Mini Drone Linear and Nonlinear Controller System Design and Analyzing

Abstract

Choosing the mini-drone for a specific payload for designing purposes is one of the most challenging for both cost and design purposes. It is important to develop and analyze the flight control systems of the quadcopter-type Parrot mini drone and how to make the drones more tolerant of adverse weather conditions. The main problem with any quadcopter is that it loses its balance when exposed to any external influence, even if that influence is weak. Where the controller is the most important part of the drone, six plane controllers cover the six degrees of freedom (6dof) in the movement of the drone. In our research, we have improved the height controller in the drone, thus improving the altitude controller by using (PD) and increasing the values of (Kp and Kd) in the altitude controller of the Parrot Mini Drone Mambo to make it more bearable to external influence and to maintain its altitude. We assumed that the aircraft was exposed to bad weather conditions, such as snowfall and dust, which led to an increase in the speed at which the drone fell. We also increased the free fall constant of the object in the simulation design of the drone from (-9.81 m/s2 to -12.81 m/s2) and used Matlab R2021a Simulink to undertake the tuning of the (Kp and Kd) values. This study yielded good results, as illustrated in the results section. Therefore, this research paper suggests adopting the PD controller in the altitude controller and the new values of Kp and Kd to make the drone more tolerant of weather conditions. We tested these results in practice and got good results.

Full text

Journal of Robotics and Control (JRC)
Volume 3, Issue 2, March 2022
ISSN: 2715-5072 DOI: 10.18196/jrc.v3i2.14180 212
Journal Web site: http://journal.umy.ac.id/index.php/jrc Journal Email: jrc@umy.ac.id
Mini Drone Linear and Nonlinear Controller System
Design and Analyzing
Esraa H. Kadhim 1, Ahmad T. Abdulsadda 2
1,2 Department of Communication Engineering, Engineering Technical Collage / Al-Najaf, Al-Furat Al-Awsat Technical
University (ATU), Najaf, Iraq
E-mail: 1 esraa.kadhim.ms.ectn@student.atu.edu.iq, 2 coj.abdulsad@atu.edu.iq
Abstract—Choosing the mini-drone for a specific
payload for designing purposes is one of the most
challenging for both cost and design purposes. It is
important to develop and analyze the flight control
systems of the quadcopter-type Parrot mini drone and
how to make the drones more tolerant of adverse
weather conditions. The main problem with any
quadcopter is that it loses its balance when exposed to
any external influence, even if that influence is weak.
Where the controller is the most important part of the
drone, six plane controllers cover the six degrees of
freedom (6dof) in the movement of the drone. In our
research, we have improved the height controller in the
drone, thus improving the altitude controller by using
(PD) and increasing the values of (Kp and Kd) in the
altitude controller of the Parrot Mini Drone Mambo to
make it more bearable to external influence and to
maintain its altitude. We assumed that the aircraft was
exposed to bad weather conditions, such as snowfall and
dust, which led to an increase in the speed at which the
drone fell. We also increased the free fall constant of the
object in the simulation design of the drone from (-9.81
m/s2 to -12.81 m/s2) and used Matlab R2021a Simulink to
undertake the tuning of the (Kp and Kd) values. This
study yielded good results, as illustrated in the results
section. Therefore, this research paper suggests adopting
the PD controller in the altitude controller and the new
values of Kp and Kd to make the drone more tolerant of
weather conditions. We tested these results in practice
and got good results.
Keywords—PID controller; quadcopter; Matlab-Simulink;
Altitude controller.
I. INTRODUCTION
Recently, UAVs, particularly quadcopters, have elicited
the attention of people all over the world, including
researchers, students, and technology enthusiasts or
hobbyists. Responding to this extraordinary popularity,
researchers have created a plethora of novel control
algorithms, ranging from the model-based controller to the
model-free controller, to effectively and efficiently control
the quadcopter system.
A large number of users have used this design to study
the characteristics and components of drones and to develop
and use them in different fields. The most famous of these
researches are: Several deep learning architectures were
used in this paper to identify the quadcopter UAV system.
Overall, the CNN-LSTM model has been found to
outperform all other architectures, with average tested MSE
and MAE values of 0.0002 and 0.0030, respectively [1],[2].
A paper proposed a UAV-based smart healthcare scheme for
COVID-19 monitoring, cleansing, social distancing, data
study, and statistics group in the control area. The frame
collects information via wearable sensors, drive sensors
deployed in battered areas, or thermal appearance processing
[3],[4].
In the other paper, the observer (linear parameter-varying
(LPV)) was deployed on a Parrot® Rolling Spider mini
drone, and a series of flying tests were performed to evaluate
the (Fault Detection and Diagnosis (FDD)) competencies in
real-time using the onboard processing power. Flight tests
validated the simulation results and demonstrated that the
sliding style observer could provide reliable fault rebuilding
for quadrotor mini-drone organizations [5]. The modified
adaptive sliding approach algorithm was developed in the
other paper using a version law based on the Lyapunov
strength approach, which allowed the controller's nonlinear
adaptive performance to compensate for disturbances and
parameter perturbations. Matlab simulations are used to
validate the utility of the suggested regulator strategy in
comparison to the old approach [6]. The sensors, such as
ultrasonic and barometric pressure sensors, as well as their
data, played a vital part in calculating the altitude of the
Parrot Mambo micro drone in the other study. Utilized
Simulink software and block sets like the Simulink support
package for Parrot micro drones to keep the drone at a
constant height. Apart from the hardware and software
descriptions, the drone's equipment, capabilities, and
performance have also been discussed [7].
The Vortex Ring State (VRS) and Windmill-Brake State
(WBS) have been examined in the context of quadcopters in
the other work. Following that, wind tunnel tests were used
to develop a quadcopter model that is independent of the
floppy load and blade disk sizes. A basic model was then
developed for trajectory de-signs. Thereafter, the GPOPS-II
program was used as an arithmetical solver to construct
optimum 2D and 3D descent trajectories due to the
challenging optimum issue aimed at minimal time path
design. Finally, conducted flying tests were conducted to
demonstrate that the VRS is current in quadcopters. Further
claimed that the flight fluxes might stand decreased by
raising the plane speed of the blade floppy.
As an ideal falling trajectory, a helix-type trajectory is
used [8]. Low-cost instruments, such as a 10-DOF Mems

