UNIVERSITY OF BOLTON. ENGINEERING, SPORTS and SCIENCES BSC(HONS) MECHATRONICS TOP-UP TRIMESTER 1 EXAMINATION 2013/2014 ADVANCED MECHATRONIC SYSTEMS

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1 [kh37] UNIVERSITY OF BOLTON ENGINEERING, SPORTS and SCIENCES BSC(HONS) MECHATRONICS TOP-UP TRIMESTER 1 EXAMINATION 2013/2014 ADVANCED MECHATRONIC SYSTEMS MODULE NO: MEC6002 Date: 19 December 2013 Time: 10:00 12:00 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.

2 Page 2 of 14 Q1. (a) Explain three advantages and three disadvantages of a closed loop speed control system over an open loop speed control system. (5 marks) (b) The steering control system of an automobile can be represented by the block diagram shown in Figure Q1 (b). Using block diagram reduction techniques, find the transfer function of the following control system: Y(s)/R2(s). where Y(s) is the output signal and, R1(s) and R2(s) are the two separated input signals. Figure Q1 (b) An automobile steering control system (15 marks) (c) A spring-damper system has the following transfer function. Please sketch the output displacement over the time when the impulse input is applied to the system. θo 10 G( s) = = θi 5s + 1 (5 marks) (Total 25 marks)

3 Page 3 of 14 Q2. (a) The block diagram of a machine position control system can be shown in Figure Q2 (a), where 0.16 and K = 3. G c G( s) = s( s + 0.2) Figure Q2 (a) A machine position control system (i) Establish the transfer function (C/R) of the system. (5 marks) (ii) Find the natural angular frequency ω n. (2 marks) (iii) Find the damping ratio ζ. (2 marks) (iv) Find the 100% rise time t r. (2 marks) (v) Find the percentage maximum overshoot. (2 marks) (vi) Find the 2% settling time t s. (2 marks) (b) A human-arm control system can be simplified to a block diagram as shown in Figure Q2 (b), where s + 3 G( s) = 3 2 s + 2s + 4s + K Figure Q2 (b) A human-arm control system (i) Apply Routh-Hurwitz stability criterion to determine the range of values of K for the above system which will result in a stable response. (6 marks) Question 2 continued overleaf

4 Page 4 of 14 Question 2 continued (ii) If the above system input R(s) is a unit step and K is 6, determine the steady-state error. (4 marks) (Total 25 marks) Q3. (a) A RLC circuit is shown in Figure 3(a) below. where C is the Capacitance, L is the Inductance, R is Resistance, i(t) is the current and v(t) is voltage. Figure 3(a): RLC electrical circuit (i) Develop a differential equation for V in terms of the RLC electrical circuit shown in Figure 3(a) above. (8 marks) Question 3 continued overleaf

5 Page 5 of 14 Question 3 continued (ii) Determine the Laplace transforms of the differential equations obtained from (i) above. Assume that the system is subjected to a unit step input,the initial conditions of the system are zeros (i.e. at time = 0, x, x, x are all zeros) and the capacitor is initially discharged as the following expression. vc ( t) dt = t 0 v ( t) dt c (2 marks) (iii) Determine the transfer function G(s) = V c (s)/v(s) (2 marks) (b) A suspension system for a scooter is shown in Figure 3(b). where f(t) is the input force y1(t) and y2(t) represents the output displacements. k1, k2 and k3 are the spring stiffness constants. C is the viscous damping coefficient. Figure 3(b) A suspension System Question 3 continued overleaf

6 Page 6 of 14 Question 3 continued (i) (ii) Develop the differential equations for the suspension system (3 marks) Determine the Laplace transforms of the differential equations obtained from (i) above. Assume that the system is subjected to a unit step input, y(0) =0 and y (0)=0. (6 marks) (iii) Determine the transfer function G(s)=Y1(s)/F(s) (4 marks) (Total 25 marks) Q4 Figure Q4 shows a mechatronic control system, in which the G 2 ( s) = P 10s s and a controller Gc(s) is applied into the system. Input(s) + - Gc(s) Gp(s) Output(s) Figure Q4 A Mechatronic Control System (a) If a PI controller is used (K d = 0), determine the integral gain K i causing the system s steady state error to be less than The system is 1 subject to a unit parabolic input function (θ i = ). (5 marks) 3 s Question 4 continued overleaf

