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