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MicroCART. IRP Presentation Spring 2009 Andrew Erdman Chris Sande Taoran Li. MicroCART Overview. Autonomous Helicopter Functional Requirements / IARC 09-06 Semester Goals. MicroCart. Dec09-06 Goals. Obtain Simulink Model of X-Cell 60 Helicopter Derive Dynamics of Flight

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Microcart

MicroCART

IRP Presentation

Spring 2009

Andrew Erdman

Chris Sande

Taoran Li


Microcart overview

MicroCART Overview

  • Autonomous Helicopter

  • Functional Requirements / IARC

  • 09-06 Semester Goals


Microcart1

MicroCart


Dec09 06 goals

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


General functional requirements

General Functional Requirements

  • Precise mathematical model of system

  • Model should be able to assist in testing and designing controllers

  • Understandable by other MicroCART teams


Benefits

Benefits

  • Estimation of the hovering equilibrium points

  • Finding parameters for stable hovering

  • Simulation of the helicopter’s behavior

  • Valuable testing tool


Model obtainment

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


Model solution

Model Solution

  • Modify existing model for R-50 helicopter


Parameter modification

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


Control modification

Control Modification

  • Reverse engineer existing MicroCART control software

  • Insert existing MicroCART controller in Simulink model

  • Observe behavior

  • Advanced Controller?


  • Model with pid controllers

    Model With PID Controllers


    Pid control

    PID Control


    Results of actions

    Results of Actions

    • PID controllers provide decent control of helicopter

    • Test systems

      • Hovering Stability

      • Waypoint Seeking

    • H∞ controller would be more robust


    Model outputs

    Model Outputs


    Advanced control overview

    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


    Linearization

    Linearization

    • First need to derive the thrust and drag equations for the main rotor

      • TMR

      • QMR


    Linearized main rotor thrust and drag equations

    Linearized Main Rotor Thrust and Drag Equations

    • TMR = 1080*(u_col+(m*g+26)/1080)-26;

    • QMR = -(0.0671*u_col+0.2463);


    Linearization methods

    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


    Linearization process

    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


    State space matricies

    State Space Matricies


    Full model

    Full Model


    Outputs

    Outputs


    Schedule

    Schedule


    Questions

    Questions?


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