Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 9, No. 2 2024 

44 

Classical	PID	Control	of	A	Quadcopter	UAV	Under	
Variable	Load	Conditions	
Haoyang Zhao1, a 

1College of Mechatronics and Vehicle Engineering, East China Jiaotong University, Nanchang, 330013, China 
azhy18612713011@outlook.com 

Abstract: In recent years, the application of UAVs has become more and more extensive, resulting in a number of special 
operation UAVs. Quadrotor aerial robots have become one of the most popular vehicles at home and abroad because of their 
small size, light weight, simple structure, low cost, low requirements for takeoff and landing, and good maneuverability. UAVs 
are required to perform different tasks in the current complex environment, so variable loads are inevitable, and the stability of 
the UAV body is especially important when performing variable loads, and there are many ways to help and verify the attitude 
of the UAV during flight. In this paper, in order to more intuitively see the self-generated stability of the UAV under variable 
load conditions, the dynamics model of the UAV will be established first, and the simulation results show that the movement of 
the UAV has a very good stability. However, in the previous research, it is not possible to visualize the stability and flight state 
of the UAV when it is flying under variable load, this paper will make the UAV keep its own flight stability under two kinds of 
loads through the PID design model. At the same time, the function of the UAV's own mass change during flight is found, and 
the design function is used to show the stability curve of the UAV when it flies with its own changing mass. Through the final 
simulation and calculation, the experiment found that through the PID control, the flight state of the UAV when flying with 
variable load can be observed more intuitively, and the stability state of the UAV when flying can also be observed. 

Keywords: Quadcopter UAV, Classical PID control, Variable loads. 

1. UAV Power Model

Figure 1. Axis Definitions 

PID modeling through quadcopter UAV dynamics 
formulation 

This paper use a quadcopter UAV and set the earth as the 
reference system and place the origin at the center of the UAV 
to produce the above figure. The flight of the UAV provides 
lift through four propellers to maintain a safe altitude while 
flying, and different motions are achieved through different 

rotational speeds of the four propellers. The motion of the 
UAV is categorized into roll, pitch and yaw where the roll rate 
is P, roll angle is Φ, pitch rate is q, pitch angle is θ, yaw rate 
is r, yaw angle is Ψ. to want the UAV to hover in the air it 
needs the total thrust Ft to be all the way with its own gravity 
and Ft = F1+F2+F3+F4. the angular equation of motion of the 
UAV can be derived when the UAV is unaffected by any other 
situation 

𝐼𝑥𝑝 = (𝐼𝑦 – 𝐼𝑧) 𝑞𝑟 + 𝜏𝑝         (1) 

𝐼𝑦𝑞= (𝐼𝑧 – 𝐼𝑥) 𝑝𝑟 + 𝜏𝑞             (2) 

𝐼𝑧𝑟 = (𝐼𝑥 – 𝐼𝑦) 𝑝𝑞 + 𝜏r            (3) 

where 𝜏 is the moment denoting the product of the force 
arm and force from the starting point of the UAV coordinates 
to the propeller, 𝐼𝑥, 𝐼𝑦 , and 𝐼𝑧 is the rotational inertia of the 
UAV in the x,y,z plane. This leads to the equations of motion 
of the UAV, which are modeled on the PID based on the 
physical equations. 

2. Flight Design and PID Control

[5] 
Figure 2. PID control 



 

45 

 

There are many ways to control the flight of UAV, it can be 
a low-cost way to realize the flight control of quadcopter UAV 
hanging load system by using on-board sensors and 
calculators for the purpose of the experimental platform, 
especially the visual measurement platform for observing the 
hanging, as well as the position and suppression of pendulum 
controllers, and the feasibility of the low-cost flight system is 
proved through simulation and flight experiments. [1] The 
second one can model the dynamics of the quadcopter UAV, 
based on which, a suitable reference coordinate system is 
selected, the coupling relationship between the suspended 
weight and the quadcopter UAV is analyzed, and finally the 
Newton-Eule method is used to obtain the dynamic model of 
the variable-load suspended rotor UAV. Then, the controller 
was designed by using the feedback linearization control 
method for the above dynamics model. The position tracking 
control of the variable-load suspended rotor UAV is realized 
by using the outer-loop position controller and inner-loop 
attitude controller with the position and yaw angle of the UAV 
specified. [2] Stability control can also be performed by the 
derived UAV dynamics model with robotic arm using 
conventional PID control algorithm and expert PID control 
algorithm respectively. The model is built in Matlab/Simulink 
and simulation experiments are conducted to compare the 
superiority and robustness of the two control algorithms. [3] 
Finally, the attitude control of UAV carrying different loads 
can also be studied, and the main research contents are as 
follows: (1) Establishment of mathematical model: To study 
the attitude control of UAV, the first step is to establish the 
dynamics model of UAV, firstly, the appropriate reference 
coordinate system is selected and the conversion matrix 
between each coordinate system is given, and then the 
relevant Newtonian kinematics formulas are utilized to 
establish the After that, the dynamics and kinematics 
equations of the multi-rotor UAV are established by using 
Newton's kinematics equations. Finally, taking into account 
the different types of loads carried by the UAV, the dynamic 
equations of the multi-rotor UAV with different loads are 
derived. (2) Attitude controller design: this paper designs two 
different controllers for comparison: firstly, it designs the 
multi-rotor UAV attitude controller based on PID control, 
considers the effects of different loads on the attitude of the 
UAV, and designs several sets of simulation experiments to 
verify the effectiveness of the controller. [4] 

