Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 7, No. 2, 2023 

 

101 

PID	Control	Algorithm	Based	on	Particle	Swarm	
Optimization	for	Quadrotor	UAV	with	Tip	Defect	
Zhenhao Qin1, a 

1Lille College, Hohai University, Nanjing, Jiangsu, 211100, China 
ae-mail: qzh974771@gmail.com 

 

Abstract: For the four-rotor UAV (Unmanned Aerial Vehicle), blade is one of the most important actuator, the four-rotor UAV 
is prone to blade tip defect during use, which will directly affect the reasoning size of the four-rotor UAV, resulting in the flight 
quality or performance decline of the four-rotor UAV, ordinary PID control in the case of blade tip defect, it can still be optimized 
by other algorithms. In this paper, particle swarm optimization will be used to optimize PID parameters in the case of tip defect 
of quadrotor UAV, and simulation experiments will be conducted in MATLAB Simulink to verify the reliability of particle swarm 
optimization by comparing and optimizing data curves such as forward and backward roll Angle and yaw Angle. 

Keywords: Quadrotor UAV PID control, Particle swarm optimization, Tip defect. 
 

1. Introduction 
In recent years, the rapid development of UAV technology 

has shown a wide range of application potential in many fields, 
especially the four-rotor UAV, as an important vertical take-
off and landing UAV, has gradually become an ideal platform 
for various tasks. The four-rotor UAV has the characteristics 
of good motion performance, small size, light weight, low 
price, easy manufacturing and environmental friendliness, 
and is widely used in various fields, such as: aerial 
photography, detection, urban environmental monitoring [1] 
and so on. In recent years, it has been a research hotspot in 
the field of aviation, but the production accuracy of quadrotor 
UAV is high, and the failure or missing of any component may 
lead to the performance of quadrotor UAV. At the same time, 
the problem of flight control of four-rotor UAVs remains one 
of the key challenges in the field of UAVs. 

For four-rotor UAVs, blade is one of the most important 
actuators and an important component that generates thrust 
for UAVs. However, due to factors such as excessive 
rotational speed, blade often vibrates during rotation, which 
will lead to accelerated blade wear and reduced service life. 
Therefore, blade tip defects or fractures are likely to occur 
during the use of four-rotor UAVs. This will directly affect the 
inference size of the quad-rotor UAV, resulting in a decline in 
flight quality or performance of the quad-rotor UAV, or even 
out of control [2]. In the four-rotor UAV, the main controls 
include PID control, fuzzy control, fuzzy PID control [3], PID 
control has been widely used many years ago [4] 

In recent years, the research on intelligent PID control has 
gradually deepened and strengthened. PID controller has low 
requirements for model accuracy and strong adaptability. PID 
controller is widely used in quad-rotor UAV because of its 
good adaptability to some parameters which cannot be 
accurately measured. Even though PID control is so widely 
used in quadcopters, it can still be optimized using other 
algorithms. 

Particle swarm optimization (PSO) has the advantages of 
fewer parameters, easy operation and design, and fast 
convergence. In this paper, the PID algorithm of the four-rotor 
UAV is optimized by particle swarm optimization under the 
condition of blade tip defect, and the corresponding data is 

obtained by using Simulink simulation tool in MATLAB, and 
then compared with the data after particle swarm optimization. 
Explore the advantages and disadvantages of particle swarm 
optimization. 

2. Uav Modeling and Pid Control 

2.1. Principle and model of four-rotor UAV 
Four-rotor UAV is a vertical take-off and landing multi-

rotor aircraft, which is composed of four symmetrical rotors. 
Each rotor is driven by a motor to generate thrust, and the 
flight control can be achieved by adjusting the speed. 

The structure of the four-rotor UAV: 
Fuselage: The fuselage of a quadrotor drone is the main 

body of the entire aircraft and is usually made of lightweight 
materials such as carbon fiber or aluminum alloy to reduce 
overall weight and improve flight performance. 

Rotors: The quadrotor UAV has four symmetrically 
arranged rotors, each driven by a motor, attached to the four 
brackets of the fuselage. The rotors are the source of flight 
power, which enables the drone to hover and fly in the air by 
generating upward thrust. 

Motor and electric modulation: Each rotor is equipped with 
a motor and corresponding electrical modulation (electronic 
governor). Electric regulation controls the speed of the motor, 
thus controlling the thrust of the rotor. By adjusting the speed 
of the motor, the drone can achieve actions such as rising, 
falling, hovering and steering. 

