For the single link robot arm system given in Figure 1 mass of the system is m, and length is 1. The angle between the robot and ground is 0. The angular velocity is . Control torque applied at the joint to the system is T. Also additional torque has the damping effect in the opposite rotation of the system due to air friction, which can be modeled as -b0. Physical parameters for the given system are m = 0.5kg, l m T (external torque) 3 Figure 1: Single Link Robot Arm 1 = 0.3m, g = 9.8m/s, b = 0.01 Nms. The torque is limited by T 1Nm. Considering the given system it is expected to solve the following questions. a) For the given system, resulting linearized equation of motion is given as follows: ml -0 - 60 =T- 0 gravity c) Consider that a PID controller is applied to the system; K S Evaluate the transfer function of the system giving the relation between input 7 and output 0. Please find your resulting transfer function with system parameters, then substitute the given system parameters for final result. Plot and explain the step response and pole zero map. F(s) = Kp + b) Design a controller that results to place the poles of the closed loop system to -3 and -4. Plot the resulting closed loop step response and pole zero map. Use a design methodology covered during the course and explain the reason for the design methodology you have chosen. (1) + Kas (2) By using the open loop transfer function obtained in parametric form, apply the PID controller, and determine the type of the system (Do not design controller, only evaluate the system type).