TMMS04
Lesson 1 – Sensors and Characteristics
2014 HT-1
1. A linear position sensor based on a potentiometer is shown in Figure 1. This potentiometer has a
total resistance of 100Ω where the wiper (middle connector) can travel in a range of [5, 95]%. The
mechanical measurement range of this sensor is [1.8, 3.0]m. The sensor is connected to the data
acquisition box with four wires. Each wire has a resistance of 1.7Ω/m and is 5m long. The two
connectors of the differential analog input (measures the difference of the voltages on the inputs)
have infinite input resistance thus no current will flow at this connectors. The data acquisition
box is exciting the sensor with 10V DC.
Figure 1: Linear position sensor (potentiometer)
(a) Draw a simple connection diagram showing the potentiometer, the resistors of the wires, and
the data acquisition box ports.
(b) Calculate the sensor gain Ks in V/m.
(c) Will the sensor gain be affected if the supply voltage used for exciting the sensor varies?
(d) What will the output signal be when a position 2.3m is measured?
(e) The data acquisition box has a input range of [0.0, 10.0]V and a resolution of 1mV. Which
resolution (distance) may this sensor system have in the best case? How many distinct
position can be measured?
2. A “HEDS 5540E” optical quadrature encoder is used to measure a linear motion. The encoder is
attached to a rack and pinion (a gear wheel that rotates with the linear motion). The diameter
of the wheel is 100mm and the gear ratio is 1:1.
(a) If the linear motion is 200mm long, how many pulses will the encoder give?
(b) What is the system’s resolution (distance) of the translational motion? Hint: Can the data
acquisition box know the position within the pulse distance?
(c) What is the velocity limit for this system? What are the requirement on the data acquisition
box to allow this velocity?
3. Measurement results from a pressure transducer IDA354-1,5C-10V are shown in Figure 2. The
transducer exhibits a non-linear behavior.
(a) By approximating the curve with a straight line an approximate linear voltage/pressure
relationship can be derived. Determine the value.
(b) Find the largest deviation (due to non-linearity) from the ideal transducer characteristics. Is
it within the limits promised by the data-sheet?
(c) In your application it is necessary to measure pressure up to 350 bar, select a suitable transducer IDA***-***-*** for that range. What is the maximum error due to nonlinearities or
hysteresis?
(d) In your application it is necessary to measure pressure up to 30 bar, select a suitable transducer IDA***-***-*** for that range. What is the maximum error due to nonlinearities or
hysteresis?
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TMMS04
Lesson 1 – Sensors and Characteristics
2014 HT-1
10
9
8
7
Volt
6
5
4
3
2
1
0
0
20
40
60
80
bar
100
120
140
160
Figure 2: The pressure transducer measurement showing the nonlinear characteristic.
Input
Output
1
Value []
0.5
0
-0.5
-1
0
0.1
0.2
0.3
0.4
0.5
Time [s]
Figure 3: Actuator dead-band
4. Sensors and actuator may have a deadband or neutral zone.
(a) What are the dead-band limits in the actuator response shown in figure 3.
(b) How could this be compensated in the controller generating the input signal to the actuator?
Can this rise any problems?
5. Bias (offset) in a sensor signal can cause problems if not handled correctly. In this example,
figure 4, a robot arm is rotating between four stations making a very brief stop at each one.
Measurements from an angular velocity sensor (gyro), figure 5, are integrated to determine the
absolute robot arm angle, however, a bias is affecting the measurement.
2
TMMS04
Lesson 1 – Sensors and Characteristics
2014 HT-1
500
Integrated Angle [degrees]
400
300
200
100
0
Biased integration
Un−biased integration
−100
0
2
4
Time [s]
(a)
6
8
(b)
Figure 4: (a) A robot arm rotates between four stations. (b) Comparison between biased and unbiased
integrated measured angular velocity, (absolute angle).
Signal with bias
Angular Velocity [rad/s]
1.5
1
0.5
0
0
1
2
3
4
Time [s]
5
6
7
8
Figure 5: Angular velocity signal with an unwanted bias
(a) Find the seemingly constant bias value
(b) Find the actual angular velocity motion frequency and determine the signal function. Subtract
the bias “in your head”. Hint! The actual signal amplitude is π4 .
(c) Approximately calculate the integrate angle values (with and without bias) at t = 2s and at
t = 5s. Comment on the deviation between true and biased results. Why are they different
at the two time instances?
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TMMS04
Lesson 1 – Sensors and Characteristics
2014 HT-1
6. Comprehension questions
(a) Potentiometer:
Why are four wires used to connect the sensor? What are the advantages to use four wires
compared to use three, two or . . . wires to connect the sensor? What is the minimum amount
of wires to connect the sensor to make a reading possible?
For further information: This thought are relevant when connecting strain gauge, too.
(b) Quadrature Encoder: Which problem may arise at low speed?
(c) Quadrature Encoder: Explain two methods of determining the speed / velocity from a quadrature encoder signal. What are the advantages of each method?
(d) Which characteristic does an integrator have so bias may become an infinite problem?
(e) How does an offset influence the result when differentiating a signal with offset?
(f) How does noise influence the result when integrating / differentiating a signal with high
frequency noise?
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