Flight control system: The flight control system is the core 
control part of the four-rotor UAV, which is usually composed 
of the Flight Controller and related sensors. The flight 
controller is responsible for receiving sensor data and 
calculating control instructions, and then adjusting the speed 
of each motor through electrical regulation to achieve stable 
control of the UAV and flight tasks. 

Sensors: Drones are equipped with a variety of sensors to 
sense the environment and flight status. Common sensors 
include Gyroscope, Accelerometer, Compass, Barometer, and 
GPS positioning systems. These sensors provide the data 
needed by flight controllers to monitor the drone's attitude, 
altitude, position and speed in real time. 



 

102 

Dynamic equation of four-rotor UAV, based on Newton-
Euler equations [5] and model proposed in [6]. 

The six equations for the angular motion: 
 

𝐼 𝑝 𝐼 𝐼 𝑞𝑟 𝜏                    (1) 
 

𝐼 𝑞 𝐼 𝐼 𝑝𝑟 𝜏                    (2) 
 

𝐼 𝑟 𝐼 𝐼 𝑝𝑞 𝜏                    (3) 
 

Φ 𝐩 𝐫 𝐪 sin ϕ tanθθθ𝛉           (4) 
 

θ q cos ϕ r sin ϕ              (5) 
 

Ψ rcos 𝛟 q / cos 𝛉              (6) 
 

The six equations for the linear motion: 
 

x 𝑉                     (7) 
 

y 𝑉                     (8) 
 

z 𝑉                     (9) 
 

𝑚𝑣 𝐹 cos ϕ cos Ψ sin θ sin ϕ sin Ψ     (10) 
 

𝑚𝑣 𝐹 cos ϕ sin θ sin Ψ cos Ψ sin ϕ     (11) 
 

𝑚𝑣 𝑚𝑔 𝐹 cos ϕ cos θ          (12) 
 

In the above formula, p stands for roll rate, q stands for 
pitch rate, r stands for yaw rate, τp stands for rolling moment, 
τq stands for pitching moment, τr stands for yawing moment, 
stands for Roll angle, stands for Pitch angle, stands for Yaw 
angle. 

2.2. Establishment of tip defect model of four-
rotor UAV 

According to the paper [8], ρf is defined as the ratio 
between the thrust generated by the propeller after the 
propeller tip defect fault and the original thrust: 

 
ρ θ k /3 θ k /4 λk /2 / θ /3 θ /4 λ/2  (13)[8] 

 
Where θ0 represents the zero incidence Angle of the 

blade, θtw represents the torsional incidence Angle, λ 
represents the ratio of the incoming flow velocity to the tip 
velocity, and k represents the ratio between the blade radius 
after the defect and the initial blade radius. In this paper, the 
blade parameters of the four-rotor UAV in paper [6] will be 
taken as an example. The parameters are specifically set as 

θ0= 0.67rad, θtw= 0.29rad, λ=0.05, and the k value is 
assigned as 0.7 

The mathematical form of this fault can be expressed as: 
 

T  ρ T                  (14) 
 

Where Tn is the lift force generated by a propeller under 
normal conditions 

2.3. PID control 
PID controller is the most used in UAV control. PID control 

algorithm is a common feedback control algorithm, which is 
used to realize the stability control of the system. PID stands 
for proportional (P), integral (I), and differential (D) control 
terms, which are combined to compute the control signal and 
adjust the output of the control system so that it is as close as 
possible to the expected value. 

Proportional (P) item: The proportional control acts on the 
current error (deviation), and its output is proportional to the 
size of the error. When the error is large, the output of the 
proportional term will also increase, thus speeding up the 
system response. 

Integral (I) item: Integral control is used to eliminate 
steady-state errors in the system. It controls the cumulative 
error, that is, the cumulative value of the error over time is 
integrated. The integral term can eliminate the steady-state 
error caused by the proportional term and the differential term. 

Differential (D) term: Differential control is used to 
suppress overharmonic oscillations of the system. It predicts 
the development trend of future error by detecting the rate of 
change of error, and adjusts the control signal to slow down 
the system response speed. 

2.4. PID control of UAV 
Position varies with speed, Angle varies with speed. 

Therefore, we divide the variables into: 
Inner ring: Speed and posture rate. 
Outer ring:Position, posture, Angle. 
Velocity varies with attitude Angle, so the ring of attitude 

Angle is also the inner ring of velocity. 
Rate control: Controls p,q,r 
The figure 1 below considers the control for example. treat 

the plant as a black-box.  
 

