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January 2026.
P-ISSN : 2502-3470.
E-ISSN : 2581-0367
Development of a Type-2 Fuzzy Algorithm for Quadplane Attitude Control System in VTOL to Cruising Transition Meilaillatul Rohmah1.
Purwadi Agus Darwito2
1, 2
Industrial Technology and Systems Engineering Department.
Institut Teknologi Sepuluh Nopember.
Surabaya.
Indonesia 1meilaillatulr@gmail.
com (*) 2padarwito@gmail.
Received: 2025-01-18.
Accepted: 2025-11-26.
Published: 2026-01-09 AbstractAi The Quadplane uncrewed aerial vehicle (UAV) is a combination of a quadcopter system and a conventional aircraft.
The Quadplane UAV has three phases: vertical take-off, transition, and cruise.
In the transition phase, the Quadplane Tilt-rotor tilts the two front motor axes for forward propulsion.
During this transition phase, the aircraftAos balance changes, potentially causing it to crash.
This study proposes using a type-2 fuzzy control method.
The type-2 fuzzy control method is better at handling uncertainties in the Quadplane, known as the Footprint of Uncertainties (FOU), than the type-1 fuzzy method.
In this study, simulations were conducted using MATLAB Simulink, and the results of the type-2 fuzzy control method and the PID method from previous studies were compared.
The results of the z-position tracking response using the type-2 fuzzy method yield a rise time of A3 s, an overshoot of <2%, and a steady-state error of A0.
5 m.
The results of the x-position tracking response using the type-2 fuzzy method yield a rise time of A2.
5 s, an overshoot of almost 0%, and a steady-state error of <0.
2 m.
The results of the Quadplane pitch angle position tracking response using the type-2 fuzzy method produce a rise-time value of A1.
5 s, overshoot A0.
05A, steady state error A0.
02Overall, the type-2 fuzzy controller is proven to be more effective, accurate, and efficient in controlling the hybrid Quadplane in the transition phase, so it is worthy of being implemented in a real prototype with hardware-in-theloop testing as further research.
KeywordsAi Uncrewed Aerial Vehicle.
Quadplane Attitude.
Control System.
VTOL.
Transition Phase.
Fuzzy Type-2.
PID Method.
INTRODUCTION
A Quadplane UAV is a combination of a quadcopter system and a conventional aircraft .
The merger of these two systems is intended to produce an uncrewed aerial vehicle (UAV), commonly known as a Quadplane, capable of vertical take-off and landing (VTOL), also with longer flight endurance.
This merger resulted in an aircraft system with a forward thrust mechanism added after take-off .
The advantage of the VTOL system on a quadcopter is that it can be used in urban areas and confined spaces .
In addition, the VTOL system can be used in mountainous areas .
and on small landing areas, and it does not require runways for take-off and landing .
However, quadcopters can only fly for short periods, which limits their ability to carry out missions that require a wide range and long endurance.
Quadplane UAVs offer several advantages, including lower operating costs than other models, the ability to operate effectively even in unfavourable and dangerous conditions, and greater flight endurance .
Due to the addition of a forward thrust mechanism after takeoff, the Hybrid Quadplane undergoes a transition phase in which the aircraft changes from VTOL to hovering to cruising.
This transition-phase scenario starts with a vertical take-off using 4 propellers to the desired altitude, then the quadplane is in a hovering position.
Then the propeller accelerates to the required airspeed.
At this phase, the lift force of the hover engine is substituted by the lift force of the aircraftAos wings.
The propellers slowly reduce their speed to maintain altitude during this period .
When the Quadplane transitions from hover mode to cruising mode, or forward flight, the unstable aerodynamic effects change significantly .
In this transition phase, the aircraftAos balance condition changes over time, requiring an appropriate control method to stabilize it .
In addition, this phase is susceptible to external disturbances, such as wind.
The impact of wind disturbances on UAVs is becoming increasingly significant .
and is gradually becoming a major cause of UAV accidents .
Quad-Plane is very sensitive to wind disturbances at ground level, making it challenging to keep the aircraft stable in the air, let alone complete its work.
In addition, the aircraft may crash .
In previous research, several control methods have been used in quadcopter UAV systems.
These include PID control .
, linear quadratic control .
