1) Assume that a system below has a phase margin of 65° at a crossover frequency of 3 rad/s. R(s) 10 F -15 We now include a sensor in the feedback path that has dynamics H(s). The modified block diagram is shown below and the frequency response of H(s) is given. R(s) Y(s) -30 -75 G S 10 Lead/lag compensator G Lead/lag compensator H(s) sensor Bode plot of H(s) G, (s) plant Frequency (rad/s) G, (s) plant Y(s) Q1) Estimate the new phase margin of the modified loop

r bsp G = .5 Kp J = .0000221 kg*m² K = .0502 Kf K RJs + K² R = 10.6 (motor) @n bsp = 1 1² en y 1.1 Hand Calculation Write the closed loop transfer function in terms of the parameter symbols. Do this by writing the open loop transfer function first and then using it to write the closed loop TF.

Do as Many you can.. Within 10 minutes.

(b) Block diagram of a system with unity feedback is illustrated as R(s) Y(s) K G(s) Figure Q3(b) and the transfer function is given as 50000 G(s) = s² + 150s + 5000 From the given block diagram and transfer function, sketch an approximate magnitude and phase of Bode Plot. Choose any value of K that you might think will simplify your sketching. There is no requirement of K value in this sketching process. The selection of Kis only necessary if you have a particular design requirement.