance even though further opportunities for optimizations
are left.
I. I NTRODUCTION
The induction machine fulfils many industrial requirements
and today mostly sets up the standard for variable speed
drives [1]. This drive has been investigated to a large extent.
Nevertheless research still continues. The issue of controlling
electrical drives is nowadays widely solved with the so-called
field oriented control (FOC). It was introduced in [2] and
has been thoroughly investigated meanwhile [3]. The basic
idea is to use a coordinate system aligned to the rotor flux
vector. It enables the asymptotic decoupled control of the rotor
flux and motor torque or speed, respectively. The transformed
system variables are controlled with PI-controllers whereas
the control structure commonly consists of inner current and
outer speed/torque and flux control loops. Due to the inherent
nonlinearity of the machine model control design requires different time constants of the inner and outer loops. Furthermore
decoupling between flux and speed is only achievable if the
flux is kept constant.
In recent years nonlinear control methods were applied
to the speed and flux control of the induction machine.
The assumptions of different time constants of the loops
or a constant rotor flux are not necessary. The feedback
linearization methods [4][5] use transformations in appropriate
coordinates in which a nonlinear feedback is designed to
exactly linearize the system and exactly decouple the control
variables. Then an outer controller can be designed by linear
methods. The passivity-based control [6][7] uses the property
passivity to design a feedback control that guarantees stability.
An iterative Lyapunov design method is called backstepping
[8][9]. The design starts with a small subsystem which will
be expanded stepwise till the control for the complete model
is determined. Stability is proven in every iteration step. The
sliding mode control [10] is a discrete control method. The
control objectives are expressed in state space as a sliding
surface. The control algorithm is designed to lead the system
to it and keep it there asymptotic stable. A rather new control
method uses the system property flatness [11] to design the
control. In [12] and [13] the flatness was used to design a
dynamic feedback linearizing scheme. Another approach is to
design at first a feedforward control using the flatness to lead
the system to the (in general time varying) reference trajectory,
so the system may be linearized around it [14]. With focus
on eliminating tracking errors a linear feedback control is
inserted. Application of this flatness-based control (FBC) to
the induction machine is presented in [15] and [16]. Based
on the research in the field of modern control of electrical
drives the FBC is expected to offer advantages over the other
methods shown above concerning tracking behaviour, rejection
of perturbations and robustness. Therefore in this paper the
FBC of the voltage-fed induction machine will be presented,
analyzed and compared to the standard method of FOC.
The preceding investigation is structured into five sections.
Section II describes the system modelling. In section III the
FOC and in section IV the FBC is presented and designed.
The performance and characteristic features of the FBC are
analyzed and compared to the FOC by simulations in section
V. This paper is completed by a conclusion in section VI.
II. I NDUCTION M ACHINE M ODEL
In this section the model of a three-phase voltage source
inverter-fed squirrel cage induction machine with an isolated
neutral point will be described. It is assumed to be symmetric
and to have a linear magnetic behaviour and constant resistances. Since the sum of the phase voltages equals zero, the
system can be described by two-dimensional space vectors
[17]. The following notation will be used for a space vector in
an a/b-reference frame rotating with ωK : x→K = xa + jxb . The
model parameters are specified in the appendix (see TABLE I).
In the stationary reference frame (ωS = 0) the stator voltage
vector can be expressed
vsS = Rs isS + ψ̇sS
→
→
(1)
→
whereas →
isS and ψ→sS are the stator current and stator flux
vectors. In the same way the rotor voltage vector can be
expressed in the rotor fixed reference frame rotating with ωR
vrR = Rr irR + ψ̇rR
→
→
(2)
→
R
whereas→irR and ψ
are the rotor current and rotor flux vectors.
→r
The transformation in an arbitrary reference frame rotating
with ωk yields [17]:
vsk
→
vrk
→
= Rs isk + ψ̇sk +jpωk ψsk
=
→
Rr irk
→
→
+ ψ̇rk
→
(3)
→
+jp(ωk − ωR ) ψrk
→
(4)
the voltage-fed induction machine are θR and δ = ρ − p ωR
[12]. Note that the derivative of δ is known as slip frequency.
