SITUATION STATEMENT: (Just read the situation, the question is at the bottom part of the problem) Convert this transfer function to a state-space representation. G(s) Y(s) R(s) (s²+as+ b)(s+d) R(s) = After taking the expansion of the denominator, the transfer function maybe simplified to the below diagram, s+c 1 Polynomial expansion, s W(s) s+c Y(s)

Introductory Circuit Analysis (13th Edition)
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Publisher:Robert L. Boylestad
Chapter1: Introduction
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SITUATION STATEMENT: (Just read the situation, the question is at the
bottom part of the problem)
Convert this transfer function to a state-space representation.
G(s) =
=
R(S)
Y(s)
S+C
R(s) (s²+as+b) (s+d)
=
After taking the expansion of the denominator, the transfer function
maybe simplified to the below diagram,
1
Polynomial expansion, s
W(s)
S+C
Y(s)
Transcribed Image Text:SITUATION STATEMENT: (Just read the situation, the question is at the bottom part of the problem) Convert this transfer function to a state-space representation. G(s) = = R(S) Y(s) S+C R(s) (s²+as+b) (s+d) = After taking the expansion of the denominator, the transfer function maybe simplified to the below diagram, 1 Polynomial expansion, s W(s) S+C Y(s)
Question:
Functions; r(t), w(t) and y(t), may be evaluated. Determine the differential equation at
the first block (left) using r(t) & w(t).
d^3w/dt^3 + (ab+d)d^2w/dt^2 + (b+ad) dw/dt + bdw(t) = r(t)
d^3w/dt^3 + (a+c)d^2w/dt^2 + (b+d) dw/dt + bdw(t) = r(t)
d^3w/dt^3 + (ab+d)d^2w/dt^2 + (ab+d) dw/dt + bdw(t) = r(t)
d^3w/dt^3 - (a+d)d^2w/dt^2 + (b+ad) dw/dt - bdw(t) = r(t)
d^3w/dt^3 + (a+d)d^2w/dt^2 + (a+d) dw/dt + abdw(t) = r(t)
d^3w/dt^3 + (a+d)d^2w/dt^2 + (b+ad) dw/dt + bdw(t) = r(t)
Transcribed Image Text:Question: Functions; r(t), w(t) and y(t), may be evaluated. Determine the differential equation at the first block (left) using r(t) & w(t). d^3w/dt^3 + (ab+d)d^2w/dt^2 + (b+ad) dw/dt + bdw(t) = r(t) d^3w/dt^3 + (a+c)d^2w/dt^2 + (b+d) dw/dt + bdw(t) = r(t) d^3w/dt^3 + (ab+d)d^2w/dt^2 + (ab+d) dw/dt + bdw(t) = r(t) d^3w/dt^3 - (a+d)d^2w/dt^2 + (b+ad) dw/dt - bdw(t) = r(t) d^3w/dt^3 + (a+d)d^2w/dt^2 + (a+d) dw/dt + abdw(t) = r(t) d^3w/dt^3 + (a+d)d^2w/dt^2 + (b+ad) dw/dt + bdw(t) = r(t)
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