Flight Reliability of Multi Rotor UAV Based on Genetic Algorithm

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DOI:_{10.12928/TELKOMNIKA.v14i2A.4354} ₂₃₁

Flight Reliability of Multi Rotor UAV Based on Genetic

Algorithm

Huang Ronghui*, Li Xun, Zhang Xin, Pei Huikun Shenzhen Power Supply Co., Ltd., Shenzhen 518048, China

*Corresponding author, e-mail: [email protected]

Abstract

The UAV system has been widely applied in various military and civil fields. This technology mainly is applied to radar positioning, wild fire management, agricultural monitoring, environmental monitoring, aerial photography and search and rescue mission. It conducts real-time monitoring and control on the inclination angle, inclination angle speed and accelerated speed of inclination angle based on the flight attitude control of the multi rotor UVA. Secondly, it controls the swing deflection of rotor, motor speed, inclination angle control and speed based on the optimal solution ability to overall search of the genetic algorithm to achieve the real time optimization of parameters. Then, it establishes the servo unit with direct torque current which will be combined with the sliding mode controller to reconfigure the sliding mode variable structure controller with direct torque to carry out control on the motor balance in advance. The experiment results show that the servo unit with direct torque current together with genetic algorithm realizes the error correction of the hovering rotor of UVA; during the dynamic control of the UAV fight, the gyroscope is sensitive to the change of the aerial carrier attitude and then the correction to the drift of gyroscope can be realized to provide stable reliability control for the whole UAV flight.

Keywords: UAV; Flight reliability; Genetic algorithm; Motor speed; Angle; Controller

1. Introduction

UAV is the abbreviation of Unmanned Aerial Vehicle also known as “UAV” which is a new blood of modern aircrafts [1]. In recent years, with the technological progress, the performance of UAV has been substantially improved and various new types of UAV with high speed, small size and high duration of flight emerge in endlessly and the application scope of UAV has been continuously extended. In the military field [2-4], the UAV can be used as training target drone aircraft for such purposes as military reconnaissance, disturbance induction and bomb dropping; in civil field, the UAV can carry out aerial photography, surveying and mapping and environmental monitoring, As the UAV has such advantages as low cost and easy-maintenance, focus on it becomes increasingly higher. The selection of a stable control scheme is of vital importance to UAV. Only when the stable control scheme I is determined, can the mechanical analysis and modeling be carried out. However, the mathematical modeling is the basis of the controller design [5]. Accurate mathematical model can provide convenience for the system design and analysis. The reliability testing refers to a series of test behavior based on the software for the detection of whether the software reaches the specified reliability requirement under the simulation environment simulating the real environment [6]. For the multi rotor flight controller with excellent performance, its attitude during the flight process must be relatively stable with less vibration. Meanwhile, when there is external disturbance, the multi rotor will generate strong resistance to counteract the disturbance; when the disturbance disappears, the resistance will rapidly disappear without causing incorrect resistance. This text designs a kind of multi rotor UAV with balancing reliability control based on genetic algorithm.

2. Flight Control of Multi Rotor UAV Based on Genetic Algorithm 2.1. Modeling of UAV Flight Condition

The balancing control of the multi rotor UAV requires the real-time collection of the information of inclination angle, inclination angle speed and accelerated speed of inclination angle. Therefore, different sensors are required to carry out the real-time measurement [7, 8]. However, different sensors have different characteristics. For example, the rotor has good

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dynamic performance which is suitable for collecting signals with rapid changes but easy to cause drift error; inclinometer has good static performance which is suitable for collecting signals with slow changes but easy to cause white noise during the collection process. Therefore, different sensors can complement with each other to collect signals and jointly conduct real-time measurement of the attitude signal of multi rotor UAV. Genetic algorithm is a kind of method for the complementary filtering of signals collected by various sensors with rapid convergence speed and strong capacity of resisting disturbance [9].

In the sensor system, the rotor meter measures the inclination angle speed of the fuselage, the main errors of which are drift error and scale error [10] and the output characteristic of which is as shown in equation (1).

(1) Where, is output value of the rotor meter; is the real inclination angle speed measured by the rotor meter; is scale error and  is drift error. After the difference algorithm of equation (1), it can be contained that the difference equation model of the difference equation model of motor in one cycle is as shown in equation (4).

