Karl Time Domain Flashcards

1
Q

What is the R(s) of an impulse signal

A

1/s

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2
Q

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

A

1 / s^2

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3
Q

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

A

2 / s^3

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4
Q

What is the settling time?

A

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

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5
Q

What is the rise time?

A

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.

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6
Q

What is the peak time?

A

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

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7
Q

What is Steady State error?

A

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

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8
Q

What is Peak Response?

A

It is the magnitude of the peak overshoot.

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9
Q

What is the % overshoot?

A

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

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10
Q

What is the equation for Steady State Error?

A
Ess = lim(s->0) s * R(s) * (1-T(s))
Where T(s) is the closed loop transfer function.
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11
Q

When can we apply the final value theorem?

A

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

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12
Q

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

A

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

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13
Q

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

A

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

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14
Q

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

A

Impulse: finite

ramp: infinite
parabolic: infinite

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15
Q

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

A

Impulse: 0
Ramp: finite:
Parabolic: infinite

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16
Q

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

A

Impulse: 0
Ramp: 0
Parabolic: finite

17
Q

What is the pole zero form of a transfer function?

A

T(s) = b / s + a

18
Q

What is the time constant form of a transfer function?

A

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

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

19
Q

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

A

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.

20
Q

What is the formula for 2% settling time?

A

Ts(2%) = 4 * Tau

21
Q

What is the formula for rise time?

A

Tr = 2.2 * Tau

22
Q

What is the general form of a second order system?

A

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

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

23
Q

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

A

The damping ratio.

24
Q

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

A

Yss = K

where K is the system Gain

25
Q

What are the pole locations for a second order system?

A

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

26
Q

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

A

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.

27
Q

What makes a system unstable?

A

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

28
Q

What is the definition of a stable system?

A

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

29
Q

What is the definition of an unstable system?

A

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

30
Q

What is the definition of a marginally stable system?

A

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

31
Q

What makes a system stable?

A

If all of its poles have negative real parts.

32
Q

What makes a system marginally stable?

A

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