, and predictive control .
When using these three control methods, they produce good results in running the quadcopter, but only to a certain extent, because most of their system models assume no external or internal uncertainty and treat the system model as correct.
However, in actual quadcopter control, there are uncertainties in operation and environmental disturbances.
Meanwhile, fuzzy control is considered an alternative.
This method is simple and effectively addresses operational uncertainty in quadcopters .
Research .
found that the fuzzy logic method achieved 88.
89% accuracy.
The implementation of fuzzy algorithms can yield an output value that serves as a reference for the actuatorAos logic in maintaining the system condition at the set point .
Based on previous research on control methods for VTOL UAVs, this research proposes a fuzzy control method.
This method is divided into type-1 and type-2 fuzzy sets.
The type2 fuzzy control method can better handle the uncertainty encountered in the quadcopter, also known as the Footprint of Uncertainties, than type-1 .
This control method also DOI : https://doi.
org/10.
25139/inform.
Inform : Jurnal Ilmiah Bidang Teknologi Informasi dan Komunikasi Vol.
xx No.
xx July 2020.
P-ISSN : 2502-3470.
E-ISSN : 2581-0367 handles higher levels of uncertainty compared to type-1 fuzzy control methods .
This research will use a type-2 fuzzy control method to address the uncertainty of the Quadplane UAV during the transition phase.
The results of the Euler quadplane angle control response using the type-2 fuzzy control method will be compared with those of the previously implemented PID control method in MATLAB.
This research aims to determine the effectiveness of type-2 fuzzy control methods on the stability of the Quadplane during the transition phase.
because the angle affects the QuadplaneAos direction of movement while cruising.
The parameters required for the transition phase are the z value as the Quadplane hovering coordinate point, the x value as the Quadplane destination coordinate point when cruising, and the pitch angle () of the propeller axis, which needs to be controlled in the transition phase because it affects the direction of the QuadplaneAos movement when cruising.
The y value and yaw angle (O) are ignored in this study.
Table I for the set point values used in this study.
II.
RESEARCH METHODOLOGY
Mode Take-off Transition Cruising Design and Parameter Quadplane This research uses a Quadplane design reference from Pavan NAos 2020 research.
The Quadplane UAV researched this time uses the concept of a fixed-wing aircraft with tilted rotors for Vertical Take-off and Landing and as an aircraft thruster during cruising: data, statistics, and aircraft standards based on Pixhawk aircraft in Fig.
TABLE I
Parameter X.
Y, and Values Z Value X Value Value This study uses IMU and GPS sensors to detect the QuadplaneAos position and orientation in 3 dimensions (X.
Z).
These two sensors will produce signals ycyca , ycuyca , yuEyca , which are the actual z-position, x-position, and pitch angle of the QuadplaneAos propeller axis, respectively.
The error between the set point and the QuadplaneAos actual value will generate an input signal for the controller.
In this study, the control method used is type-2 fuzzy control.
The controllerAos output signal will serve as the input to servo actuators 1 and 2, as well as motor actuators 1, 2, 3, and 4, to control the speed of these motors during the transition phase.
The block diagram of the Quadplane system control during the transition phase is shown in Fig.
Quadplane Configuration Fig.
Quadplane Attitude Control Block Diagram During Phase Transition Fig.
2 illustrates the block diagram of the quadplane attitude control system during the transition phase.
The sensor block, controller, actuator, and input and output signals in the Quadplane position control system during the transition phase.
When the Quadplane reaches the z value corresponding to the setpoint, the Altitude Controller will generate a ycOyuE control The ycOyuE will command Servo 1 and Servo 2 to tilt the two front motor axes of the Quadplane, known as the tilt The ycOyc becomes the control signal input for actuator motors 1, 2, 3, and 4.
The ycOycu becomes the control .
Quadplane Force Direction Fig.
Quadplane Design This study will design a Quadplane control system for the transition phase .
overing to cruisin.
using a type-2 fuzzy control method.
The purpose of designing this control system is to stabilize the Quadplane so it can hover and move forward without falling.
To maintain the QuadplaneAos position so it does not fall, the main thing is to control its pitch angle.
This is DOI : https://doi.
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P-ISSN : 2502-3470.
E-ISSN : 2581-0367 signal input for motors 1 and 2.