If the stator current dynamics are much faster than the speed
and flux dynamics a fast inner current control loop can be
designed using only equations (10) and (11) and assuming the
speed and flux as constants [17]. For the outer speed and flux
control design the stator currents are treated as new control
inputs and the system behaviour is described by equations (8),
(9), (12) and (13). This system of lower order is also flat with
ψrd and θR as flat outputs [16]. The benefits of using the
property flatness for the design of the control algorithms will
be shown in the section about FBC.
The voltage source inverter (VSC) is approximated as a
continuously three phase variable voltage source modelled by
a PT1 -lag element with TV SC = 1/(2 fp ) as time constant,
whereas fp is the switching frequency. Moreover all state
variables are assumed to be measurable, the flux may be
measured indirectly.
The flux vectors may be expressed:
ψsk
= Ls isk +M irk
(5)
ψrk
= Lr irk +M isk
(6)
→
→
→
→
→
→
In the following the so-called d/q-reference frame which is
aligned to the rotor flux vector will be used and the superscript
will be omitted, i.e.
ψr = ψrd + j0 = ψrS e−jρ
→
→
(7)
whereas ρ is the rotor flux angle in the stationary reference frame. Substituting the stator flux and rotor current
vectors in (3) and (4) using (5) and (6) and introducing
σ = 1 − (M 2 /(Ls Lr )), γ = (M 2 Rr /σLs L2r ) + (Rs /σLs ),
α = (Rr /Lr ) and β = (M/σLs Lr ) gives:
dψrd
= −α(ψrd − M isd )
dt
is
dρ
= pωR + αM q
dt
ψrd
(8)
(9)
i2s
disd
vs
= −γisd + αβψrd + pωR isq + αM q + d (10)
dt
ψrd
σLs
is is
vs
disq
= −γisq −βpωR ψrd −pωR isd −αM q d + q (11)
dt
ψrd
σLs
The mechanical dynamics may be described by
dωR
Tl
= µψrd isq −
(12)
dt
J
dθR
= ωR
(13)
dt
whereas µ = (3pM/2JLr ) and θR is the rotor angle and Tl
the load torque. Equations (8)-(13) completely describe the
induction machine dynamics. In [12] the voltage-fed induction
machine was shown to be a flat system. Such systems are characterized by the fact that all system states and control inputs
may be expressed as functions only of the flat outputs and
model parameters. In other words the trajectory of the vector
consisting of the flat output determines the state trajectory and
by that it determines the system behaviour. The flat outputs of
III. F IELD -O RIENTED C ONTROL
The principle of field orientation was already introduced in
[2] and is nowadays the standard way of controlling electrical
drives. As can be seen in (8) and (12) using the d/q-reference
frame enables the decoupled control of ωR and ψrd by isq
and isd , respectively, if a constant rotor flux is assumed. The
basic control structure is shown in Fig. 1. Basically it consists
of inner stator current control loops and outer speed and rotor
flux PI-control loops. Assuming different time constants of the
inner and outer loops they are designed separately.
A. Current Control
The current control design is done with (10) and (11) in
which couplings between both current components can be
seen. Therefore a decoupling network is used which gives
vsd,Dec ∗ and vsq,Dec ∗ (neglecting the time constant TV SC ):
i2sq
∗
(14)
vsd,Dec = σLs −αβψrd − pωR isq − αM
ψrd
isq isd
∗
vsq,Dec = σLs βpωR ψrd + pωR isd + αM
(15)
ψrd
In Fig. 1 the decoupling is combined with the transformation
of the measured three-phase stator currents into the d/qreference frame for which in general informations about the
speed and the rotor flux are necessary. Assuming perfect
decoupling and using (14) with (10) and (15) with (11) yields
the resulting current dynamics:
vs
disd
= −γisd + d,c
(16)
dt
σLs
vs
disq
= −γisq + q,c
(17)
dt
σLs
These first order dynamics are controlled by PI-controllers,
that is
1
vsd,c ∗ = kpd isd − i∗sd +
isd − i∗sd dt (18)
TId
1
∗
∗
vsq,c
= kpq isq − isq +
isq − i∗sq dt (19)
TIq
Smoothing
*
Filter
~
`
r,d
~
a
R
*
`r,d
*
Speed &
Flux
Controller
aR
Current
Controller
*
isd
+
-
vsd,c
*
+
*
+
-
isq
+
-
vsq,c
vs,123
*
+
+
vsd,Dec
isq
isd
Fig. 1.
