Lecture 3

Question 1

In the motor model, what is represented by: 
t(m)
b 
J 
omega?

Answer 1

t(m): motor torque (input)
b: resistance to motion
J: mass moment of inertia
omega: speed of rotation

Question 2

What is the momentum equation for the motor model?

Answer 2

tm(t) - b*omega(t) = J(domega/dt)

Question 3

What must be known in order to solve the momentum equation for the motor model?

Answer 3

How t(m) changes with time

Question 4

What is the integration by parts formula?

Answer 4

Int{b a} u(dv/dt) dt

= [uv]{b a} - Int{b a} v(du/dt) dt

Question 5

What is f(0)?

Answer 5

The initial condition when t = 0

Question 6

What does a unit step function represent physically?

Answer 6

A torque of 1Nm for all time t > 0

Question 7

What does e^(-t) tend to as t tends to infinity?

Answer 7

0

Question 8

What is K(mv)?

Answer 8

The motor constant

Question 9

What is b?

Answer 9

The viscous friction

Question 10

What does the final speed depend on without gain used?

Answer 10

The viscous friction b and the motor constant K(mv)

Question 11

What is K?

Answer 11

Gain

Question 12

What happens to the speed as K is increased?

Answer 12

As gain is increased, the final speed tends towards unity (the desired speed)

Question 13

What happens to the speed of response as K increases and why?

Answer 13

It improves because the exponential term is more negative

Question 14

What do lapalace transforms do

Answer 14

Take differential equations and turns them into algebraic equations, these can then be rearranged and through inverse Laplace transforms give a solution

Question 15

What is the Laplace transform of 1

Answer 15

1/s

Question 16

Laplace transform of y. + 4y = x

Answer 16

sY(s) + 4Y(s) = X(s)

Y(s)/X(s) = 1/s+4

Question 17

If the input to a motor is a unit step function what must you multiply the Laplace transform output by

Answer 17

1/s