Journal of Robotics and Control (JRC) ISSN: 2715-5072 213
Esraa H. Kadium, Mini Drone Linear and Nonlinear Controller System Design and Analyzing
(Micro-electro-mechanical systems), IMU (Inertial
Measurement Unit), and a LIDAR (light detection and
ranging) were fitted on a minor unmanned rotorcraft in other
research and synchronized at a 10-Hz measurement rate to
estimate the location of the platform and its space from a
hitch or a landing field. Kalman filtering was used to correct
the IMU data for systematic errors (bias) and dimension
noise, as well as to obtain predicted locations from the
accelerometer data. The technique was created on an aboard
microprocessor (Arduino Mega 2560), and it enables low-
cost hardware applications of many sensors for usage in
aerospace requests [7].
The other study looks at a proportional and derivative
PD controller that uses a quadrotor UAV to regulate the
adjustment of the quadrotor UAV while in flight. To be
stable and have high performance, the PD controller's gain
parameters, the proportional gain Kp, and the derivative
gain Kd is used. Unmanned aerial vehicles (UAVs) are
becoming more popular, and they come in a wide variety of
sizes and designs. The quadcopter settles the time of roll,
pitch, and yaw system after incorporating PD controllers
into the systems. After the research, the simulation results
and a comparison of X, Y, and Yaw control approaches are
shown. Plemented. The optimum estimate technique, which
was built on an aboard microprocessor (Arduino Mega
2560), enables low-cost hare operations of many sensors for
usage in a variety of requests [10], [11].
In other studies, the controller has been tweaked to
handle the tracking trajectory problem. The primary idea
behind this control system is to allow the robot to trace the
target trajectory with the least amount of error possible. The
robustness and effectiveness of the created method, as well
as the responsiveness of the suggested sliding mode
controller, are demonstrated using simulation results
produced using MATLAB software [10], [12]–[14]. In [15]–
[18], the outcomes of the autonomous swarming flights in
the open air are discussed. The designed mini-drone is small
in size, with a wheelbase of 130 mm and a mass of 76 g, and
it comes equipped with all of the sensors required for
autonomous flying. The suggested controller compensates
for nonlinearity in dynamics, allowing for accurate velocity
control. Furthermore, the results of the swarming flight tests
revealed that the produced mini-drones and the suggested
controller perform flawlessly under real-world flying
circumstances. Another author found the results impressive:
using the audio signal's Mel-frequency cepstral coefficients
(MFCCs) and various support vector machine (SVM)
classifiers, it was possible to achieve a minimum
classification accuracy of 98% in the detection of the
specific payload class carried by the drone with an
acquisition time of only 0.25 s; the performance improved
when longer acquisition times were used [19]. The key
references that the author used are [20]–[23]. Moreover,
some studies created an embedded system for a quadrotor
UAV flight controller. The controller was built with readily
available low-cost components, open hardware design, and
open software, allowing users to test and implement new
control algorithms, which distinguish it from the most
prevalent alternatives on the market. A sensing system was
created for taking and recording the quadrotor’s odometer.
An architecture for sending angular velocity instructions to
the motors through the PWM was designed, and everything
was processed everything on a Raspberry Pi 3 [24-26].
Many research studies focus on improving the design of
the control system in drones because these aircraft reach
dangerous places that humans cannot reach. During their
flight, they are exposed to different and dangerous weather
conditions. In addition, the drone system under actuated is
challenging to control.
In this paper, we will improve the control system for
determining the position and altitude of the aircraft (PD) by
making the aircraft maintain its stability even after exposure
to bad weather conditions such as falling dust or snow on it.
II. MATERIALS AND METHOD
A. Material
In this research paper, we use a mini drone called
Parrot mini drone-Mabo (Fig. 1). The Mambo is controlled
by a computer running the PyParrot interface through a Wi-
Fi or Bluetooth connection. A built Simulink model is
utilized to simulate the desired flight route for this study.
This program enables simulated runs with various
parameters to identify the Parrot mini drone's intended
response. This is performed by controlling the Simulink
model's numerous subsystems [4].
Fig. 1. Parrot mini-drone fly
Maintaining control of a UAV is necessary for a variety
of reasons. UAVs must have fewer independent control
inputs than grades of freedom, which causes a controller
difficulty when tiresome to retain control of wholly six
degrees of freedom. This opens up the possibility of
including design elements to regulate the axes, as well as
yaw, pitch, and roll. Fig. 2 shows a simple block chart of the
needed inputs and wanted outputs that a controller will
require to successfully manage a UAV.
Fig. 2. Quadrotor control system design.
The focus of this study is on the Parrot mini drone-Mabo
control implementation. Simulink is used to create the
programmed controller based on a Parrot model. The block
diagram for the procedure for each flight alteration made by

