UNIVERSITY OF BOLTON ENGINEERING, SPORTS & · PDF fileBSc (Hons) Mechatronics Top-Up Semester 1 Examination 2014/2015 Advanced Mechatronic Systems Module No. MEC6002 ... A unit impulsefunction

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UNIVERSITY OF BOLTON

ENGINEERING, SPORTS & SCIENCE ACADEMIC

GROUP

BSc(HONS) MECHATRONICS TOP-UP

SEMESTER 1 EXAMINATION 2014/2015

ADVANCED MECHATRONIC SYSTEMS

MODULE NO: MEC6002

Date: 20 January 2015 Time: 10.00 INSTRUCTIONS TO CANDIDATES: There are SIX questions. Answer ANY FOUR questions. All questions carry equal marks. Marks for parts of questions are shown

in brackets. This examination paper carries a total

of 100 marks. All working must be shown. A

numerical solution to a question obtained by programming an electronic calculator will not be accepted.

Page 2 of 12

Engineering, Sports & Science Academic Group BSc (Hons) Mechatronics Top-Up Semester 1 Examination 2014/2015 Advanced Mechatronic Systems Module No. MEC6002

Q1.

(a) Describes three advantages and three disadvantages of a digital control

system over an analogue control system.

(6 marks)

(b) An Automobile brake control system can be represented by the block diagram

shown in Figure Q1(b). Using block diagram reduction techniques, find the

following transfer functions for this control system.

(i) Y(s)/R(s) (7 marks)

(ii) Y(s)/D(s) (7 marks)

Figure Q1 (b) An automobile brake control system.

Where R(s) is the input, D(s) is the disturbance and Y(s) is the output.

(c) A mercury-in-glass thermometer has the following transfer function. Please

sketch the output temperature over the time when a impulse input is applied

to the system.

(5 marks)

Total 25 marks

Please turn the page

43

2)(

ssG

i

o

Page 3 of 12


Q2

(a) The differential equation for a car suspension system is :

Where θo is the output and θi is the input.

(i) Find the transfer function of this system. (4 marks)

(ii) Find the damping factor. (2 marks)

(iii) Find the damped frequency. (2 marks)

(iv) Find the subsidence ratio. (2 marks)

(v) Find the 5% settling time ts. (2 marks)

(b) The block diagram of a servo control system can be shown in Figure Q2(b).

Figure Q2 (b) A servo motor control system

Determine the steady state error (ess) for a ramp function response of the above system. (7 marks)

(c) Apply Routh-Hurwitz stability criterion to determine the range of values of K

for a robot control system with the transfer function of T(s)

which will result in a stable response.

(6 marks)

Total 25 marks


iooo

dt

d

dt

d

29104

2

2

Ksss

s

s

ssT

i

o

84

7

)(

)()(

23

Page 4 of 12


Q3 (a) A suspension system for a Pushchair is shown in Figure 3(a). where F is the input force y1(t) and y2(t) represents the output displacements. k1 and k2 are the spring stiffness constants. c1 and c2 is the viscous damping coefficient.

Figure 3(a) A suspension System of a Pushchair

(i) Develop the differential equations for the suspension system

(6 marks)

(ii) Determine the Laplace transforms of the differential equations obtained

from (i) above. Assume that the system is subjected to a unit step input

and the initial conditions of the system are zeros (i.e. at time = 0, x, x’, x’’

are all zeros).

(3 marks)

(iii) Determine the transfer function G(s)=Y2(s)/F(s)

(4 marks)

Total 25 marks


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Q4 Figure Q4 shows a CNC control system, which requires high accuracy for

position and velocity response. If the CNC system has a transfer function of:

)5)(62(

1)(

sssGp

and a controller is used in the system.

Figure Q4 A CNC Control System

(a) If a PI controller is used (Kp = K, Kd, = 0) determine the integral gain Ki

to control the system’s steady state error be less than 0.5. The system

subjects a unit ramp input. (7 marks)

(b) Design a PD controller (Ki = 0) that will meet the system design

specifications ts = 0.8 s and percentage overshoot = 5%. Determine the

proportional gain Kp and the derivative gain Kd. The system subjects a

unit step input. (12 marks)

(c) In a PID controller, explain:

For which purpose a P is needed

For which purpose an I is needed

For which purpose a D is needed

(6 marks)

Total 25 marks


i(s) CNC system

Gp(s)

Controller

Gc(s)

o(s)

-

Page 6 of 12


Q5. (a) A DC motor needs to be selected to drive a conveyor for a drink filling

system. Figure Q5 (a) shows the conveyor system with a compound gear train.

