A hybrid thrusting system for increasing the endurance time of multirotor unmanned aerial vehicles

Abstract

One of the most significant disadvantages of electric multirotor unmanned aerial vehicles is their short flight time compared to fuel-powered unmanned aerial vehicles. This is mainly due to the low energy density of electric batteries. Fuel has much more energy density when compared to batteries. Electric-powered motors in multirotor unmanned aerial vehicles cannot be replaced with fuel-based engines because the stability and control of multirotor unmanned aerial vehicles rely on the high response rates of electric motors. One of the possible solutions to overcome this problem of short endurance times is by using hybrid thrusting systems that combine the advantages of both fuel and electrical propulsion systems, where high maneuverability and long endurance flight time could be achieved. In this work, hybrid thrusting and power systems for multirotor unmanned aerial vehicles are studied. Targeted hybrid thrusting systems consist of combustion engines, electric motors, and their power sources. Then a hybrid thrusting system-based quadrotor unmanned aerial vehicle model is developed. The article presents the altitude and attitude control systems of the developed hybrid thrusting system-based unmanned aerial vehicle. The presented hybrid quadcopter model comprises four electric motors and one fuel engine. The fuel engine used in this work is a 4.07 cc internal combustion engine targeting 2–3 kg unmanned aerial vehicles with up to 5 kg maximum takeoff weight. The developed hybrid quadrotor unmanned aerial vehicle achieved a 139% improvement in flight time when compared with traditional electric-based quadrotor unmanned aerial vehicles. The article also reports on other flight time-related issues such as the optimal fuel mass to battery size ratio to maximize the endurance time of the quadrotor unmanned aerial vehicles.

Introduction

Over the past two decades, there has been significant growth in the development of unmanned aerial vehicles (UAVs) in general, and multirotor vertical takeoff and landing (VTOL) UAVs in particular. ^{1 –5} UAVs are increasingly used in various military and civilian applications, ^{6 –9} including precision agriculture spraying, cargo transportation, rescue, and firefighting, due to their high maneuverability, low cost, and ease of maintenance. ^10,11 Also, many research in the field of UAV regulations, governance, and integration in the public air traffic is actively and continuously ongoing. ^{12 –21} Many of UAV applications require high maneuverability and long flight times. In multirotor UAVs, maneuverability is better achieved with electrical thrusting systems. This is due to the fast response of electrical motors. Also, many of the applications using electrical thrusting UAVs require long flight times.

UAVs vary in size, ranging from micro UAVs designed for short entertainment flights, lasting only a few minutes, to larger drones utilized by the military that can fly for more than a day. Despite their usefulness, one of the primary challenges to the extensive utilization of electric multirotor UAVs is their limited endurance time, which is often less than an hour. ⁹

Multirotor UAVs consist of electric motors because of their fast response, which is the main enabler of high maneuverability, in addition to a power source that is usually electric batteries. Fuel engines have high energy densities, but they are not being used in multirotor UAVs due to their slow response and low efficiency for small engine sizes. Many efforts targeted VTOL aircraft in manned and unmanned aerial vehicles to increase their flight times. Saeed et al. ³ present a survey study of hybrid UAVs. Many of these UAV types are of large size. Studies and work in the field of hybrid UAVs that combine fuel engine(s) with electric rotors could be found in the literature. ^{22 –30} Other approaches of using fuel cells as auxiliary power sources are presented in the literature. ^{31 –34}

In this work, a quadrotor UAV with a hybrid thrusting system is modeled and developed along with its altitude and attitude control systems. The presented work utilizes the advantages of electric-based and fuel-based thrusting systems, targeting longer flight times that would enable the expansion of multirotor UAVs in a broader range of different fields.

The rest of the article is organized as follows. The second section reviews the literature. The third section presents the quadrotor model. The proposed hybrid system is presented in the fourth section. The simulation and results are shown in the fifth section. Finally, the article is concluded in the final section.

Literature review

Many research has been conducted on enhancing the endurance of UAVs. ^{23,25 –29,31 –37} Various approaches were proposed. Many of these approaches involve incorporating specialized internal combustion engines (ICEs) or additional power sources, such as fuel cells, photovoltaic solar panels, supercapacitors, or a combination of these.

Kim ³¹ designed and tested a fuel cell system for small-winged UAVs, which flew for up to 80 min during various modes of flight. Improvements were made to minimize fuel sloshing and weight, with a focus on fuel cell development.

