Introduction, Laplace Transform & Transfer Functions Flashcards
Explain how the cruise control system in a car work?
The system takes the desired speed as an input and then subtracts the measured speed from it. This value then goes into the cruise controller which then changes the gas flowrate to the engine, allowing the car to drive
What is the difference between open loop control and closed loop control?
Closed loop control has a sensor which provides a feedback value, whereas the open loop control has no feedback
What are the conditions to satisfy to have a linear system?
f(x+y) = f(x) + f(y)
f(kx) = kf(x), k is a real number
What is the difference between a time varying system and a time invariant system?
Time invariant: Parameters of the system don’t change over time
Time varying: Parameters of the system change over time
What is a time continuous system?
State variables change continuously over time
What is a discrete system?
State variables change only at a discrete set of points in time
What is meant by the linearity of Laplace Transforms?
L{a.f(t) + b.g(t)} = a.F(s) + b.G(s)
How do we account for a shift in time with a Laplace Transform?
L{f(t-T) = e^-Ts * F(s)
What does L[e^-at f(t)] equal?
F(s+a)
How do we differentiate a Laplace Transfors in respect to the first order?
sF(s) - f(0)
How do we differentiate a Laplace Transfors in respect to the second order?
s^2 * F(s) - sf(0) - f’(0)
What is the Laplace Transform of an integral?
1/s * F(s)
What is the Final Value Theorem?
lim f(t) as t tends to infinity is equal to lim sF(s) where s tends to 0
What does the Final Value Theorem represent?
This is for when the system is stable and what will occur at the end of the cycle
It’s representative of the final value of the system
What is the general formula of a transfer function?
G(s) = Y(s) / U(s)
Transfer Function = Output / Input