This is because in cruising flight mode, only the two front motors of the Quadplane provide state input will be generated using Equation .
for the desired Quadplane control system.
Mathematical Model of Quadplane The mathematical model of a 6 DOF quadplane .
in all modes can be expressed in Equation .
Where, ycU is represent state variables, ycOycy is plane control variable, and ycOycE is quadcopter control variable.
State variables composed of several variables.
First, position variables .
cu, yc, y.
relative to the inertial frame.
Second, linear velocity .
c, yc, y.
relative to the body frame.
Third.
Euler angles .
uo, yuE, yu.
And fourth, angular velocity .
cy, yc, y.
relative to the body frame .
The control variables are divided into several variables.
First, the rotation speed of the four lift motors in quadcopter mode .
co1 , yco2 , yco3 , yco4 ) .
Second, the rotation speed of the pusher motor .
yuycEayc , elevator deflection .
uyce ) , aileron deflection .
uyca ), and rudder deflection .
uyc ).
ycAycycuycoyco ycy ycy ycyN .
cN ] = ya Oe1 (Oe .
c ] y .
c ]) .
cAycyycnycycaEa ]) yc yc ycAycycayc ycN To obtain a mathematical model of Quadplane motion, kinematic and dynamic models were developed.
This resulted in kinematics defined by coordinate-frame transformations in Equations 2 and 3 .
, as follows:
1 sin yuo tan yuE cos yuo [ yuEN ] = .
yuo sec yuE cos yuo sin yuE cos yue sin yuo sin yue yc cos yuo sin yuE sin yue Oe sin yuo cos yu.
[ yc ] yc cos yuo cos yuE cos yuo tan yuE ycy Oe sin yuo ] .
c ] cos yuo sec yuE yc ycIN] ycu = .
cU ycU ycI]ycN ya= .
yayc = ycy ycu2 ya4 yaycE = yuU ycu2 ya5 yaycE = yuU ycu3 ya5 The analysis of quadplane kinetics, mathematical modelling of the quadplane is also obtained from the differential Equations of quadplane dynamics using Equation .
Where ycN , ycN , ycN are the first derivative of the linear velocity of quadplane with respect to the quadplane body axis.
yaycu , yayc , yayc represent the forces on the axis x, y, z the quadplane body frame, yaycu ycyc Oe ycyc Oe yci sin yuE ycN [ ycN ] = .
cyyc Oe ycyc yci sin yuo cos yuE ] .
ayc ] yco ycyc Oe ycyyc yci cos yuo cos yuE yayc ycN ycUN Propulsion System The propulsion motors used in this simulation consist of 4 Emax MT3515 650kv motors with 12x3.
8 SF APC propellers.
For simplicity, it is assumed that the geometry of the aircraft itself does not interfere with the operation of the propellers.
When developing the model, the propeller performance was assumed to depend only on the magnitude and direction of the incoming airflow.
Also, the propeller data for the APC 12x3.
SF propeller was taken from the manufacturerAos website .
The raw data was used to find the advance ratio (J), thrust coefficient .
ayc ), torque coefficient .
ayc ), power coefficient .
aycE ), and efficiency .
uC ).
The definitions of these coefficients are given in Equations .
ycUN = yce.
cU, ycOycE , ycOycE ) .
ycU = .
cu yc yc yc yc yc yuo yuE yue ycy yc y.
ycN ycOycy = .
uyca yuyce yuyc yu.
ycN , ycOycE = .
co1 yco2 yco3 yco.
ycN cos yuE cos yue sin yuo sin yuE cos yue Oe cos yuo sin yue cN ] = [ cos yuE sin yue sin yuo sin yuE sin yue cos yuo cos yue Oe sin yuE sin yuo cos yuE ycuN = .
cUN ycE ya ya yuC= yc The dynamics of the quadplane in fixed-wings mode .
fter transitio.
remain closely related to those in VTOL mode.
In a broader sense, the aircraftAos 6DoF can be separated into two.
The first involves the longitudinal axis, and the second involves the lateral and directional axes.
Based on the quadplane configuration in Fig.
, there are four control variables for aircraft control during fixed-wing mode: Aileron.
Elevator.
Rudder, and Throttle .
