AUTOMAT I C S and AUTOMATIC CONTROL

and AUTOMATIC CONTROL

is the transient output response y of the system when

⇒

u(t) = δ(t)

y(t) = g(t)

For linear system with transfer function:

When :

u(t) = δ(t)

then :

is the transient output response y of the system when

⇒

u(t) = 1(t)

y(t) = h(t)

For linear system with transfer function:

When :

u(t) = 1(t)

then :

final value of step response?

of a system or device in response to a stimulus,

Frequency responses

u(t) = Asin(ωt)

y(t) = Bsin(ωt+φ)

If a sine wave is injected into a system at a given frequency, a linear system will respond at that same frequency with a certain amplitude and a certain phase angle relative to the input

where:

- angular frequency

with coordinates P(ω) = Re [G(j ω)] and Q(ω) =

the form of:
a) magnitude:

[dB]

b) phase: