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The Floating Dutchmen: Three Dimensional Arm Driven Pendulum

Explore the development of a control system for balancing a 3D arm-driven pendulum, including objectives, design specifications, modeling, validation, and optimization process.

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The Floating Dutchmen: Three Dimensional Arm Driven Pendulum

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  1. The Floating Dutchmen:Three Dimensional Arm Driven Pendulum Teresa Bernardi Brian Lewis Matthew Rosmarin Control System Design May 3, 2006

  2. Presentation Overview • Introduction • Objectives • Design Specification • Design Approach • Results • Assessment of Accomplishments • Conclusion

  3. Introduction • Inverted pendulum • Classic control problem • Inherently unstable • Motivation • Challenge of 3D balancing • Similar to RPI Mechatronics spherical inverted pendulum

  4. Objectives • Balance 2D pendulum • Lower configuration • Upper configuration • Balance 3D pendulum • Implement swing up

  5. Design Specifications • Ability to balance • Accommodation of disturbances • Non-zero initial angle • Arm inertia variation • Impulse perturbation

  6. Design Approach • Modeling • Model Validation • Control Design • Control Optimization

  7. Modeling • MATLAB SimMechanics model • 2D system • 3D system • SolidWorks model • 2D equations of motion

  8. Model Validation • Compare state-space matrices • 2D equations of motion • 2D MATLAB model • Compare natural frequencies • Parameter identification • 2D MATLAB model

  9. Control Design • Input system parameters into MATLAB • Arm lengths • End weight • Generate K-matrix using LQR()

  10. Control Optimization • Fine-tune overall system gain • Insert window of control • Adjust proportional gains • Position • Velocity • Zero system

  11. Results • Balancing angle limits • Actuating Arm: ±50° • Balancing Arm: ±50° • Swing up balancing angle limits • Actuating Arm: ±30° • Balancing Arm: ±30°

  12. Initial 2D Balancing in Lower Configuration

  13. Balancing in 2D with Pan Axis in Upper Configuration

  14. Balancing in 2D with Tilt Axis in Upper Configuration

  15. Testing Robustness

  16. Swing Up with No End Weight

  17. Swing Up with End Weight

  18. Assessment of Accomplishments • 2D balancing • Lower configuration • Upper configuration • Swing up

  19. Conclusions • Significant vibration introduced • Backlash • Play • 3D balancing possible • More rigid structure • Direct drive • Redesign actuator stage

  20. Questions?

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