UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BSC (HONS) MECHATRONICS TOP-UP SEMESTER 1 EXAMINATION 2017/2018 ADVANCED MECHATRONIC SYSTEMS

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1 ENG08 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BSC (HONS) MECHATRONICS TOP-UP SEMESTER EXAMINATION 07/08 ADVANCED MECHATRONIC SYSTEMS MODULE NO: MEC600 Date: 7 January 08 Time: INSTRUCTIONS TO CANDIDATES: There are 6 questions. Answer 4 questions. All questions carry equal marks. Marks for parts of questions are shown in brackets. This examination paper carries a total of 00 marks. All working must be shown. A numerical solution to a question obtained by programming an electronic calculator will not be accepted.

2 Page of 5 Q. (a) Explain the Open loop and Closed loop control systems with the aids of block diagram. (6 mark (b) A steering control system of an automobile can be represented by the block diagram shown in Figure Q (b). Using block diagram reduction techniques, find the transfer function Y(/R( of the following control system, where Y( is the output signal and, R( and R( are the two separated input signals. Figure Q (b) Automobile steering control system (5 mark (c) A DC motor of a prosthetic hand can be described by using the following first order differential equation: d 0 5 o 0 i dt Where the θo and θi are the output and input responses of the system. Find the corresponding transfer function of this system. (4 mark Total 5 Marks

3 Page 3 of 5 Q (a) The block diagram of a machine position control system can be shown in Figure Q (a), where 0.6 and K = 3. G c G( s ( s 0.) Figure Q (a) A machine position control system (i) Establish the transfer function (C/R) of the system. (5 mark (ii) Find the natural angular frequency ωn. ( mark (iii) Find the damping ratio ζ. ( mark (iv) Find the 00% rise time tr. ( mark (v) Find the percentage maximum overshoot. ( mark (vi) Find the % settling time ts. ( mark (b) A human-arm control system can be simplified to a block diagram as shown in Figure Q (b), where s 3 G( 3 s s 4s K Figure Q (b) A human-arm control system (i) (ii) 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 mark If the above system input R( is a unit step and K is 6, determine the steady-state error. (4 mark Total 5 Marks

4 Page 4 of 5 Q3 (a) A suspension system for a mountain bicycle is shown in Figure Q3 (a). F(t) is the input force and Y(t) represents the output displacement. Figure Q3 (a) A Suspension System (i) (ii) (iii) Develop the differential equations for the suspension system (6 mark 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 zero. (3 mark Determine the transfer function G(=Y(/F( (4 mark Question 3 continued over page

5 Page 5 of 5 Question 3 continued (b) An RLC circuit is shown in Figure Q3(b) below. where C is the Capacitance, L is the Inductance, R is Resistance, i(t) is the current and v(t) is voltage. Figure Q3(b): An RLC electrical circuit (i) (ii) Develop a differential equation for the RLC electrical circuit shown in Figure Q3 (b) above. (6 mark 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 zero. ( mark (iii) Determine the transfer function G( = Vc(/V( (4 mark Total 5 marks

6 Page 6 of 5 Q4 A PID controller designed to control a position of a moving mechatronic system is shown in Figure Q4 (a). The transfer function of the plant is G ( s(0s 4) Input( + - Gc( Gp( Output( Figure Q4 (a) The design criteria for this system are: Settling time < 5.0 sec Overshoot < 0% Steady state error < % (for a unit parabolic input = /s 3 ) (a) (b) (c) Design a PID controller to determine the parameters Kp, Ki, and Kd and clearly identify the design procedure. (5 mark If a velocity feedback is introduced into Figure Q4, draw a block diagram with the velocity feedback and explain the effects on a control system of including the velocity feedback. (3 mark In a PID controller, one part relates to the system s past behaviour, one to its present and one to its future. Briefly explain which one is for what and why. (7 mark Total 5 marks

7 Page 7 of 5 Q5 Figure Q5 shows a production system which includes a processing centre, a sensor system, and a controller. Processing Centre Gp( Sensor System Gs(z) Controller Figure Q5 Part of a Production System The processing centre (an analogue system) is controlled by the controller (a computer numerical control). The sensor system (a digital system) detects the processing conditions and feedback the detected information to the controller. (a) Draw a closed-loop control system, with the help of a block diagram, for the production system shown in Figure Q5. Clearly identify all the components and explain how the whole closed-loop control system works. (6 mark (b) If the computer control system s resolution required is 0 mv, and the range varies between - Volt to + Volt, (i) Design an Analogue to Digital Converter with suitable bits for the production controller. (4 mark (ii) (iii) What integer number represented a value of +6 Volts? What voltage does the integer 500 represent? (3 mark (3 mark Question 5 continued over page