Journal of Robotics and Control (JRC) ISSN: 2715-5072 214
Esraa H. Kadium, Mini Drone Linear and Nonlinear Controller System Design and Analyzing
the Parrot mini drone Mabo is shown in Fig. 3. Two control
rings, an external loop, and an internal loop flow continually
into apiece throughout the system. The system inputs are the
location reference, estimated yaw, yaw reference, and
altitude reference. The Simulink simulation's state estimator
is divided hooked on numerous filter blocks. A
complementary filter and a Kalman filter remain employed
[4].
Fig. 3. controller subsystem [11]
To identify inaccuracies, it compares the reference
signals generated by the path planning algorithm to the
estimated states. These are fed into the PID controllers,
which generate the commands for the actuators. The signals
are then sent to the pitch/roll (or attitude) internal loop
controller by the X-Y position outer loop controller. There
is also a yaw controller and a height controller that work
independently of these controllers. A total of six PID
controllers control the position and attitude of the micro
drone. Fig. 4 and Fig. 5 illustrate how to set up the altitude
controller as PID. In this approach, the proportional gain is
multiplied by the altitude error generated from the sonar
sensor, while the derivative gain is multiplied by the rate of
altitude of the gyroscope, which is a less noisy signal than
the ultrasound signals. It is important to note that the z-axis
in the coordinate system of the drone points downwards,
which means the altitude value in the control system will
always have a negative sign in front of it (expressed in
meters) [2].
Fig. 4. Altitude controller block [27].
B. The Mathematical Model of PID (Proportional
Integrated and Derivative) and PD (Proportional and
Integrated) controller
1) PD controller
It is a series controller, proportional and derivative
controller. If we assume that we have the system shown in
Fig. 6, the PD controller is connected in series with the
system.
Fig. 5. Altitude controller structure [11]
Fig. 6. PD Controller block diagram.
󰇛󰇜  