(2) The first-order auto-regression AR (1) model of the drift error of rotor meter can be established in accordance with the AR (1) estimation method of the drift error of rotor meter, as shown in equation (2).

(3) Where,  is the auto-regression model parameter which is set to be equal to  =0.9185; ; is the measured white noise with a mean value of zero.

The state equation of genetic algorithm can be established in accordance with the difference equation model of the attitude signal of motor and drift error model of rotor meter.

(4)

Where, is the Gaussian white noise with a mean value of zero. The covariance of Gaussian white noise is:

(5)

Where, , Where, and are respectively the noise

covariance of the inclinometer and rotor meter; is the standard deviation of inclination angle; is the standard deviation of the Gaussian noise density of rotor meter; is the standard deviation of the noise in the drift error AR (1) model of rotor meter. The key is to establish the relationship between pseudo-control variable and actual accelerated speed of the system through the equation description of the quad-rotor linear motion and angular motion; introduce

(1 )

o i

      

 i



0( 1) ( 1)

( ) ( 1) ( ) 1

n n

n n T

 

      



(n 1) ( )n ( )n

    

( ) ( 1)

1 0

1 1

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0 1 0 ( 1)

( ) 0 0 1 0 ( 1) ( ) 0 0 0 ( 1)

T T n n n n T n n n n n                    _       _ _                       _                   ฀฀ ฀฀ 0

{ ( 1) ( 1)}

T Ci

C E n n

C g

   

   

 

 

3 2 3 2

2 2 ₀

3 2

2 _; 2 2 ₀

1 ₂ 2

0 0

T T

C T C T

i g T                   _ _ _{ } _   _ _         i

(3)

un-modeled error and put forward a final pseudo-control input form containing reference model, PD controller and neural network compensator to obtain the optimal estimation of motor attitude and measure the drift error of rotor meter to realize the correction of drift error.

2.2. Rotating Speed Control Based on Genetic Algorithm

Genetic algorithm (GA) is a kind of calculation method simulating heredity and evolution process of biology, the principle of which is the evolution principle of “Natural selection and survival of the fittest” in the biological universe [11,12]. PID controller is a kind of linear controller. R (t) is process quantity while Y (t) is the set value quantity and the difference value between them is the deviation of the system [13-17]. The deviation is formed to be the controlled quantity u (t) of the controlled object through the controller after the linear combination of three links (P), (I) and (D), the regularity of which is:

dt t de K dt t e K t e K t u d t i p ) ( ) ( ) ( ) ( 0



   (6)

Where, is the proportionality coefficient, is integral coefficient and differential coefficient [10].

In the engineering control, the absolute integral error is generally adopted as the performance index of evaluation (ITAE):

dt t e t J 



0 ( ) (7)

To avoid overshooting, the function of penalty is adopted. In case of overshooting, the overshoot will serve as an item of objective function. The optimal index at that time is:

dt t e Ct dt t e t ITAT

J( ) t () ()

0 



_

(8)

It can be obtained after the discretization of equation (8):



() ( )



( ) ( 1)





) ( 1     



 k e k e T T j e T T t e K t u d k j i p (9)

In equation (8), C is penalty coefficient and when , C=0; in equation (9), , are respectively the integral and differential time coefficient.

Step 1: calculate PID parameter values in accordance with Z-N method: _, , _, and _, ;

Step 2: population quantity of ant is m and each ant k (k=1~m) has 15 attributes to store ordinate values of 15 nodes of paths of ants and crawling path.

Step 3: parameter initialization of mixed algorithm: set t=0 and ; assign and initial time (i=1~15, j=0~9); set ∆ , _, and put all ants at the initial point O.

Step 4: set variable i=1, if , calculate the probability for the ants to transfer towards each node of the line segment in accordance with equation (6); otherwise, adopt Roulette Wheel Selection to select the next node in accordance with equation (1) and store the value of the selected node in the tabu table at the same time.