Protonex^® provides portable fuel cell systems from 0.1 to 1 kW. They optimized proton exchange membrane (PEM) fuel cells to increase small unmanned ground vehicles (UGVs) and UAVs endurance, with results demonstrating two to eight times better performance than battery-powered systems. Protonex^® researchers achieved 600 W of power from only 450 g of material, reducing weight and increasing output. Their power sources are used in various platforms. ³²

Dudek et al. ³³ developed a winged UAV with an AEROPACK^® hybrid system, using a fuel cell and a battery. They studied various fuel sources and found that a pressurized composite cylinder is best for short flights and a chemical fuel cartridge for longer ones. The fuel cell supplied most of the power, with batteries serving as backup. The best result was a 2-h flight, with further research ongoing for optimal performance. ³³

Arat and Surer used a hybrid system of PEM fuel cell and lithium battery pack to increase a quadcopter’s flight duration. They completed 12 flights and improved flying time by an average of 2 min. ³⁴

The FEV Group utilized a lightweight Opposed Piston Opposed Cylinder engine design ³⁸ that has a high power density and power-to-volume ratio. The engine worked well on the first try and could be used as a primary power source in a UAV with other sources like batteries. ³⁸

Other researchers tested a 13.6 kg drone with wings featuring a rule-based controller and hybrid propulsion system. Their design saved 54% energy in a 1-h ISR flight and 22% in a 3-h mission compared to traditional gasoline-powered drones. ³⁹

Khaday proposed a hybrid power system of a battery and a supercapacitor for the Cheerson CX-10 micro quadcopter. The hybrid system outperformed the battery by 106% at a voltage threshold of 3.6 V and was 26% more efficient in the second test. The proposed solution is ideal for acceleration and power-intensive flights, but less effective at constant altitudes. ³⁵

Jones et al. created a hybrid quadrotor UAV for marine environments that rides sea currents and connects with nearby nodes. The Aqua-Quad has a solar panel for extended battery life, allowing for 30–32 min of flight time. It can recharge while riding water and fly for 80 min per 24 h. ⁴⁰

The patent described by Von Novak and Irish ²² introduces a hybrid UAV with a battery pack and fuel engine. The primary rotor harvests energy when the auxiliary rotors rotate its blades, which is then stored in the batteries for longer battery life.

A hybrid system with eight rotors, combining a gas engine and a brushless DC (BLDC) motor for higher lift and longer flight duration, is presented by Lin et al. ²³ The system, called Quad-in-Quad, uses engine-driven quadrotors for lift power and motor-driven quadrotors for flight control. Although preliminary flight tests were brief, the authors expect it to fly up to 90 min with a 40 kg payload. ²³

Kim and Hong designed a hybrid multicopter with four electric rotors and two gas engines for longer flight endurance. The UAV is expected to fly for 72 min with the engine and 58 min without it. Experimentally it achieved about 65 and 60 min, respectively. ²⁴

Recoskie et al. designed a low-cost, lightweight hybrid system for a dirigible UAV, consisting of a gasoline engine, a BLDC motor, and a variable pitch propeller to maximize power. Compared to electric power systems, the designed hybrid system had 674% higher energy density, resulting in a proportional increase in flight duration. ²⁵

The work presented by Abdilla et al. ⁴¹ studies dividing a battery into smaller batteries that shall be sequentially discharged and released. Thus, the overall weight of the UAV will continuously reduce and hence reduce power consumption.

Lu et al. studied parameters matching for a hybrid quadcopter with a coaxial centered engine and a generator to run the BLDC motors. They used a parameters matching algorithm to select the proper generator, engine, and rotors based on the required power source, flight performance, and pulling force demands. The hybrid UAV achieved a 1 h flight time. ²⁶

Commercially, the Perimeter 8 UAV is a gasoline-hybrid drone with eight rotors. It can fly for 5 h with no payload and can travel up to 110 miles. ²⁷ Also, HYBRIX 2.1 UAV is a hybrid drone with a gasoline engine that charges its batteries. It can hover for 2–4 h. It has a max payload of 5 kg, and a 20 kg MTOW. ²⁸ The X1-H UAV is a 25 kg MTOW hybrid coaxial quadrotor with batteries and an ICE. The UAV’s maximum endurance time is 4 h with no payload and maximum fuel of 10 L (2.64 gal). ²⁹ THEA HEX is a 5-kg hexacopter hybrid UAV equipped with a 2 kW generator and an 11 L (2.9 gal) fuel tank that charges two 5000 mAh batteries to power six BLDC motors. THEA HEX can fly up to 7 h without payload and 2 h with maximum 5 kg payload. The UAV’s MTOW is 22 kg. ³⁰

In the reviewed literature, researchers worked on different approaches. Some of them added a fuel cell as a range extender. Those have different ways of designing a fuel cell system, such as Protonex^® and AEROPACK^® for winged or multirotor UAVs. Other researchers tend to put effort into developing the UAV structure or algorithms. None of the mentioned commercial UAVs used a centered engine to lift the UAV or share thrust with other rotors. In this work, we utilize a centered coaxial fuel engine to take care of the lift demand as illustrated in Figure 3.

