# Creation of dynamic model of system of stable flight control in by malj

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```									        CREATION OF DYNAMIC MODEL OF SYSTEM OF STABLE FLIGHT
CONTROL IN PLANES WITH THE AUTOPILOT

1,3
Azerbaijan Technical University, 2Azerbaijan National Aviation Academy, Baku, Azerbaijan
1
prfqurbanov@mail.ru, 3vusala0@gmail.com

The carried out researches show that occurrence of mechanical fluctuations in a
fuselage at change of speed is one of lacks arising during performance of tasks of flight in
planes with the autopilot. The first harmonic is the most operating from these mechanical
fluctuations, the frequency of this harmonics is rather small and the amplitude is big. For the
purpose of elimination of this problem in planes with the autopilot has been used the stabilising
gyrocompass and has been created the automatic control system of planes with stabilising
gyrocompass. The block diagramme of such control system is shown in figure 1.
Transfer functions of links of the block diagramme are resulted as following.
Taking into consideration the first harmonic of mechanical fluctuations arising during
flight transfer function of the plane can be written down in the following form:
k b Tc p  1

k1
Wt ( p)                                    

p T p  2Tp  1
2       2
       p  12
2

Part of the block diagramme in the figure 1, concerning to this transfer function is
shaded. The transfer function of the steering machine is:
k sm
Wsm ( p)                         ,
T p  2 smTsm p  1
2
sm
2

The transfer function of gyroscope which is dempfering mechanical fluctuations arising
in a fuselage:
kdg
Wst . g ( p)                                   ,
Tdg p 2  2 dgTdg p  1
2

Transfer function of a gyroscope defining a course is:
U cg ( p)
Wcg ( p)  ~         kcg
  p
Transfer functions of the correcting devices:
           U c1 ( p) T1 p  1
Wc1 ( p)  U  p   T p  1
             dg        2

W ( s)  U c 2 ( p)  T3 p  1
 c2
           U cg  p  T4 p  1
Transfer functions of the intensifying device:
U g ( p)
Wg ( p)                       kg
Ue  p
For formation of the closed system is used the following equation:
U e ( p)  U t ( p)  U c1 ( p)  U c 2 ( p)
Converter:
kc             k
Wc ( p)                            c
(Tc p  1)(TIPMS p  1) 1  p

1
1
Where:   Tc  TIPMS , Tc                         , f –is frequency , m-number of phases.
mf
Transfer functions rather opposition moment is:
n( p )     km 1  T1 p 
Wom ( p)             
M  p  TmT1 p 2  Tm p  1
Transfer functions of the rectifier:
U d ( p)
Wrect ( p)                    krect
U gyrosc  p 
Transfer functions of the operational amplifier:
U G ( p)
WOA ( p)                kamp
Uв  p
Transfer functions of the rheostat:
U r ( p)
Wrheostat ( p)               krheos
x p 
Transfer functions of the reducer and the hydraulic device are:
Wred ( p)  kred
Wh.d ( p)  kh.d
In the figure 1 is shown the scheme of automatic control of the plane with the autopilot.
Using transfer functions of links it is possible to write down the general transfer function
concerning the simplified block diagramme.
To receive the general transfer function we must accept some simplifications:

Wt   2
1       k1


p 2  12  k1 p     
p p  12          p p 2  12                
WhdWredWTC                 khd  kred  kc
W0                            
1  WhdWredWTCWrheos 1  p  khd  kred  kc  krheos
1
W1  Wcon1Wstab.devWplane
s
W plane
W1          
1  W1


                                                             
p TmT1 p 2  Tm p  1 kb Tc p  1 p 2  12  k1 p T 2 p 2  2Tp  1      
                                          
p 2 TmT1 p 2  Tm p  1 T 2 p 2  2Tp  1 p 2  12  kcon1            k 1  T p k T p  1 p     k pT
m   1

b       c
2   2
1   1
2

p 2  2Tp  1
1    
W2  WsmWcon2W0Wrect                W1
Wsg
W1                                          W1
W2            
1  W2 1                    kcon2  krect  k sm  khd  kred  kc
 W1
                                    
k sg Tsm p  2 smTsm p  1 1  p  khd  kred  kc  krheos 
2  2

kamp  k sm
W3  WampWsmW2                                                 W2
T p  2 smTsm p  1
2
sm
2

2
W3
W4                                               
1  W3Wcon2Wsg  Wcon1Wst . gW plane 

W3

1                  
             
 k sg T3 p  1 kdg T1 p  1 p 2  12  k1 p kdg T1 p  1 
W3

 T p  1
       4                  
p p 2  12 Tdg p 2  2 dgTdg p  1 T2 p  1 
2
                                      
k  k 1  T1 p 
Wgeneral  W4Wcon1Wst .m  con1 2 m              W4                                 (1)
TmT1 p  Tm p  1
The equation (1) expresses dynamic model of a control system of flight providing
stability and compensating mechanical fluctuations arising during flight of the plane with the
autopilot.

Stabilizing gyroscope                                                                                                                      W4
uc1
Wk1(p) udg        Wst.g(p)       
           Wplane(p)

W2
W1
ue                                        ug           U3             Wp                                              1                   g                   Ucon1

b                                                                          Wcon1(p)
ut                    Wamp(p)           Wsm(p)                                                        Wplane(p)                        +
s
0
k1                  
g                                                        exit
Uc2             W3                                                                               s 2  12                                                           Wst.dev(p)
Wst.mach(p)
1                Wcon1(p)       Wst.device(p)
Wc2(p)
s
1/Wsg(p)
Ucon2
usg
Wcon2(p)
W(p)
Wsg(p)
x3               x2                x1                UOA         Urectifier
Whm(p)            Wred(            W(p)          
p)
Wrheos(p)       Urheostat
W0

Fig. 1. The general block -diagramme of simplified dynamic model of a plane with the autopilot

References
1. N.N.Popov, O.E.Nosco, D.N.Popov. Pilotless flying machines. Taganroq,
(1999).
2. R.A.Mur. Prospects of development of pilotless flying machines//The space
technics, №2 , February (1990).
3. Global hawk vanguard of unmanned aerial reconnaissance//Global Defence
Review, London (1998).
4. 1993 Airborne reconnaissance a vision for the 21st century//Global Defence
Review, London (1998).

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