multiple subsystem 2 14
DESCRIPTION
Feedback ControlTRANSCRIPT
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Multiple Subsystem 2Dr. Aaron Don M. Africa
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Basic Feedback ControlG1 = U / E
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Superposition of Multiple InputsUsed to evaluate system performance when several inputs are simultaneously applied at a different points of a system
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Step 1Set all inputs except one equal to zero We determine the output C due to inputs U and RPut U = 0
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Step 2 Transform the block diagram to canonical form The system reduces to:
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Step 3Calculate the response due to the chosen input acting aloneCR = [G1G2 / (1 + G1G2)] R
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Step 4Repeat Steps to 3 for each remaining inputsPut R = 0 and Put a -1 into a block, representing a negative feedback effect.Rearranging the block diagram
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Let the -1 block be absorbed by the summing pointThe output CU due to input U is CU = [G2 / (1 + G1G2)]U
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Step 5Algebraically add all the responses
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Example 1Determine the output C due to U1 , U2 and R for the figure
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Let U1 = U2 = 0CR = [G1G2 / (1 G1G2H1H2) ] R
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Let R = U2 = 0C1 = [G2 / (1 G1G2H1H2) ] U1
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Let R = U1 = 0C2 = [G1G2H1 / (1 G1G2H1H2) ] U2
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Analysis and Design of Feedback Systems
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Example 2For the system shown in the figure find Peak TimePercent OvershootSettling Time
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Natural FrequencyDamping RatioPeak TimePercent OvershootSettling Time
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Example 3Design the value of gain K, for the feedback control system in the figure so that the system will respond at 10% overshoot (The damping ratio of 10% overshoot is 0.591)
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10% overshoot has a damping ratio of 0.591
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Example 4Determine the a) Loop Transfer Function b) Control Ratioc) Error Ratio d) Primary Feedback ratio
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a) Loop Transfer Functionb) Control Ratio
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c) Error Ratiod) Primary Feedback Ratio