IRP Presentation
Spring 2009
Andrew Erdman
Chris Sande
Taoran Li
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Autonomous Helicopter
Functional Requirements / IARC
09-06 Semester Goals
Obtain Simulink Model of X-Cell 60 Helicopter
 Derive Dynamics of Flight
 Model current PID controller for testing
 Explore other control structure
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Precise mathematical model of system
Model should be able to assist in testing and
designing controllers
Understandable by other MicroCART teams
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Estimation of the hovering equilibrium points
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Finding parameters for stable hovering
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Simulation of the helicopter’s behavior
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Valuable testing tool
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We require a Simulink model
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Helicopter dynamics are extremely complex
 To derive or not to derive?
 Model from scratch requires meticulous measurement
and testing of helicopter properties
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No readily available X-Cell 60 Simulink model
 Simulink models available for different types of
Helicopters
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Modify existing model for R-50 helicopter
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Initial parameters for R-50 are incompatible
with X-Cell 60
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Research parameters for X-Cell 60
Scaling rules
Change parameters and update flight dynamics
equations
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Reverse engineer existing MicroCART control
software
Insert existing MicroCART controller in
Simulink model
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Observe behavior
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Advanced Controller?
T_MR
T_MR
T_TR
T_TR
V
V
Tau
Tau
w
w
Beta_1s
Beta_1s
Beta_1c
Beta_1c
Position
u
F
Theta
Flapping and Thrust
Helicopter_translation
F
Helicopter_rotation
Theta
Forces and Torques
VR system
RBM
Flapping
V_sensor
V
V
Accelerometer
w_sensor
u
w
w
Translatory velocities
Gyro
Rotary velocities
Theta
Attitude
Control
Input
6
Pitch
1
Feedback
Feedback
out
X
Setpoint
out
Setpoint
X PID
Pitch PID
5
Roll
2
Feedback
Feedback
out
Y
Setpoint
out
Setpoint
Y PID
Roll PID
1
Servos
3
Feedback
out
Z
Setpoint
Z PID
4
Feedback
out
Yaw
Setpoint
X PID5
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PID controllers provide decent control of
helicopter
Test systems
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Hovering Stability
Waypoint Seeking
H∞ controller would be more robust
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Robust autonomous control for hovering
requires advanced control methods
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PID controllers are functional, yet not desirable
Linearization of acceleration equations yield
the closed system at a hovering equilibrium
point
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Can use Taylor approximation for most elements
Thrust and drag equations require numerical
analysis
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First need to derive the thrust and drag
equations for the main rotor
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TMR
QMR
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TMR = 1080*(u_col+(m*g+26)/1080)-26;
QMR = -(0.0671*u_col+0.2463);
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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
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Derive non-linear state derivative equations
Substitute small angle approximations for the
states
Cos(θ) ≈ 1
 Sin(θ) ≈ θ
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Products of small signal values are assumed
equal to zero