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Solution_to_problem_11.7

# Solution_to_problem_11.7 - The regulator problem relates...

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11.7 – 1 Solution to problem 11.7 a) Servo problem : The servo problem relates the output with the setpoint, SP Y Y , assuming that there is no disturbance, i.e. 0 D = . Using the general procedure to solve the closed-loop system (starting from Y and going backwards) we will find ourselves in a loop involving U: ( ) ( ) p p c p c sp p Y G U G G E G G Y Y G U = = = - - tildenosp If we now continue substituting U we are in a loop. Therefore, U must be solved before calculating Y . That can be done starting from U and going backwards, as follows: ( ) ( ) c c sp p U G E G Y Y G U = = - - tildenosp Now the terms with U can be grouped, thereby solving U : c sp c c p U G Y G Y G G U = - + tildenosp ( ) 1 c p c sp c U G G G Y G Y - = - tildenosp 1 c sp c c p G Y G Y U G G - = - tildenosp Now we can solve Y : 1 c sp c p p c p G Y G Y Y G U G G G - = = - tildenosp We just need to group together the terms containing Y : ( ) 1 c p p c sp p c Y G G G G Y G G Y - = - tildenosp ( ) 1 c p p c p c sp Y G G G G G G Y - + = tildenosp 1 p c sp c p p c G G Y Y G G G G = - + tildenosp b) Regulator problem :

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Unformatted text preview: : The regulator problem relates the output with the disturbance, Y D , assuming that there is no set point change, i.e. sp Y = . The procedure is similar. U was determined already in the previous question, however now the set point is zero because it does not change (remember we use deviation variables). 11.7 – 2 1 1 c sp c c c p c p G Y G Y G Y U G G G G--= =--t t Now we can solve Y : 1 c d p d p c p G Y Y G D G U G D G G G-= + = +-t As before, now we just need to group terms and solve: ( ) 1 1 1 d c p p c d c p d p c c p c p G D G G G G Y G D G G G D G G Y Y G G G G----= =--t t t t ( ) 1 c p p c d c p d Y G G G G G D G G G D-+ =-t t 1 d c p d c p p c G G G G Y D G G G G-=-+ t t...
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Solution_to_problem_11.7 - The regulator problem relates...

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