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B.ENG DEGREE IN ENGINEERING EG32001 CONTROL AND DYNAMICAL SYSTEMS 3B AUGUST 2007 TWO HOURS ANSWER THREE QUESTIONS Only calculators meeting the published Faculty regulations are permitted to be used in examinations Log Linear Paper will be provided [The numbers given in square brackets indicate the mark allocated for that part of the question]  1. (a) Derive valid expressions for the magnitude and phase of the frequency response for the closed loop system shown in Figure Q1(a). These expressions do not need to be simplified, as long as they are valid. [8] Figure Q1(a) (b) Derive simplified expressions for the output ,C(s) in Figure Q1(b) for (i) the case where the input, R(s) is zero. [5] (ii) the case where the disturbance, D(s) is zero. [5] (iii) the case where D(s) is zero and R(s) is a unit step input. [2] Figure Q1(b) 2. An automotive company is considering developing new, modern control systems to integrate into their motor vehicles. Describe in detail, using diagrams where necessary, the sensors that may be incorporated into the following control systems. Include in your answer the parameters that need to be measured and how feedback may be incorporated to adjust the control system. (a) managing the engine temperature [5] (b) controlling the fuel intake into the cylinders of the engine. [5] (c) monitoring the exhaust emissions [5] (d) automatic windscreen wiper control [5] 3. For the system of figure Q3, m = 10kg; k = 100 kN; I = 0.1 kgm2; r = 10cm. (a) Determine the corresponding equations of motion. [8] (b) Calculate the frequencies of normal mode vibration. [8] (c) Find the corresponding mode shapes. [4] Figure Q3 4. The closed loop transfer function of a unity feedback system is: where K is controller gain (a) Plot the asymptotic approximations of the Bode plots, both gain and phase on the log-linear paper provided. Clearly show the break frequencies and attenuation of each asympto