(a) Figure Q.3a illustrates a circuit for representing an electrical system consisting of capacitor (C), resistor (R), and inductor (L). The voltage V (t) and V, (t) are the input to the system, u(t) = The output is the current that pass through the resistor y(t) = ir (t). Identify a state space representation of the system using x() = [8] as the state variables. R ee ww- İL(t) İR(t) ic(t) Vý(t) Va(t) Vc(t) C 表达为最 Figure Q.3a

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(a) Figure Q.3a illustrates a circuit for representing an electrical system consisting of
capacitor (C), resistor (R), and inductor (L). The voltage V (t) and V, (t) are the
input to the system, u(t) =
The output is the current that pass through
V½(t)]
the resistor y(t) = iR (t). Identify a state space representation of the system using
x(1) = [81
as the state variables.
R
İL(t)
İR(t)
Va(t)
Vc(t)
ic(t)
~) Vo(t)
表达为最
Figure Q.3a
(b) Determine the state space representation of the system shown in Figure Q.3b,
where the input torque is f(t) and the output is x3(t).
r(1)
X3(1)
4 N/m
N-s/m
A1).
4 kg
3 N/m
3 kg
2 kg
3 N/m
2 N'm
4 Nm
3 N-s/m
2 N-s/m
I N-s m
Figure Q.3b
please ignore the background text Bartleby and solve black part only.
x+y"- °c, x^-k yt 2x°+3x+4=y (x+y). a*+b²-(a+b)(a2=ab+b2)
reametime-
8
x+6
y=sinx
Ga+b?
X+2
reamstime
2
16
Transcribed Image Text:(a) Figure Q.3a illustrates a circuit for representing an electrical system consisting of capacitor (C), resistor (R), and inductor (L). The voltage V (t) and V, (t) are the input to the system, u(t) = The output is the current that pass through V½(t)] the resistor y(t) = iR (t). Identify a state space representation of the system using x(1) = [81 as the state variables. R İL(t) İR(t) Va(t) Vc(t) ic(t) ~) Vo(t) 表达为最 Figure Q.3a (b) Determine the state space representation of the system shown in Figure Q.3b, where the input torque is f(t) and the output is x3(t). r(1) X3(1) 4 N/m N-s/m A1). 4 kg 3 N/m 3 kg 2 kg 3 N/m 2 N'm 4 Nm 3 N-s/m 2 N-s/m I N-s m Figure Q.3b please ignore the background text Bartleby and solve black part only. x+y"- °c, x^-k yt 2x°+3x+4=y (x+y). a*+b²-(a+b)(a2=ab+b2) reametime- 8 x+6 y=sinx Ga+b? X+2 reamstime 2 16
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