7 Page 7 of 14 Question 4 continued (b) Use K i obtained from Question (a) above, design a PID controller that will meet the system design specifications: Settling time t s < 5 seconds and Percentage Overshoot P.O. < 10%. Determine K P and K d. (10 marks) (c) If a velocity feedback is introduced into the system around the Gp(s) of the Figure Q4 and the Gc is a Proportional controller (K i = K d = 0): i) Draw a block diagram with the velocity feedback and determine the transfer function for the whole system. (5 marks) ii) Determine the velocity gain Kv for the natural angular frequency ω n is 1.6 rads/s, and the damping ratio ζ is about 0.8, when the system subjects to a unit step input. (5 marks) (Total 25 marks) Q5. Figure Q5 shows a manufacturing system which includes a CNC machining centre, a sensor system, and an industrial robot with its control system. CNC Machining Centre Gm Sensor System Gs Industrial Robot and Controller Gc Figure Q5 A Manufacturing System The CNC machining centre is controlled by its digital controller. The sensor system detects the types of component on CNC machine table and sends the detected analogue information to the robot controller. The robot picks and places the components from the CNC machine table and sends digital control signals to the CNC machining centre. Question 5 continued overleaf

8 Page 8 of 14 Question 5 continued (a) (b) Draw a closed-loop control system, with the help of a block diagram, for the manufacturing system shown in Figure Q5. Clearly identify all the elements and explain how the whole closed-loop control system works. (7 marks) If the robot controller has a 10 bit Analogue to Digital Converter with the signal range between -12 Volt to +12 Volt: (i) What is the resolution of the AD converter? (2 marks) (ii) What integer number represents a value of -8 Volts? (2 marks) (iii) What voltage does the integer 1000 represent? (3 marks) (iv) What voltage does represent? (3 marks) (c) If the CNC machining centre consists of a Digital to Analogue Converter with zero order element in series with the sensor system which has a transfer function 4 G p ( s) = s( s + 4) find the sampled-data transfer function, G(z) for the digital control system. The sampling time, T, is 0.01 seconds. (8 marks) (Total 25 marks) Q6. (a) An automated assembly line is assembling a car model. The line involves the processes of: plastic mould arriving, spray painting, and metal logo fixing. Question 6 continued overleaf

9 Page 9 of 14 Question 6 continued You are asked to select sensors to detect the following: the arrival of a plastic moulding the presence on the model of paint of the correct colour the correct presence, orientation and position of the metal logo Use your answer to part a) above to justify your recommendation for each sensor selected. (9 marks) (b) Figure Q6(b) shows the driven system with a compound gear train for this automated assembly line, you are asked to select a DC motor for the system. The output torque T L requires being 5Nm, the output speed being 60 rpm. Output Ι m = 0.2 Kgm 2 T L T m D A DC Motor B C I L = 6 Kgm 2 Gear Train Figure Q6(b) The driven system Where the first driver Gear A has 20 teeth, Gear B 40 teeth, Gear C 16 teeth and Gear D 48 teeth. (i) (ii) If the viscous friction has been measured as b m = 0.05 Kgm/s and b L = Kgm/s, determine the maximum torque and the speed of the motor. (10 marks) Select the DC motor from the Table Q6(b) to meet the requirement of above, and explain the reason supported by all calculation procedure. (6 marks) Question 6 continued overleaf

10 Page 10 of 14 Question 6 continued Table Q6(b) DC Motors Type Voltage V Power Output W Torque Nm Speed rpm ZT PT MP RT TYU (Total 25 marks) END OF QUESTIONS

11 Page 11 of 14 DC Motors (Dynamic Equations) α M ωm G = = α ω L L Formula Sheet Power = (I m + I L /G 2 )α m ω m T L = I L α L T m = (I m + I L /G 2 )α m + (b m + b L /G 2 )ω m Blocks with feedback loop Go( s) G(s) = (for a negative feedback) 1+ Go( s) H ( s) G(s) = Go( s) (for a positive feedback) 1 Go( s) H ( s) Steady-State Errors ess = lim[ s(1 GO ( s)) θi ( s)] (for an open-loop system) s 0 1 ess = lim[ s θ i ( s)] (for the closed-loop system with a unity feedback) s 0 1+ G ( s) e e ss ss o 1 = lim[ s θi ( s)] (if the feedback H(s) 1) s 0 G1 ( s) G ( s)[ H ( s) 1] G2 ( s) = lim[ s s 0 1+ G ( s) G Laplace Transforms A unit impulse function 1 1 A unit step function s 1 A unit ramp function 2 s First order Systems 1 1 t /τ θ = G (1 e ) (for a unit step input) O ss 2 θ d ](if the system subjects to a disturbance input) ( s)

12 Page 12 of 14 t /τ θ = AG (1 e ) (for a step input with size A) O ss Performance measures for second-order systems ω d t r = 1/2π; ω d t p = π; 4 t s = ζω n ; ω d = ω n (1-ζ 2 ) P.O. = exp ( ζπ ) 100% 2 (1 ζ )

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