Automatic Control Projectaurelied/Finalpresentation.pdf · Automatic Control Project 2005 / 2006....
Transcript of Automatic Control Projectaurelied/Finalpresentation.pdf · Automatic Control Project 2005 / 2006....
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Automatic Control ProjectAutomatic Control Project
2005 / 2006
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The PendubotThe Pendubot
Aurélie Dufour
Erik Henriksson
Eric Blanquer
Jacob Riback
Benjamin Mairesse
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Final PresentationFinal Presentation
Modeling
Control
Implementation
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Objectives with the projectObjectives with the project
Stabilize in up-up and down-up
Swing-up
Peripheral movement
Safety net
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Description of the PendubotDescription of the Pendubot
One motor
Two links
Two encoders
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ModelingModeling
Lagrange method Energy based method:
{qi} is a set of parameters that entirely describes the system.
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State-Space FormState-Space Form
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Linearized equations:
Where the matrices A and B were computed using Maple as follows:
LinearizationLinearization
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Model validationModel validation
No satisfying friction model found.
Chaotic system. Model good enough for
control purpose.
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Control strategyControl strategy
Before implementation with LabView, the strategies were developed using Matlab & Simulink
Balancing controlSwing-up controlSafety netSwitched system
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Balancing controlBalancing control
LQ approach:Linearization + State-feedback
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Underactuated system: Partial feedback linearization
Feeding the system with the input:gives the new following set of equations:
Partial feedback linearizationPartial feedback linearization
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Global SchemeGlobal Scheme
An inner-loop to linearizeAn outer-loop to control
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Swing-upSwing-up
Partial feedback linearization to control the inner link PD-control tuned to handle the outer link
Suitable reference signals (static and dynamic)
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Safety netSafety net
Engage an emergency procedure when the system is unsafe
unsafe = supply voltage > 9.9 Volts (10 Volts Max)
Force the inner link to point downwards and catch it with a balancing controller
Switching areas - inner and outer links -
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Switched systemSwitched system
For peripheral movement
Multiple sectors needed
One controller per sector
Final control system is hybrid automata
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Crossing the uncontrollable stateCrossing the uncontrollable state
Go as close as possible to the uncontrollable state with a balancing controller
‘Jump’ using the partial feedback linearization
Catch the Pendubot with a new balancing controller
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ImplementationImplementation
Using LabView
100 Hz Sampling frequency
Program consists of three main building blocks
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Overall structureOverall structure
Flow chart
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Front PanelFront Panel
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ResultsResults
All the ordered functionality is implemented and working.
Documentation is handed for comments.
Software is ready for distribution.
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ConclusionsConclusions
The group had good knowledge entrance.
Feedback linearization is the key to success.
Friction is very hard to model.
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Conclusions cont.Conclusions cont.
Implementation is the large part. About 40% of the total time spent.
Large difference between having all parts of a program working and having a working program.
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QuestionsQuestions