 
Figure 1. Rate Control 

 
Attitude controls. Treat the rate control loop as the inner 

loop as shown in Figure 2. 
 

 
Figure 2. The rate control loop 

 
 



 

103 

 
Treat the rate control loop and the plant as the black box 

as shown in Figure 3. 
 

 
Figure 3. The rate control loop and the plant 

 
And then do the same for the Position Control  Repeat the same procedure for velocity and position 

control loops as shown in Figure 4. 
 

 
Figure 4. Velocity and position control loops 

 

3. Particle Swarm Optimization 

3.1. Introduction 
The study of bird foraging behavior led to the invention of 

particle swarm optimization (PSO), because birds can find the 
best destination through the sharing of collective information. 

The PSO algorithm has six important parameters, which 
are the position of the i th particle, the speed of the i th particle, 
the optimal position searched by the i th particle, the optimal 
position searched by the group, the adaptation value of the 
optimal position searched by the i th particle and the 
adaptation value of the optimal position searched by the group 

In particle swarm optimization, each candidate solution is 
called a "particle" that represents a point in D-dimensional 
space if D is the number of parameters to optimize. We can 
use the following vector to represent the position of the I-th 
particle, and the population is formed: 

 
𝑥 𝑥 𝑥 𝑥 . . . 𝑥            (15) 

 
X x , x , . . . , x             (16) 

 
In the process of finding an optimal solution to the problem, 

the particle will redefine its trajectory in parameter space (i.e. 
update its position iteratively) according to the following 
equation of motion[7]: 

 
𝑥 𝑡 1 𝑥 𝑡 𝑣 𝑡 1         (16) 

 
the velocity of the ith particle is defined as[7]: 
 

vi(t+1)=vi(t)+c1(pi-xi(t))R1+c2(g-xi(t))R2       (17) 
 

Where pi refers to the best fit value of the particle, that is, 

the coordinates at which the particle has obtained the best 
solution so far, G is expressed as the overall optimal solution, 
c1 and c2 are learning factors, usually between 0 and 4, and 
R1 and R2 are random numbers distributed in the range of 0 
to 1. 

The flow of particle swarm optimization is as follows: (1) 
Initialize particle swarm parameters,(2) randomly initialize 
the position and velocity of each particle,(3) update the 
velocity and position of each particle according to the 
conditions met, and calculate the current fitness of each 
particle,(4) update the individual historical optimal fitness 
value and position of each particle,(5) for each particle, 
Compare its adaptation value with the historical best 
adaptation value (6) If a good enough solution is reached or 
the number of iterations reaches the maximum, end; 
otherwise, go to step (3).[4] 

3.2. The optimized simulation results 
The particle swarm optimization of PID control of a 

quadrotor UAV with tip defect is carried out under simulink 
simulation in MATLAB. The following 5 data comparison 
graphs are obtained 

The particle swarm optimization functions are 
respectively: 

delta_max_T = max(T)/11.5*100; 
 

    delta_max_tau_p = 0;  %max(tau_p)*200;      (18) 
 

  delta_max_tau_q = 0;  %max(abs(tau_q))*100;    (19) 
 

    delta_max_tau_r = abs(min(tau_r))*20000;      (20) 
 

obj_ij = 
1/(delta_max_T+delta_max_tau_p+delta_max_tau_q+delta_

max_tau_r)*1000;  (21) 
 



 

104 

tau_p stands for this rolling moment,tau_q stands for this 
pitching moment,tau_r stands for this yawing moment. The 
experimental data is shown in Figure 5-9 

 

 
Figure 5. The convergence process 

 
The curve becomes regionally stable at about 40 iterations, 

which is 4.09 
 

 
Figure 6. Experimental data of tau_p 

 

 
Figure 7. Experimental data of T 

 
Figure 8. Experimental data of tau_q 

 

 
Figure 9. Experimental data of tau_r 

 
The overshoot time of the four diagrams did not change 

much, and the overshoot decreased slightly by about 6%The 
results show that PSO has a slight optimization effect on PID 
control of the four-rotor UAV with tip defect. 

4. Conclusion 
In this paper, PSO is used to optimize PID control in the 

case of blade tip defect of the four-rotor UAV, and various 
parameters of PID are optimized to different degrees, and 
certain results are obtained after optimization., but there are 
still some shortcomings in this paper.The main reason is that 
the number of iterations of particle swarm optimization 
algorithm is small, and the optimization of some modules may 
have a weakening effect on other modules. 

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