EE C128 / ME C134 Spring 2014 HW7 UC Berkeley Homework 7 Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s)= K s(s + 5)(s + 11) do the following: (a) Find the gain, K, for the uncompensated system to operate with a 30% overshoot. (b) Find the peak time and K v for the uncompensated system. (c) Design a lag-lead compenator to decrease the peak time by a factor of 2, decrease the percent overshoot by a factor of 2, and improve the steady-state error by a factor of 30. Specify all poles, zeros and gains. 2. Compensators (9 points) The unity feedback system shown in Problem 1, with G(s)= K (s 2 +4s + 8)(s + 10) is to be designed to meet the following specifications: Overshoot: Less than 25% Settling Time: Less than 1 second K p = 10 Do the following: (a) Evaluate the performance of the uncompensated system operating at 10% overshoot. (b) Design a passive compensator to meet the desired specifications. (c) Use MATLAB to simulate the compensated system. Compare the response with the desired specifications. 3. Bode Form (3 points) Express the following transfer functions in their Bode forms. (a) G(s)= 1 s(s + 2)(s + 4) (b) G(s)= (s + 5) (s + 2)(s + 4) Rev. 2.0, 04/13/2014 1 of 4