Q.3 (a) Figure Q.3a illustrates a circuit for representing an electrical system consisting of capacitor (C), resistor (R), and inductor (L). The voltage Va (t) and V,(t) are the input to the system, u(t) 6 UTM 경0 The output is the current that pass through the resistor y(t) = ir(t). Identify a state space representation of the system using x(t) = 6 UTM U as the state variables. UTM UTM & UTM & UTM UTM &UTM ee R 5 UTM UTM Va(t) İL(t) UT İR(t) Vc(t) ic(t) C UTM &UTM Vo(t) & UT 77M ㅎ UTM 6UTM UT UTM UTM TM 3 UT

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Q.3
(а)
Figure Q.3a illustrates a circuit for representing an electrical system consisting of
capacitor (C), resistor (R), and inductor (L). The voltage Va (t) and V, (t) are the
input to the system, u(t)
[Va(t)
the resistor y(t) = ir(t). Identify a state space representation of the system using
UTM U
The output is the current that
UTM
%3D
[vc(t)]
S UTS
pass through
x(t)
as the state variables.
6 UTM
UTM
UTM UTM UTM
UTM &UTM
le
İL(t)
UTM UTM
Va(t)
3 UT
İR(t)
Vc(t)
ic(t)
C
Vp(t)
5 UT
5 UTM UTM
6 UTM UTM UTM
(b) Determine the state space representation of the system shown in Figure Q.3b,
UT
Figure Q.3a
UTM UTM
where the input torque is f (t) and the output is x3(t).
UTM 5 UTM UTM
&UTM UT
UTM 3 UT
UTM
(1)'x'
x,(1)
UT
8 UTM U
x;(1)
4 N/m
A1) 4 kg
000
3 N-s/m
3 N/m
& UTM &U
3 kg
3 N/m
2 kg
2 N/m
4 N/m
Transcribed Image Text:Q.3 (а) Figure Q.3a illustrates a circuit for representing an electrical system consisting of capacitor (C), resistor (R), and inductor (L). The voltage Va (t) and V, (t) are the input to the system, u(t) [Va(t) the resistor y(t) = ir(t). Identify a state space representation of the system using UTM U The output is the current that UTM %3D [vc(t)] S UTS pass through x(t) as the state variables. 6 UTM UTM UTM UTM UTM UTM &UTM le İL(t) UTM UTM Va(t) 3 UT İR(t) Vc(t) ic(t) C Vp(t) 5 UT 5 UTM UTM 6 UTM UTM UTM (b) Determine the state space representation of the system shown in Figure Q.3b, UT Figure Q.3a UTM UTM where the input torque is f (t) and the output is x3(t). UTM 5 UTM UTM &UTM UT UTM 3 UT UTM (1)'x' x,(1) UT 8 UTM U x;(1) 4 N/m A1) 4 kg 000 3 N-s/m 3 N/m & UTM &U 3 kg 3 N/m 2 kg 2 N/m 4 N/m
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