1. Name three advantages of frequency response techniques over the root locus.

a. Transfer functions can be modeled easily from physical data;

b. Steady-state error requirements can be considered easily along with the design for transient response;

c. Settles ambiguities when sketching root locus;

d. Valuable tool for analysis and design of nonlinear systems.

2. Define frequency response as applied to a physical system.

A sinusoidal input is applied to a system. The sinusoidal output's magnitude and phase angle is measured in the steady-state. The ratio of the output magnitude divided by the input magnitude is the magnitude response at the applied frequency. The difference between the output phase angle and the input phase angle is the phase response at the applied frequency. If the magnitude and phase response are plotted over a range of different frequencies, the result would be the frequency response for the system.

3. Each pole of a system contributes how much of a slope to the Bode magnitude plot?

Negative 6 dB/octave which is the same as 20 dB/decade

4. A system with FOUR poles and two zeros would exhibit what value of slope at high frequencies in a Bode magnitude plot?

Negative 12 dB/octave or 40 dB/decade

(TO FIND get 4 poles - 2 zeros = 2 * 6dB/octave=12 dB/octave and for other its zeros (0 is 60 dB, 1 is 40 dB, and 2 is 20 dB/decade)

5. Describe the asymptotic phase response of a system with a single pole at -2.

Zero degrees until 0.2; a negative slope of 45o/decade from a frequency of 0.2 until 20; a constant -90o phase from a frequency of 20 until ∞

6. What are two differences between Bode magnitude plots for first-order systems and for underdamped second-order systems?

Second-order systems require a correction near the natural frequency due to the peaking of the curve for different values of damping ratio. Without the correction the accuracy is in question.

7. Briefly state the Nyquist criterion.

Z = P - N, where Z = # of closed-loop poles in the right-half plane, P = # of open-loop poles in the righthalf plane, and N = # of counter-clockwise encirclements of -1 made by the mapping.

8. What simplification to the Nyquist criterion can we usually make for systems that are open-loop stable?

We need only map the positive imaginary axis and then determine that the gain is less than unity when the phase angle is 180o.

The amount of additional open-loop gain, expressed in dB and measured at 180o of phase shift, required to make a closed-loop system unstable.

10. Define phase margin.

The phase margin is the amount of additional open-loop phase shift, ΦM, required at unity gain to make the closed loop system unstable.

11. Name two different frequency response characteristics that can be used to determine a system's transient response.

Transient response can be obtained from (1) the closed-loop frequency response peak, (2) phase margin

12. Briefly explain how to find the static error constant from the Bode magnitude plot.

For Type zero: Kp = low frequency gain; For Type 1: Kv = frequency value at the intersection of the initial slope with the frequency axis; For Type 2: Ka = square root of the frequency value at the intersection of the initial slope with the frequency axis.

13. Describe the change in the phase margin if time delay is added to the plant.

No change at all