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Fuzzy Logic Control of Coupled Dynamic Systems

Fuzzy Logic Control of Coupled Dynamic Systems. Project # 3 Andrew Janson Nicklas Stockton FM: Dr. Kelly Cohen. Motivation. Structural dynamics problems can be represented by second-order dynamic systems Damp oscillations in flexible body structures

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Fuzzy Logic Control of Coupled Dynamic Systems

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  1. Fuzzy Logic Control of Coupled Dynamic Systems Project # 3 Andrew Janson Nicklas Stockton FM: Dr. Kelly Cohen

  2. Motivation • Structural dynamics problems can be represented by second-order dynamic systems • Damp oscillations in flexible body structures • Fuzzy systems exhibit marked robustness in the case of uncertain conditions

  3. Why Fuzzy? Sensing Action Universal Mapping • Fuzzy Logic • Linguistic Reasoning • Simple • Robust Universal Mapping

  4. Objectives • Develop simulation of dynamic structure model • Analyze proposed control solutions • Develop an effective non-linear active structural control methodology • Demonstrate robustness of fuzzy systems

  5. Problem Formulation (1 of 5) Two mass, spring connected system traversing distance L

  6. Problem Formulation (2 of 5) • Inputs: • Car 1 distance traveled • Car 2 distance traveled • Car 1 velocity • Car 2 velocity • Output: • Force on car 2 Input: Output:

  7. Problem Formulation (3 of 5) • Initial Conditions: • Final Conditions:

  8. Problem Formulation (4 of 5) • Equations of motion:

  9. Problem Formulation (5 of 5) • Cost Function: (Minimize J) • Goals: • Minimize settling time • Get as close to wall as possible

  10. Theoretical Limits • Travel 100m, 3 kg system, 1 N force • Max acceleration = 1/3 m/s2 • Best time (without slowing) ~ 24s • Best time (with slowing) ~32s

  11. Previous Solution Comparison • C • = 42.000s • = 99.965200m • J = 0.32797 • A • = 32.550s • = 99.998766m • J = 0.32797 • B • = 32.366s • = 99.984220m • J = 0.35522 Controller Time History Force (N) Time (s)

  12. Fuzzy Rules

  13. Linear Controller (1 of 2)

  14. Linear Controller (2 of 2) • Janson/Stockton • = 32.269s • = 99.9983m • J = 0.32590

  15. Fuzzy Results • = 32.303s • = 99.999821m • J = 0.32339

  16. Robustness Test • Measure the systems’ ability to adapt to changes in the environment • Vary value of spring constant “K” by 40% • Measure percent change of cost from nominal and compare to that of linear

  17. Robustness Test Results

  18. Lessons Learned • Professional Growth • Critical Thinking • Research Experience

  19. Questions?

  20. References • http://flysonthewater.com/sites/default/files/Bunny.jpg • http://gust.engin.umich.edu/research/hale_gust.html • http://www.gis.ba/en/applications-of-fuzzy-logic-in-geographic-information-systems-for-multiple-criteria-decision-making/ • http://www.lpa.co.uk/fln_det.htm • http://www.gnurf.net/v3/clip-art/free-clip-art-vintage-race-car-041.html • http://www.clker.com/cliparts/z/7/8/1/U/P/satellite-dish-hi.png • http://us.123rf.com/400wm/400/400/3drenderings/3drenderings1203/3drenderings120303403/12958784-3d-render-of-cartoon-character-with-robotic-arm.jpg

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