# Mid-term presentation

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```					Midterm review

2E1242 – Automatic Control
Helicopter Project
Introduction

The Helicopter team:

   David Höök
   Pontus Olsson
   Henric Jöngren
   Vivek Sharma
   Ksenija Orlovskaya
Resources
   Helicopter with two degrees of freedom (Humusoft)
   Input voltage to two DC motors driving the main and tail propellers (MIMO-
system)
   Output horisontal and vertical angles
   Labview (communicating with process)
   Matlab (simulation, model validation)
Main objective

   The helicopter is supposed to:
 Follow a prespecified trajectory that illustrates its performance limitations.
 Attenuate external disturbances
Modelling

Subsystems
 Main motor and vertical movement

 Tail motor and horisontal movement

 Two systems corresponding to the cross coupling between the
movements
Mathematical modelling of the helicopter

Tupp
Subsystem #1
Vertical angle
Main motor and vertical movement
1

Tresulting TuppTmg T f TgyroTtail
Tgyro             Ttail
   Order of transfer function                                            T
f   Tf
   Matlab identification toolbox ==>                         Tmg
g11 and g12
Mathematical modelling of the helicopter

Tmain
Tgyro
Subsystem #2

Tail motor and horisontal movement
Horisontal angle
Thorizontal
Tresulting  Thorisontal  T f  Tgyro  Tmain                           2

   Order of transfer function
   Matlab identification toolbox ==>
g22 and g21                                                               Tf
Step response, real and simulated system
Transfer function matrix

  vertical   g 11 ( s ) g 12 ( s )  umain 

            
 
       
 utail 
 horisontal   g 21 ( s ) g 22 ( s )        
            
G(s)
   Decoupling: minimizing effect of g12 and g21 in system
Step response, model

0.015

0.01

0.005                                                    um
ut

0
0   10   20   30   40   50   60   70   80   90         100

20

15

10
fi1
5
fi2

0
0   10   20   30   40   50   60   70   80   90         100
Decoupling, approach 1

A simpler method to reduce the cross coupling,

   Neglect influence from tail motor in elevation.

   Find required u to tail motor to compensate torque from main propeller at
different main rotor velocities.

   Efficient in the static case, has to be enhanced to also reduce cross coupling
when accelerating/decelerating main propeller because of the extra torque from
rotational intertia.
U2(u1)

u2  reg vertical ( 2 ,  2 )  f (u1 , u1 )
               
Decoupling matrix, approach 2

 w11 ( s)   w     ( s) 
W ( s) 

12      
 w21 (s)    w  22
( s) 

w11  w22  1
w12   g12 / g11
w12   g 21 / g 22
Decoupling, new system - decoupled

Gny (s)     g ( s)
 11
 g ( s)
 21
g
g
12

22
( s)   w11 ( s)
.
( s)   w21 ( s)

w
12

w
22
( s)   g11 ( s)

( s)   0
 
0     

g 22 (s) 


•The cross coupling has been eliminated
•Strange behaviour of outsignals
Future work

   Enhance model
 Model corresponding to actual process
 Use model for control deriving

   Design optimal controllers for different regions
 transfer functions for different angle segments
 Find smooth transition between the segments

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