VSC
*
+
+
*
vsq,Dec
*
`r,d
Induction
Machine
aR
is,123
Coordinate
transform
+Decoupling
Control structure of Field-Oriented control of an voltage-fed induction machine
whereas the controller gains kpd , kpq , 1/TId and 1/TIq may be
tuned by standard tuning methods [17] [18]. Here the technical
optimum [17] is used and the VSC time constant taken into
account to prevent unrealizable voltage references. See (34) in
the appendix for the gains.
B. Speed and Flux Control
The speed and flux control is designed with (8) and (12)
whereas the inner closed current loops are modelled as PT1 lag elements with time constants Tid and Tiq . Assuming ψrd =
ψr∗d = const. both PI-controllers can be treated separately and
are tuned with the symmetrical optimum [17]:
1
∗
∗
isd
= kpψ ψrd − ψrd +
ψrd − ψr∗d dt (20)
TIψ
1
∗
∗
∗
isq
dt
(21)
= kpω ωR − ωR +
ωR − ωR
TIω
For the controller gains see (35) in the appendix. According
to [17] using first order filters with time contstants Tf,ψ =
Tf,ω = 4 TV SC to smooth the references enhances the system
behaviour.
IV. F LATNESS - BASED C ONTROL
The property of flatness [11] can effectively be used for
designing control algorithms. In general the control structure
consists of a feedforward and a feedback part [14]. Since
flatness allows to formulate the control inputs as functions
of only the flat outputs this can be used to design the feedforward even for nonlinear systems. Under ideal conditions
the feedforward can track the (time varying) reference if it is
smooth enough. Otherwise due to derivatives in the references
and limitations in the control inputs tracking errors would
appear. Even if the references are smooth enough deviations
from perfect tracking will appear due to disturbances, model
uncertainties and other perturbations. Therefore feedback is
introduced. Since the system is near to the reference trajectory
via feedforward, thus linearizable around it, the feedback can
be designed with linear methods also for nonlinear systems
[14].
Even though the voltage-fed induction machine is flat and
the application of FBC to the complete, nonlinear model would
be possible, here a cascade is used due to its simplicity and
comparability to the FOC. The control structure used is shown
in Fig. 2.
A. Current Control
As can be seen in Fig. 2 the current control consists also of
a feedforward and a feedback. For the current control design
∗
and ψrd ≈ ψr∗d is assumed. At first the feedforward
ωR ≈ ωR
is determined using (10) and (11):
i∗sq 2
di∗sd
∗
∗
∗
∗ ∗
vsd,f = σLs
+γisd −αβψrd −p ωR isq −αM ∗
(22)
dt
ψrd
∗
disq
i∗s i∗s
∗
+γi∗sq+p ωR
[βψr∗d+i∗sd ]+αM q ∗ d (23)
vs∗q,f = σLs
dt
ψrd
Combining (22) with (10) and (23) with (11) and neglecting
TV SC yields the dynamics of the current tracking errors
∆isd = (isd − i∗sd ) and ∆isq = (isq − i∗sq ):
vs
d∆isd
= −γ∆isd + d,c
dt
σLs
vs
d∆isq
= −(γ + α)∆isq + q,c
dt
σLs
(24)
(25)
These resulting dynamics for the tracking errors are controlled
by PI-controllers:
1
∆isd − ∆i∗sd dt (26)
vs∗d,c= Vpd ∆isd − ∆i∗sd +
τId
1
vs∗q,c= Vpq ∆isq − ∆i∗sq +
∆isq − ∆i∗sq dt (27)
τIq
whereas the controller gains Vpd , Vpq , 1/τId and 1/τIq are also
tuned with technical optimum [17] and may be found in (36)
in the appendix. Note that in contrast to FOC the controllers
do not have to perform tracking tasks since ∆i∗sd = ∆i∗sq = 0
(tracking is done by feedforward). The controller gains should
therefore be tunable to be more robust against perturbations
as with FOC (not investigated here).