Step 5: after each ant finishes a node, update local information element in accordance with equation (7); make an adaptive adjustment to the local information volatilization coefficient in accordance with equation (8);

Step 6: set i=i+1, if i≤15, go to step 3; otherwise, execute step 7;

Step 7: calculate the corresponding PID parameters ( , , ) of the path in accordance with array and equation (9); carry out computer simulation to obtain the performance index , steady-state regulation error and overshoot of the system; calculate the corresponding objective function of ant k in accordance with equation (9); record the optimal path and optimal path performance index in this loop and store , , in

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Step 8: if and the whole ant colony has not converged to walk in the same path, set all ants at the initial point O again and go to step 4: otherwise, the loop is ended and output the optimal path and its corresponding optimal PID parameters ∗, ∗, ∗.

2.3. Direct Torque Control Current Servo

Decompose torque current / of the left/right motor into common/differential mode current / ; decompose armature voltage / of the left/right motor into common/differential mode voltage / ; decompose torque speed / of the left/right motor into common/differential mode angular speed / , the equations of which are as shown in equation (10).

(10)

It can be seen from equation that the motor system can be decomposed into balance system and steering system. It can be considered that the common modulus is used for balancing control and differential modulus is used for steering control. The comprehensive equations (1), (2) and (8) and mathematical model of motor reducer are as shown in equation (11) [18-20].

(11) The nonlinear direct torque current model of the balance system can be obtained. In equation (11),  is the transmission efficiency of motor; is the reduction ratio of motor; is the electromagnetic torque coefficient of motor; is the rotary inertia of motor reel; _/ is the torque current of the left/right motor. When  5, the linearization of the nonlinear direct torque current model can be achieved (that is:  = 0, cos = 1 and sin = ). Then, the system model of the direct torque current of motor after linearization is as shown in equation (12).

(12) Where, , , and are the motor coefficients of the system.

According to DC servo motor equation (12) of the direct-current motor during the steady-state operation:

(13) Combine the system model of the direct torque current with the direct torque current equation to establish the direct torque current servo unit, as shown in Figure 1. The controlled quantity is the given torque current which directly conducts driving control on the motor through PD regulator, PI regulator and motor driver element.

;

2 2

;

2 2

;

2 2

i_{d m} i_{d m}

i_R i_{c m} i_L i_{c m}

u_{d m} u_{d m}

u_R u_{c m} u_L u_{c m}

d m d m

R c m  L c m 

   

 _ _ _ _

 

 _ _ _ _

 

 _ _ _ _



2 2

( )

l e l t l

r e r t r

J N K i I N J

T N K i I N J

  

    

 



  



1 2

3 4

c c

i i

   

   

    



      

c c c c c c

u R i L K

dt 

(5)

Sensor system

Motor driver element

Motor

Current detectio

Figure 1. Structure chart of the direct torque current servo unit

2.4. Rotating Speed Control of Rotor Based on Genetic Algorithm

The motor system of multi rotor self-balancing aircraft is a kind of typical multivariable, nonlinear, unstable and self-unbalanced system with strong coupling, the balancing control of which requires short adjusting time, no overshooting and strong robustness after disturbance to the system. However, the sliding mode variable structure control has such advantages as rapid response, strong robustness and adaptation to the nonlinear system. The sliding mode variable structure controller with direct torque current can be obtained after the combination of the direct torque current servo unit and genetic algorithm.

(1) Determination of the Sliding Mode Surface: The sliding mode surface with sliding mode variable structure control established by phase plane is as shown in equation (14).

(14)

Where, and are odd numbers.

In the sliding mode surface, set , it can be obtained:

(15)

Set Lyapunov function as and it can be calculated:

(16)

As and are odd numbers, . Therefore, the system is

asymptotically stable under the Lyapunov meaning.

(2) Determination of Reaching Law: To suppress the high-frequency shaking of the system under sliding mode, the exponential reaching law is established based on the genetic algorithm, as shown in equation (15).

(17) Where,  > 0 and  > 0; is sliding mode surface and is sign function. Through the change of parameters  and , the dynamic quality during the sliding mode can be adjusted and high-frequency shaking of the system under sliding mode can be suppressed.

The equation (18) can be obtained in accordance with the exponential reaching law. (18) As  > 0 and  > 0, . Set the Lyapunov function to be:

 

q p

s  H 

   

q p H    

1 2 v 

/ q p

v   H  

 

     

[ ( )]

s s sign s



  

[ ] | |

s s ss sign s  s



(6)

(19) It can be obtained:

(20) Therefore, the exponential reaching law is also asymptotically stable under the Lyapunov meaning.

