parameters optimization for small helicopter

7/29/2019 Parameters Optimization for Small Helicopter

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Parameters optimization for small helicopter

highly controller based on genetic algorithm

Weiping Zhao

General Aviation Key Laboratory

Shenyang Aerospace University

Shen yang , [email protected]

Dongzhou Yu

Electronics and Information Engineering


Shen yang, [email protected]

Zhanshuang Hu

Electronics and Information Engineering,


Shen yang, China

[email protected]

Abstract —We introduce genetic algorithm to the problem of

small unmanned helicopter height control in this paper. In

base on the stability of pitching angle control loop, we gain

the parameters of flying height outside loop controller which

is constituted by height feedback signal. Aim at the features

of highly stability control model for small unmanned

helicopter, we select the system rise time, steady-state error

and the combination of overshoot proportion as the

optimization objective function. The simulation results

showed that the PID controller using genetic algorithm

design has better adaptability and stability, ensure the

system control effect and improve the system performance.

Keywords-Genetic Algorithm; Optimal Control;

Unmanned Helicopter

I. I NTRODUCTION

In recent years, because of wide application in themilitary[1], civil and scientific research, the research of Unmanned Aerial Vehicles has become a hotspot in globalscope.

Unmanned Aerial Vehicle flight control system iscomposed by rudder loop, stable circuit and control(guidance) circuit[2]. All kinds of control circuit

performance restricts the Unmanned Aerial Vehicle flightcontrol system’s overall performance directly, therefore[3],the setting of control parameters in SAV control loop is

particularly important for SAV control system[4].Generally speaking, we must consider the angle motioncontrol if we want to control the aircraft motions first,make its flight attitude changed, and then make its focustrack changes correspondingly [5]. So we called flightattitude and control loop (namely inside loop) as corecontrol circuit of flight control system which is based onattitude angle feedback.

The inside loop of flight control system is the basis of outside loop control which contains flying height, heading,track and so on[6].

Among these, the height hold of UAV is achieved bythe method of introducing a highly feedback signal and

compose a flying stable outside loop which based on thecontrol of inside loop by the pitch angle.

We use genetic algorithm for PID parametersoptimization for two times because that the process of classic setting method tedious and we can't ensure that weget the controller is optimal. In the basis of the pitchingAngle control loop stability, we get the flying heightoutside loop controller parameters constituted by highlyfeedback signal. It is shown that the result which simulatedis effective.

II. SMALL UNMANNED HELICOPTER MODEL AND

CONTROL PRINCIPLE

According to papers, the longitudinal simplified modelof some type unmanned helicopter are shown in type 1:

{ x = A x + B u

y = C x + D u

(1)

1

α -0.8823 1 0.0041 0 α -0.04293

J -4.01756 0.7621 -0.00066748 0 J -5.50577= + B

J 0 1 0 0 J 0

h -1.3665 0 1.3665 0 h 0

⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥

⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦

(2)

In the type, α is fuselage angle, θ is pitch angle, h isflying height, B1 is longitudinal cycle change of rotor.

The pitch control and high control diagram are shownin figure 1 and figure 2.

When the pitch attitude control design completed, onthe basis of it we can add height hold control mode. Thehold of height can't complete simply by the stability of the

pitch, because in the process of flying, there are verticalairflow interference which will produce highly drift, so weneed to get the flying height of helicopter in using height

measurement device, and control helicopter attitude byhighly deviation, changing the track occurred of helicopter and make the plane back to the scheduled height.



We can see that the height hold control mode isdesigned on the basis of pitch control system, not only the

process of classic setting method tedious, but we can'tensure that you get the controller is optimal, therefore, weuse genetic algorithm for PID parameters optimization.

III. GENETIC ALGORITHM

Genetic algorithm adopt a "Build + Test" model, its basic operation includes encoding, create the initial population, calculate fitness and judge whether meet theoptimal conditions, if so then return, if it is not satisfied,then return to the initial population and calculate fitness,order cycle through genetic operators (selection, crossover and mutation). Figure3 is the genetic algorithm flow chart.

