timeresponse16 - + + = (2) Rearranging equation (2), the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 - +
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 = + + (3) Time Response The settling time is 4 0.001 s n T = = s. If L = 1 H, R = 2 n and R = 8000 . 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 -- = = = + + (1) Therefore, the natural frequency is rad 8774 2 s n R = = and 2 1 0.012F 8774 C = = . 2...
View Full Document

Page1 / 2

timeresponse16 - + + = (2) Rearranging equation (2), the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online