System Identification of Model Helicopter

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System Identification of Model Helicopter
Qingyun Li 2007.8.10
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Procedure of System Identification

• The choice of model structure depends on the end
  application of the model, the frequency range of
  applicability, and the associated key vehicle
  dynamic characteristics.
• The test input is one of the major factors
  influencing the accuracy of estimated parameters.
• Select the appropriated parameter estimation
  methods.
• Assess the predictive quality of the extracted
  model. If the result isnt satisfied with the
  requirement, redo the above procedure.

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Structure of dynamic model

• There are many theories to explain the helicopter
  dynamics model, for example, the computational
  fluid dynamics (CFD). They can accurately
  simulate the behavior of the helicopter in some
  fields, but are too complex to act as the
  control model.
• We devise the model structure using the
  simplified analytic expressions for the forces
  and moments, which the aerodynamic expressions
  are based on 2-D analysis, is appropriate for low
  bandwidth control.

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Assumption

• The helicopter is strict bilateral symmetry and
  the center of mass locates at the main shaft.
• The sensor MTi location in the body frame is
• The speed of the main rotor is kept as a constant
  .
• Ignore the air resistance when the helicopter
  hovering.

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Model Helicopter
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• are the servos
  inputs PWM signals
• are the collective pitch
  control, lateral cyclic control and longitudinal
  cyclic control of the swashplate, respectively.
  is the pitch control of the
  tail rotor.

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General rotor flapping motion

• The top view of the rotor disc (the tip-path
  plane) is shown.
• is the longitudinal disc tilt
• is the lateral disc tilt.

• Tilting the swashplate gives rise to a
  one-per-rev sinusoidal variation in blade pitch.
• is the blade azimuth angle, where
  is the main rotor speed.

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• The first-harmonic approximation of the rotor
  flapping motion in the quasi-steady-state form
  is
• Where is the rotor coning.

• Note the tip-path plane approximation for a
  two-bladed rotor is generally valid for only low
  frequency excitation.

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Thus, the flybar flapping angle is and,

• A simple model may be obtained by simply setting
• in the low frequency region.
  The result is

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Force and moment generated by main rotor

• The structure of the model helicopters
  cyclic/collective control system.

The main blade pitching angle is
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Force and moment generated by main rotor
Where,
is the collective pitch,
is the cyclic angle of the rotor blades
The average rotor thrust is controlled by the
collective pitch .

• The expression for main rotor thrust near hover
  is obtained using the blade element theory

.
.
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Force and moment generated by main rotor
The cyclic pitch of the main rotor blades
creates different amounts of lift in
different regions
.
These differing amounts of thrust create pitch
and roll
moments on the helicopter.
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Force and moment generated by main rotor

• The average moment created by the two main rotor
  blades around a revolution can be expressed as
  follows

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Force generated by tail rotor

• There is no cyclic input for the tail rotor
  blades, only a collective pitch angle .
  The thrust generated by the tail rotor is found
  in a similar manner to the thrust of the main
  rotor
• And, ignore the opposing torque of the tail
  rotor.
• In addition, there is a electronic gyro used on
  the tail rotor to stabilize the yaw axes, as the
  following figure shown.

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Force generated by tail rotor

• Because the model of the gyro is sophisticated
  and unknown, only a simple damping term is used
  here
• So, the expression for tail rotor thrust is

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Rigid body dynamics
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From the sensor--MTi, we can get the acceleration
of the point S. Note the sensor measures all
accelerations, including the acceleration due to
gravity-- , i.e., the absolute
acceleration of point S is

• Newton-Euler equations for the rigid body motion
  are

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• To sum up the above arguments, the attitude
  dynamic system is described in state space as

where cant be measured.
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Or, substitute the PWM signals into model (1) ,
the whole model of the attitude dynamic system
can be expressed as follows
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Parameter estimation
the fourth-order Runge-Kutta method is used to
get the solution of state equation.
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Acoocding the dynamics equations, we get
following model(because of the GPS absent)
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The augmented state vector is then defined as
The extended system is represented as


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The standard UKF algorithm can be summarized as
follows
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Simulation

• Here I use the UKF joint filter test our model
• First Generate states, input and observation
  data from the model
• Second Use the observation data to estimate the
  parameters and states.
• From the figures, we know that most parameters
  can be estimated to the original value well, but
  some one not.
• I think it is caused be the state 7 state 8,
  because they can not be observed, also estimated
  as the parameters. So the parameters can not be
  estimated clearly.

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Parameters0-10
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Parameters10-20
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Parameters20-30
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Experiment

• First we check the data, to find out which part
  is better for our experiment, and get 2 parts ,
  the input and IMU data is as follow.
• Here I only show you the first part, the second
  part you can find in my report

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States estimation
Parameters(1-10) estimation
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Parameters(11-20) estimation
Parameters(21-30) estimation
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Problems future work

• The algorithm is valid in simulation for most
  parameters.but some paratmers producted with the
  states7,8. I will find out some method to solve
  it..
• For the experiment. The estimation Euler-angle
  has big error with the real. May be the error is
  bigger than what is shown on the companys manual.

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