In the research presented in this article, a multirotor quadcopter UAV is modeled and developed to integrate a fuel engine to add extra thrust and aid the electrical thrusting system. The research presented in the literature ^{22 –26} showed different designs of electrical thrusting systems combined with fuel-powered rotors to increase endurance time. The difference between the work in the literature and the work presented in this article is mainly in the design of the UAV incorporating four electrical motors and one fuel-based engine. Moreover, the attitude and altitude control systems for the newly developed Hybrid-Based UAV are presented and evaluated. Furthermore, the fuel engine used in the presented Hybrid-Based UAV is a 4.07 cc ICE that weighs 197 g targeting 2–3 kg UAVs of a maximum 5 kg MTOW. The ICE we utilize in this work is extremely small when compared with the large ICEs used in the relatively large commercial UAVs (>20 kg MTOW) presented in the literature. ^{27 –30} The developed Hybrid-Based UAV achieved a 139% improvement in flight time compared with the same UAV without the ICE.

Quadrotor model

The fully electric quadcopter UAV base model that this work builds on is presented in the study by Alzu’bi et al. ⁴ Figure 1 illustrates the base model. Block (1) has the governing equations of the quadrotor with the dynamic equations that control the UAV’s behavior. In addition, external disturbances to the quadrotor dynamics are introduced. The disturbances are related to the rotors’ inertia, moments’ inertia, and attitude (roll and pitch) angles. This is to simulate external real-life disturbances that come from various weather conditions like wind for example. Block (2) has all sensors that detect the status of the UAV. An inertial measurement unit senses the pitch, roll, and yaw angles. For altitudes less than 6 m, the UAV takes feedback from an ultrasonic sensor. It also has an integrated pressure sensor to read the altitude and GPS for the position, then adds some noise and delay to these readings to imitate real-life. All data gathered by sensors are directed to block (4) with proportional integral derivative (PID) controllers for altitude, trajectory, and attitude (roll, pitch, and yaw). Block (4) takes the reference trajectory from block (3) and the sensors’ readings from block (2) to make the proper feedback control signal to achieve the desired trajectory. The UAV parameters are given as follows:

Weight:	2.375 kg
Arm length:	0.288 m
Moment of inertia:	$I_{xx}=51.2\times {10}^{-3}kg\cdot {\text{m}}^2$ $I_{yy}=44.1\times {10}^{-3}kg\cdot {\text{m}}^2$ $I_{zz}\text{=}3.8\times {10}^{-2}kg\cdot {\text{m}}^2$
Thrust coefficient:	$7.8\times {10}^{-5}N\cdot {\text{s}}^2$
Drag coefficient:	$7.5\times {10}^{-7}N\cdot {\text{s}}^2$

Figure 1.

Base model of the quadrotor.

The weights of the batteries used in the simulations are added to the UAV weight as detailed in Table 1. These weights are based on batteries sold online by HRB USA and PowerHobby online stores. The modeling and equations of the quadcopter are based on the work presented in the literature. ^36,42,43

Table 1.

Battery capacities versus weight.

Battery capacity (mAh)	Battery weight (g)
1300	172
3000	319
3300	376
3800	411
4000	437
5000	527
6000	550
6500	600
7000	600

Quadrotor kinematics

There are two frames to be defined to model the quadrotor UAV, the body frame attached to the body of the UAV and the reference frame, which is fixed to the ground. Figure 2 illustrates a quadrotor with two frames, the UAV frame attached to the body and the reference ground frame. The velocity states are studied in the frame of the UAV body, while the position states are studied in the ground frame. The rotation matrix $R_G^b$ is coupling the two frames and given in equation (1)

$R_G^b=R(\varnothing )R\left(\theta \right)R\left(\psi \right)$

1

where

$R(\varnothing )=\left[\begin{array}{ccc}1& 0& 0\\ 0& c\varnothing & s\varnothing \\ 0& -s\varnothing & c\varnothing \end{array}\right]$

$R\left(\theta \right)=\left[\begin{array}{ccc}c\theta & 0& -s\theta \\ 0& 1& 0\\ s\theta & 0& c\theta \end{array}\right]$

$R\left(\psi \right)=\left[\begin{array}{ccc}c\psi & s\psi & 0\\ -s\psi & c\psi & 0\\ 0& 0& 1\end{array}\right],c\text{ is cosine},s\text{ is sine}$

where ∅, θ, and ψ are the roll, pitch, and yaw angles, respectively.

Figure 2.

Quadrotor drawing of body and ground frames.

The multiplication of these three rotations yields the rotational matrix from the ground frame to the body frame shown in equation (2)

$R_G^b=\left[\begin{array}{ccc}c\psi c\theta & s\psi c\theta & -s\theta \\ c\psi s\varphi s\theta -s\varphi c\psi & s\varphi s\theta s\psi +c\theta c\psi & c\theta s\varphi \\ c\varphi s\theta c\psi +s\varphi s\psi & c\varphi s\theta s\psi -c\psi s\varphi & c\varphi c\theta \end{array}\right]$

2

Assuming that the time derivatives of the Euler angles on the body frame are too small, then multiplying the angular velocities ( $\dot{\eta }$ derivatives of roll, pitch, and yaw with respect to time) by the rotational matrix gives the body’s angular velocity that would be expressed using equation (3)