The elevator deflection and thrust motor affect the aircraftAos longitudinal control.
The aileron and rudder affect control in the lateral direction axis.
The following are the Equations to determine the deflection of the aileron, elevator, and rudder using Equations .
, respectively, to produce roll, pitch, and yaw angle values.
For the quadplaneAos rotational motion dynamics.
Equation .
relates to moment balance .
Symbol I is defined as the matrix of moments of inertia.
The symbols ycAycycuycoyco , ycAycyycnycycaEa , and ycAycycayc are the moments of inertia with respect to the x, y, and z axes relative to the quadplane body frame, respectively.
The quadplane kinematics and dynamics Equations .
will produce a state output using Equation .
, and the integrated yuyca = yuyca,ycycycnyco yuyuo yuyce = yuyce,ycycycnyco yuyuE DOI : https://doi.
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E-ISSN : 2581-0367 yuyc = yuyc,ycycycnyco yuyue The total moment acting on the aircraft due to propulsion is then calculated using Equation .
Propulsion System Forces and Moments Based on the actuator configuration in Fig.
, there is a force on the motor axis that must be converted into force and moment relative to the centre of gravity of the aircraft .
The aircraftAos motors are at right angles to its centre of The distance between the motors along the x- and yaxes is 0.
75 m.
The motor positions are given in Equations .
The thrust force vectors are given in Equations .
The total force generated by the propulsion system is given by Equation .
ycN yc1 = .
yc2 = .
Oe0.
yc3 = [Oe0.
Oe0.
yc4 = [Oe0.
ya1 = ya1 .
in yuI1 ycAycy = ycE1 ycE2 ycE3 ycE4 ycA1 ycA2 ycA3 ycA4 Transition Phase Simulation The transition phase is when the Quadplane dynamics change from quadcopter to aeroplane dynamics.
In this phase, the Quadplane must execute the Quad-to-Plane transition at an airspeed of 0 O ycOyca O 13 ycoAEyc .
In the Quad-to-Plane transition phase, the airspeed is higher than the trim speed .
cOycayca = ycOycaO 2 ycoAEyc ) controlled by the quad-mode controller, and the pusher motor will ramp up until the Quadplane position stabilizes.
this condition, the quad motor is prevented from dropping to zero to prevent an unstable quadplane.
Once the airspeed reaches the threshold of 11.
2 ycoAEyc .
The aircraft switches to plane-mode control and monitors the trim condition, while quad-mode control drops to zero .
In this research, a Quadplane control simulation is conducted in MATLAB Simulink.
In this simulation, parameters are specified, including the wind model used and the x, y, and z values.
This simulation uses two wind models.
The first is the 1-cos discrete wind model.
The second is the Von Kyrmyn continuous wind model.
The continuous-discrete wind model is defined by Equation .
Where yc0 is defined as the time when the wind starts to blow.
ycOycO ycoycaycu is defined as the highest wind speed.
OIyc is the interval of time when the wind speed changes.
ycN .
ycN .
Oe cos yuI1 ]ycN .
ya2 = ya2 .
in yuI2 cos yuI2 ]ycN .
ya3 = ya3 .
Oe.
ycN .
ya4 = ya4 .
Oe.
ycN .
yaycy = ya1 ya2 ya3 ya4 ycOycO .
OIy.
= { The moment generated due to propulsion is a combination of the torque generated by the propeller and the moment generated by the thrust force acting at a distance from the CG of the The moment acting on the aircraft due to each propeller is given as Equations .
ycE1 = ycE1 .
in yuI1 Oe cos yuI1 ]ycN .
ycE2 = ycE2 .
in yuI2 cos yuI2 ]ycN .
ycE3 = ycE3 .
Oe.
ycN .
ycE4 = ycE4 .
Oe.
ycA2 = yc2 y ya2 ycA3 = yc3 y ya3 ycA4 = yc4 y ya4 ycOycO ycoycaycu yc < yc0 , yuU.
cOeyc0 ) .
Oe cos ) yc0 < yc < yc0 OIyc .
OIyc yc0 OIyc < yc, ycO ycO ycoycaycu This study uses the Von Kyrmyn continuous wind model to simulate unstable winds.
