1. Roberto - Balancing Robot RIT Computer Engineering Senior Design Project

2. Group Members Jeff Mahmood Paul Krausman Dave Froman

3. Project Description Two-wheel balancing robot – Balances on any angled surface – Remains balances indefinitely Remote controlled “Inverted Pendulum” PID Controller

4. Physical Layout

5. PID Algorithm Means to control some output from a combination of different factors Differential equations solved in the frequency domain We will solve experimentally

6. PID Algorithm (cont.) PID is “Proportional Integral Derivative” Output based on the aggravate of 3 factors – Error – Error Derivative – Error Integral PID algorithm combines these 3 factors to determine appropriate output

7. Error Definition Error: Difference between set point and actual Error can be positive or negative Error Set Point Actual

8. PID Equation Proportional Integral Derivative Output = P*Θ + I*Θ + D*Θ’ – P is the Proportional constant Current error – I is Integral constant Sum of past errors – D is Derivative constant Rate of change of error

9. Proportional Torque applied to motors is proportional to amount of error Θ 0°0° 40°

10. Integral Sum of all errors over time Biases output so all errors cancel over time

11. Derivative Torque applied to motors proportional to derivative of error Velocity of error 0°0° 300°/sec

12. Tuning PID Controllers Goal: – Find coefficients for P, I, and D terms – Robot should “snap” back to set point after any disturbances – Prevent any oscillations – Robot should remain at set point indefinitely

13. Finding P Term Set I and D terms to 0 Set P term to 1 Increase P term until strong oscillations occur Some references recommend setting P to 60% of this value

14. Finding D Term Slowly increase D until oscillations begin to slow Fine-tune D – Robot will oscillate if D is too high – Robot will fall over is D is too low – Robot should “snap” back to set point after any disturbances

15. Finding I Term More difficult than P and D Generally inverse of D Limit sum to prevent saturation Sliding window

16. Increase Performance Robot may seem sluggish – If either P or D is set too low, robot will be slow to respond Robot may oscillate – If either P or D is set too high, robot will oscillate before settling on set point Tweak P and D terms until optimal performance is achieved

17. Sensors Accelerometer – Measures tilt (proportional error) – Slow response, but accurate – Gives sense of “up” Gyro – Measures velocity (derivative error) – Fast response, but inaccurate – Suffers from drift over time

18. User Interface - Remote Control Two axis control – left and right motors 2 commands for each side – move forward, back Uses 4 bit encoding/decoding(8 values used) Each switch press has unique encode value, which is transmitted and received

19. Remote Control Momentary rocker switches are used for intuitive remote controlled car feel Robot moves by pressing both switches in the same direction, turns by alternating directions

20. The End Questions???