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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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posted:3/30/2013
language:English
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