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Control Systems Engineering Chapter 4: Time Response, : - Coggle Diagram
Control Systems Engineering Chapter 4: Time Response
4.2: Poles, Zeros, and System Response
Zeros
are values of Laplace transform variable s that cause the transfer function to zero or any roots of the numerator of the transfer function that are common to roots of the denominator
Occurs when numerator is equal to zero
System Response
can either be
forced
or
natural
Forced responce
is when the pole at the origin generates a step function in the output
Natural response
is when the pole on a real axis generates an exponential output
Zeros and poles are the amplitudes these responses occur
Poles
are values of Laplace transform variable s that cause the transfer function to be infinite or any roots of denominator of transfer function that are common roots of the numerator
Occurs when denominotor is equal to zero
First order systems
A first order system without zeros can be described by transfer function in Figure 4.4(a)
A pole plot can be used to easily see the poles and zeros, where poles are represented by X and zeros are identified as O
Time Constant (T
c
) is the time it takes for e^(-at) to rise to 63% of its final value
Represented by 1/a, where a is the initial rate of change of the exponential at time = 0
Rise time (T
r
) is the time for the waveform to go from .1 to .9 of its final value
Found by 2.2/a
Settling Time is time it takes for the waveform to get within .02% of its final value and remain there
Found by 4/a
Second Order Systems
:
