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Torque (Constant)
Torque (Constant)
Purpose
Generate constant torque
Library
Mechanical / Rotational / Sources
Description
The Constant Torque generates a constant torque between its two flanges. The
direction of a positive torque is indicated by the arrow.
Note A torque source may not be left unconnected or connected in series with
aspring or any other torque source.
Parameters
Second flange
Controls whether the second flange is accessible or connected to the rota-
tional reference frame.
Torque
The magnitude of the torque, in Newton meters (Nm). The default value is
1
.
Probe Signals
Torque
The generated torque, in Newton meters (Nm).
Speed
The speed of the flange that the arrow points to with respect to the other
flange, in
rad
s
.
569
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13
Component Reference
Torque (Controlled)
Purpose
Generate variable torque
Library
Mechanical / Rotational / Sources
Description
The Controlled Torque generates a variable torque between its two flanges.
The direction of a positive torque is indicated by the arrow. The momentary
torque is determined by the signal fed into the input of the component.
Note A torque source may not be left unconnected or connected in series with
aspring or any other torque source.
Parameters
Second flange
Controls whether the second flange is accessible or connected to the rota-
tional reference frame.
Allow state-space inlining
For expert use only! When set to
on
and the input signal is a linear com-
bination of mechanical measurements, PLECS will eliminate the input
variable from the state-space equations and substitute it with the corre-
sponding output variables. The default is
off
.
Torque
The generated torque, in Newton meters (Nm).
Speed
The speed of the flange that the arrow points to with respect to the other
flange, in
rad
s
.
570
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Torque Sensor
Torque Sensor
Purpose
Output measured torque as signal
Library
Mechanical / Rotational / Sensors
Description
The Torque Sensor measures the torque between its two flanges and pro-
vides it as a signal at the output of the component. A torque flow from the
unmarked flange towards the flange marked with a dot is considered positive.
Note A torque sensor isideallyrigid. Hence, if multiple torque sensors are
connected in parallel the torque measured by an individual sensor is undefined.
This produces a run-time error.
Parameter
Second flange
Controls whether the second flange is accessible or connected to the rota-
tional reference frame.
Probe Signal
Torque
The measured torque, in Newton meters (Nm).
571
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13
Component Reference
Torsion Spring
Purpose
Ideal torsion spring
Library
Mechanical / Rotational / Components
Description
The Torsion Spring models an ideal linear spring in a rotational system de-
scribed with the following equations:
 =
c 
 =
  
0
d
dt
 =
!
where  is the torque flow from the unmarked towards the marked flange, 
is the angle of the marked flange with respect to the unmarked one, and 
0
is
the equilibrium flange displacement.
Note An torsion spring may not be connected in series with a torque source.
Doing so would create a dependency between an input variable (the source
torque) and a state variable (the springtorque) inthe underlying state-space
equations.
Parameters
Spring constant
The spring rate or stiffness c, in
Nm
rad
.
Equilibrium (unstretched) displacement
The displacement 
0
between the two flanges of the unloaded spring, in
radians.
Initial deformation
The initial deformation (torsion) 
0
of the spring, in radians.
Probe Signals
Torque
The spring torque , in Newton meters (Nm).
Deformation
The spring deformation , in radians.
572
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Transfer Function
Transfer Function
Purpose
Model linear time-invariant system as transfer function
Library
Control / Continuous
Description
The Transfer Function models a linear time-invariant system that is ex-
pressed in the Laplace domain in terms of the argument s:
Y(s)
U(s)
=
n
n
s
n
++ n
1
s+n
0
d
n
sn + +d
1
s+ d
0
The transfer function is displayed in the block if it is large enough, otherwise
adefault text is shown. To resize the block, select it, then drag one of its se-
lection handles.
Parameters
Numerator coefficients
Avector of the s term coefficients [n
n
:::n
1
;n
0
]for the numerator, written
in descending order of powers of s. For example, the numerator s
3
+2s
would be entered as
[1,0,2,0]
.
The output of the Transfer Function is vectorizable by entering a matrix
for the numerator.