As already mentioned the feedforward is only effective if the
references are smooth enough. Thus the reference trajectory
generation is very important for the FBC. In this paper besides
a first order filter a rate limiter with different settings is
*
Current
Feedforward
~
*
r,d
~
a
R
Voltage
Feedforward
*
isd,f
*
`
*
i sq,f
`r,d
Reference
Generation
*
isd,c +
+
-
aR
+
*
*
isq,c +
+
-
+
~*
isd
*
isd +
Reference
~ * Gener- *
isq
isq
+
ation
Speed &
Flux
Controller
vsd,c
vsq,c
-
*
vsd,f
*
vs,123
*
+
+
`r,d
Induction
Machine
VSC
*
+
+
Current
Controller isq
isd
Fig. 2.
vsq,f
aR
is,123
Coordinate
transform
Cascaded control structure of Flatness-based control of an voltage-fed induction machine
investigated by simulations (see section V). Additionally, it
would be desirable to include the limitations in the control
inputs directly into the reference trajectory generation [19].
B. Speed and Flux Control
For the design of the outer speed and flux loop the stator
currents are treated as new control inputs that will be realized
by the inner loops delayed by τid and τiq . From (8) and (12)
the feedforward can be determined (load torque Tl unknown):
1 dψr∗d
1
+ ψr∗d
i∗sd,f =
(28)
M α dt
∗
1 dωR
(29)
i∗sq,f =
µψr∗d dt
Assuming the system near to the reference trajectory, neglecting the delays caused by the inner current loops and
putting together (28) with (8) and (29) with (12) the resulting
dynamics of the tracking errors ∆ψrd = ψrd − ψr∗d and
∗
may be expressed:
∆ωR = ωR − ωR
d∆ψrd
= −α∆ψrd + αM i∗sd,c
(30)
dt
Tl
d∆ωR
= − + µψr∗d i∗sq,c
(31)
dt
J
As feedback PI-controllers are used only to eliminate the
tracking error caused by disturbances and other nonidealities
which are also tuned with symmetrical optimum [17]:
1
∗
∗
isd,c= Vψ ∆ψrd − ∆ψsd +
∆ψrd − ∆ψs∗d dt (32)
τψ
1
∗
∗
i∗sq,c= Vω ∆ωR − ∆ωR
+
dt (33)
∆ωR − ∆ωR
τω
See (37) in the appendix for the controller gains. Similar to
the Flatness-based current control smooth references should
be used and therefore a reference trajectory generation should
be implemented. Here first order filter and rate limiter with
different settings are investigated by the simulations (see
section V).
V. S IMULATIONS
The analysis of the designed FOC and FBR has been
carried out with simulations by means of Matlab/Simulink.
The system model was implemented according to section II
(see TABLE I for system data). To prevent stability problems
caused by saturation effects and possible wind up of the
controller integrators an anti-wind up mechanism [18] was
used. Furthermore the stator current components were limited
to the nominal stator current. If not stated different the inertia
from TABLE I is used.
A. Current Control
In a first step the FBC is analyzed with different reference
generation types and settings. The current control simulations
are performed with constant speed (ωR = 153, 20rad/s). Fig.
3 shows step responses with FBC using different first order
reference smoothing filters (τf,q ) and with FOC also using
different smoothing filters (Tf,q ). Both control schemes behave
similar if the references are either very fast or slow. In the
first case the feedforward terms of FBC containing derivatives
are too high (for a short time) and therefore limited due
to inverter voltage limitations and by that are less effective.
In the second case these terms are small and the feedback
controller is also able to track the smoothed reference. But
in between the feedforward is effectively contributing to the
tracking since no limitations appear. Analytical investigations
on the determination of the reference generation should further
enhance the FBC. In the following τf,q = TV SC and Tf,q = 0
are used.
The FBC and FOC with the selected filter settings are
compared with FBC using a rate limiter as reference generation block that transforms a step into a ramp for example.
