Karl Time Domain

Question 1

What is the R(s) of an impulse signal

Answer 1

1/s

Question 2

What is the R(s) of a ramp signal?

Answer 2

1 / s^2

Question 3

What is the R(s) of a parabolic signal?

Answer 3

2 / s^3

Question 4

What is the settling time?

Answer 4

It is the time taken for the output to settle within 2% of the steady state value.

Question 5

What is the rise time?

Answer 5

It is the time taken for the output to rise from 10%-90% of the steady state value for responses without overshoot or 0-100% for responses with overshoot.

Question 6

What is the peak time?

Answer 6

It is the time taken to reach the peak of the overshoot.

Question 7

What is Steady State error?

Answer 7

It is the difference between the steady state value and the reference value.

Question 8

What is Peak Response?

Answer 8

It is the magnitude of the peak overshoot.

Question 9

What is the % overshoot?

Answer 9

It is the amount that the peak exceeds the steady state value:
%OS = Mp - Yss / Yss

Question 10

What is the equation for Steady State Error?

Answer 10

Ess = lim(s->0) s * R(s) * (1-T(s))
Where T(s) is the closed loop transfer function.

Question 11

When can we apply the final value theorem?

Answer 11

When the denominator has negative real parts and only one root at the origin.

Question 12

If the system has a step input of 2, what is the R(s)?

Answer 12

2/s because it is two multiplied the by a unit step input which is 1/s.

Question 13

What is the type number of a system and what does it tell us?

Answer 13

The type number is the number of poles at the origin. It tells us about the steady state error of the system.

Question 14

What is the steady state error for impulse, ramp and parabolic inputs to a type zero system?

Answer 14

Impulse: finite

ramp: infinite
parabolic: infinite

Question 15

What is the steady state error for impulse, ramp and parabolic inputs to a type one system?

Answer 15

Impulse: 0
Ramp: finite:
Parabolic: infinite

Question 16

What is the steady state error for impulse, ramp and parabolic inputs to a type two system?

Answer 16

Impulse: 0
Ramp: 0
Parabolic: finite

Question 17

What is the pole zero form of a transfer function?

Answer 17

T(s) = b / s + a

Question 18

What is the time constant form of a transfer function?

Answer 18

T(s) = K / Tau * s + 1

where Tau = 1 / a and K = b / a

Question 19

What does the time constant tell us about the time response of a system and the location of the poles?

Answer 19

It tells us how quickly the system will respond. The smaller time constant means a quicker response and the poles will be further from the origin but a larger time constant means a slower response and poles closer to the origin.

Question 20

What is the formula for 2% settling time?

Answer 20

Ts(2%) = 4 * Tau

Question 21

What is the formula for rise time?

Answer 21

Tr = 2.2 * Tau

Question 22

What is the general form of a second order system?

Answer 22

K*w^2 / s^2 + 2Lws + w^2

Where L is the damping ratio and w is the natural frequency.

Question 23

What does the shape of the system response for a second order system depend on?

Answer 23

The damping ratio.

Question 24

For a second order system what is the steady state response equal to ?

Answer 24

Yss = K

where K is the system Gain

Question 25

What are the pole locations for a second order system?

Answer 25

s = -Lw +- jw * sqrt(1 - L^2)

Question 26

How can we approximate the time response of a higher order system?

Answer 26

We can treat it as a second order system if it has a dominant set of complex poles. The systems that are best approximated are the ones that have their real poles furtherest from the dominant poles.

Question 27

What makes a system unstable?

Answer 27

If it drastically changes its behaviour for tiny changes in its initial state or inputs.
If ANY of its poles have positive real parts.

Question 28

What is the definition of a stable system?

Answer 28

If the natural response of the system decays to zero as t -> infinity.

Question 29

What is the definition of an unstable system?

Answer 29

if the natural response grows to infinity as t -> infinity.

Question 30

What is the definition of a marginally stable system?

Answer 30

If the natural response neither grows nor decays as t-> infinity but remains constant or oscillates.

Question 31

What makes a system stable?

Answer 31

If all of its poles have negative real parts.

Question 32

What makes a system marginally stable?

Answer 32

If any of its poles lie on the imaginary axis and are not repeated.