The control law equation (21) of the sliding mode variable structure with direct torque current can be obtained from sliding mode surface equation (14), exponential reaching law (17) and direct torque current model equation (10).

(21)

In the above equation, when S>0, the controlled quantity under reaching mode is ; when S<0, the controlled quantity under reaching mode is ; when S=0, the controlled quantity under reaching mode is . To reduce shaking, the control rate under different modes switching shall be smoothly transited which requires to select appropriate parameters in accordance with the requirements and object model during the dynamic process.

Thus, the control system of sliding mode variable structure with direct torque current based on genetic algorithm can be established, as shown in Figure 2. The attitude information of motor detected by the sensor system is fed back to the controller which will output the given value of torque current through the control algorithm of smoothing and sliding mode variable structure and controls the motor with the direct torque current servo unit to control the body balance.

Sensor system

Contro-ller

Motor driver element

Motor

Current detection

Figure 2. Structure chart of control system

3. Analysis of Experimental Results 3.1. Balance Experiment

The introduction of reference model can make the response of quad rotor more smooth and avoid the effect of step signal on its performance. Therefore, the tracking error of the real system to the reference model and the PID controller structure can be obtained. The analysis on

2 2

1 2

( ) 2

v s s

1 2 2 0

v s s s s

  

(7)

the inner-outer loop is conducted based on the gain matrix of reference model and PD controller. Figure 3 shows the signal collected by the inclinometer when the motor is static and the inclination angle is 0. It can be seen from the figure that the noise error value of inclination angle decreases from 6 to 2.5 and that the noise error decreases significantly and the waveform is more stable.

Inclination angle measured by inclinometer Signal of inclination angle after smoothing

Time/s=0.05s Time/s=0.05s

Figure 3. Signal diagram of the inclination angle of motor in hovering

Figure 4 shows the signal collected by the rotor meter when the motor is in hovering. It can be seen from the figure that the noise error of the inclination angle speed decreases from . 5 . to . . and that the noise error decreases significantly and the zero-drift error of the rotor meter decreases from . 5 . to . 8 . and the drift error is better corrected.

Angular speed measured by gyroscope Signal of the angular speed after smoothing

gul

r sp

d/r

-1

gul

r sp

d/r

-1

Time/s=0.05s Time/s=0.05s

Figure 4. Signal of the angular speed of motor in hovering

Figure 5 shows the signal of the motor inclinometer in dynamic condition. It can be seen from the figure that when the inclination angle changes from -20 to 20, the noise error decreases 6 from to 3 and the signal waveform is more stable.

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Inclination angle measured by the inclinometer in dynamic condition

Signal of the inclination angle after smoothing in dynamic condition

Time/s=0.05s Time/s=0.05s

Figure 5. Signal of the inclination angle of motor during dynamic flight

3.2. Simulation Experiment of Different Balancing Control Methods

Establish Matlab simulation model based on sliding-mode control model with direct torque current. Substitute such physical data as actually measured quality of the motor body and radius of the airplane wheel into equation (11), (12), (18) and (20) and it can be obtained that = 8.682, = -0.0345, = -23.490, = -0.202.

The exponential part / is introduced into the sliding mode surface which can improve the rapidity of convergence of the sliding-mode control. However, when it is far away from the balance point, the speed of convergence is low, so the value is 2q>p>q; the larger the absolute value H, the better the system performance but the stronger the system shaking; the larger the and in the reaching law, the faster the speed to reach the sliding mode surface but the stronger the shaking of the sliding mode. Therefore, the rapid convergence and robustness of the system can be observed through the change of parameters. Set parameters as follows: H=10, p=17, q =15,  = -300,  = 2.

Figure 6 is the Dynamic Simulation Comparison Diagram of the inclination Angle under Different Control Methods when the control system suffers disturbance at the moment of 1s. is the sliding mode variable structure control of direct torque current; is the fuzzy control; is intelligent control and is PID algorithm control.

Recovery procedure of balance angle

Figure 6. Simulation comparison of motion state under different controls

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Table 1 is the dynamic performance index comparison under different control methods. It can be seen from the table that the adjusting time of the sliding mode variable structure control of direct torque current is shorter and the ability to suppress disturbance is better and there is basically no overshooting. This simulation comparison result has also been verified during the real object experiment. Figure 6 is the picture of real object of motor GAUAV which is independently developed by our team.