(1)
Where G(s) is the transfer function of the system, ζ is the
damping ratio, and  is the natural frequency.
󰇛󰇜
(2)
Where Gc(s) is the transfer function of the controller, KP
and KD are constant values (gain).
󰇛󰇜  󰇛󰇜󰇛󰇜  


 
(3)
Where GT(s) is the total transfer function.
󰇛󰇜
󰇛󰇜 󰇛󰇜󰇛󰇜
  󰇛󰇜󰇛󰇜

  

󰇛 
󰇜  



   

(4)
Where the Y(s) is the output signal and the U(s) is the input
signal.
To control the damping coefficient and natural
frequency, three variables (Kp, Kd, Ki) were selected in
three equations to allow for full control over the system [28].
2) PID Controller
It is a cascade controller, proportional, integrated, and
derivative controller. If we assume that we have the system
shown in Fig. 7, the PID controller is connected in series
with the system.

Journal of Robotics and Control (JRC) ISSN: 2715-5072 215
Esraa H. Kadium, Mini Drone Linear and Nonlinear Controller System Design and Analyzing
Fig. 7 PID Controller block diagram.
󰇛󰇜  


(5)
󰇛󰇜  

(6)
 󰇛󰇜󰇛󰇜

  

  
(7)
󰇛󰇜
󰇛󰇜󰇛󰇜󰇛󰇜
  󰇛󰇜󰇛󰇜

 
  

󰇛 
󰇜 



 󰇛  󰇜󰇛 
󰇜  

(8)
To control the damping coefficient and natural
frequency. Three variables are to be selected (Kp, Kd, Ki) in
three equations. Thus, we have full control over the system
[28].
C. Methods
In this paper, we developed and improved the altitude
control structure shown in Fig. 4 and Fig. 5. These PID
controllers contain force and torque commands as outputs,
which are then communicated to the mix motor algorithm
(MMA) (Fig. 3), which generates the required motor thrusts
and converts the orders into motor speeds.
We replaced the PID controller with a type PI controller
and then a type controller PD in the first step. We found the
best of the three types in system stability, ease of design,
and cost reduction. The controller was simplified, as shown
in Fig. 8. The "auto-tuning" method found the value of Kp
and Kd were found by the "auto-tuning" method.
Fig. 8. Altitude controller [12].
The second method to increase the efficiency of the
system was to apply a disturbance such as dust or snow on
the vehicle, thereby increasing the value of the block named
(g*vehicle*mass) representing the mass of the vehicle. In
doing so, the system became unstable, which led us to tune
the value of Kp and Kd until we could improve performance
through trial and error. We eventually obtained a good result
as the system was able to remain stable even as it was
affected by the bad weather. Fig. 9 summarizes the steps of
the work that was undertaken.
Fig. 9. Workflow algorithm
Tuning the PD controller: a linear model is required to
tune the controllers since nonlinear models, notwithstanding
their simulation accuracy, are not ideal for controller design.
The height controller will be tuned in this article using
Simulink's ‘PD tuner’ tool. The controller simply indicates
the height to climb or drop using a positive or negative
command. The linearized controller model used for tuning is
shown in Fig. 10 [29].
Fig. 10. Tuning is done via a Simplified Altitude Controller.
By opening the PD block, the ‘autotuner’ is launched. It
linearizes the control loop. The program then shows the
linearized version’s closed-loop response, allowing you to
tweak the system’s reaction time and transient behavior (see
Fig. 11).

