Control ENG HW_Part_27 - (a Over shoot = A = exp 1 2 B =...

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(a) Over shoot = × - = - - = 84 . 0 4 . 0 exp 1 exp 2 π ξ πξ B A = 0.254 thus % overshoot = 25.4 c)thus, max value of Y(t) = A+B = B(0.254)+B = 2.54+10 = 12.54 e) Period of oscillation = 2 1 2 ξ πτ - = 3.427 b) For rise time, we need to solve r t t t for t e = = + - - - 10 ) sin( 1 1 1 10 2 φ α ξ τ ξ = ) sin( φ α τ ξτ + - r t e r = 0 = 0 ) 1589 . 1 833 . 1 sin( 5 . 0 4 . 0 = + - r t e r τ solving we get t r = 1.082 thus SOLUTION: % Overshoot = 25.4 Rise time = 1.0842 Max Y(t) = 12.54 U(t) Y(t) = 10 Period of oscillation = 3.427 Comment : we see that the Oscillation period is small and the decay ratio also small = system is efficiently under damped .
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8.2 The tank system operates at steady state. At t = 0, 10 ft 3 of wateris added to tank 1. Determine the maximum
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