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Quantizer
Quantizer
Purpose
Apply uniform quantization to input signal
Library
Control / Discontinuous
Description
The Quantizer maps the input signal to an integer multiple of the quantiza-
tion interval:
y= q round
u
q
Parameters
Quantizationinterval
The quantum q used in the mapping function.
Step detection
When set to
on
,the Quantizer produces a zero-crossing signal that en-
ables the solver to detect the precise instants, at which the output needs
to change. This may be necessary when quantizing a continuous signal.
When set to
off
,the Quantizer will not influence the step size of the
solver.
Probe Signals
Input
The input signal.
Output
The output signal.
469
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13
Component Reference
Rack and Pinion
Purpose
Ideal conversion between translational and rotational motion
Libraries
Mechanical / Translational / Components
Mechanical / Rotational / Components
Description
The Rack and Pinion models an ideal converter between translational and ro-
tational motion. The relation between the torque, force and speeds of the two
flanges is described with the following equations:
v =
R!
 =
RF
where R is the pinion radius.
Parameter
Pinion radius
The pinion radius R. A negative value will cause the flanges to move in
opposite directions.
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Ramp
Ramp
Purpose
Generate constantly rising or falling signal
Library
Control / Sources
Description
The Ramp block generates a signal that increases or decreases linearly over
time once the start time is reached. The output can be limited to a final value.
Parameters
Slope
The slope of the signal (per second).
Start time
The time at which the ramp starts.
Initial output
The output value before the start time is reached.
Final output
The final value for the output signal. If the parameter is set to
inf
the
output signal is unlimited.
Probe Signal
Output
The output signal of the pulse generator.
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13
Component Reference
Random Numbers
Purpose
Generate uniformly distributed random numbers
Library
Control / Sources
Description
The Random Numbers block generates uniformly distributed random num-
bers. The boundaries of the generated values can be configured in the compo-
nent dialog. The figure below illustrates the distribution for two different sets
of parameters. The seed of the generator initializes the algorithm at the sim-
x
\ (x)
ï4
ï2
0
2
4
0.1
0.2
0.3
0.4
[min, max] = [+/ï 1.5]
[min, max] = [+/ï 4.0]
ulation start. For the same seed, the sequence of random numbers is repro-
duced in every simulation run. If this behavior is undesired the system time
can be used as a seed. To minimize correlation effects, it is recommended to
use different seeds if multiple random generators are used in one model.
Parameters
Minimum
The lower boundary of the random numbers.
Maximum
The upper boundary of the random numbers.
Seed
The seed used to initialize the Random Numbers generator.
Sample Time
The sampling period used for generating random output values.
Reference
Mersenne Twister: http://en.wikipedia.org/wiki/Mersenne_twister
472
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Rate Limiter
Rate Limiter
Purpose
Limit rising and falling rate of change
Library
Control / Discontinuous
Description
The Rate Limiter restricts the first derivative of the signal passing through it.
While the rate of change is within the specified limits, the output follows the
input. When the rate of change exceeds the rising or falling limit, the output
falls behind the input with a fixed slope until output and input become equal
again.
Parameters
Rising rate limit
The maximum rate of change of the output signal (typically positive).
Falling rate limit
The minimum rate of change of the output signal (typically negative).
Probe Signals
Input
The input signal.
Output
The output signal.
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13
Component Reference
Rectangular to Polar
Purpose
Convert Cartesian coordinates to polar coordinates
Library
Control / Transformations
Description
This block transforms a signal representing rectangular coordinates [x;y] into
polar coordinates [r;]:
r =
p
x2 +y2
 =
atan2(x;y)
is calculated in the range      .
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Relational Operator
Relational Operator
Purpose
Compare two input signals
Library
Control / Logical
Description
The Relational Operator compares two input signals. If the comparison is true
it outputs
1
,otherwise
0
.The first input is marked with a dot.
Parameter
Relational operator
Chooses which comparison operation is applied to the input signals. Avail-
able operators are
 equal (==),
 unequal (=),
 less (<),
 less or equal (<=),
 greater or equal (>=),
 greater (>).
Probe Signals
Input
The input signals.
Output
The output signal.
475
13
Component Reference
Relay
Purpose
Toggle between on- and off-state with configurable threshold
Library
Control / Discontinuous
Description
The output of the Relay block depends on its internal state. If the input sig-
nal exceeds the upper threshold, the relay will be in the on-state. It will be in
the off-state if the inputs is less than the lower threshold. The relay does not
change for input values between the thresholds.
Parameters
Upper threshold
The highest value that the input signal may reach before the state
changes to the on-state.
Lower threshold
The lowest value that the input signal may reach before the state changes
to the off-state.
On-state output
The value of the output signal while the relay is in the on-state.
Off-state output
The value of the output signal while the relay is in the off-state.
Initial state
The state of the relay at simulation start. Possible values are
on
and
off
.
Probe Signals
Input
The block input signal.
Output
The block output signal.
476
Resistor
Resistor
Purpose
Ideal resistor
Library
Electrical / Passive Components
Description
This component provides an ideal resistor between its two electrical termi-
nals. See section “Configuring PLECS” (on page 43) for information on how to
change the graphical representation of resistors.
Parameter
Resistance
The resistance in ohms ( ). All positive and negative values are accepted,
including
0
and
inf
(1). The default is
1
.
In a vectorized component, all internal resistors have the same resistance
if the parameter is a scalar. To specify the resistances individually use a
vector [R
1
R
2
:::R
n
]. The length n of the vector determines the width of
the component.
Probe Signals
When the resistor is probed, a small dot in the component icon marks the pos-
itive terminal.
Resistor voltage
The voltage measured across the resistor from the positive to the negative
terminal, in volts (V).
Resistor current
The current flowing through the resistor, in amperes (A). A current enter-
ing the resistor at the positive terminal is counted positive.
Resistor power
The power consumed by the resistor, in watts (W).
477
13
Component Reference
Rotational Backlash
Purpose
Ideal rotational backlash
Library
Mechanical / Rotational / Components
Description
The Rotational Backlash models an ideal symmetrical, two-sided Hard Stop
(see page 483) in a rotational system, which restricts the relative displace-
ment of the two flanges between an upper and lower limit of 
b
2
.While the
displacement is within the limits, no torque is transmitted. When the dis-
placement hits either limit, the flanges become rigidly connected until the
transmitted torque reverses.
Parameters
Total backlash
The total permitted displacement b between the flanges, in radians.
Initial displacement
The initial displacement of the flanges, in radians. May be specified in or-
der to provide proper initial conditions if absolute angles are measured
anywhere in the system. Otherwise, this parameter can be left blank.
Probe Signals
Torque
The transmitted torque flowing from the unmarked to the marked flange,
in Newton meters (Nm).
Displacement
The displacement of the marked flange with respect to the unmarked
flange, in radians.
State
The internal state of the component:
-1
in lower limit,
0
inside limits,
+1
in upper limit.
478
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