Q1. Derive the transfer function Y/X for the control system shown below. (20 marks) Q2. The set point of the control system shown in Fig. is given a step change of 0.1 unit. (25 marks) Determine (a) The maximum value of C and the time at which it occurs (b) The offset (c) The period of oscillation Draw a sketch of C(t) as a function of time.(using MATL.AB Simulnk) Q3. For the control system below determine the maximum value of K (ultimate gain) above which the system is unstable? (15 marks)