$\begin{array}{c}\omega =\left[\begin{array}{ccc}1& 0& -s\theta \\ 0& c\varphi & c\theta s\varphi \\ 0& -s\varphi & c\varphi c\theta \end{array}\right]\dot{\eta }\\ =\left[\begin{array}{ccc}1& 0& -s\theta \\ 0& c\varphi & c\theta s\varphi \\ 0& -s\varphi & c\varphi c\theta \end{array}\right]\left[\begin{array}{c}\dot{\varphi }\\ \dot{\theta }\\ \dot{\psi }\end{array}\right]\end{array}$

3

Quadrotor dynamic model

All equations presented in the kinematic model are considered here. The forces and moments of the system generated by the thrusters are added. The system has two translational and rotational motions, where the rotational motion is expressed in equation (4) as

$J\dot{\omega }+\omega \times \left(J\omega \right)+M_G=M_B$

4

where J is the inertia matrix (kg·m²), $\omega$ is the body’s angular velocity (rad/s), $\times$ is the cross (vector) product, M_G is the gyroscopic effect of rotors (N·m), M_B is the applied torques to the body of the UAV results from $\omega x{[00J_r{\text{Ω}}_r]}^{\text{T}}$ (N·m), J_r is the rotors’ inertia (kg·m²), and ${\text{Ω}}_r$ is the rotors’ relative speed, ${\text{Ω}}_r=-{\text{Ω}}_1+{\text{Ω}}_2-{\text{Ω}}_3+{\text{Ω}}_4$ (rpm).

Forces F_i and moments M_i are the forces and the moments generated by each rotor and are given in equations (5) and (6)

$F_i=K_f{\text{Ω}}_i^2$

5

$M_i=K_M{\text{Ω}}_i^2$

6

where i is the rotor number (1–4). K_f is the aerodynamic constant that depends on the lift coefficient, blade pitch angle, and air density. K_M is the aerodynamic moment constant. ${\text{Ω}}_i$ is the speed of the rotor i in (rpm).

The resultant forces from rotors two and four applied on the right and left arms of the UAV cause the roll action as shown in equation (7). The resultant forces from rotors one and three applied on the front and rear arms of the UAV cause the pitch action as shown in equation (8). The resultant moments from all four rotors cause the yaw action as shown in equation (9)

$M_{\text{roll}}=-F_{2}l+F_{4}l=l{K}_f\left(-{\text{Ω}}_2^2+{\text{Ω}}_4^2\right)$

7

$M_{\text{pitch}}=F_{1}l-F_{3}l=l{K}_f\left({\text{Ω}}_1^2-{\text{Ω}}_3^2\right)$

8

l is the arm length of the quadcopter.

$\begin{array}{c}{M}_{\text{yaw}}=M_1+M_2+M_3+M_4\\ =K_M\left({\text{Ω}}_1^2-{\text{Ω}}_2^2+{\text{Ω}}_3^2-{\text{Ω}}_4^2\right)\end{array}$

9

Newton’s second law gives equation (10) written in inertial ground frame regarding the translational motion

$m\ddot{r}=\left[\begin{array}{c}0\\ 0\\ mg\end{array}\right]+R{F}_B-k_d\dot{r}$

10

where $r={[x y z]}^{\text{T}}$ is the difference between the quadrotor and the inertial ground system. m and g are the mass and gravity acceleration 9.81 m/s², respectively. R is the rotational matrix to couple the two frames. F_B is the force applied to the body (non-gravity force), resulting from the sum of all rotors’ forces and is given in equation (11). k_d is the friction coefficient, for simplicity it is assumed that it is the same in x, y, and z

$F_B=\left[\begin{array}{c}0\\ 0\\ -K_f({\text{Ω}}_1^2+{\text{Ω}}_2^2+{\text{Ω}}_3^2+{\text{Ω}}_4^2)\end{array}\right]$

11

The kinematic and dynamic models are easier to solve using state-space representation. Twelve states given in equation (12) are sensed by the sensors and sent to the controller. Then the controller produces the thrust, roll, pitch, and yaw, as shown in equations (13), (14), (15), and (16), respectively

$X={[\varphi \hspace{0.17em}\hspace{0.17em}\dot{\varphi }\theta \dot{\theta }\psi \dot{\psi }z\dot{z}x\dot{x}y\dot{y}]}^{\text{T}}$

12

$U_1=K_f({\text{Ω}}_1^2+{\text{Ω}}_2^2+{\text{Ω}}_3^2+{\text{Ω}}_4^2)$

13

$U_2=K_f\left(-{\text{Ω}}_2^2+{\text{Ω}}_4^2\right)$

14

$U_3=K_f\left({\text{Ω}}_1^2-{\text{Ω}}_3^2\right)$

15

$U_4=K_M({\text{Ω}}_1^2-{\text{Ω}}_2^2+{\text{Ω}}_3^2-{\text{Ω}}_4^2)$

16

The total torque M_B (N·m) on the quadcopter results from the roll, pitch, and yaw actions and is given in equation (17)

$M_B=|\begin{array}{c}l{U}_2\\ l{U}_3\\ U_4\end{array}|$

17

where l (m) is the arm length of the UAV.

