Input 1 Desired Output Invert System Model Prior Knowledge brPage 5br The InversionProblem Input Desired Output Invert the known system model 0 to find input Input 1 Desired Output Invert System Model Prior Knowledge His Mom knows how she ha ID: 25166 Download Pdf

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Input 1 Desired Output Invert System Model Prior Knowledge brPage 5br The InversionProblem Input Desired Output Invert the known system model 0 to find input Input 1 Desired Output Invert System Model Prior Knowledge His Mom knows how she ha

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What is Inversion-Based Control? Input Output Consider a System --- My Nephew Let the desired output be, say, eat dinner!

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What is Inversion-Based Control? Input Output = Y Let the desired output be, say, eat dinner! Question: What input should you apply? negotiate, encourage, ?? ?)

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What is Inversion-Based Control? Input Output = Y Let the desired output be, say, eat dinner! Question: What input should you apply? negotiate, encourage, bribe always works for me !)

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The Inversion-Problem Input =? Desired Output Invert the known

system model ( 0 ) to find input. Input = -1 [ Desired Output] Invert System Model Prior Knowledge

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The Inversion-Problem Input =? Desired Output Invert the known system model ( 0 ) to find input. Input = -1 [ Desired Output] Invert System Model Prior Knowledge His Mom know’s how --- she has a reasonable model

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The Control method using Inversion Use Inverse input as the feedforward input to system Prior Knowledge Actual System Input Output Invert System Model Desired Output System -1 Nonminimum Phase System Inverse: S. Devasia, D. Chen and B. Paden “Nonlinear

Inversion-Based Output Tracking,” IEEE Transactions on Automatic Control, Vol. 41 (7), pp. 930-942, July 1996

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Feedforward is Common in Human Systems Prior Knowledge Actual System Input Output Invert System Model Desired Output System -1 Examples: Walking, Playing Baseball, Driving a Car

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Problem --- model uncertainty Is Desired output = Output? Yes if we know the model perfectly! But, we rarely know a system perfectly ( 0 , -1 -1 Prior Knowledge Actual System Input Output Invert System Model Desired Output System -1

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Resolution: Addition of

Feedback Exploit knowledge of the system through feedforward input Account for errors (uncertainties, perturbations) using feedback Input Invert System Model Desired Output System Observation Output Prior Knowledge Actual System -1

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Feedforward under Uncertainty? As the kid grows up the model gets lousy! 'Z = G 0 Z -G Z Maybe it is better to use pure feedback without feedforward? Input Output Invert Lousy Model Desired Output System Knowledge Observation -1

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Feedforward under Uncertainty? Input Output -1 Desired Output System

C(s) Inverse Ref: S. Devasia, “Should Model-based Inverse Inputs be used as Feedforward under Plant Uncertainty?” IEEE Trans. on Automatic Control, Vol. 47(11), Nov 2002 Let the Error in model be 'Z = G 0 Z -G Z For SISO Case, Feedforward always improves output tracking for any feedback if 'Z__ 0 Z_

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Key Idea: Feedforward Input is found using System Inversion (1) Feedforward input uses system knowledge to control the output (2) Feedforward should be integrated with feedback

(3) Performance better than the use of feedback alone if uncertainty is not too large 'Z__ 0 Z_ Re-Cap Input Output Invert System Model Desired Output -1

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