Denominator coefficients
Avector of the s term coefficients [d
n
:::d
1
;d
0
]for the denominator, written
in descending order of powers of s.
Note The order of the denominator (highest power of s) mustbe greater than
or equal to the order of the numerator.
Initial condition
The initial condition vector of the internal states of the Transfer Function
in the form [x
n
:::x
1
;x
0
]. The initial conditions must be specified for the
controller normal form, depicted below for the the transfer function
Y(s)
U(s)
=
n
2
s
2
+n
1
s+n
0
d
2
s2 + d
1
s+d
0
573
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13
Component Reference
a
1
a
0
a
2
b
0
b
1
b
2
1/s
+
+
+
+
1/s
+
+
+
x
1
x
0
Y(s)
U(s)
where
b
i
=
d
i
d
n
for i < n
b
n
=
1
d
n
a
i
=
n
i
n
n
d
i
d
n
for i < n
a
n
=
n
n
For the normalized transfer function (with n
n
=0 and d
n
=1) this simpli-
fies to b
i
=d
i
and a
i
=n
i
.
Probe Signals
Input
The input signal.
Output
The output signal.
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Transformation 3ph->RRF
Transformation 3ph->RRF
Purpose
Transform 3-phase signal to rotating reference frame
Library
Control / Transformations
Description
This block transforms a three-phase signal [x
a
x
b
x
c
]into a two-dimensional
vector [y
d
y
q
]in a rotating reference frame. The first input is the three-phase
signal. The second input is the rotation angle ’ of the rotating reference
frame. ’ is given in radians.
2
6
4
y
d
y
q
3
7
5
=
2
3
2
6
6
6
6
6
4
cos’
sin’
cos(’ 120)  sin(’  120)
cos(’+120
 sin(’ +120
)
3
7
7
7
7
7
5
T
2
6
6
6
6
6
4
x
a
x
b
x
c
3
7
7
7
7
7
5
Any zero-sequence component in the three-phase signals is discarded.
575
13
Component Reference
Transformation 3ph->SRF
Purpose
Transform 3-phase signal to stationary reference frame
Library
Control / Transformations
Description
This block transforms a three-phase signal [x
a
x
b
x
c
]into a two-dimensional
vector [y
y
]in the stationary reference frame:
2
6
4
y
y
3
7
5
=
2
6
6
4
2
3
1
3
1
3
0
1
p
3
1
p
3
3
7
7
5
2
6
6
6
6
6
4
x
a
x
b
x
c
3
7
7
7
7
7
5
Any zero-sequence component in the three-phase signals is discarded.
576
Transformation RRF->3ph
Transformation RRF->3ph
Purpose
Transform vector in rotating reference frame into 3-phase signal
Library
Control / Transformations
Description
This block transforms a two-dimensional vector [x
d
x
q
]in a rotating reference
frame into a three-phase signal [y
a
y
b
y
c
]. The first input of the block is the
vector [x
d
x
q
]. The second input is the rotation angle ’ of the rotating refer-
ence frame. ’ is given in radians.
2
6
6
6
6
6
4
y
a
y
b
y
c
3
7
7
7
7
7
5
=
2
6
6
6
6
6
4
cos’
sin’
cos(’  120
 sin(’  120
)
cos(’ +120
 sin(’ +120
)
3
7
7
7
7
7
5
2
6
4
x
d
x
q
3
7
5
The resulting three-phase signal does not have any zero-sequence component.
577
13
Component Reference
Transformation RRF->SRF
Purpose
Transform vector from rotating to stationary reference frame
Library
Control / Transformations
Description
This block transforms a two-dimensional vector [x
d
x
q
]from a rotating refer-
ence frame into a vector [y
y
]in the stationary reference frame. The first in-
put of the block is the vector [x
d
x
q
]. The second input is the angle ’ between
the rotating and the stationary frame. ’ is given in radians.
2
6
4
y
y
3
7
5
=
2
6
4
cos!
1
t  sin!
1
t
sin!
1
t
cos!
1
t
3
7
5
2
6
4
x
d
x
q
3
7
5
578
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