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# note10 - MEEN 364 Notes for session on Notes from Session...

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MEEN 364 Notes from Session on November 10, 2004 Notes for session on November 10, 2004. 1) Obtain a relation for the output of the system shown below in terms of the reference and the disturbance. To obtain the output of the system we apply the principle of superposition, which states that the output is given by adding the individual effects of each input and disturbance separately. To obtain the transfer function between the output, Y(s) and the reference, R(s), assume the disturbance to be zero. Hence the transfer function reduces to Therefore the transfer function is given by Y(s) R(s) 1 GH GH = + (1) Similarly, to obtain the transfer function between the output, Y(s) and the disturbance, D(s), assume the reference to be zero. Hence Therefore the transfer function is given by 1

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MEEN 364 Notes from Session on November 10, 2004 Y(s) 1 D(s) 1 GH = + (2) Therefore the output, Y(s) when both the reference and the disturbance are present is given by 1 Y(s) R(s) D(s) 1 1 GH GH GH = + + + 2) The transfer functions of a control system, between the input r(t) and the output y(t), and the disturbance d(t), and y(t), are as follows: 1 2 ( ) 2.5( 1) ( ) ( ) (0.25 1) Y s s G s R s s s + = = + 2 2 ( ) 1 ( ) ( ) Y s s G s D s s + = = Compute the steady state error for the following input and disturbance signals: r(t)=4+6t+3t 2 , d(t) = sin(t). Applying superposition, we get: Y(s) = G 1 (s) R(s) + G 2 (s) D(s) The error signal is always given by ( ) ( ) ( ) E s R s Y s = : ( ) 1 2 ( ) ( ) 1 ( ) ( ) ( ) E s R s G s G s D s = (1) The signals are: 2 4 6
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note10 - MEEN 364 Notes for session on Notes from Session...

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