Answer to Question #156532 in Electrical Engineering for Tumelo

Question #156532

The differential equation for a control system is given as follows;

d3c/dt3 + 8d2c/dt2+ 31dc/dt + 48c = d2r/dt2 + 4dr/dt +25r

Determine the following, showing ALL relevant steps

a) The corresponding transfer function in its factorized form

b) Normalized transfer function

c) Magnitude slope plot

d) Phase slope plot


1
Expert's answer
2021-03-01T02:10:00-0500

Transfer Function :

Apply Laplace Transform to the given differential equation

a)"L[\\frac{d^3c}{dt^3}+\\frac{8d^2c}{dt^2}+\\frac{31dc}{dt}+48c] = L[\\frac{d^2r}{dt^2}+\\frac{4dr}{dt}+25r]"

b)C(s)[ s3+8s2+31s+48] = R(s)[s2+4s+25]

Transfer Function = Laplace Transform of Output/Laplace Transform of Input

c)="\\frac{C(s)}{R(s)}"

d)"\\frac{C(s)}{R(s)}" = "\\frac{[s3+8s2+31s+48]}{[s2+4s+25]}"

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