Journal of Robotics and Control (JRC) ISSN: 2715-5072 216
Esraa H. Kadium, Mini Drone Linear and Nonlinear Controller System Design and Analyzing
Altitude (m)
Fig. 11. PID Tuner App on Simulink
Due to the elimination of nonlinear components, the
dashed line of the response signal does not have the same
simulation behavior as the solid line, but it is still useful for
tweaking purposes. Following gain selection and brief
hardware testing, it became clear that the hardware does not
behave as planned as it is unable to take off correctly. In this
scenario, the issue has an impact on the feedforward term. If
it is too low, the algorithm assumes that the drone's weight
is lower than it actually is or that the thrust is greater than it
actually is. As a result of the reduced proportional route, the
controller has more trouble controlling the remaining
weight, and it is unable to lift off. The drone can eventually
take off if the value is increased by approximately 25% [30].
III. RESULTS AND DISCUSSION
A. RESULTS
In the reference conditions when the drone flies in
suitable weather, we obtained the following results (Fig. 12):
Kp = 0.8, Kd = 0.3, ζ=0.707, wn= 190 Hz
Fig. 12. Reference results of PD controller
We increased the drone’s weight to impose the falling of
dust or snow due to bad weather conditions by changing the
value in the block (-g*vehicle. airframe. mass). This is the
plane’s weight multiplied by the body’s free fall constant (g
= 9.81 m/s^2). The negative sign indicates that the body is
increasing.
We increased the value of the constant (g) to -12.81 to
impose an increase in the weight of the aircraft. This resulted
in the system becoming unstable, and we attained the results
shown in Fig. 13.
Fig. 13. As a result of the disturbance, the drone falls down after 3.5
seconds of flying.
To improve the system’s response, we changed the values
of (Kp) and (Kd) via the ‘autotuner’ method. The system
responded the best when (Kp) was 1.4 and (Kd) was 1 (see
Fig. 14 and Fig. 15). We can summarize the results as shown
in Table I.
Fig. 14. The new result with disturbance after converting the value of Kp
and Kd.
Fig. 15. Illustrate the end result

Journal of Robotics and Control (JRC) ISSN: 2715-5072 217
Esraa H. Kadium, Mini Drone Linear and Nonlinear Controller System Design and Analyzing
TABLE I. EXPLAIN THE RESULT
Type of
control-
ler
Kp
Ki
Kd
System
response
-g*vehicle.airframe.mass
1
PID
0.8
0.24
0.5
Stable
-9.81*
vehicle.airframe.mass
2
PD
0.8
0
0.3
Stable
-9.81*
vehicle.airframe.mass
3
PD
0.8
0
0.3
Unstable
-12.81*
vehicle.airframe.mass
4
PD
1.4
0
1
Stable
-12.81*
vehicle.airframe.mass
B. DISCUSSION
Unmanned aerial vehicles (UAVs) may be a valuable
asset in search and release missions. However, to realize
their full potential, all parameters that can touch the flight of
UAVs must be properly accounted for, such as the
excellence of sensory operations (which can vary depending
on the location of the UAVs). Most previous studies in the
literature focused on the parts of the controllers in drones,
especially the altitude controller. Many researchers, as
explained in the introduction chapter, employed many
modern and complex techniques. In this research, we used a
parrot mini drone in our experiment, where we tested the
performance of the plane using PD, and after subjecting the
drone to some disturbance and changing the values (Kp and
Kd) by auto-tuning in the simulation, we obtained good
results by applying that in the MATLAB simulation. Fig. 12
shows the altitude of aircraft Z and the estimation altitude
dZ as well as the output of PD, where it can be noted that
the drone is flying at a fixed altitude until the end of the
specified implementation time, but when we introduce
disturbance in the altitude controller (increase g to -12.81),
the drone falls down after 3.5 seconds of flying, as shown in
Fig. 13. Fig.14 presents the results obtained after a change
of values. Kp and Kd are exactly identical to the original
results before the disturbance was added. Therefore, we
suggest changing the values of the altitude controller to the
new values to make the drone more stable in bad weather.
IV. CONCLUSIONS
Our modification of the PD controller shows that our
results can be enhanced. This research uses a dynamic model
of a quadcopter-type Parrot mini drone Mabo to construct a
durable cascade PD control technique. The key benefit of the
cascade PD control scheme is its high tolerance to external
disturbances. In addition, the efficacy of the developed
controller was demonstrated by comparing conventional and
cascade PID to PD control systems. To summarize, the
cascade PD control approach gives the quadcopter system a
significant performance gain. The focus of future research
will be to build on the other controllers in the dynamic
system of the quadcopter so that the quadcopter system's
resilience and performance against parameter uncertainty and
external disturbances may be increased.
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