multiloop_control

# multiloop_control - Multiloop Control Systems 1 2 3 4 5 6...

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Multiloop Control Systems 1. Introduction 2. The relative gain array (RGA) 3. Pairing input-output variables 4. Dynamic considerations 5. Multiloop controller tuning 6. Reducing control loop interactions

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Introduction Multiloop control approach » Pair input and output variables together » Design SISO controller for each input/output pair » Attempt to minimize interactions between controllers Challenges » Often not obvious how to pair variables to minimize control loop interactions » Number of possible parings for n x n system = n ! » Detuning of SISO controllers often necessary due to interactions
Distillation Column Example Controller outputs – x D , x B , P , h D , h B Manipulated inputs – D , B , R , Q D , Q B Best pairings not obvious Number of possible pairings = n! = 5! = 120 Need efficient method to screen possible pairings

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The Relative Gain Quantifies the change in steady-state gain between an input-output pair that occurs when other control loops are closed Provides a measure of steady-state process interactions from only gain information Relative gain between input j and output i » is the open-loop gain with all other control loop open » is the closed-loop gain with all other control loop closed ( 29 ( 29 ] , 1 [ , n j i u y u y y j i u j i ij = λ ( 29 u j i u y ( 29 y j i u y
Relative Gain Calculation for 2x2 System Steady-state model Open-loop gain Closed-loop gain Relative gain 2 22 1 21 2 2 12 1 11 1 u K u K y u K u K y + = + = ( 29 11 0 1 1 2 K u y u = = - = - = - = = = 22

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multiloop_control - Multiloop Control Systems 1 2 3 4 5 6...

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