timeresponse16

# timeresponse16 - =(2 Rearranging equation(2 the transfer...

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Time Response Q UESTION 16 Find the values of R and C that yield a 20% overshoot and a 1 ms settling time for the current in the electrical network shown in Figure 16.1 if L = 1 H. L R C e i (t) + - Figure 16.1 Denote the current in the electrical network as I ( t ) and the current as being positive when it flows in the clockwise direction. Apply KVL ( 29 ( 29 ( 29 ( 29 0 i R L C e t e t e t e t - + + + = (1) where v R ( t ), v L ( t ), and v C ( t ) are the voltage drops across the resistor, inductor, and capacitor, respectively. Applying the constitutive laws for these elements in the Laplace domain, assuming zero initial conditions, equation (1) can be written as ( 29 ( 29 ( 29 ( 29 0 i I s E s RI s LsI s Cs - +

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Unformatted text preview: + + = (2) Rearranging equation (2), the transfer function ( 29 ( 29 i I s E s is ( 29 ( 29 2 1 1 i I s s R E s L s s L CL = Ã· + + (3) Time Response The settling time is 4 0.001 s n T Î¶Ï– = = s. If L = 1 H, R = 2 Î¶Ï‰ n and R = 8000 Î©. The damping ratio for 20% overshoot is 2 2 2 2 % 20 ln ln 100 100 0.4559 % 20 ln ln 100 100 OS OS Î¶ Ï€ -- = = = + + (1) Therefore, the natural frequency is rad 8774 2 s n R Ï– = = and 2 1 0.012Î¼F 8774 C = = . 2...
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timeresponse16 - =(2 Rearranging equation(2 the transfer...

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