ENG0016 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) IN BIOMEDICAL ENGINEERING SEMESTER 1 EXAMINATION 2017/2018 ADVANCED BIOMECHATRONIC SYSTEMS MODULE NO: BME6003 Date: Friday 19 January 2018 Time: 10.00 am 12.00 noon INSTRUCTIONS TO CANDIDATES: There are 6 questions. You are required to answer any 4 questions. All questions carry equal marks. Marks for parts of questions are shown in brackets. CANDIDATES REQUIRE : Property tables provided Formula Sheet (attached) Take density of water as 1000 kg/m 3
Page 2 of 10 Q1 (a)explain, helped by sketches, what amplitude, gain, phase and phase shift is and why frequency response is useful for bio mechatronic systems control. [8 marks] (b)the following graph shows a sinusoidal input and output of a system. Given the input frequency is 4 rad/sec, please determine the gain and phase. [4 marks] (c) Figure Q1(c) shows an open loop Bode plot. i) Estimate the gain margin and the phase margin. [4 marks] ii) Explain the functions of gain margin and phase margin in systems control. [4 marks] iii) Explain the system s Peak Resonance M p and Bandwidth. [3 marks] iv) Comment on the system s stability performance. [2 marks] Q1 continued over the page Please turn the page
Page 3 of 10 Figure Q1(c) A Bode Plot Q2 A simplified model of a Prosthesis limb system is shown in Figure Q2. The control system for the prosthesis limb dynamics is given by: G p (s) = 1 s(s + 5)(s + 3) Input (s) + - Prosthesis limb ControllerG c (s) Prosthesis limb Dynamics G p (s) Output (s) Measurement =1 Figure Q2 A Prosthesis limb a) If Gc(s) is a proportional controller only, find the range of the gain Kp making the system to be an underdamped system for unit step input. Q2 continued over the page [7 marks]
Page 4 of 10 Please turn the page 1 b) Find the Ki for a unit parabolic input (θi = s 3 steady state error is less than 0.01. ) if Gc(s) is a PI controller and the c) The designer needs to achieve less than 20% overshoot and ts less than 5 seconds. Design a PID controller by determining Kp and Kd (using the Ki obtained from (b) above) to satisfy these requirements. [8 marks] d) Describe how the error item is handled by (i) proportional, (ii) integral and (iii) derivative controllers. Q3 (a) Using block diagrams, briefly explain discrete time signal processing for feedback and feedforward system. [6 marks] (b) Explain what is meant by a zero-order hold (ZOH) system. [4 marks] (c) A controller has an 10 bit Analogue to Digital Converter with the signal range between 0 Volt to +24 Volt: (i) (ii) (iii) (iv) What is the resolution of the AD converter? What integer number represents a value of +12 Volts? What voltage does the integer 854 represent? What voltage does 1011011011 represent? [2 marks] [2 marks] [2 marks] [2 marks] (d) A controller of biomechatronic system consists of a Digital to Analogue Converter with zero order element in series with the processing centre which has a transfer function s G p (s) = (s + 2) Find the sampled-data transfer function, G (z) for the digital control system. The sampling time, T, is 1 seconds. [7 marks]
Page 5 of 10 Please turn the page Q4 Q5 a) Draw the equivalent circuit of an ideal operational amplifier including the assumed characteristics. b) Draw the circuit diagram of the implementation of an instrumentation amplifier using three operational amplifiers. [10 marks] c) Derive an expression for an instrumentation amplifier using three operational amplifiers. [10 marks] a) What is meant by the half power point in relation to filters? b) If a voltage of 12Vrms is input to a system and the output produced is 1.2Vrms. What is the gain of the system in db? c) A passive low pass filter can be constructed from a single resistor and capacitor. i) Draw the circuit diagram for a passive Low Pass filter and derive an equation for the gain v out v in.. ii) iii) Design the filter to have a cut-off frequency of 1000Hz. The Resistor should have a value between 100 Ohms and 1000 Ohms. Calculate the gain at appropriate frequencies and hence plot the bode diagram (magnitude only) for the circuit.
Page 6 of 10 Please turn the page Q6 a) Memory used in microprocessor systems can be divided into two basic types, volatile and non-volatile. Describe these two basic types of memory and explain how each one is used. [10 marks] b) Show using a diagram the two computer architectures used in computer systems. Describe the advantages and disadvantages between the two systems. [10 marks] c) Describe the term Special Function Register in relation to a PIC microcontroller. Blocks with feedback loop END OF QUESTIONS PLEASE SEE BELLOW FOR FORMULAE SHEETS Formula Sheets G(s) = G(s) = G o (s) 1 + G o (s)h(s) G o (s) 1 G o (s)h(s) (for a negative feedback) (for a negative feedback) Steady-State Errors e ss = lim s 0 [s(1 G o (s))θ i (s)] (for an open loop system) e ss = lim s 0 [s 1 1 + G o (s) θ i(s)] (for the closed loop system with a unity feedback) e ss = lim s 0 [s e ss = lim s 0 [ s 1 θ G 1 + 1 (s) i (s)] (if the feedback H(s) 1) 1 + G 1 (s)[h(s) 1] G 2 (s) 1 + G 2 (G 1 (s) + 1) θ d(s)] (if the system subjects to a disturbance input)
Page 7 of 10 PLEASE TURN THE PAGE FOR MORE FORMULAE SHEETS First order Systems G(s) = θ o θ i = G ss(s) τs + 1 τ ( dθ o dt ) + θ o = G ss θ i t τ θ o = G ss (1 e ) (for a unit step input) t τ θ o = AG ss (1 e ) (for a step input with size A) θ o = G ss ( 1 ) e (t τ ) (for an impulse input) τ Second- order Systems d 2 θ o dt 2 + 2ζω n dθ o dt + ω n 2 θ o = b o ω n 2 θ i G(s) = θ 2 o(s) θ i (s) = b o ω n s 2 + 2ζω n s + ω2 n ω d t r = 1/2π ω d t p = π p.o.= exp( ζπ (1 ζ 2 ) ) 100% t s = 4 ζω n ω d = ω n (1 ζ 2 )
Page 8 of 10 PLEASE TURN THE PAGE FOR MORE FORMULAE SHEETS
Page 9 of 10 PLEASE TURN THE PAGE FOR MORE FORMULAE SHEETS
Page 10 of 10 END OF FORMULAE SHEETS