control

Question 1

what does gain compensation achieve

Answer 1

Adding a gain compensator will not change original root locus, but can
change stability, time response, and steady state error

Question 2

what is the difference between the bode and nyquist plot, give some advantages and disadvantages

Answer 2

Nyquist: plots real vs imaginary part as frequency varies
Pros: easy to tell if the system is stable
cons: hard to choose key values of frequency

Bode: has a magnitude and a phase plot with gain (dB) vs frequency and phase shift (degs) vs frequency
pros: large range of frequency, easy to see the effects of the controller, easily see PM/GM#
cons: 2 seperate plots

Question 3

what does phase lag compensation achieve

Answer 3

Adding a phase-lag compensator will slightly change original root locus to
the right of original root locus, making system tend to become unstable, but
can reduce the steady-state error.

Question 4

what does phase lead compensation do

Answer 4

Adding a phase-lead compensator will change original root locus to the left
of original root locus, making system become more stable, meeting more
dynamic specifications.

Question 5

what is the purpose of compenation design

Answer 5

Dynamic system itself may not directly satisfy required performance
specifications. There often exist inherent trade-off among performance
specifications. The purpose of compensation design is to meet more
performance specifications, e.g., steady-state error, overshoot, and settling
time

Question 6

State the difference between a practical phase-lead compensator and an ideal phase-lead compensator

Answer 6

Implementation using different circuit such as RC, different method of choosing
added zero location (ideal case by using angle criterion directly, and practical
case by using own choice but instead choosing added pole by using angle
criterion)
Their time responses are also different in terms of overshoot and settling time
etc.
Ideal phase-lead compensator (also PD controller) is sensitive to step changes
with input and sensitive to noise. Practical lead compensator can mitigate these
effects

Question 7

definition of gain margin

Answer 7

Gain margin is a factor by which the system gain can be increased before
driving the system unstable

Question 8

what is the definition of phase margin

Answer 8

Phase margin is the amount of additional phase lag that can be introduced
into the system at the gain crossover frequency before making the system
unstable

Question 9

how do you read gain margin from a nyquist plot

Answer 9

For finding gain margin, you need to find the phase cross-over frequency
w_pi where the phase is -180 degree, the gain margin can be calculated by
1/|GH(i*w_pi)|.

Question 10

how do you read phase margin from a nyquist plot

Answer 10

For finding phase margin, you need to find the gain cross-over frequency
w_1, where the gain is unit. The phase margin is the difference between the
phase of GH(i*w_1) and -180 degree