steadystateerror8

# steadystateerror8 - Steady State Error QUESTION 8 For the...

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Steady State Error Q UESTION 8 For the system shown in Figure 8 calculate e (∞) for the following sets of inputs: r ( t ) = 1 and d ( t ) = 0, r ( t ) = t and d ( t ) = 0, r ( t ) = 0.5 t 2 and d ( t ) = 0, r ( t ) = 0 and d ( t ) = 1, r ( t ) = 0 and d ( t ) = t , r ( t ) = 0 and d ( t ) = 0.5 t 2 . + + + - 1 s 8 8 s + 2 5 3 1 s s + + R(s) D(s) Y(s) Figure 8 Let ( 29 ( 29 1 2 5 3 1 G s s s s = + + and ( 29 2 8 8 G s s = + . From the block diagram, ( 29 ( 29 ( 29 E s R s Y s = - and ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 Y s D s G s R s G s Y s = + - Combining equations, ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 1 2 1 2 1 1 1 1 G s G s G s E s R s D s G s G s G s G s + - = - + +

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Steady State Error E ( s ) can be rewritten as ( 29 ( 29 ( 29 ( 29 ( 29 2 4 3 2 4 3 2 4 3 2 3 1 8 11 25 3 32
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steadystateerror8 - Steady State Error QUESTION 8 For the...

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