System modelling and time domain analysis

Question 1

How can we find the transfer function from loop reduction?

Answer 1

Y/U = A(s)/ 1+ AB(s)
-where A(s) is the top of the loop and B(s) is the negativ feedback

Question 2

What does it mean if a TF is said to be strictly proper?

Answer 2

if the order of the numerator is less than that of
the denominator

Question 3

What does it mean if a TF is proper?

Answer 3

if the order of numerator = order of denominator

Question 4

What does it mean if a TF is non-proper

Answer 4

if the order of the numerator is greater than that of
the denominator

Question 5

Define a stable TF

Answer 5

when the natural response decays to zero as time tends to infinity

Question 6

define a marginally stable TF

Answer 6

when the natural response oscillates with constant bounds as time tends to infinity

Question 7

Define an unstable TF

Answer 7

when the natural response grows without bounds as time approaches infinity

Question 8

How can we see if a TF is stable?

Answer 8

-Find the poles of the TF
-plot on pole-zero map
-sketch step response using inverse laplace

Question 9

In the s-plane, where should stable TFs be plotted?

Answer 9

Strictly on the LHS of the s-plane

Question 10

For a second order system, what is the response defined by?

Answer 10

Wn - natural frequency
zeta - damping ratio

Question 11

How do we test the performance of systems?

Answer 11

1. Provide uniform input
2. Record Response
   3.Quantify and evaluate response to input
3. Vary system and re-evaluate

Question 12

What are typical test inputs?

Answer 12

Impulse
Step
Ramp/Slope
Parabola

Question 13

Define rise time

Answer 13

time to go from 10% to 90% of outputs final value

Question 14

Define overshoot

Answer 14

% over final value

Question 15

Define setting time

Answer 15

time to reach and stay within 2% of final value

Question 16

What are the netwon/euler equations for torque?

Answer 16

Tm(t) = Kt*i(t)

Tm(t) - bw(t) = Jw(dot)(t)

Kti(t) - bw(t) = J*w(dot)(t)