Gathering all that was presented and substituting it in equation (4), the result is shown in equation (18)

$\left[I\right]\left[\ddot{\eta }\right]+\left[\dot{\eta }\right]\times \left(\left[I\right]\left[\dot{\eta }\right]\right)+\left[\dot{\eta }\right]\times \left[\begin{array}{c}0\\ 0\\ J_r{\Omega }_r\end{array}\right]=\left[\begin{array}{c}l{U}_2\\ l{U}_3\\ U_4\end{array}\right]$

18

where

$I=\left[\begin{array}{ccc}{I}_{xx}& 0& 0\\ 0& I_{yy}& 0\\ 0& 0& I_{zz}\end{array}\right]$

$\eta =\left[\begin{array}{c}\varphi \\ \theta \\ \psi \end{array}\right]$

$I_{xx}, I_{yy},and I_{zz}$ are the inertia of the quadcopter body along the x, y, and z axes (kg·m²) and $\times$ is the cross (vector) product.

After simplifying equation (18) and equating the left-hand side with the right-hand side, the angular accelerations are obtained and shown in equations (19) to (21)

$\ddot{\varphi }=\frac{l}{I_{xx}}{U}_2-\frac{J_r}{I_{xx}}\dot{\theta }{\text{Ω}}_r+\frac{I_{yy}}{I_{xx}}\dot{\theta }\dot{\psi }-\frac{I_{zz}}{I_{xx}}\dot{\theta }\dot{\psi }$

19

$\ddot{\theta }=\frac{l}{I_{yy}}{U}_3-\frac{J_r}{I_{yy}}\dot{\varphi }{\text{Ω}}_r+\frac{I_{zz}}{I_{yy}}\dot{\varphi }\dot{\psi }-\frac{I_{xx}}{I_{yy}}\dot{\varphi }\dot{\psi }$

20

$\ddot{\psi }=\frac{l}{I_{zz}}{U}_4+\frac{I_{xx}}{I_{zz}}\dot{\theta }\dot{\varphi }-\frac{I_{yy}}{I_{zz}}\dot{\theta }\dot{\varphi }$

21

Using equation (10), substitute the values inside it to get equation (22), and by arranging the result and equating the two sides, the translational accelerations are obtained in equations (23) to (25)

$m\left[\begin{array}{c}\ddot{x}\\ \ddot{y}\\ \ddot{z}\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ mg\end{array}\right]+\left[R\right]\left[\begin{array}{c}0\\ 0\\ -U_1\end{array}\right]+\left[\begin{array}{c}-k_d\dot{x}\\ -k_d\dot{y}\\ -k_d\dot{z}\end{array}\right]$

22

where R is

$\left[\begin{array}{ccc}c\varphi c\psi & s\varphi s\theta c\psi & c\varphi s\theta c\psi +s\varphi s\psi \\ c\theta s\psi & s\varphi s\theta s\psi +c\theta c\psi & c\varphi s\theta s\psi -s\theta c\psi \\ -s\theta & s\varphi c\theta & c\varphi c\theta \end{array}\right]$

$\ddot{x}=\frac{-1}{m}\left[\left(\text{cos}\hspace{0.17em}\varphi \text{cos}\psi \text{sin}\theta +\text{sin}\varphi \text{sin}\psi \right)U_1-k_d\dot{x}\right]$

23

$\ddot{y}=\frac{-1}{m}\left[\left(\text{cos}\varphi \text{sin}\psi \text{sin}\theta -\text{cos}\psi \text{sin}\varphi \right)U_1-k_d\dot{x}\right]$

24

$\ddot{z}=g-\frac{1}{m}\left[\left(\text{cos}\hspace{0.17em}\varphi cos\hspace{0.17em}\theta \right)U_1+k_d\dot{x}\right]$

25

Taking the equations (19) to (25), the 12 states are expressed as shown in equations (26) to (37)

${\dot{x}}_1=\dot{\varphi }=x_2$

26

${\dot{x}}_2=\ddot{\varphi }=x_4{x}_6{a}_1-x_4{\text{Ω}}_r{a}_2+b_1{U}_2$

27

${\dot{x}}_3=\dot{\theta }=x_4$

28

${\dot{x}}_4=\ddot{\theta }=x_2{x}_6{a}_3-x_2{\text{Ω}}_r{a}_4+b_2{U}_3$

29

${\dot{x}}_5=\dot{\psi }=x_6$

30

${\dot{x}}_6=\ddot{\psi }=x_2{x}_4{a}_5+b_3{U}_4$

31

${\dot{x}}_7=\dot{z}=x_8$

32

${\dot{x}}_8=\ddot{z}=g-\frac{1}{m}\left[\left(\text{cos}{x}_1\text{cos}{x}_3\right)U_1+k_d\dot{x}\right]$

