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Deduce the state space representation and state variable matrices A, B, C, and D of the RLC circuit connected with two voltage sources vi(t) & vz(t), as shown in Figure Q3(b). Assume that the outputs are the currents flowing in R1, and R2.

Question-Answer › Category: Electrical Engineering › Deduce the state space representation and state variable matrices A, B, C, and D of the RLC circuit connected with two voltage sources vi(t) & vz(t), as shown in Figure Q3(b). Assume that the outputs are the currents flowing in R1, and R2.
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Alejo asked 1 year ago

Deduce the state space representation and state variable matrices A, B, C, and D of the RLC circuit connected with two voltage sources vi(t) & vz(t), as shown in Figure Q3(b). Assume that the outputs are the currents flowing in R1, and R2.

b) Deduce the state space representation and state variable matrices A, B, C, and D of the RLC circuit connected with two vol

 

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S gill answered 1 year ago

Vc and iL are the state variables.

i1 and i2 are the outputs.
11(t) = ilt)
-Vi(t) + Rii(t) + Lil(t) + V (t) = 0 Läl
d Til(t) is represented dt as 2L
LiL = -Riil(t) – V (t) + Vi(t)
R1 ii 1 iz(t) – Ve(t) +Vict) (1)
KCL at node:
il(t) = ict) + 12(t)
ic(t) = il(t) – iz(t)
CV c(t) = il(t) - iz(t) dt
V c(t) = VC
iz(t) V c(t) R2 V2(t) R2
V c(t) V2t) Vc = il(t) - + R2 R2 (2)
Outputs:
Current through R1 is iL
i1(t) = iL(t) (3)
Current through R2 is
-VC + R212(t) + V2(t) = 0
iz(t) V c(t) R2 V2(t) R2 (4)
X = AX + BU
2L R1 L 21 Vc + 1 Vi V2 Vc R2 R2
= CX + DU
21 0] =B + 2M V1 V2
————————————————-
Go through the answer.
If there are any doubts, please let me know in the comment box.
Do not forget to upvote.

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