Academic Year 2014/15
ENG742s1 Industrial Control Systems
Second Attempt Coursework
Deadline For Submission: Friday 24th
July 2015
Hand-in Instructions: Work may be submitted via the ENG Office, or a scanned version
may be uploaded via the ENG742s1 Moodle site.
Instructions for completing
assessment:
Answer ALL of the following questions. Work should be
handwritten. The work should be well presented, showing the
detail of the working used to solve the problems.
Examiners: Dr KI Alkadhimi and Dr EJM Geddes
2014-15 Page 1 of 5
1. Consider the unity negative feedback nuclear reactor control system shown in Figure Q1.
Figure Q1
The system has to meet the following specification to a unit step input:
i. a transient specification with a 2% settling time of less than 1/3 second and a percentage overshoot 5%; and
ii. a steady-state specification with 5% steady-state error.
Design a compensator () which, when placed in series with the system open-loop transfer function will produce a closed-loop system that meets both of the specifications (i)
and (ii) simultaneously.
[25 Marks]
2. The block diagram shown in Figure Q2 represents a radar-tracking antenna with velocity and
position feedback.
Figure Q2
(a) Determine the values of and such that the system response to a step input has
a 2% settling time 2 seconds and a damping ratio of =
.
[10 Marks]
(b) With the parameters of part (a), the system has a steady-state tracking error of 5 for a tracking rate demand of 10 per second. Show that, by incorporating an additional compensator of the form /( + ) in the inner rate feedback loop, the transient specification can be met and the steady-state tracking error can be
reduced.
[15 Marks]
)(siAntenna
+
)(so
Tachogenerator
vsk
)3( +ssk
+
Gain
)(sGC
Actuator
)10(1+s
)(si+
Reactor Core
)2(4
+s
)(so
2014-15 Page 2 of 5
3. The angular position of a robotic arm (measured in radians) is to be controlled in a
unity negative feedback scheme, and an in-series compensator is to be designed to
achieve a particular set of time domain requirements. The transfer function of the
open-loop robot arm is not known, although corresponding frequency response data
is available in the form of a Bode diagram, shown in Figure Q3 on page 4.
(a) The specification requires that a rise time of = 0.21 seconds and a 2% settling time of = 0.52 seconds are achieved in response to a step input. Translate this specification to an equivalent frequency domain specification.
[5 Marks]
(b) Design a single-stage, in-series, lead compensator to meet the frequency
response specifications of part (a). Explain the important steps in the method.
Annotate Figure Q3 as appropriate.
[7 Marks]
(c) Sketch the effect of the compensator on the open-loop frequency response by
annotating Figure Q3. Highlight the important compensator characteristics on
the sketch.
[4 Marks]
(d) Sketch the closed-loop response of the compensated system to a step input
demand of 10 radians. Include estimates of the peak time, the percentage
overshoot and the steady-state error. The actual step response may not achieve
these estimates, or indeed may not achieve the transient specification. What
are the reasons for this?
[5 Marks]
(e) Instead, a compensator is required which will achieve a gain crossover
frequency of = 30rad/s, but still achieves the same damping ratio. Explain how your design above would need to be modified to achieve this new
requirement, but do not design the compensator.
[4 Marks]
2014-15 Page 3 of 5
4. A dc servo system is shown in Figure Q4.1. The system is modelled with a transfer function
() =5
( + 1)( + 2)
A Bode diagram of () is shown in Figure Q4.2 (on page 5). A closed-loop specification requires that the steady-state error to a ramp input of 10 radians per second is 0.5 radians.
Additionally, a phase margin of 50 should be achieved.
Figure Q4.1
(a) Show that a value of = 8achieves the steady-state error requirement. [5 Marks]
(b) Adjust Figure Q4.2 to reflect the choice of from part (a) and estimate the corresponding phase margin and gain cross over frequency.
[5 Marks]
(c) Give the transfer function of a lag compensator and sketch its Bode diagram
identifying the important characteristics in terms of the compensator parameters.
Note: you do not need to use semi-logarithmic graph paper; a sketch of the general
shape of the Bode diagram is adequate.
[4 Marks]
(d) Design a lag compensator which achieves the required phase margin whilst also
satisfying the steady-state requirement achieved in part (a). Annotate Figure Q4.2 as
appropriate.
[6 Marks]
(e) Estimate the step response characteristics (percentage overshot, settling time, peak
time, rise time and final value) of the compensated systems from part (c).
[5 Marks]
Motor and Load
k+
)(si )(so)(sG
Amplifier
2014-15 Page 4 of 5
Student Registration Number:
Figure Q3
2014-15 Page 5 of 5
Student Registration Number:
Figure Q4.2
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