IRP Presentation Spring 2009 Andrew Erdman Chris Sande Taoran Li

 Autonomous Helicopter  Functional Requirements / IARC  Semester Goals

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

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

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

 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

 Modify existing model for R-50 helicopter

 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

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

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

 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

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

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

 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

 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