This article uses the classical PID control method, which is 
a common control method in quadcopter UAVs. It is a control 
system that is controlled by the proportionality, integration 
and differentiation of the error generated by comparing the 
information collected from the real-time data of the controlled 
object with the given value. It is used to regulate the attitude 
(i.e., the angle of the vehicle) and the altitude of the UAV in 
order to achieve a stable and smooth flight. Attitude control 
of a quadcopter UAV typically uses three PID controllers 
corresponding to pitch, roll and yaw angles. Each controller 
receives the error signal between the target angle and the 
actual angle and calculates the controller outputs to adjust the 
rotational speeds of the four motors to control the attitude of 
the vehicle. The proportional term controls the magnitude of 
the error signals, the integral term controls the accumulation 
of the error signals, and the differential term controls the rate 
of change of the error signals. The principle of PID control is 

based on the idea of feedback control, in which the controller 
outputs are continuously adjusted to make the attitude or 
altitude of the vehicle as close as possible to the target value. 
The basic idea is that at each time step, the error signal is 
computed and the controller output is calculated based on the 
weights of the proportional, integral and differential terms. 
These weights usually need to be manually adjusted in order 
to achieve optimal control in different environments and 
application scenarios. 

All of the above studies have done a good job of 
demonstrating the stability of the UAV while in flight, but it 
is not possible to visualize the state curves while in flight. To 
show the flight curve, we use the UAV power model with 
simulink to design the flight model of the UAV and simulate 
the reality by changing the function and function value in the 
model. So change the mass of the UAV in flight to realize the 
variable load of the UAV. In simulink the mass m of the UAV 
is changed to a matrix so that the mass of the UAV is changed 
to achieve variable load, due to the change in m the angular 
velocity and the angle of rotation of the UAV at different 
moments is also changed, so a variable i is introduced with a 
for loop to reflect the change of two physical quantities under 
the change of m. In real life, the variable load of the vehicle 
can be roughly categorized into two cases, which are 
persistent variable load and sudden mass variable load, and 
this paper discuss these two cases separately. 

(1) Finding the UAV variable load as a function of mass 
when changing the UAV mass continuously. In order for the 
UAV to reflect the variable load curve with continuity within 
the function, the matrix of m is introduced such that the initial 
value is 0.5kg, the interval is 0.01s, and the final value is 
1.5kg, and these data can be expressed as the UAV's m under 
the continuity change without 

(2) Mass change function of the UAV in a certain time in 
the case of abrupt changes 

After getting persistent change in the state of the UAV 
change the value of the m matrix of the UAV, in the case of 
the initial value of 0.5 kg at an interval of 0.5 s final value of 
1.5 kg, the resulting data can be seen in the state of the UAV 
in the case of a sudden change in its own mass. 

3. Simulation Results 
The flight status of the quadrotor UAV with variable load 

is shown in Fig 3and Fig 4. Figure three is the flight state of 
the UAV in the case of continuous variable load, in every 
0.01s the mass change can be seen that the UAV fluctuation 
but every moment through the adjustment makes the UAV in 
all aspects of the flight is smooth, there is no loss of control, 
can be very good to continue to fly. Figure 4 shows the flight 
status of the UAV in the case of sudden change of load, in the 
case of the change of mass every 0.5 seconds, it can be seen 
that the flight status of the UAV fluctuates greatly, but then 
the UAV can quickly return to a smooth flight. Through 
experiments using UAV flight models it can be found that, the 
UAV can quickly adjust the flight state, so that it has been 
flying smoothly without losing control, which also proves that 
the model can be visualized to observe that the UAV will not 
affect the stability of the UAV's flight because of the changes 
in its own mass when it changes loads. 

 



 

46 

 
Figure 3. Continuous Variable Load 

 

 
Figure 4. Shows the mutation load 

 

4. Conclusion 
This paper establishes an approach for UAV flight state 

detection with variable load. The power model of UAV flight 
is established through MATLAB/Simulink, and the flight 
curves of two variable loads are demonstrated through the 
design, and the curves can intuitively detect the state of the 
UAV, and detect the stability of the UAV's fuselage in the case 
of variable load, which provides evidence for the stability of 
the UAV. It makes the variable load flight of the quadrotor 
UAV more intuitive, which provides convenience for the 
subsequent research on the variable load of the quadrotor 
UAV. 

References 
[1] Huang Z.H. (2022). Flight control and realization of quadrotor 

UAV with suspended load. Engineering Science and 
Technology Ⅱ Series 1-2 

[2] Wu Y.Z. (2021) Research on adaptive fuzzy self-immunity 
control of variable load UAV. Engineering Science and 
Technology Ⅱ Series 1-2 

[3] Chen B. (2022) Research on modeling and cooperative control 
method of quadrotor unmanned aircraft system with robotic 
arm. Engineering Science and Technology Ⅱ Series . 1 

[4] Guo SJ. (2018) Attitude stabilization control of multi-rotor 
UAV with variable loads. Engineering Science and 
Technology Ⅱ Series . 1 

[5] Developer Community. 2021. An article to understand the PID 
control algorithm. https://cloud.tencent.com/