Figure Q5 (a) A conveyor system

Where the first driver Gear A has 24 teeth, Gear B 36 teeth, Gear C 18 teeth

and Gear D 54 teeth. L is the rotational velocity of the conveyor and m is the rotational velocity of the motor.

(i) If the maximum speed of the conveyor needs to be 120 rpm and the angular acceleration αL is 6 rad/s2, determine the maximum torque and speed of the motor. (8 marks)

(ii) Assume that the viscous friction in the system can be ignored,

determine the power needed to accelerate the whole system at the maximum speed of the conveyor from rest. (2 marks)

(iii) If the viscous friction has been measured as bm = 0.005 Kgm/s and bL = 0.06 Kgm/s, and using the gear ratio determined by (i) above, determine the new maximum torque of the motor and new power required for the system.

(3 marks)

Question 5 continued over page

Conveyor

D Tm, m

m = 0.03 Kgm2 L

IL = 10 Kgm2

A

B C

Gear Train

Motor

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Question 5 continued

(b) Suppose that the drink system involves the processes of: paper cup arriving, liquid filling, plastic lid covering, and paper logo fixing.

i) You are asked to select sensors to detect the following:

the arrival of a paper cup

the right level of liquid filled

the correct position of the plastic lid covering

the correct presence, orientation and position of the metal logo

(4 marks)

ii) Use your answer to part i) above to justify your recommendation

for each sensor selected. (8 marks)

Total 25 marks

Q6 (a) Give one example of analogue system and one example of digital system and explain, helped by sketches, how the signal is carried both in the analogue system and in the digital system. (6 marks)

(b) The controller has a 12 bit Analogue to Digital Converter with the signal range between -10 Volt to +10 Volt: (i) What is the resolution of the AD converter? (2 marks) (ii) What integer number represented a value of 6 Volts? (2 marks)

(iii) What voltage does the integer 2000 represent? (2 marks)

(iv) What voltage does 101110101101 represent? (2 marks)

Question 6 continued over the page

Page 8 of 12


Question 6 continued

(c) A controller (as shown in Figure Q6(c)) consists of a Digital to Analogue

Converter with zero order element in series with the processing centre which has a transfer function

)6.0(

6.0)(

sssG

(i) Find the sampled-data transfer function G(z) for the digital

control system. The sampling time, T, is 0.02 seconds. (7 marks)

(ii) Find the steady-state error for the feedback control system as shown in Figure Q6(c), if the input to the system is a unit step input.

(4 marks)

Figure Q6(c) Digital Feedback Control System

Total 25 marks

END OF QUESTIONS

U(z) X(z)

-

Page 9 of 12


Formula Sheet

DC Motors (Dynamic Equations)

G =

Power = (Im + IL/G2)αmωm

TL = ILαL

Tm = (Im + IL/G2)αm + (bm + bL/G

2)ωm

Blocks with feedback loop

G(s) = (for a negative feedback)

G(s) = (for a positive feedback)

Steady-State Errors

(for an open-loop system)

(for the closed-loop system with a unity feedback)

(if the feedback H(s) ≠ 1)

(if the system subjects to a disturbance input)

Laplace Transforms

A unit impulse function 1

A unit step function

A unit ramp function

First order Systems

(for a unit step input)

L

M

L

M

)()(1

)(

sHsGo

sGo

)()(1

)(

sHsGo

sGo

)]())(1([lim0

ssGse iOs

ss

)]()(1

1[lim

0s

sGse i

os

ss

)](

]1)()[(1

)(1

1[lim

1

10

s

sHsG

sGse i

sss

])()(1

)([lim

21

2

0d

sss

sGsG

sGse

s

1

2

1

s

)1( / t

ssO eG

Page 10 of 12


(for a step input with size A)

Performance measures for second-order systems

dtr = 1/2; dtp = ; ts = ;

d = n(1-2)

P.O. = exp

)1( / t

ssO eAG

n

4

%100))1(

(2

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UNIVERSITY OF BOLTON ENGINEERING, SPORTS & · PDF fileBSc (Hons) Mechatronics Top-Up Semester 1 Examination 2014/2015 Advanced Mechatronic Systems Module No. MEC6002 ... A unit impulsefunction