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pre-report

# pre-report - Stanley Martin April 11,2008 Inner Loop Close...

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Stanley Martin April 11,2008 Inner Loop Close small loop: Θ L V m 1 + Θ L V m K v s = 61 . 54 s 2 +35 . 1 s 1 + 61 . 54 s 2 +35 . 1 s K v s = 61 . 54 s 2 + 35 . 1 s + 61 . 54 K v s Inner loop transfer function: Θ L Θ d = K p 61 . 54 s 2 +35 . 1 s +61 . 54 K v s 1 + K p 61 . 54 s 2 +35 . 1 s +61 . 54 K v s = K p 61 . 54 s 2 + 35 . 1 s + 61 . 54 K v s + K p 61 . 54 = K p 61 . 54 s 2 + s (35 . 1 + 61 . 54 K v ) + K p 61 . 54 Comparing equation to standard form: K p 61 . 54 = ω 2 n = (22 . 2) 2 K p = (22 . 2) 2 61 . 54 = 8 . 0084 2 ζω n = 35 . 1 + 61 . 54 K v K v = 2( . 707)(22 . 2) - 35 . 1 61 . 54 = - . 0603 1

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Outer Loop Close small loop: X ( s ) α ( s ) 1 + K vbb s X ( s ) α ( s ) = 5 g 7 s 2 1 + K vbb s 5 g 7 s 2 = 5 g 7 s 2 + K vbb s 5 g = 5 7 g s 2 + 5 7 gsK vbb Outer loop transfer function: X ( s ) U ( s ) = K pbb 5 7 g s 2 + 5 7 gK vbb s + K pbb 5 7 g First set of requirements: ζ = . 707 ω n = 2 . 96 rad s K pbb 5 7 g = ω 2 n = (2 . 96) 2 K pbb = (2 . 96) 2 7 5 g = 1 . 25 K vbb 5 7 g = 2 ζω n = 2( . 707)(2 . 96) K vbb = 2( . 707)(2 . 96)(7) 5 g = . 598 Second set of requirements:
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pre-report - Stanley Martin April 11,2008 Inner Loop Close...

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