Karl Time Domain Flashcards
What is the R(s) of an impulse signal
1/s
What is the R(s) of a ramp signal?
1 / s^2
What is the R(s) of a parabolic signal?
2 / s^3
What is the settling time?
It is the time taken for the output to settle within 2% of the steady state value.
What is the rise time?
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.
What is the peak time?
It is the time taken to reach the peak of the overshoot.
What is Steady State error?
It is the difference between the steady state value and the reference value.
What is Peak Response?
It is the magnitude of the peak overshoot.
What is the % overshoot?
It is the amount that the peak exceeds the steady state value:
%OS = Mp - Yss / Yss
What is the equation for Steady State Error?
Ess = lim(s->0) s * R(s) * (1-T(s)) Where T(s) is the closed loop transfer function.
When can we apply the final value theorem?
When the denominator has negative real parts and only one root at the origin.
If the system has a step input of 2, what is the R(s)?
2/s because it is two multiplied the by a unit step input which is 1/s.
What is the type number of a system and what does it tell us?
The type number is the number of poles at the origin. It tells us about the steady state error of the system.
What is the steady state error for impulse, ramp and parabolic inputs to a type zero system?
Impulse: finite
ramp: infinite
parabolic: infinite
What is the steady state error for impulse, ramp and parabolic inputs to a type one system?
Impulse: 0
Ramp: finite:
Parabolic: infinite
What is the steady state error for impulse, ramp and parabolic inputs to a type two system?
Impulse: 0
Ramp: 0
Parabolic: finite
What is the pole zero form of a transfer function?
T(s) = b / s + a
What is the time constant form of a transfer function?
T(s) = K / Tau * s + 1
where Tau = 1 / a and K = b / a
What does the time constant tell us about the time response of a system and the location of the poles?
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.
What is the formula for 2% settling time?
Ts(2%) = 4 * Tau
What is the formula for rise time?
Tr = 2.2 * Tau
What is the general form of a second order system?
K*w^2 / s^2 + 2Lws + w^2
Where L is the damping ratio and w is the natural frequency.
What does the shape of the system response for a second order system depend on?
The damping ratio.
For a second order system what is the steady state response equal to ?
Yss = K
where K is the system Gain
What are the pole locations for a second order system?
s = -Lw +- jw * sqrt(1 - L^2)
How can we approximate the time response of a higher order system?
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.
What makes a system unstable?
If it drastically changes its behaviour for tiny changes in its initial state or inputs.
If ANY of its poles have positive real parts.
What is the definition of a stable system?
If the natural response of the system decays to zero as t -> infinity.
What is the definition of an unstable system?
if the natural response grows to infinity as t -> infinity.
What is the definition of a marginally stable system?
If the natural response neither grows nor decays as t-> infinity but remains constant or oscillates.
What makes a system stable?
If all of its poles have negative real parts.
What makes a system marginally stable?
If any of its poles lie on the imaginary axis and are not repeated.
