Problem 1 [20 marks] The control block diagram of an Anti-lock Braking System (ABS) for an automo- bile is depicted in Figure 1. Brake Torque T K 1 8+0.5 s(s+1) 8+2 Reference Slip Ratio ABS Controller Brake Modulator Brake Cylinder Actual Slip Ratio Feedback Sensor Figure 1: Anti-lock Braking System (ABS). a) Refer to Figure 1 and identify the objective, controlled variable, and control variable to the system. [3 Marks] b) Determine the total closed-loop system transfer function for the ABS system, if feedback sensor transfer function is unity feedback, i.e., H(s) = 1. [4 Marks] c) Determine the characteristic equation of the control system, if feedback sensor transfer function is unity feedback. [4 Marks] d) Determine the poles and zeros of the total closed loop transfer function, if feed- back sensor transfer function is unity feedback and ABS controller K = 1. Hint: s3+3s2+3s+0.5= (s+0.21)(s+2.8s +2.45)