33

${\dot{x}}_9=\dot{x}=x_{10}$

34

${\dot{x}}_{10}=\ddot{x}=\frac{U_1}{m}\left(\text{sin}\hspace{0.17em}{x}_{1}sin\hspace{0.17em}{x}_5+\text{cos}{x}_1\text{cos}{x}_3\text{sin}{x}_5\right)$

35

${\dot{x}}_{11}=\dot{y}=x_{12}$

36

$\begin{array}{c}{\dot{x}}_{12}=\ddot{y}\\ =\frac{U_1}{m}\left(\text{sin}\hspace{0.17em}{x}_{1}cos\hspace{0.17em}{x}_5+\text{cos}\hspace{0.17em}{x}_{1}sin\hspace{0.17em}{x}_{3}sin\hspace{0.17em}{x}_5\right)\end{array}$

37

where

$a_1=\frac{I_{yy}-I_{zz}}{I_{xx}}$

38

$a_2=\frac{J_r}{I_{xx}}$

39

$a_3=\frac{I_{zz}-I_{xx}}{I_{yy}}$

40

$a_4=a_2=\frac{J_r}{I_{yy}}$

47

$a_5=\frac{I_{xx}-I_{yy}}{I_{zz}}$

42

$b_1=\frac{l}{I_{xx}}$

43

$b_2=\frac{l}{I_{yy}}$

44

$b_3=\frac{l}{I_{zz}}$

45

Proposed hybrid system

The proposed hybrid thrusting quadrotor UAV model consists of the base model of the electric-based quadrotor, the battery and fuel consumption model, and the coaxial glow engine with the fuel consumption model. The fuel ICE and consumption model was developed in Simulink^®, Simscape^™, and MATLAB^®. The proposed Hybrid-Based UAV with the forces and moments is depicted in Figure 3.

Figure 3.

Forces and moments acting on the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

Battery and fuel consumption models

The battery model has the initial full capacity value. The model also comprises a consumption model that is dependent on time and the RPM of the electrical motors. The rate of discharge of the batteries is subject to various factors, including the overall weight of the UAV, temperature, flight mode, and numerous other variables. In this study, the speed of the four electric motors was considered for the battery consumption rate. Accordingly, the relationship between the flight time and the battery level was experimentally derived, as shown in equation (46)

$\begin{array}{l}{\text{CurrBatt}}_t\\ =\left[{\text{ PrevBatt}}_{t-1}-\left(C\times {\displaystyle \sum }_{\text{All motors}}\text{RPM}\right)\right]/\text{per second}\end{array}$

46

where CurrBatt is the instantaneous status of battery capacity in (mAh), PrevBatt is the previous battery status, RPM is the rotation per minute for each motor, and $C=1.1806\times {10}^{-4}$ derived experimentally.

The glow fuel consumption was taken from Wiegand ⁴⁴ and modified to suit the proposed engine O.S. MAX-25LA-S with a displacement of 4.07 cc. The relation between engine displacement and fuel consumption is almost linear, according to an experiment by Khaday. ³⁵

The battery and fuel subsystem’s functionality is illustrated in Figure 4. The illustration shows how battery and fuel consumption work.

Figure 4.

The internal function of the battery and fuel system.

The Hybrid-Based UAV’s thrust in equation (13) was modified to include the fuel engine thrust, and the new equation is shown in equation (47), where ${\text{Ω}}_E$ is the rotational speed of the added glow engine. The fuel engine model is invoked in the dynamics to give a share in lifting the UAV without affecting the roll, pitch, as it is mounted on the center of the UAV, or yaw actions, because it has coaxial propellers.

The controller subsystem takes the sensed-and-altered states from the quadrotor dynamics subsystem and compares them with the desired values to take the decision for the control signal. The controller subsystem was altered to have a PID control signal for the fuel engine, as shown in Figure 5.

$U_1=K_f({\text{Ω}}_1^2+{\text{Ω}}_2^2+{\text{Ω}}_3^2+{\text{Ω}}_4^2+{\text{Ω}}_E^2)$

47

Figure 5.

The PID controller for roll, pitch, yaw, and altitude. ²

A control parameter named electric motors thrust share (EMTS) is used to control the electrical motors’ speed, where EMTS will limit the amount of the electric motors’ thrust contribution to the overall thrust by the fuel engine and electric motors. The EMTS is calibrated to achieve the best endurance time.

Simulation and results

The full hybrid model was tested in MATLAB^® and Simulink^®. A total of 2835 simulation iterations were done to study the optimum fuel amount with the battery’s capacity. In the first part of this section, the UAV control performance results are presented. We also overview the results of the optimum fuel amount in relation to the battery capacity, and finally, the results of the optimum EMTS to achieve the best endurance time are presented.

UAV control performance results

In this study, a mission was simulated wherein the UAV climbs to an altitude of 100 m before starting to fly in a circular flight path with a radius of 10 m. A constant flight speed was assumed at all time. The results are to be shown for both the Electric-Based UAV and the Hybrid-Based UAV.