Table 1. Dynamic performance comparison

Control methods Adjusting time/s Overshoot Disturbance suppression

Sliding-mode control of direct torque current 4.0 0 0.02

Fuzzy control 5.6 0 0.03

Intelligent PID control 7.0 0.011 0.032

Genetic algorithm control 9.0 0.045 0.024

Figure 7. Picture of real object of multi rotor UAV

4. Conclusion

The thesis analyzes the force during the balancing control of multi rotor UAV and establishes the optimal estimation of the fuselage information based on genetic algorithm which integrates signals of multiple sensors and comprehensively detects the attitude information of the fuselage and globally searches solution with the genetic algorithm; designs the balancing control system of UAV: firstly establish the direct torque current servo unit which is combined with the sliding mode controller to reconstruct sliding mode variable structure controller of direct torque to determine the speed of each rotor and control the balance of motor. The experiment results show that the zero-drift error of the hovering rotor is better corrected through the servo unit control with direct torque current together with genetic algorithm and that the output waveform of inclinometer during the dynamic control of flight; the simulation result of the comparative test with other methods indicates that: compared with other traditional methods, the adjusting time is shorter and the robustness is stronger without overshoot and the dynamic performance of the control system is improved and more stable when the system suffers disturbance.

References

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(1)

Sensor system

Motor driver element

Motor

Current detectio

Figure 1. Structure chart of the direct torque current servo unit

2.4. Rotating Speed Control of Rotor Based on Genetic Algorithm

(1) Determination of the Sliding Mode Surface: The sliding mode surface with sliding mode variable structure control established by phase plane is as shown in equation (14).

(14)

Where, and are odd numbers.

In the sliding mode surface, set , it can be obtained:

(15)

Set Lyapunov function as and it can be calculated:

(16)

As and are odd numbers, . Therefore, the system is

asymptotically stable under the Lyapunov meaning.

The equation (18) can be obtained in accordance with the exponential reaching law. (18) As  > 0 and  > 0, . Set the Lyapunov function to be:

  /

q p

s  H 

   

q p H    

2 1 2 v 

/ q p

v   H  

 

     

[ ( )]

s s sign s



  

[ ] | |

s s ss sign s  s



(2)

(19) It can be obtained:

(20) Therefore, the exponential reaching law is also asymptotically stable under the Lyapunov meaning.

(21)

Sensor system

Contro-ller

Motor driver element

Motor

Current detection

Figure 2. Structure chart of control system

3. Analysis of Experimental Results 3.1. Balance Experiment

The introduction of reference model can make the response of quad rotor more smooth and avoid the effect of step signal on its performance. Therefore, the tracking error of the real

2 2

1 2

( )

v s s

1 2 2 0

v s s s s

  

(3)

Inclination angle measured by inclinometer Signal of inclination angle after smoothing

Time/s=0.05s Time/s=0.05s

Figure 3. Signal diagram of the inclination angle of motor in hovering

Angular speed measured by gyroscope Signal of the angular speed after smoothing

gul

r sp

d/r

-1

gul

r sp

d/r

-1

Time/s=0.05s Time/s=0.05s

Figure 4. Signal of the angular speed of motor in hovering

(4)

Inclination angle measured by the inclinometer in dynamic condition

Signal of the inclination angle after smoothing in dynamic condition

Time/s=0.05s Time/s=0.05s

Figure 5. Signal of the inclination angle of motor during dynamic flight

3.2. Simulation Experiment of Different Balancing Control Methods

Recovery procedure of balance angle

Figure 6. Simulation comparison of motion state under different controls

(5)

Table 1. Dynamic performance comparison

Control methods Adjusting time/s Overshoot Disturbance suppression

Sliding-mode control of direct torque current 4.0 0 0.02

Fuzzy control 5.6 0 0.03

Intelligent PID control 7.0 0.011 0.032

Genetic algorithm control 9.0 0.045 0.024

Figure 7. Picture of real object of multi rotor UAV

4. Conclusion

References

[1] Dadkhah M, Obeidat MM, Jazi MD, Sutikno T, Riyadi MA. How can we identify hijacked journals? Bulletin of Electrical Engineering and Informatics. 2015; 4(2): 83-87.

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