MicroCART

1. MicroCART IRP Presentation Spring 2009 Andrew Erdman Chris Sande Taoran Li

2. MicroCART Overview • Autonomous Helicopter • Functional Requirements / IARC • 09-06 Semester Goals

3. MicroCart

4. Dec09-06 Goals • Obtain Simulink Model of X-Cell 60 Helicopter • Derive Dynamics of Flight • Model current PID controller for testing • Explore other control structure

5. General Functional Requirements • Precise mathematical model of system • Model should be able to assist in testing and designing controllers • Understandable by other MicroCART teams

6. Benefits • Estimation of the hovering equilibrium points • Finding parameters for stable hovering • Simulation of the helicopter’s behavior • Valuable testing tool

7. Model Obtainment • We require a Simulink model • Helicopter dynamics are extremely complex • To derive or not to derive? • Model from scratch requires meticulous measurement and testing of helicopter properties • No readily available X-Cell 60 Simulink model • Simulink models available for different types of Helicopters

8. Model Solution • Modify existing model for R-50 helicopter

9. Parameter Modification • Initial parameters for R-50 are incompatible with X-Cell 60 • Research parameters for X-Cell 60 • Scaling rules • Change parameters and update flight dynamics equations

10. Control Modification • Reverse engineer existing MicroCART control software • Insert existing MicroCART controller in Simulink model • Observe behavior • Advanced Controller?

11. Model With PID Controllers

12. PID Control

13. Results of Actions • PID controllers provide decent control of helicopter • Test systems • Hovering Stability • Waypoint Seeking • H∞ controller would be more robust

14. Model Outputs

15. Advanced Control Overview • Robust autonomous control for hovering requires advanced control methods • PID controllers are functional, yet not desirable • Linearization of acceleration equations yield the closed system at a hovering equilibrium point • Can use Taylor approximation for most elements • Thrust and drag equations require numerical analysis

16. Linearization • First need to derive the thrust and drag equations for the main rotor • TMR • QMR

17. Linearized Main Rotor Thrust and Drag Equations • TMR = 1080*(u_col+(m*g+26)/1080)-26; • QMR = -(0.0671*u_col+0.2463);

18. Linearization Methods • Use Taylor approximation to linearize accelerations • Lateral Acceleration • Vertical Acceleration • Angular Acceleration about x, y, z axes • Linearization of Euler Rate about x, y, z axes

19. Linearization Process • Derive non-linear state derivative equations • Substitute small angle approximations for the states • Cos(θ) ≈ 1 • Sin(θ) ≈ θ • Products of small signal values are assumed equal to zero

20. State Space Matricies

21. Full Model

22. Outputs

23. Schedule

24. Questions?