TW2 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING MSc SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2015/2016 ADVANCED CONTROL TECHNOLOGY MODULE NO: EEM7015 Date: Monday 16 May 2016 Time: 10.00 12.00 INSTRUCTIONS TO CANDIDATES: There are 4 questions. Answer any 3 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.
Position Page 2 of 8 1 Figure Q1 shows an open-loop output response for a position control system, where the system experiences a unit step input. As a system design engineer: 1 Step Response of a Position Control System 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 Time (sec) Figure Q1 The Open-loop Output Response (a) (b) (c) Comment on the system s transient and steady state responses. (5 marks) Suggest, with reasons, two possible approaches to improve the system performances. (4 marks) If a PID controller will be applied into this mechanical system: (i) Draw a closed-loop control system, with the help of a block diagram, and clearly identify all blocks and signals, and explain how the whole closed-loop control system works. (4 marks) Question 1 continued over page
Page 3 of 8 Question 1 continued (ii) (iii) Suggest, with reasons, the procedure that you will use to select the three terms of the PID controller K p, K i, and K d. (8 marks) Explain clearly for which PID term could be used to improve the particular system response performance/s (6 marks) (d) Recommend with explanation two alternative controllers which can be used for the application. (6 marks) (Total 33 marks) 2. (a) Design a Fuzzy Logic Controller (FLC) by using Sugeno s method to control the speed of a DC motor drive. The inputs of the controller are: the speed error (e) and the derivative of the speed error (de/dt). The output of the controller is the change in the voltage V. In the design, you should clearly state each FLC design stage; however, the detailed membership functions and the operations of the membership functions are not required. 3-5 control rules are required. (15 marks) (b) Consider two fuzzy subsets of the set Z, Z = {a, b, c, d, e} referred to as A and B A = {0.3/a, 0.6/b, 1.0/c, 0.2/d, 0.5/e } and B = {0.1/a, 0.9/b, 0.5/c, 0.2/d, 0/e } Conduct the following Fuzzy Set Operations: (i) The support of A and B (2 marks) (ii) The core of A and B (2 marks) (iii) The cardinality of A and B (2 marks) (iv) The complement of A and B (2 marks) Question 2 continued over page
Page 4 of 8 Question 2 continued (v) The union of A and B (1 mark) (vi) The intersection of A and B (1 mark) (vii) The new set C, if C = A 2 (1 mark) (viii) The new set D, if D = 0.3B (1 mark) (ix) The new set E, for an alpha cut at A 0.5 (2 marks) (c) If a fuzzy subset of the set F, F = {-4, -3, -2, -1, 0, 1, 2, 3, 4} referred to as G G = {0.3/-4, 0.5/-3, 0.5/-2, 0.8/-1, 0.8/0, 0.6/1, 0.6/2, 0.5/3, 0.4/4 } Defuzzyfication of the set G by using the central of gravity (COG) technique. (2 marks) (d) If a fuzzy subset of set Z, Z = {5, 10, 20, 25, 30, 50} referred to as X X = {0.1/5, 0.4/10, 0.5/20, 0.6/25, 0.7/30, 0.9/50} Defuzzyfication of the set X by using the Sugeno method. (2 marks) 3. The differential equations for a non linear system are given by: (Total 33 marks) 2 d L 2 dt Px L 2 V dx H Kx dt The input of the system is V and outputs of the system are L, x, and d L/dt. Question 3 continued over page
Page 5 of 8 Question 3 continued (a) Using Taylor s series approximation to linearise this nonlinear system. (12 marks) (b) (c) Select the state variables and transfer the differential equations obtained from (a) above to the relevant first-order differential equations. (8 marks) Determine the system matrices A, B, C and D, where A, B, C, and D have their usual meaning. (10 marks) (d) Determine the outputs of L, x, and d L/dt. (3 marks) (Total 33 marks) 4. Figure Q4-1 shows a unity feedback system with the open loop transfer function G p (s) = 1 s(0.2s 1) Inp - G c (s) G p = 1 s(0.2s 1) Outp Figure Q4-1 A Unity Feedback System The Design Specifications for the system are: Accuracy for a unit ramp input < 2%, i.e. steady-state error < 0.02. Maximum percent overshoot = PO < 10%. Figure Q4-2 presents Bode plots with the G c (s) controller. Question 4 continued over page
Page 6 of 8 Question 4 continued a) Identify the controller, plant and controlled plant on the plot. (3 marks) b) Distinguish the type of the controller used and provide an equation for the controller. (8 marks) c) Explain, with the detailed procedure, whether the design specifications have been achieved or not under this G c (s) controller. (8 marks) d) Design an improved controller on the Bode plot, to achieve the required performances of the system. (14 marks) (Total 33 marks) END OF QUESTIONS PLEASE TURN THE PAGE
Phase (deg) Magnitude (db) Page 7 of 8 You can write your answers in the Bode diagram attached. Please make sure that you have written down your ID number on the sheet. ID: 80 Bode Diagram 60 40 20 0-20 -40-60 90 45 0-45 -90-135 -180 10-2 10-1 10 0 10 1 10 2 10 3 Frequency (rad/sec)
Page 8 of 8 Phase Margin in Degrees VS Percent Overshoot (PO)