ELEC 207 INSTRUMENTATION & CONTROL SECOND SEMESTER EXAMINATIONS 2018/19
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ELEC 207
SECOND SEMESTER EXAMINATIONS 2018/19
INSTRUMENTATION & CONTROL
PART A
1. a) Explain the difference between systematic and random errors affecting a measurement result. Describe a possible method to decrease systematic errors and a possible method to decrease random errors.
b) Is the precision of a measurement instrument improved by decreasing the systematic errors or the random errors? Why?
c) An Analog-to-Digital Converter (ADC) has 16 bits, an input voltage range from -2.5 V to 2.5 V, an accuracy of 0.1 mV and a maximum sampling frequency of 250 kHz.
i) Calculate the resolution of this ADC.
ii) Calculate the standard uncertainty corresponding to the indicated accuracy, assuming a uniform probability distribution of the errors within the accuracy range.
iii) Can this ADC be used to correctly acquire a sinusoidal signal with a frequency of 150 kHz? Why?
d) A measurement signal is affected by high-frequency noise arising from inductive coupling with a nearby power circuit.
i) Sketch the frequency response (magnitude) of a suitable filter designed to clean the signal from this noise. Label the axes.
ii) With the aid of a diagram, design and explain another method to decrease this noise, without using any additional device in the circuit.
e) A current transducer provides an output voltage that varies from 0 to 10 V when the current to be measured varies from 0 to 50 A. The current-voltage relationship is linear. Calculate the sensitivity of the transducer.
Total 25
2. a) A strain gauge is designed to have a 1% resistance increase when a strain of 4500 microstrain is applied to it. What is the gauge factor of this strain gauge?
b) A full bridge that employs four active strain gauges (of nominal resistance R and gauge factor G) is shown in Figure Q2.1. The operating (source) voltage of the bridge is Vs . Derive the following relationship between the applied strain e and the bridge output voltage Vout = VB – VA :
Vout = VS Ge
Figure Q2.1
c) With the aid of a diagram, describe the working principle of a thermocouple.
d) The output voltage of a thermocouple with its reference junction at 32 ºC is 1.187 mV. Using Table Q2, determine the temperature measured by the thermocouple.
Table Q2: Thermocouple output voltage (in mV) with reference junction at 0 ºC
e) A temperature sensor, initially at 25 ºC, is introduced into a fridge at 5 ºC. The sensor has a first-order transient response, with a time constant of 10 s. Calculate the waiting time required for the sensor to reach a temperature of 6 ºC.
f) An accelerometer with natural angular frequency ωn = 200 rad/s, damping ratio ξ = 0.4 and static sensitivity K = 3 V/g is subject to a step acceleration of 0.5 g. With reference to the normalised step response curves shown in Figure Q2.2, determine approximate estimates of:
i) The maximum output voltage of the accelerometer during the transient.
ii) The time required for the output voltage to reach the maximum value calculated in question 2.f.i) above.
Figure Q2.2
Total 25
PART B
3. You are part of a team designing a controller for a servo motor in a disk drive. The servo motor can be modelled as having a transfer function of G3(s) where:
a) What is the order of G3(s)?
b) What are the zeros and poles of G3(s)?
c) Draw the block diagram for a unity-gain negative feedback controller. Assume that the servo motor is the plant and that the transfer function of the controller is P(s). Clearly indicate the input, X(s), the output, Y(s), the error signal, E(s), and the control signal, U(s).
d) Draw the root locus of G3(s). Clearly indicate how increasing the gain of the proportional controller, KP, from zero to infinity will alter the position of the closed loop poles. There is no need to calculate the position of any breakaway points.
e) What feature of the root locus means that it will be important that the proportional gain is not too large?
f) What is the velocity constant for G3(s)?
g) It is required that the steady-state error in response to a ramp input must be less than 1. Deduce an inequality in a that must hold. Express the inequality as a function of the proportional gain, KP.
Total 25
4. You have been asked to use a lead compensator to improve the overshoot associated with a sensitive fifth-order system for detecting earthquakes.
a) The system has two dominant poles. What does that tell you about the position of these poles relative to the others?
b) The system is well approximated as a second-order system with a damping coefficient of ζ = 0.1. Is such a second-order system undamped, under-damped, over- damped or critically damped?
c) What is the overshoot without a compensator?
d) What is the phase margin, ΦM, without the compensator? Note that:
e) What value of damping coefficient is needed to reduce the overshoot to 20%?
f) What is the minimum phase margin, ΦM, that will achieve this overshoot?
g) Write the transfer function of a lead compensator with a pole at s = p and zero at s = z.
h) Plot the lead compensator’s pole and zero on the complex s-plane. Clearly label the axes.
i) Sketch the bode plot of a lead compensator that will satisfy the overshoot requirement. Clearly indicate the low-frequency gain and the maximum phase lead.
j) Why is it advantageous to use a lead compensator and not a PD controller?
Total 25
2023-08-29