Figure 6 shows the roll controller response in the Hybrid-Based UAV. The actual roll angle follows the desired roll angle with some little noise that usually does not exceed $0.0154\left(\text{rad}\right)\cong {0.88}^{\circ }$ during normal flight.

Figure 6.

Roll controller’s response for the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

Figure 7 shows the roll controller’s response for the Electric-Based UAV. The response of the Electric-Based UAV is smoother than the Hybrid-Based UAV. The noise in the observed roll response is within $0.0047\left(\text{rad}\right)\cong {0.27}^{\circ }$ .

Figure 7.

Roll controller’s response for the Electric-Based UAV. UAV: unmanned aerial vehicle.

The largest error in the response of both the Hybrid-Based and the Electric-Based UAV is due to the sudden change in the desired response. This difference lasted for a very short amount of time (0.11 s) and did not affect the stability. The same note will be observed in the pitch response in Figures 8 and 9.

Figure 8.

Pitch controller’s response for the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

Figure 9.

Pitch controller’s response for the Electric-Based UAV. UAV: unmanned aerial vehicle.

Figure 8 shows the pitch angle control response in the Hybrid-Based UAV. The actual pitch angle follows the desired pitch angle with some noise of $0.0194\left(\text{rad}\right)\cong {1.112}^{\circ }$ in the steady flight situation.

Figure 9 depicts the desired and actual pitch angle response for the Electric-Based UAV. During normal flight the difference is less than $0.0053\left(\text{rad}\right)\cong {0.303}^{\circ }$ . It can be observed that the level of noise in the pitch response of the Electric-Based UAV is lower than that of the Hybrid-Based UAV. The higher level of noise in the Hybrid-Based UAV comes from the mechanical vibration caused by the ICE.

For the yaw controller response in the Hybrid-Based UAV, the UAV is desired to always point toward the north. The desired yaw angle is fixed to be zero, and the actual value was most of the time varying between $0.0063\cong {0.361}^{\circ }$ and $-0.0027\left(\text{rad}\right)\cong -{0.1547}^{\circ }$ as shown in Figure 10. This variation was within the acceptable range as it did not affect the UAV stability.

Figure 10.

Yaw controller’s response for the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

The response of the yaw controller in the Electric-Based UAV is shown in Figure 11.

Figure 11.

Yaw controller’s response for the Electric-Based UAV. UAV: unmanned aerial vehicle.

Controlling the roll, pitch, and yaw angles of the UAV in addition to its altitude result in the desired trajectory. Figure 12 shows the desired altitude being followed by the actual altitude in the Hybrid-Based UAV. Figure 13 shows the altitude response of the Electric-Based UAV.

Figure 12.

The UAV’s desired and actual altitudes for the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

Figure 13.

The UAV’s desired and actual altitudes for the Electric-Based UAV. UAV: unmanned aerial vehicle.

The total thrust required during the climb of the UAV is proportional to the desired altitude. As the desired altitude increases, the amount of thrust required also increases. Additionally, a greater climbing slope will necessitate a greater amount of thrust to reach the desired altitude on time. Figure 14 illustrates the altitude controller response in the Hybrid-Based UAV. It shows how the generated engine thrust was higher during the climbing phase than when it was during the steady flight phase. The variation of the engine’s thrust while climbing was double the variation in the steady flight, and the maximum generated thrust from the engine when climbing was 56% more than the maximum produced thrust in the steady flight.

Figure 14.

The Hybrid-Based UAV’s desired and actual altitudes with engine thrust. UAV: unmanned aerial vehicle.

The Hybrid-Based UAV’s trajectory following response is illustrated in Figures 15 and 16. The X coordinate and Y coordinate follow the desired values as shown in Figures 15 and 16, respectively.

Figure 15.

The Hybrid-Based UAV’s desired and actual trajectory X coordinate. UAV: unmanned aerial vehicle.

Figure 16.

The Hybrid-Based UAV’s desired and actual trajectory Y coordinate. UAV: unmanned aerial vehicle.

Figure 17 summarizes the actual X, Y, and Z coordinates of the UAV versus the engine thrust. The dashed line is when the time at which the UAV reached the desired altitude. The left side of the dashed line shows the climbing period, where X and Y coordinates have no change, and their values are zeros (Note that the figure’s values are scaled, they appear to be 0.5. The actual values are shown in Figures 15 and 16.). The Z coordinate (altitude) increases to reach the desired altitude. The engine thrust shows higher values as expected to lift the UAV in the climbing phase. The right side of the dashed line shows a constant Z coordinate illustrating a steady altitude, and X and Y coordinates are changing their values to generate a circular motion as desired. In the steady flight region, the thrust produced by the engine decreased as the UAV was not increasing its altitude.

Figure 17.

Fuel engine thrust with actual X, Y, and Z coordinates (scaled between 0 and 1).

The desired trajectory of the Hybrid-Based UAV was achieved successfully. Figure 18 shows the desired and actual trajectory for the Hybrid-Based UAV.

Figure 18.

