NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER
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NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER L. Mederreg, F. Diaz and N. K. M’sirdi LRV Laboratoire de Robotique de Versailles, Université de Versailles Saint Quentin en Yvelines, 10, avenue de l’Europe 78140, Vélizy, France.
description
NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER L. Mederreg, F. Diaz and N. K. M’sirdi LRV Laboratoire de Robotique de Versailles, Université de Versailles Saint Quentin en Yvelines, 10, avenue de l’Europe 78140, Vélizy, France. 1. Introduction. - PowerPoint PPT Presentation
Transcript of NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER
NONLINEAR BACKSTEPPING CONTROL WITH OBSERVER DESIGN FOR A 4 ROTORS HELICOPTER
L. Mederreg, F. Diaz and N. K. M’sirdiLRV
Laboratoire de Robotique de Versailles,Université de Versailles Saint Quentin en Yvelines,
10, avenue de l’Europe 78140, Vélizy, France.
11 Introduction.Introduction.
22 4 rotors Helicopter model Presentation4 rotors Helicopter model Presentation
33 Back stepping controller synthesisBack stepping controller synthesis
44 Back stepping controller synthesis with observerBack stepping controller synthesis with observer
55 Simulation and resultsSimulation and results
66 Conclusion.Conclusion.
OUTLINEOUTLINE
Introduction
• Thanks to its special configuration, the 4 rotor helicopter allows to achieve many tasks in different fields.
Symmetry of the platform geometry Low weightLow cost
•Autonomous flight Non linear control law Synthesis.
Complexity of the dynamical system Presence of Perturbations due to the wind Unavailability of some state variables
4 rotors Helicopter model Presentation
0 0 0( , , )Tu v w Absolute velocities / Earth frame
( , , )T Orientation angels: Yaw, Roll, Pitch.
State vector:
0 0 0 0 0 0( , , , , , , , , , , , )Tx x y z u v w p q r
Gravity center coordinates0 0 0( , , )Tx y z
( , , )Tp q r Angular velocities / Helicopter frame
( , , )Tx y zA A A Aero dynamical forces
( , , )Tp q zA A A Aero dynamical Momentums
0
0
0
0
0
x
y
z
x u
w
p
q
r
The state representation is given by:0
0
0
1
2
3
4
sin sec cos sec
cos sin
sin tan cos tan
1( )(cos cos sin sin sin )
1( )(cos sin sin cos sin )
( ) 1( )( , , )
( )
( )
( ) 1
y z
x x
z x
y y
x y
y y
u
v
w
q r
q r
p q r
m
mF x
gm
u
qr I I du
I I
pr I I du
I I
qp I Iu
I I
( )x F x
2
( )
12
dE y y
V E
System of 4 equations 4 unknowns
0i j i j i j i j ja u bu c u d u h , :1 4i j
System outputs: 0 0 0
( , , , )y x y z
Desired outputs: ( , , , )d d d dy x y z
Control laws: 1 2 3 4( , , , )u u u u u
Back stepping controller synthesis
We consider that all the state vector is measurable
SIMULINK bloc diagram of the controller
2
( )
12
dE y y
V E
• We include in the expression of V the observing errors to be cancelled
Back stepping controller synthesis with observer
• We shall observe the absolute velocity vector
0 0 0ˆ ˆ ˆ( , , )Tu v w : Difficult to measure
• We consider that all the other parameters are measurable
Where V is a LYAPUNOV candidate function
System 4 equations 4 unknowns
Convergence of the tracking errors
Convergence of observing errors
Simulation and results
Simulation of a vertical helix trajectory flight in presence of perturbations (7 newton front wind blowing)
The controller gains are adjusted by doing intensive simulations
cos( )
sin( )2
10
3
d
d
d
d
x t
ty
tz
Tracking Trajectory : Initiales positions:
0
0
0
0
0
0
0
x
y
z
3D Tracking trajectory
Tracking errors for the BACKSTEPPING controller
Observation Errors for the BACKSTEPPING Observer
Tracking Errors for the BACKSTEPPING controller with Observer
Conclusion :
This approach has shown :
Good robustness of the Controller
Good convergence of the couple controller observer
allows to decrease the number of the required sensors
