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Inverted Pendulum
Inverted Pendulum
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Thesis presentation on inverted pendulum

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Stabilization and balancing of Linear and Rotary Inverted Pendulum System.

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Thesis presentation on inverted pendulum

  1. 1. Stabilizing and balancing of Linear and Rotary Inverted Pendulum system. Presented by- Nowab Md. Aminul Haq Student ID. -1010130 Ashik-E-Rasul Student ID. 1010132 Department of Mechanical Engineering Bangladesh University of Engineering and Technology (BUET) 1 Supervised by- Dr. Md. Zahurul Haq Professor & Head. Department of Mechanical Engineering, BUET.
  2. 2. What is an Inverted Pendulum ? 2 A Pendulum that has its center of mass above its pivot point. • Inherently unstable. • Must be actively balanced in order to remain upright. • Must have a feedback system to keep it balanced. Criteria for Balancing • Moving the Pivot point . • Applying torque at the Pivot point. • Generating a net torque on the Pendulum. • Vertically Oscillating the Pivot point.
  3. 3. Real life Examples 3
  4. 4. Types of Inverted Pendulum 4 In general two types- 1. Linear Inverted Pendulum 2. Rotary Inverted Pendulum Moving the pivot point horizontally Applying a torque at the pivot point
  5. 5. Our Thesis Work 5 Inverted pendulum pivoted on cart Rotary Inverted pendulumSelf Balancing Vehicle prototype Linear Inverted Pendulum
  6. 6. Linear Inverted Pendulum 6
  7. 7. Methodology of work 7 Study of System dynamics Mathematical Modeling MATLAB Simulation PID Controller design in MATLAB Application of Controller in Experimental Setup.
  8. 8. System Dynamics and Mathematical Modeling 8 • 2D problem, where the pendulum is constrained to move in the vertical plane. • Control input is the force , F that moves the cart horizontally. • Outputs are the angular position of the pendulum and the horizontal position , of the cart . • Pendulum is vertically upright , when = pi System Transfer Functions
  9. 9. MATLAB Simulation of the System. 9 Time phi • No Feedback, No Controller. • The System goes without bound. • The pendulum falls down within seconds. Fig: System behavior without Feedback and Controller.
  10. 10. PID Controller Design 10 Angle Fig: Simulink Model of the system with PID controller and Feedback Fig: System block diagram with PID controller and Feedback PID Controller Proportional gain , KP Integral gain, KI Derivative gain, KD • Angular displacement is sent as a feedback. • Displacement can me measured by using Sensor( Potentiometer, Encoder , Gyroscope etc. )
  11. 11. PID Controller design in MATLAB 11 Initialization KP = 1,KI= 1,KD =1 Tuning KP between( 1-100) Tuning KD between( 1-20)
  12. 12. 12 PID Controller design in MATLAB Tuned Response, with KP=100, KI=1, KD=20
  13. 13. Application of Controller in Experimental Setup. 13 Res ult
  14. 14. Rotary Inverted Pendulum 14 Fig: ExperimentalFig: Rotary Inverted Pendulum
  15. 15. Mathematical Modeling 15 Equation of Motion Linearization State Space Model Open loop poles MATLAB Plot Fig: Mathematical modeling result
  16. 16. Pole Plotting on MATLAB 16 Fig: Open Loop Poles
  17. 17. Controller Design(Pole Placement Method) 17 Controll ability Desired Poles • ζ = 0.7. • ωn = 4 rad/s • |α| < 15 deg. • Gain Calculat ion • To move the poles to desired location Simulati on • Simulate The result To Model • Apply on the system 2 . . . ] ( ) [ n Ran T B k AB A B A B T n   3 430, 40p p   
  18. 18. Simulink Model 18
  19. 19. Simulation Result 19
  20. 20. Implementation on Model 20
  21. 21. Poles and Stability 21
  22. 22. Designing an optimal controller 22 Linear Quadratic Regulator(LQR) Cost Function Design Matrices • Design Matrices(Q and R) with trial and error • Control effort(Vm) is limited Gain • Calculate Controller Gain Using MATLAB Simulation • Done in Simulink To Model • Apply on the Model
  23. 23. Simulation Results 23
  24. 24. 24 Simulation Results
  25. 25. 25 Simulation Results
  26. 26. 26 Motor Voltage
  27. 27. 27 PendulumAngle
  28. 28. 28 ArmAngle
  29. 29. 29 Concluding Remarks • Experiment study of Linear Inverted Pendulum, considering both the Pendulum Angle and cart position. • Balancing can be studied with other modern controllers, ex. Fuzzy Controller, Neural Network etc. • A comperative study of different controllers can also be done, to analyze which controller provides the best Balancing.
  30. 30. Thank you!! 30

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