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MP2013
NANYANG TECHNOLOGICAL UNIVERSITY
SEMESTER 2 EXAMINATION 2009-2010
MP2013 - MECHATRONICS SYSTEMS INTERFACING
April/May 2010
Time Allowed: 2½ hours
INSTRUCTIONS
1.
This paper contains FOUR (4) questions and comprises FIVE (5) pages.
2.
Answer ALL questions.
3.
All questions carry equal marks.
4.
This is a RESTRICTED-OPEN BOOK examination.
5.
One double-sided A4 cheat sheet is allowed.
1.
A temperature measurement system comprises a temperature sensor and meterpointer. The temperature sensor input range is 0 to 100 °C and the corresponding
output range is 0 to 500 mV. Its equivalent output impedance is 100 Ω. It has a time
constant τ = 8 sec.
The meter, with input impedance of 1000 Ω, has an input range of 0 to 500 mV. It
displays temperature on a dial, with full scale deflection of 0 to 100 °C. It is modeled
as a 2nd order system with damping ζ = 0.1 and natural frequency ωn = 1000
radians/sec. If a step voltage is applied to it, the pointer will oscillate and take
4/(ζ·ωn) sec to reach steady state.
(a)
At time t = 0, its sensing element is suddenly transferred from air at 20 °C to boiling
water at 100°C. Forty (40) seconds later it is suddenly transferred back to air. Assume
that the meter at t = 0 reads 20 °C and that the transfer time is negligible.
(i)
Find the sensor static sensitivity K1 V/°C and the meter-pointer K2 °C/V.
(4 marks)
(ii)
Sketch the system output (pointer motion) versus time and explain your sketch.
(8 marks)
(iii)
If the period of the temperature change of 80°C is taken to be 80 sec, explain
your pointer response with the aid of a sensor magnitude ratio plot M1(ω) and
a meter-pointer plot of M2(ω).
(5 marks)
Note: Question 1 continues on page 2.
1
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MP2013
(b)
The meter-pointer system is to be replaced by a digital display, which has a 10-bit, 05 V Analogue-Digital Converter (ADC) with a 1 MΩ input impedance.
(i)
Find the quantization error of the ADC, Q.
(2 marks)
(ii)
2.
If the sensor resolution is 0.1 °C, determine if an amplifier or/and a buffer
circuit is needed. If required, design the amplifier or/and buffer circuit. If not,
explain.
(6 marks)
A computer system is to read in a signal given by the expression y(t) and shown
below (for 2 complete cycles):
y(t ) = A sin (100πt ) , where A is 10 V
Volts (V)
10
t (sec)
0.01
0.02
Figure 1: The signal y(t)
(a)
Express y(t) by its Fourier Series, and sketch the amplitude spectrum from DC
to the 12th harmonics.
(10 marks)
(b)
If the computer is to sample the signal at a rate of fs = 420 Hz, comment on
whether the computer will be able to capture the original signal accurately. For
your discussion, use a sketch of the amplitude spectrum of the sampled signal
components with frequencies up to the Nyquist frequency, 210 Hz and
compare with the amplitude spectrum of the original signal.
(6 marks)
(c)
A low pass filter is used to remove frequency components higher than the 10th
harmonics. Design a low pass RC filter so that the amplitude of the 10th
harmonics is reduced by 50%. Provide suitable values of R and C. Explain
how a higher order RC low pass filter can be designed
(5 marks)
(d)
Propose a suitable sampling frequency of fs Hz and determine the amplitude of
the 10th harmonic or its alias after sampling.
(4 marks)
2
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MP2013
3.
A steel cantilever beam with rectangular cross-section A=100 mm2 is supported as in
Figure 2a. One end of the cantilever is fixed while the other end is subject to a pulling
force at an angle θ with respect to the horizontal plane. The pulling force is due to the
action of a mass M, subject to the gravity (g) and connected to the cantilever through
a wire (via a pulley, as in Figure 2a).
Two similar strain-gauges (R1 and R2, for both assume gauge factor GF=2) are
mounted axially on the top and on the bottom side of the beam and electrically
connected in a Wheatstone bridge configuration as shown in Figure 2b. Two regular
resistors (R0, in Figure 2b) of similar value are used to balance the bridge. The
Young’s modulus for steel is 2.1x 109 N/m2.
(b)
(a)
Figure 2: Cantilever beam
(a)
Provide a Yes/No answer and a brief explaination to the following two questions:
(i)
Is the proposed configuration of strain-gauges sensitive to bending strains?
(ii)
Is the proposed configuration of strain-gauges sensitive to temperature
changes?
(7 marks)
(b)
Assuming that the bridge is balanced for a no-load condition, determine the bridge
output voltage Vo assuming an input voltage Vi=10V, a pulling angle θ = 30 degrees
and a suspended mass equal to M=10 kg.
(11 marks)
(c)
Suppose that the signal Vo from the bridge is first amplified by a factor GAIN=100
and then numerically converted via an 8-bit ADC with operating voltage range 0-10V.
What is the minimum value for the mass M that such a system would be able to detect?
(7 marks)
3
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MP2013
4.
A permanent magnet DC Motor is powered at nominal voltage and, without load, the
angular speed is Ω0 = 4000 rpm. It is known that, at nominal voltage, for a load
torque T1 = 3 Nm the corresponding speed is Ω1 = 1000 rpm. Such values are
represented as operating points on the speed-torque plot in Figure 3.
5000
(0 , Ω0)
speed [rpm]
4000
3000
2000
(T1 , Ω1)
1000
0
-1
0
1
2
torque [Nm]
3
4
5
Figure 3: speed-torque plot
(a)
What is the stall torque Ts for nominal voltage condition?
(5 marks)
(b)
The motor is attached to a viscous load, for which linearity can be assumed, and that
is known to dissipate 2618 Watts to run at 5000 rpm. Determine the final operating
point of the motor (i.e. both the torque T2 and speed Ω2) for the motor when driving
such a load. In addition, also represent (on your answer book) the speed-torque curves
for both the load and the motor (at nominal voltage) on a plot similar to Figure 3.
(15 marks)
Figure 4: PWM driver
(c)
With reference to Figure 4, a pulse generator is used to periodically (T=10-3 sec) fully
discharge a capacitor C with short pulses of negligible duration. An ideal comparator
CMP compares the voltage across the capacitor with Vpot, the output of a
potentiometer (0<Vpot<V0). Such signal is then amplified by the amplifier P-AMP
and used to drive a DC Motor (DCM) via Pulse Width Modulation (PWM).
Note: Question 4 continues on page 5.
4
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MP2013
(i)
Considering an ideal current source I0=100mA and an operating voltage
V0=10V, what is the minimum value of the capacitance C that allows a 100%
duty-cycle for the maximum value of Vpot?
(ii)
For such a value of capacitance, sketch the time change of the voltage across
the capacitor and the voltage across the motor, with respect to the input pulses,
when the output of the potentiometer is set at Vpot=7V.
(5 marks)
End of Paper
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