lomework3: A second-order series RLC circuit, shown in Figure below, has some damping due to the resistor. Determine: 1. The key parameters for this circuit in terms of R, L, and C. 2. The time response and the error signal for this system if it is called over damped system. R V. Vi

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Computer Technology Eng. Dept.
-z- 2 - 1)W? – 1)/
Homework3: A second-order series RLC circuit, shown in Figure below, has some
damping due to the resistor. Determine:
1. The key parameters for this circuit in terms of R, L, and C.
2. The time response and the error signal for this system if it is called over
damped system.
R
Vo
C
Vị
8.
Scanned with CamScanner
Control Engineering Fundamentals
Third Class
Hint:
We can modify the denominator term of the transfer function as follows:
s2 + 23wns + wn2 = [s? + 23wns+ w,²] + (3@n)² - ((wn)“
= [s + 2(s)(3Wn) + (3wn)²] + w,? - ((w,)? = (s + (wn)² – wn² (² – 1)
Answer:
1
1+
2(3+ J?-1)(
u(t)
1
le-Ban-V²-1)t
1
e-(kantanv-1)
e(t) =
2(3+ J? -1)(J-1),
u(t)
e-Cwn--1)t
- 1)W? – 1)/
Transcribed Image Text:Computer Technology Eng. Dept. -z- 2 - 1)W? – 1)/ Homework3: A second-order series RLC circuit, shown in Figure below, has some damping due to the resistor. Determine: 1. The key parameters for this circuit in terms of R, L, and C. 2. The time response and the error signal for this system if it is called over damped system. R Vo C Vị 8. Scanned with CamScanner Control Engineering Fundamentals Third Class Hint: We can modify the denominator term of the transfer function as follows: s2 + 23wns + wn2 = [s? + 23wns+ w,²] + (3@n)² - ((wn)“ = [s + 2(s)(3Wn) + (3wn)²] + w,? - ((w,)? = (s + (wn)² – wn² (² – 1) Answer: 1 1+ 2(3+ J?-1)( u(t) 1 le-Ban-V²-1)t 1 e-(kantanv-1) e(t) = 2(3+ J? -1)(J-1), u(t) e-Cwn--1)t - 1)W? – 1)/
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