Lecture 4

Question 1

What do y and r represent in the differential equations used in transfer functions?

Answer 1

y is the response (output signal)
r is the excitation (input signal)

Question 2

How is the transfer function of a system derived?

Answer 2

Assume 0 initial conditions for y, r, and their derivatives
Take Laplace transforms of each
Factor out Y(s) and R(s)
Collect terms

Question 3

For Y(s)/X(s) = abc, which side of the abc block do Y(s) and X(s) respectively go?

Answer 3

Y(s): right (after)
X(s): left (before)

Question 4

What is the transfer function?

Answer 4

The ratio of the Laplace transform of the output variable to the Laplace transform of the input variable (assuming zero initial conditions)

Question 5

What does (X(s) - Y(s)) represent in a spring-mass-damper system?

Answer 5

Relative displacement

Question 6

What’s the advantage of a second order system

Answer 6

The steady state response reached to a step input matched the desired input, with just proportional control get steady state error