Fig. 4 shows the comparison whereas the max. slope of the
rate limiter was tuned to give the fastest response. The faster
responses to a step in i∗sq of FBC (with both filters) becomes
apparent, but at the same time slightly higher osscillations
occur. The coupling between the d- and q-components of the
stator current are somewhat higher with FOC. Altogether, both
control methods yield comparable results in current control. In
the following only the flatness-based current control with first
order reference smoothing will be investigated.
B. Speed and Flux Control
The design of the outer loops was performed with the
approximation of the inner loops as P T1 -lag elements (FOC:
FBC
FBC
21
FOC
820
820
800
800
18
17
Reference
τf,q = 0
16
τf,q = TVSC
ωR/min−1
isq/A
19
τf,q = 4 TVSC
15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
ωR/min−1
20
780
780
760
760
740
740
reference
Tiq = 0.2 ms
Tiq = 0.3 ms
Tiq = 0.4 ms
2
FOC
0
21
2
4
6
8
10
0
2
4
6
8
10
20
30
30
20
20
17
Reference
Tf,q = 0
16
T
10
10
f,q
=T
VSC
Tf,q = 4 TVSC
15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
t/ms
Fig. 3.
Current control with different first order reference filters
isq/A
18
isq/A
isq/A
19
0
0
−10
−10
−20
−20
−30
0
2
4
6
8
−30
10
Tiq = 0.2 ms
Tiq = 0.3 ms
Tiq = 0.4 ms
0
2
4
t/ms
21
11
Reference
FBC (first order)
FBC (rate limiter)
FOC
20
10.9
19
10.8
i /A
17
sd
isq/A
18
6
8
10
t/ms
Fig. 5.
Step response to a filtered speed reference step using different
approximations of the inner current loops (Tf,ω = 4 Tiq ; τf,ω = 4 τiq )
10.7
16
10.6
15
FBC
14
3
0
600
200
0
800
800
3
FBC (first order)
FBC (rate limiter)
FOC
400
usd/V
780
760
reference
τ =2τ
740
τf,ω = 3 τiq
f,ω
720
iq
τf,ω = 4 τiq
200
0
1
2
3
780
760
reference
Tf,ω = 2 Tiq
740
Tf,ω = 3 Tiq
Tf,ω = 4 Tiq
720
4
0
1
2
3
4
0
2
3
−200
0
1
2
3
30
30
20
20
10
10
t/ms
Fig. 4. Current control: FBC (first order reference filter τf,q = TV SC ),
FBC (rate limiter, max. slope: 30A/1ms) and FOC without filter
isq/A
t/ms
0
τf,ω = 2 τiq
−10
τ
f,ω
−20
−30
iq
τf,ω = 4 τiq
0
1
2
t/ms
3
T
−20
Tf,ω = 3 Tiq
−30
4
f,ω
=2T
iq
Tf,ω = 4 Tiq
0
1
2
t/ms
3
4
Fig. 6. Step response to a speed reference step using different smoothing
filters (J = 100 kg cm2 ; Tiq = 0.3 ms ; τiq = 0.2 ms)
820
800
800
780
760
reference
τ =2τ
740
τf,ω = 3 τiq
720
sq
FOC
820
f,ω
iq
τf,ω = 4 τiq
0
1
2
3
780
760
reference
Tf,ω = 2 Tiq
740
Tf,ω = 3 Tiq
Tf,ω = 4 Tiq
720
4
30
30
20
20
10
10
isq/A
ωR/min−1
FBC
i /A
Tid and Tiq ; FBC: τid and τiq ). Fig. 5 shows the response
to a speed reference step, filtered with Tf,ω = 4 Tiq (FOC)
and τf,ω = 4 τiq (FBC), respectively, using different approximations. If the inner loop is modelled to fast there arise
considerable oscillations in the speed controlled with FOC
while the FBC still works properly. In the following analysis
Tiq = 0.3 ms and τiq = 0.2 ms is used.
The influences of the smoothing filter time contants on
the speed tracking behaviour are shown in Fig. 6 and Fig.
7 using different inertias. In Fig. 6 the behaviour of FBC
is only slightly better than that of FOC. Using a machine
with a reduced inertia (Fig. 7) shows that the FBC slightly
outperforms the FOC under this conditions. It gives a higher
dynamic behaviour.
