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ch07 - S E V E N Steady-State Errors SOLUTIONS TO CASE...

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S E V E N Steady-State Errors SOLUTIONS TO CASE STUDIES CHALLENGES Antenna Control: Steady-State Error Design via Gain a. G(s) = 76.39K s(s+150)(s+1.32) . System is Type 1. Step input: e( ) = 0; Ramp input: e( ) = 1 K v = 1 76.39K 150 x 1.32 = 2.59 K ; Parabolic input: e( ) = . b. 1 K v = 2.59 K = 0.2. Therefore, K = 12.95. Now test the closed-loop transfer function, T(s) = 989.25 s 3 +151.32s 2 +198s+989.25 , for stability. Using Routh-Hurwitz, the system is stable. s 3 1 198 s 2 151.32 989.25 s 1 191.46253 0 s 0 989.25 0 Video Laser Disc Recorder: Steady-State Error Design via Gain a. The input, 15t 2 , transforms into 30/s 3 . e( ) = 30/K a = 0.005. K a = 0.2*600 20000 * K 1 K 2 K 3 = 6x10 -3 K 1 K 2 K 3 . Therefore: e( ) = 30/K a = 30 6x10 3 K 1 K 2 K 3 = 5x10 -3 . Therefore K 1 K 2 K 3 = 10 6 . b. Using K 1 K 2 K 3 = 10 6 , G(s) = 2x10 5 (s + 600) s 2 (s + 2x10 4 ) . Therefore, T(s) = 2x10 5 (s + 600) s 3 + 2x10 4 s 2 + 2x10 5 s + 1.2x10 8 . Making a Routh table,
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