UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING MSC SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2016/2017
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1 UNIVERSITY OF BOLTON TW16 SCHOOL OF ENGINEERING MSC SYSTEMS ENGINEERING AND ENGINEERING MANAGEMENT SEMESTER 2 EXAMINATION 2016/2017 ADVANCED CONTROL TECHNOLOGY MODULE NO: EEM7015 Date: Monday 15 May 2017 Time: 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.
2 Page 2 of 9 Q1. Question 1 has two forms - (a) and (b). You only need to answer one form Q1 (a) or Q1 (b). Don t try to answer both. (a) For the circuit shown in Fig.1(a) below: i) From Kirchhoff s current law write down the second order differential equation that describes the relationship between capacitor voltage and the current source. [8 marks] ii) Construct the state space equations and find the A, B, C and D matrices. [12 marks] iii) If R=XL=XC=30 ohms for 50 Hz frequency, find the system transfer function and determine its stability from the examination of system characteristic equation. [5 marks] Fig.1 (a) Parallel RLC circuit iv) Build up the discrete-time state-space model defining the Ad, Bd matrices. [8 marks] Please turn the page
3 Page 3 of 9 Question 1 (b) (b) For the circuit shown in Fig.1 (b) below: i) From the mass-spring-damping system law write down the second order differential equation that describes the relationship between mass displacement and the applied force u(t). [8 marks] ii) iii) Construct the state space equations and find the A, B, C and D matrices. [12 marks] If k=3 N/m, f=0.75 N/(m/s), M=2 N/(m/s 2 ), find the system transfer function and determine its stability from the examination of system characteristic equation. [5 marks] K friction f/2 y(t) M mass u(t) force Fig.1b Mass-spring-damping system iv) Build up the discrete-time state-space model defining the Ad, Bd matrices. [8 marks] Please turn the page
4 Page 4 of 9 Q2. A specific plant is given by x = A. x + B. u Where A = [ ], B = [ 0] The system uses the state feedback control u = Kx i) Is the system controllable? [10 marks] ii) Design the regulator system shown in Fig.2 below if the desired closedloop poles are: s = 3 j2, s = 12 Fig.2 Regulator system [15 marks] iii) Find the new transfer function of the regulated plant and prove its stability using the factorization of its characteristic equation. [8 marks] Please turn the page
5 Page 5 of 9 Q3. (a) Consider three fuzzy subsets of the set X, X = {a, b, c, d, e, f, g} = {-3, -2, -1, 0, 1, 2, 3} referred to as A1, A2 and A3 A1 = {0.1/a, 0.4/b, 0.8/c, 1.0/d, 0.5/e, 0.2/f, 0/g} A2 = {0.3/a, 0.9/b, 0.1/c, 0.3/d, 0.6/e, 0.4/f, 0.1/g} and A3 = {1.0/a, 0.8/b, 0.6/c, 0.4/d, 0.3/e, 0.2/f, 0.1/g} Conduct the following Fuzzy Set Operations: (i) The support of A1, A2 and A3 [2 marks] (ii) The core of A1, A2 and A3 [2 marks] (iii) The cardinality of A1and A3 [2 marks] (iv) The complement of A2 and A3 [2 marks] (v) The union of A1, A2 and A3 [1 mark] (vi) The intersection of A1, A2 and A3 [1 mark] (vii) The new set B, if B = A1 2 [1 mark] (viii) The new set C, if C = 0.5A2 [1 mark] (ix) The new set D, for an alpha cut at A30.8 [1 mark] (x) Defuzzyfication of the set A1 by using the central of gravity (COG) technique. [2 marks] (xi) Defuzzyfication of the set A3 by using the Sugeno method. [2 marks] Question 3 continued over page
6 Page 6 of 9 Question 3 continued (b) Identify, using examples, the Mamdani-style fuzzy inference with Sugeno-style fuzzy inference in i) Fuzzy rules [4 marks] ii) Aggregation of rule outputs [4 marks] iii) Defuzzification [2 marks] iv) Discuss the advantages and disadvantages of these two Fuzzy inferences [6 marks] Q4. (a) In the assignment, you are asked to control the water temperature and level in a water tank. Using the water tank control system as an example, critically explain the following two control systems, identify their differences and specify their particular application areas: (i) (ii) a conventional PID control system a Fuzzy Logic control system [16 marks] (b) Figure Q4 (b) - 1 shows a unity feedback system with the open loop transfer function Gp(s) = 20 ( s 1)( s 2) Question 4 continued over the page
7 Page 7 of 9 Question 4 continued Inp Gc (s) Gp = Outp - Figure Q4 (b) -1 A Unity Feedback System The Design Specifications for the system are: The static position error constant Kp is 10. Maximum percent overshoot = PO < 12%. Figure Q4 (b) - 2 presents Bode plots for the Gp(s) Design a Lead Compensator, with detailed procedure, to achieve the required performances of the system. You may use Ogata s lead compensation form Ts 1 Gc(s) = Kcα Ts 1 [17 marks] Question 4 continued over the page
8 Page 8 of 9 Question 4 continued 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: Figure Q4 (b) 2 The Bode diagram for Gp(s) END OF QUESTIONS
9 Page 9 of 9 Phase Margin Degrees VS Percent Overshoot (PO)
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