The temporal variations in wind speed are divided into two components, as described by Equation .
i Where ycO ycO is the average wind speed over a time period and is defined in Equation .
ycN is defined as the duration of the gust.
OIycOycO is the fluctuating wind condition.
The average time value of OIycOycO is zero.
OIycOycO is also used to represent the magnitude of the fluctuation in Equation .
i ycOycO = ycO ycO OIycOycO , .
1 ycN i ycOycO = O0 ycOycO .
yccyc, .
ycN The moments acting on the aircraft due to the thrust force of each propeller are given in Equations .
ycA1 = yc1 y ya1 1 ycN O (OIycOycO .
)2 yccyc, ycNIeO 2ycN OeycN = lim Equation .
defines a spectrum function of the Von Karman wind model.
Symbols yayc , yayc , and yayc are defined as the length scales of turbulence in three directions.
The symbols yuayc,ycO .
yuayc,ycO .
yuayc,ycO are intensity fluctuation functions and altitude-dependent functions.
ya ycyc () = yuayc,ycO 2 yc yuU .
339yayc )2 ]5AE6 DOI : https://doi.
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339y2yayc )2 ycyc () = yuayc,ycO 2 yc ycyc () = yuayc,ycO yuU .
339yayc )2 ]11AE6 2 yayc 1 8AE3.
339y2yayce ) yuU .
339yayc )2 ]11AE6 first presented by Zadeh in 1975 .
The classification of type-2 fuzzy sets allows for superior and inferior membership functions.
both of these functions can be represented by the respective membership functions of type-1 fuzzy sets.
This new concept was introduced by Mendel and Liang in their research .
The interval between these two functions is used to describe type-2 fuzzy sets and represents the uncertainty trace (FOU) .
Equation .
is defined as the fluctuation intensity and turbulence length scale when the altitude is below 1000 feet.
as the unit is defined as the flying altitude.
u_6 is defined as the wind speed at an altitude of 6 meters.
yayc = Ea.
Ea yayc = yayc = .
yuayc,ycO = 0.
1yc6 , yuayc,ycO = yuayc,ycO = yuayc,ycO .
Fuzzy Logic Controller Fuzzy logic is a logic with membership degrees in the range 0 to 1, unlike classical Boolean logic .
Variables in fuzzy logic are represented in the form of fuzzy sets.
Commonly used fuzzy sets are Gaussian, trapezoidal.
Gaussian bell, triangular, and sigmoid.
In fuzzy logic, the Membership Function (MF) indicates the degree of membership for each value in a variable.
The function of the designed fuzzy set is required to determine the degree of membership of fuzzy sets .
Fig.
3 is an FLC diagram that explains the stages of fuzzy logic control .
fuzzy sets A and B .
AOB Fig.
4 Type-2 Fuzzy Membership Function Type-2 fuzzy control systems are commonly defined as an extension of type-1 fuzzy control systems .
Type-2 fuzzy logic has two membership functions: primary and secondary.
The degree of secondary membership in a type-2 fuzzy logic is The Type-2 fuzzy membership degree is depicted as a uniform shading, as shown in Fig.
4, called the footprint of uncertainty (FOU) .
This system also uses an AuIf-ThenAy fuzzy rule base.
The difference in type-2 fuzzy logic and type-1 fuzzy logic lies in the reduction step after the inference step.
Reduction steps convert the output of a type-2 fuzzy set into a type-1 fuzzy set, yielding crisp output values.
RESULT AND DISCUSSION
Fig.
3 Fuzzy Logic Control Diagram A Fuzzy Logic Controller, commonly abbreviated FLC, is a control system that uses the concepts of fuzzy set theory in its There are three steps in an FLC, namely fuzzification, inference mechanism, and defuzzification.
Fuzzification is the initial step that converts crisp values into fuzzy values.
These fuzzy values are then used as input for the inference mechanism.
At this step, decisions are made based on the available inputs using a designed logical rule base.
Lastly, the fuzzy inference mechanismAos output is defuzzified to crisp values .
In FLC, a rule base connects input and output values during the fuzzy inference stage.
The rules used in this FLC are in the form of AuIf-ThenAy .
Type-2 Fuzzy Logic Controller Type-2 fuzzy logic can better handle systems with uncertainty and imprecision.
