CHEN 3701 Lecture 17: 2015_10_5 Lecture
9 Oct 2015
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Document Summary
-> defined as the ultimate response of the system that is forced by a sinusoidal input. For a linear system forced by a forcing function u(t) = asin(wt), omega = radian frequency the output will ultimately also be a sine wave w/ the same frequency, omega, but w/ different amplitude and some phase angle. Approach 1: direct: through partial fraction expansion, inversion, (how we showed that. Approach 2 --> for a general, stable transfer function g(s) Amplitude ratio (ar) = phi = avg g(j*omega) = argument of g(j*omega) Aside complex number z = a + jb verify that it holds for set s = j*omega. Calculate can do this for any transfer function can find sinusoidal response. Chen4601_processcontrol page 1 special case of interest: systems in series polar form of complex number theta correponds to overall function g. Chen4601_processcontrol page 2 facilitates the calculations a lot.
