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 Kv 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

(s2 + 4s + 8)(s + 10)is to be designed

to meet the following specifications:

Overshoot: Less than 25%

Settling Time: Less than 1 second

Kp = 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)

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EE C128 / ME C134 Spring 2014 HW7 UC Berkeley

(c) G(s) =(s + 3)(s + 5)

s(s + 2)(s + 4)

4. Sketching Bode Plots (9 points)

For each of the functions given in Problem 3, sketch the Bode asymptotic magnitude and asymptotic

phase plots.

5. Nyquist Plots (6 points)

Sketch the Nyquist diagram for each of the systems given below, and using the Nyquist Criterion,

determine whether or not each system is stable.

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EE C128 / ME C134 Spring 2014 HW7 UC Berkeley

6. Bode Plot Analysis (6 points)

For the Bode plots shown below, determine the transfer functions by hand, and confirm your answers

via MATLAB.

(a)

(b)

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EE C128 / ME C134 Spring 2014 HW7 UC Berkeley

7. Bode Plot Analysis (6 points)

The Bode plots for a plant, G(s), used in a unity feedback system are shown below.

Do the following:

(a) Find the gain margin, phase margin, zero dB frequency, 180◦ frequency, and the closed-loop

bandwidth.

(b) Use your results in Part (a) to estimate the damping ratio, percent overshoot, settling time,

and peak time.

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