Scaled Helicopter Mathematical Scaled Helicopter Mathematical Model and Hovering ControllerModel and Hovering Controller
Brajtman Michal & Sharabani Yaki
Supervisor : Dr. Rotstein Hector
Project GoalsProject Goals
Simulation using Matlab’s Simulink
Studying the small scale helicopter’s dynamicsModeling the system
Regulator implementation
Studying the small scale Studying the small scale helicopter’s dynamics. helicopter’s dynamics.
A universal model is hard to develop
The dynamics of different types ofhelicopters differ
Options for modeling the systemOptions for modeling the system
Downscaling from full size helicopters
Identification by measurements
Decoupling
Helicopter’s ComponentsHelicopter’s Components
Yaw, Pitch and Roll Yaw, Pitch and Roll
Symmetrical AirfoilSymmetrical Airfoil
Coning & Flapping Coning & Flapping
Main Rotor ControlMain Rotor Control
Axes SystemsAxes Systems
Dynamics equations Dynamics equations
cos/)cossin(
sincos
tancostansin
)(
)()(
)(
coscos
cossin
sin
22
rq
rq
rqp
NNqrpqpr
MMrpprq
LLpqqrrp
TZgqupvwm
TYgrupwvm
TXgvrwqum
TAxzxxyyxzxx
TAxzzzxxyy
TAxzyyzzxzxx
Z
Y
X
Mathematical modelMathematical model
Simulink implementationSimulink implementation
12
wb3
11
wb2
10
wb1
9
psy
8
theta
7
phi
6
dz
5
dy
4
dx
3
z
2
y
1
x
s +27.7s+57602
442000
Transfer Fcn
hover_model
S-Function
1973.3
Gain1
-0.178
Gain
f(u)
Fcn3
f(u)
Fcn2
f(u)
Fcn1
f(u)
Fcn
Demux
4
del_psy
3
del_theta
2
del_phi
1
del_o
beta_max
phi
theta
wb1
wb1
wb2
wb2
wb3
wb3
Mpsy
Tt
Mthata
Mphi
Tow_m
T
Results – open loop Results – open loop
Closed loop systemClosed loop system
[Xtrim;0;0] trin condition
K
state space
del_o
del_phi
del_theta
del_psy
x
y
z
dx
dy
dz
phi
theta
psy
wb1
wb2
wb3
l inear model
Step
Scope
Demux
0
0
Closed loop – after tuning Closed loop – after tuning
ConclusionsConclusions
The system and the controller (linear & nonlinear) were verified
A mathematical model was constructed
A full state feedback LQ controller was designed
THE ENDTHE END