This type-2 fuzzy set is essentially a Aufuzzy fuzzy.
Ay This means that the membership degree of a type-2 fuzzy set is a type-1 fuzzy set.
This type-2 fuzzy set was Design of Quadplane Transition Phase This study will design a quadplane control system for the transition phase .
rom hovering to cruisin.
using a type-2 fuzzy controller.
The control system design aims to stabilize the quadplaneAos hover and forward motion.
The control system design focuses on controlling the Z.
X, and pitch angles of the To implement the transition phase, the simulation requires the x and z coordinate point parameters as reference points for the hovering/transition phase, along with the angle of the front propeller axis.
The x- and z-coordinate values and the propeller axis angle have been determined and are presented in Table I.
The parameters controlled by this system include the quadplaneAos Z and X positions and pitch angle.
And the control parameters used in this study are: 4 propellers as the drive during take-off.
2 front propellers tilted forward and 2 rear propellers slowly slowing to perform the transition phase.
front propellers moving constantly.
and 2 rear propellers remaining stationary during the cruising phase.
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E-ISSN : 2581-0367 Type-2 Fuzzy Logic Controller Data Representation .
Fuzzification: At this stage, crisp inputs will be converted into fuzzy sets.
For each FLC parameter input, all three use the Gaussian membership function to achieve Each parameter has one input.
The input is the difference between the reference position value and the actual position value for each parameter.
The three membership functions for each parameter, namely: x-position, z-position, and tilt angle, are shown in Fig.
Inference and Rule-Based: Fuzzy rules in the form of AuIf-ThenAy are used to connect inputs with outputs at the fuzzy inference stage.
In this study, the rule base used to generate the control signal is shown in Fig.
X Position .
Z Position .
X Position .
Pitch Angle Position Fig.
Rule-Based .
Type Reduction and Defuzzification: In type-2 fuzzy logic, there is an additional Type-Reduction step that converts the output from a type-2 fuzzy set to a type-1 fuzzy set.
This step is necessary to produce a definite output signal.
This study also refers to previous research that used the Karnik-Mendel Algorithm for type reduction.
Fuzzy Type-2 Simulation Results After determining the data and performing simulations in MATLAB, this section presents the results.
Fig.
7 shows the results obtained using the type-2 fuzzy method.
Fig.
shows that the controllerAos output can move the Quadplane to the set point at an altitude of 50.
However, the altitude value obtained is negative.
This is because the flight coordinate system .
specially in aircraft and drone simulation.
uses the NED (North-East-Dow.
convention, where the Z-axis points To reach the altitude set point, the Quadplane takes 11 seconds.
There is no overshoot or drastic change in altitude.
Thus, this test shows that the type-2 fuzzy logic can execute the transition phase well, and the Quadplane does not experience a stall .
However, there is an error of 0.
5 meters.
Therefore, the steady-state error value during take-off is 1%.
Fig.
shows the QuadplaneAos response during cruising along the x-axis.
The blue line represents x_reff, which is the .
Z Position .
Pitch Angle Position Fig.
Membership Function DOI : https://doi.
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The x-axis set point is 0 m when the Quadplane takes off and 100 m when it is hovering.
A red signal indicating the QuadplaneAos actual x position.
During cruising, the QuadplaneAos actual x position differs from the set point, resulting in an error or a time difference.
This causes the QuadplaneAos rise time to be about 2 seconds slower than the set point value.
However, in reaching the x coordinate point: 10.
Fig.
shows the pitch angle of the Quadplane during take-off until it reaches an altitude of 50 meters, hovering, and cruising for 100 meters.
During take-off, the pitch angle changes from 0A to 0.
When hovering, the QuadplaneAos pitch angle changes drastically from 0.
2A to -0.
During cruising, the pitch angle of the Quadplane reaches a steady state in accordance with the set point and does not experience PID Simulation Results This section presents the results for the PID method.
Fig.
shows the simulation results for the Z-position Quadplane.
Xposition Quadplane, and pitch-angle position Quadplane using the PID method.
Based on previous simulations, the same response was obtained using type-2 fuzzy logic.
First.
Fig.
shows that the controllerAos output can move the Quadplane to the set point at an altitude of 50.
The time needed for the Quadplane to reach the set point is 11 seconds.