Fig. 8 shows the behaviour of FBC and FOC responding to
speed reference steps (Tf,ω = 2 Tiq ; τf,ω = 3 τiq ) and load
torque steps. At t = 10 ms a load torque Tl = Tn /2 is
applied to the rotor and t = 20 ms the load torque is reduced
to Tl = 0 Nm. Both control schemes properly eliminate the
speed tracking error.
=3τ
0
−10
R
1
ω /min−1
0
sq
usq/V
2
600
400
−200
1
820
R
2
820
ω /min−1
1
ωR/min−1
0
i /A
13
FOC
10.5
0
τf,ω = 2 τiq
−10
τ
f,ω
−20
−30
=3τ
iq
τf,ω = 4 τiq
0
1
2
t/ms
3
4
0
1
2
3
4
0
−10
T
−20
Tf,ω = 3 Tiq
−30
f,ω
=2T
iq
Tf,ω = 4 Tiq
0
1
2
t/ms
3
4
VI. C ONCLUSION
In this paper a rather new nonlinear control method called
flatness-based control was applied to the induction machine
Fig. 7. Step response to a speed reference step using different smoothing
filters and reduced inertia (J = 50 kg cm2 ; Tiq = 0.3 ms ; τiq = 0.2 ms)
Parameter
Stator resistance Rs
Rotor resistance Rr
Mutual inductance M
Stator inductance Ls
Rotor inductance Lr
Pole pair p
Mechanical power Ps
Stator phase voltage Vs
Torque Tn
Stator frequency ωs
Rotor speed ωR
Power factor cos(φ)
Inertia J
Switching frequency fp
Voltage limit
850
R
ω /min−1
800
750
reference
FBC
FOC
700
0
5
10
15
0
5
10
15
20
25
30
35
25
30
35
30
20
sq
i /A
10
0
−10
−20
−30
FBC
FOC
20
t/ms
Fig. 8. Response to speed reference steps and load torque steps (from t = 10
ms till t = 20 ms: Tl = Tn /2; )
fed by a voltage source converter. Due its simplicity and comparability to the conventional field-oriented control a cascaded
control structure was used. Here the flatness-based control was
used for the inner current and outer flux and speed loops.
The control design and tuning was presented. A simulation
study concerning the influence of different control subsystems
and parameters was carried out. The field-oriented control was
included for comparison issues.
The flatness-based control was shown to be always competitive to the conventional field-oriented control, actually outperforms it slightly for special cases like small inertias. Designing
a flatness-based control without using the cascade structure is
possible due to the flatness of the complete machine model
and could further enhance the system behaviour. Especially
for small inertias this could be a promising possibility. Further
investigations should be done on designing the reference trajectory generation. To exploit the possibilities the control input
limmitations should be directly taken into account. Additionly,
a different tuning of the feedback parts could offer advantages
in perturbation rejection and robustness.
A PPENDIX
Controller gains (FOC):
= kpq
= TIq
kpd
TId
kpψ =
1+(α Tid )2
α2 M Tid ;
kpω =
=
=
TIψ =
1
2Tiq µ ;
σLs
2TV SC
2 TV SC
γσ Ls
1+(α Tid )2
kpψ (1+α Tid )3
(34)

4Tid 

2
TIω = 8Tiq
µ
(35)
Controller gains (FBC):
Vpd = Vpq =
τId =
Vψ =
2 TV SC
γσ Ls
1+(α τid )2
α2 M τid ;
Vω =
1
2τiq µ ;
σLs
2TV SC
; τIq =
2 TV SC
(γ+α)σ Ls

1 + (α τid )2

τψ =
4τid 
Vψ (1 + α τid )3

2

τω = 8τiq
µ
(36)
(37)
Value
0.399 Ω
0.45 Ω
0.1585 H
0.1616 H
0.1676 H
2
22 kW (rated)
230 V (rated)
143 Nm (rated)
2π 50Hz(rated)
153,20 rad/s (rated)
0,869 (rated)
100 kg cm2
5 kHz
565 V
TABLE I
N OTATION AND S YSTEM DATA
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