4. A Controller K is used to control the angle y, of a motor by providing the required voltage to the motor. The bode plot of the openloop system GK is shown below: a. b. What happens to the phase margin of the system as the time delay increases? Explain why. If there is time delay between the controller and the plant, what is that maximum time delay this controller can handle before it becomes unstable. (Do not do Pade Approximations). Show all your calculations. c. If there is time delay introduced by the sensor that measures the angle, then what is the maximum time delay this system can handle before it becomes unstable. (Do not do Pade Approximations) Magnitude (dB) Phase (deg) 50 O -50 -100 -90 -135- -180k 10 -2 Bode Diagram Gm= Inf dB (at Inf rad/sec), Pm= 48.5 deg (at 0.882 rad/sec) 10 10 Frequency (rad/sec) 10

Fig: 1