Transfer Function Question
Transfer Function Question
(OP)
Why we don't need the initial conditions for the transfer function ?
Thanks
Thanks
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RE: Transfer Function Question
TTFN
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RE: Transfer Function Question
As commonly used the transfer function is basically the frequency response of a single input/single output system.
You can extend the concept to generalized time response including initial conditions, but that is more for specific applications and performance modeling, as the transfer function is now a matrix.
RE: Transfer Function Question
Thanks
RE: Transfer Function Question
TTFN
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RE: Transfer Function Question
Use of null initial conditions is only common when considering the dynamic steadystate response, whether Laplace, Heaviside, Ztransforms, or the sinusoidal steadystate where the effect of the initial conditions have damped out.
Ignoring them is easier for the student and suitable for a broad range of practical problems, but hardly a complete solution to your problem.
RE: Transfer Function Question
Given a linear timeinvariant differential equation model, any nonzero initial conditions must be included when taking the Laplace transform of any derivative terms. This is how they end up in the system output signal as the zeroinput response term. However, they end up dropping out of the response equation if set to zero, and only the transfer function and its accompanying arbitrary input signal remain.
Zero initial conditions can be created by using deviation variables, finding the zerostate response, then adding the initial conditions back to the zerostate response. Deviation variables can be created by subtracting the steadystate equation from the differential equation, and are often created by linearization of nonlinearities that are differentiable around the linearization point.
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RE: Transfer Function Question