Desired versus actual trajectory of the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

Fuel amount versus battery capacity

The flight time is proportional to the battery capacity and the thrust share from the fuel engine. The relation between the flight time and the engine weight is inversely proportional. Equation (48) depicts these relations

$\text{Flight time}\propto \frac{\left(B\times a+c\right),\text{ engine thrust share}}{\text{engine weight}}$

48

where B is the battery capacity (mAh) and a and c are constants.

Several mission simulations were performed at various battery capacities and fuel masses. Figure 19 summarizes the flight times of the Electric-Based UAV at different battery capacities. It shows that the UAV flight time increases linearly with the increase in battery capacity. The relation between the battery capacity and the achieved flight time is presented by the linear polynomial shown in equation (49)

$T_f=0.332\times B+173.58$

49

where T_f is the total expected flight time (s) and B is the mounted battery capacity (mAh).

Figure 19.

Final flight time with different battery capacities for Electric-Based UAV. UAV: unmanned aerial vehicle.

For the Hybrid-Based UAV, the simulation results show that the flight time keeps increasing as the fuel mass increases until an optimal value is reached. Afterward, the flight time starts decreasing with more fuel mass because the battery dies before the fuel is consumed. Figure 20 shows the achieved flight times at various fuel masses with a 3000 mAh battery capacity.

Figure 20.

Total flight time versus fuel mass with a battery of 3000 mAh for the Hybrid-Based UAV. UAV: unmanned aerial vehicle.

The simulation results show that the relation between the optimum fuel amount and the battery capacity is almost linear, as shown in equation (50). To visualize the results, Figure 21 illustrates the optimum fuel amount for various battery sizes. These data were fitted to a first-order polynomial as in equation (50)

$F=a\times B+c$

50

where F is the optimal fuel mass (kg), $a=0.0188$ , B is the given battery capacity (mAh), and $c=73.874$ .

Figure 21.

The optimum fuel amount for each battery capacity.

Figure 22 illustrates a comparison of the achieved flight time for both the Electric-Based UAV and the Hybrid- Based UAV using the optimal fuel mass. The improvement in flight time was between 103% and 163%. The best improvement was achieved in the 5000 mAh battery, where a 163% extra time was attained. These results were achieved based on the fuel engine and electric motors’ contribution to the total thrust as detailed in the control strategy discussed in the fourth section.

Figure 22.

A comparison of achieved flight time for both the Electric-Based and the Hybrid-Based UAVs. UAV: unmanned aerial vehicle.

Thrust share control performance results

The control strategy presented in Figure 5 shows that the altitude PID controller’s correction command is cascaded with a P controller before the command is sent to the four electric motors. As a result of this strategy, the Electric motors’ contribution to the thrust is governed by the cascaded P controller. The gain of the mentioned controller is referred to as EMTS. The EMTS gain is a calibratable value that depends on the mass of the UAV.

Figure 23 illustrates different calibration values of the EMTS gain versus flight time at 3000 mAh battery capacity.

Figure 23.

EMTS calibration at 3000 mAh battery capacity. EMTS: electric motors thrust share

For the 3000 mAh battery, which is the used battery on the Electric-Based UAV we have presented in our work by Alzu’bi et al., ⁴ several simulations were performed with different values of the fuel mass and the electrical motors’ thrust share. The achieved endurance time is 2870s (47.8 min), whereas the base model was only 1200s (20 min). The proposed hybrid model has achieved 139% extra time improvement in flight time by adding a 116 g of fuel and adjusting the electrical motors’ share to be 0.02 of the total thrust. Figure 24 shows the behavior for the Electric-Based UAV. Figure 25 shows the behavior of the Hybrid-Based UAV during the total flight with the optimum configuration of:

Fuel mass: 116 g.

EMTS: 0.02 of the motor’s capability.

Battery capacity: 3000 mAh.

Figure 24.

X, Y, and Z coordinates with the longest flight time for Electric-Based UAV. UAV: unmanned aerial vehicle.

Figure 25.

X, Y, and Z coordinates with the longest flight time for Hybrid-Based UAV. UAV: unmanned aerial vehicle.

Conclusion

Flight time endurance is a key in the success of VTOL multirotor UAVs. These UAVs are mostly battery powered and thus have limited flight times. In this work, a small size quadrotor Hybrid-Based UAV was modeled and developed. The Hybrid-Based UAV features a small 4.07 cc fuel engine that is used to help four other electric motors in lifting the UAV via a fifth coaxial rotor. A control strategy was presented to control the thrust attained from both the fuel engine and the electric motors. Several experimentation were performed to study the effect of fuel mass, battery capacity, and the EMTS on the total flight time of the newly developed Hybrid-Based UAV.

The developed Hybrid-Based UAV achieved 139% extra flight time compared to an Electric-Based UAV of the same features excluding the hybrid thrusting system.

The work presented the newly developed UAV model and the control algorithm and its performance in addition to other recommendations such as the optimal fuel mass relevant to the used battery capacity.