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

2.  Autonomous Helicopter  Functional Requirements / IARC  09-06 Semester Goals

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

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

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

7.  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.  Modify existing model for R-50 helicopter

9.  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.  Reverse engineer existing MicroCART control software  Insert existing MicroCART controller in Simulink model  Observe behavior  Advanced Controller?

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

15.  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.  First need to derive the thrust and drag equations for the main rotor  TMR  QMR

17.  TMR = 1080*(u_col+(m*g+26)/1080)-26;  QMR = -(0.0671*u_col+0.2463);

18.  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.  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