Concrete steps are followed:

• 1. Randomly generate certain amount of initial population and calculate the fitness of eachindividual.

• 2. Select populations according to certain rules, weusually use the roulette wheel method to select

populations.• 3. Cross the population selected in a certain

probability and generate new species.

• 4. Individual in new population occurred variationin a certain probability.

• 5. Judge whether meet the optimal conditions, endif satisfied, if not satisfied then go to the secondstep.

In the genetic algorithm, the objective function has agreat impact on the genetic algorithm, it is the target of

parameters the genetic algorithm optimize for. However,the use of the objective function is embodied throughevaluation of individuals’ fitness. Now, the objective

function is shown in type 3.

t t e J 210

)( λ λ += ∫∞

(3)

In the type (3), λ 1, λ 2 are weighting coefficients, e (t) issystem error.

To ensure the effect of controller, reduce the oscillationof the system, Introduce the oscillation frequency of

system ω, and multiplied the penalty function λ3, then

the objective function eventually become:

τ λ λ λ 3210 )( ++= ∫

∞

t t e J (4)

We make the number of parameters population is 30,iterative algebra is 500, the probability of crossover andmutation respectively is pc=0.8 and pm=0.02, then we get

the optimal solution of the objective function. Figure 4shows the optimal convergence curve of the objectivefunction with genetic algorithm.

We finally get the highly PID controller parameters inabove conditions is [4.5214, 1.7621, 1.4575], highlySIMULINK simulation is shown in figure9. Thesimulation results are shown in figure 5 and figure 6. Thecontroller parameter which is obtained according toclassical setting method given in reference [1] is [2, 6.5, 0.02]. The transfer function of pitching angle feedback isratio 1, the simulation results is shown in figure 7 andfigure8. The diagram of simulation system is shown infigure 9. The simulation results show that: Setting PID

parameters base on genetic algorithm, control heightchannel of unmanned helicopter, getting pitch angle andhigh order step response after optimization, shown infigure 5. Through the results of optimization we can seethe rise time is faster and the jitter is smaller, PID control

parameters based on genetic algorithm is better than theclassical PID control.

IV. CONCLUSION

Genetic algorithm is introduced to the high control problem of small unmanned helicopter, using geneticalgorithm to optimize PID controller parameters twice. In

base on the pitching Angle control loop stability, we gainthe flying height outside loop controller parametersconstituted by highly feedback signal. It needs to choosethe objective function exactly, select the system rise time,steady-state error and the combination of overshoot

proportion as the optimization objective function for highly stability control model features of small unmannedhelicopter, to ensure the control effects, we introduce

penalty function of restrictions system oscillation. Thesimulation results: the PID controller using geneticalgorithm design has better flexibility, adaptability,stability and ensure that the system control effect.

R EFERENCES

[1] Liang Li, “Unmanned helicopter flight control method and GPSapplication research” China agricultural mechanization researchinstitute.

[2] Katsuhiko Ogata <Modern Control Engineering> (Fourth Edition)Publishing House of Electronics Industry in USA 2003.7

[3] Gnen F.Franklin,J.David Powell,Abbas Emami-Naeini <Feedback Control of Dynamic Systems> (Fourth Edition) Publishing Houseof Electronics Industry 2004.5

[4] Yongzhe Tang, “Helicopter Control System Design,” National

Defence Industry Press August 2000,pp137-145.[5] Tao Zhou “Simplified model of micro-and small-scale unmanned

helicopter control system,” Zhejiang University May 2005

[6] Jinkun Liu, “Advanced PID Control and MATLAB Simulation,”Electronic Industry Press January 2003,pp89-109.



Figure1. The pitch angle control diagram

Figure2. The height control diagram

Figure3.Genetic algorithm flow chart

Figure4. The optimal convergence curves of objective Figure5. High order step response curve

function in genetic algorithm after genetic algorithm setting



Figure6. The pitch curve Figure7. The PID controller high order stepresponse

curve of classic method setting

Figure8. The PID controller pitch curve of classic method setting

Figure9. High level SIMULINK simulation diagram

parameters optimization for small helicopter

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