There is no overshoot or drastic change in altitude.
Therefore, this test shows that type-2 fuzzy logic performs well during the transition phase, and the Quadplane does not experience a stall .
Z Position .
X Position .
Z Position .
Pitch Angle Position Fig.
Simulation Results .
X Position DOI : https://doi.
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Comparison
A3 s Overshoot
A0,05A
A0,3A
Error steady A0,02A A0,1A Fuzzy is faster PID oscillates Fuzzy is more Metric Pitch Angle Position Based on simulation results, the z, x, and pitch angle positions of the Quadplane using the two control methods above, namely the type-2 fuzzy method and PID, are shown in Table II.
The control system parameters observed and written in the table include: the rise time value of the system in reaching the setpoint, the overshoot that occurs in the system, and the magnitude of the error after reaching the setpoint .
teady state Table II shows the control response for tracking the QuadplaneAos x, z positions, and tilt angle.
The type-2 fuzzy method yields better results than the PID method.
The rise time of the type-2 fuzzy method is faster than that of the PID method in reaching the set point.
The overshoot value in the type-2 fuzzy method is relatively smaller than that of the PID method.
The steady-state error in the type-2 fuzzy method is smaller than that in the PID method.
In addition, in motor and servo control, the type-2 fuzzy method achieves faster rise times than the PID method.
The overshoot and steady-state error values using type-2 fuzzy are smaller than those using PID.
Pitch Angle Position Fig.
PID Simulation Result Fig.
shows that the set point of the x-axis when the Quadplane takes off is 0 m, whereas when the Quadplane is hovering, the set point is 100 m.
A red signal indicating the QuadplaneAos actual x-position.
During cruising, the QuadplaneAos actual x-position differs from the set point, resulting in an error or a time difference.
This causes the QuadplaneAos rise time to be 2 seconds slower than the set point However, at the x-coordinate 10, there is no overshoot.
Fig.
shows the results of testing the Quadplane pitch angle position using the PID method.
The results of this test show that the red signal corresponds to the Quadplane pitch angleAos actual position, and the blue signal corresponds to the Quadplane pitch angleAos set point.
A change in the Quadplane angle position during take-off.
The angle change reached 0.
Meanwhile, when the Quadplane is in a hovering condition, the pitch angle changes from 0.
01A to 0.
This may be due to a change in the direction of the propeller movement, which was initially vertical and then tilted by the servo motor to become However, at 12 seconds, the QuadplaneAos pitch angle returns to 0A, and it then cruises and follows the track IV.
CONCLUSION
The designed type-2 fuzzy algorithm successfully controlled the Quadplane hybrid system during the transition phase .
overing to cruisin.
The controller generated the appropriate thrust distribution across the four motors and adjusted the servo tilt angle responsively, allowing the quadplane to smoothly transition from hovering to cruising without excessive Compared to PID control, type-2 fuzzy control shows superior performance with smaller steady-state error, faster settling time, and lower overshoot.
The system controlled by the type-2 fuzzy method maintains the balance of X position.
Z position, and pitch angle more precisely and efficiently.
The simulation results show that the type-2 fuzzy method effectively validates the Quadplane hybrid system design.
This controller provides more accurate tracking, a more stable response, and smoother control signals than PID.
This proves that type-2 fuzzy control is an effective method for controlling the Quadplane during the transition phase.
Comparison of PID and Fuzzy Type-2 Responses Fig.
7 and Fig.
8 show the simulation results for the Type-2 Fuzzy Control and PID control methods.
Table II below
compares the control responses generated by the two control
TABLE II
COMPARISON OF SIMULATION RESULTS USING FUZZY TYPE-2 METHOD AND
PID CONTROL METHOD
Fuzzy Parameter Metric
PID
Comparison
Type-2
X Position Rise Time
A3 s A5 s Fuzzy is faster
PID has a greater
Overshoot
< 2%
A10%
Error steady Fuzzy is more A0,5 m
2Ae3m
Z Position Rise Time
A2,5 s A4 s Fuzzy is faster
Almost Fuzzy is more Overshoot
A8%
Error steady Fuzzy is more < 0,2m A1m
PID
Rise Time
Fuzzy Type-2
A1,5 s Parameter REFERENCES