8 Page 8 of 5 Question 5 continued (c) If the controller consists of a Digital to Analogue Converter with zero order element in series with the processing centre which has a transfer function G p ( s( s ) as shown in Figure Q5(c), find the sampled-data transfer function, G(z) for the digital control system. The sampling time, T, is 0.0 seconds. (9 mark Input + - Output Figure Q5 (c) Total 5 marks Q6 (a) A DC motor needs to be selected to drive a conveyor for an assembly line. Figure Q6 (a) shows the conveyor system with a compound gear train. Tm m = 0. Kgm A D L Conveyor DC Motor B C IL = Kgm Gear Train Figure Q6 (a) A Conveyor System Question 6 continued over page

9 Page 9 of 5 Question 6 continued Where the first driver Gear A has teeth, Gear B 36 teeth, Gear C 6 teeth and Gear D 3 teeth. (i) (ii) If the maximum speed of the conveyor needs to be 500 rpm, the angular acceleration αl is 3 rad/s, the viscous friction has been measured as bm = 0.0 Kgm/s and bl = 0.06 Kgm/s, determine the maximum torque and speed of the motor. (8 mark Determine the power needed to accelerate the whole system at the specified rate from rest. ( mark (b) If a brushed DC motor is selected to drive above conveyor system. A DC supply voltage of 40 V is available. Referring to the DMT catalogue, the motor to achieve this power rating is the PM 40 series. Some of the motor specifications are reproduced in Table Q6 below TABLE Q6 DMT PM 40 Series Motor Specifications No-load 40V n0 (rpm) 400 No-load current I0 (A) 0. The starting current Ia (A) 3. Terminal resistance R (Ω) Torque constant Km (Nm/A) 6 Speed constant Ke (rpm/v) 3 Output power P0 (W) 00 Maximum winding temperature, Tmax ( o C) 85 The ambient air temperature Tamb ( o C) 0 Thermal resistance: housing ambient, Rth ( o C/W) Thermal resistance: winding housing, Rth ( o C/W) Question 6 continued over page

10 Page 0 of 5 Question 6 continued (i) (ii) (iii) Check if the PM40 motor meets the requirement of the design specifications of the Power and Speed. (6 mark Check whether the motor will be able to accommodate the heat rise in the coils. (5 mark Check the efficiency of the motor, and check if the PM40 motor is operated at the region of maximum efficiency. (4 mark Total 5 marks END OF QUESTIONS

11 Page of 5 FORMULA SHEETS Go( G( = (for a negative feedback) Go( H( G( = Go( Go( H( (for a positive feedback) Steady-State Errors e lim[ s( G ( ) ( ] (for an open-loop system) ss s 0 O i e e e ss ss ss lim[ s s 0 G o i ( ] (for the closed-loop system with a unity feedback) ( lim[ s i ( ] (if the feedback H( ) s 0 G ( G ( [ H( ] G ( lim[ s d ] (if the system subjects to a disturbance input) s 0 G ( G ( ) Laplace Transforms A unit impulse function A unit step function s A unit ramp function s First order Systems O G ss ( e t / ) (for a unit step input) t / AG ( e ) (for a step input with size A) O ss ( t) G o ss ( ) e ( t / )

12 Page of 5 (for an impulse input) Second-order systems d dt o d o n n o b o n dt o( G( ( s i bo n s n n i dtr = / dtp = P.O. = exp ( ) 00% ( ) ts = 4 n d = n (- ) The current through the motor I = (T/Km) + I0 The motor speed n = nv IRKe The power dissipated in the motor Pdis = I R The heat rise under steady-state conditions Temp = Pdis(Rth + Rth) The motor winding temperature Temp/motor = Temp/amb + Temp The motor efficiency η = ωkm/vf The maximum efficiency of motor ηmax = (- (I0/Ia)) The starting torque Ts = KmIa The region of maximum efficiency of motor T/Ts

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