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steadystateerror1 - Steady State Error QUESTION 1 For the...

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Steady State Error Q UESTION 1 For the system shown in Figure 1 with ( 29 ( 29 ( 29 ( 29 2 17 6 3 11 s s F s s s s + + = + + , calculate e (∞) for the following inputs: r ( t ) = 3, r ( t ) = 7 t , and r ( t ) = 24 t 2 . + - R(s) F(s) Y(s) E(s) Figure 1 The closed–loop transfer function is ( 29 ( 29 ( 29 ( 29 ( 29 2 3 2 17 6 1 31 50 102 s s Y s F s R s F s s s s + + = = + + + + . From the Routh Table below, it can be seen that the closed–loop system is stable and, therefore, the steady–state error can be calculated. 3 2 1 0 1 50 31 102 46.71 0 102 0 s s s s ( 29 ( 29 ( 29 1 1 E s R s F s = +
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Steady State Error ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 0 0 3 11 1 lim lim 17 6 3 11 17 6 1 3 11 s s s s s e s R s s R s s s s s s s s s s s + + ∞ = = + + + + + + + + + + For r
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