Having recently reached the commercial mainstream, drones will be utilized in different aspects of human beings’ lifestyles in the future. New advanced delivery systems designed and being used to safely get packages to customers in 30 min or less using unmanned aerial vehicles have a great potential to enhance the services provided to millions of customers in the future. This system also will increase the overall safety and efficiency of the transportation system [1
]. There is also wide interest in flying robots in the toy industry. The different types of quadrotors and toy drones will help children to be creative, excited, and familiarize themselves with this cutting-edge technology [2
]. The use of unmanned aerial vehicles (UAVs) for capturing visual information in areas that are hard to reach or dangerous for humans is another interesting application of drones [3
]. This application would bring a huge advantage in terms of time saving, cost, and human risk when it is necessary to inspect areas that are either dangerous or difficult to reach for humans, such as power lines, power plant boilers, bridges, tunnels, hydraulic dam walls, and pipelines [4
]. The potential impacts of future aerial robots on other applications such as aerial photography and firefighting are also clear [6
In the last two decades, quadcopters (also called quadrotor helicopters or quadrotors) have been considered to be the most practical form of aerial robots [8
]. The modeling and simulation [9
], control and stabilization [10
], and dynamic behavior prediction [12
] of these aerial robots have been widely studied and investigated in the literature. Thus, different aspects of performance prediction and optimization of these robots are completely understood. The main conclusion of the literature has been that for aerial robots to become a standard tool in everyday use, it is vital that they can be operated efficiently by a non-expert pilot and that the navigation system be robust enough to remain operational in rough, industrial conditions. Consequently, the most important challenge for the development phase of this technology is the control system. In other words, having an accurate and precise control strategy is a “must” for safe and efficient operation of all types of aerial robots. In order to design a reliable control structure, a dynamic model (a control-oriented model (COM)) is needed to simulate the behavior of the drone in different working conditions. This model should be reliable, precise, and accurate to enable control experts to develop an effective control strategy for this mechatronic product. This model should also be fast enough to be used in iterative procedures of control system design.
In 2016, a new type of aerial robots was introduced and patented: JetQuads (JQs). The JetQuad is a quadrotor in which the propellers are replaced with jet engines [13
]. Thus, it is a jet engine-powered drone that could have a revolutionary impact in the next generation of aerial robots. The main advantage of using jet engines in drones is that the turbines can run on ordinary diesel fuel. As a result, the drone is mechanically simple and very powerful. The JetQuad outperforms conventional electrical drones in two aspects, energy density and power-to-weight ratio:
The energy density measures energy storage in a unit mass. The JetQuad uses diesel fuel with an energy density of 40 MJ/kg, whereas electrical drones use solid lithium-based batteries that at most have an energy density of 1 MJ/kg. Thus, for the same on-board mass of fuel (or battery) storage, the JetQuad stores 40 times more energy than the equivalent electrical drone. Although jet engines are heavier than electrical motors, they have much higher power-to-weight ratios, so this penalty is insignificant. The U.S. Department of Energy (DOE) has recently initiated a five-year research project to develop next-generation battery technology. The DOE targets an energy density achievement of 3 MJ/kg energy density. This is still 1/10 of the energy density of diesel. As a result, the JetQuad will remain competitive for many years to come [13
The power-to-weight ratio determines how much power a given engine outputs for a given mass of that engine. Electrical drones have a large penalty in this regard. A brushless electrical motor, on its own, has a very large power-to-weight ratio. However, when added to the weight of propeller, electronic speed controllers, and batteries, this ratio is greatly decreased. Turbine-based engines, such as jet engines, do not suffer from this problem. More specifically, the JetQuad uses microturbines that have an ultrahigh rotation rate and lead to vast amounts of power produced from a small engine. In addition, electrical drones must limit current flow to prevent the overheating of electronics that support smooth motor operation. In contrast, fuel flow rate is the limiting factor for turbine-based engines. It gives jet-engine designers the flexibility to extract much more power from smaller motors [13
However, the dynamic behavior and control requirements for the JQ are different from those of quadrotors. This topic has not been considered in the literature yet. Thus, the main contribution of this paper is to focus on control requirements and control mode identification of the JQ to enable researchers to focus on control system designs and optimization for this promising concept.
The JQ is a quad jet engine-powered drone proposed by FusionFlight in 2016 [13
]. It is based on patented air booster (AB) technology that allows for stable and high-performance flight through the atmosphere. It will push the frontiers of drone technology to a whole new level in the future. The main structure of a JQ is shown in Figure 1
. It is composed of a main body and four microjet engines. Each microturbine uses an electric starter as well.
The modeling and simulation of the JQ was presented and discussed in detail in References [14
]. The bond graph as a graphical representation tool for physical dynamic systems was utilized to model and simulate the dynamic behavior of the JQ.
A bond graph is a very suitable approach to modeling mechatronic systems, as it allows the conversion of the system into state-space representation [17
]. The bond graph has been used in turbomachinery applications widely: Gas turbine modeling and analysis [22
], noise prediction and control [25
], and surge prediction and control [27
] are topics in which a bond graph has been successfully used. In previous studies by the authors, both propulsion and the main body of the JQ were modeled in a bond graph, and these models were then combined to predict the dynamic behavior of the system [14
]. This model was used for this paper to generate more results in order to develop the control requirements for the JQ as well as to identify control modes that should be satisfied simultaneously for safe and optimal operation of the JQ.
For this purpose, a brief summary of the modeling approach is first presented, and the developed model is explained in detail. Two different scenarios for thrust profile are then defined to analyze the dynamic behavior of the JQ from compatibility and robustness points of view. Based on the simulation results, the Jet Quad control requirements are identified and prioritized, and essential control modes are defined. A control structure with its associated control algorithm to satisfy all control modes simultaneously is finally proposed.
2. JetQuad Modeling
As a case study, the JQ developed by FusionFlight, “AB4 JetQuad: Quad-Turbine Drone”, is used in this paper. The characteristics of the AB4 are shown in Table 1
. As mentioned earlier, the model of the JQ was developed using a bond graph in previous studies by the authors. Full details about the modeling procedure can be found in References [14
]. The main assumptions used in the modeling approach are as follows:
Heat loss in components is negligible.
Inlet pressure drop is negligible.
The compressor mass flow rate is constant.
The turbine mass flow rate is constant and has no effect on energy storage.
The nozzle mass flow rate is constant, with no effect on energy storage.
The schematic of the jet engine and the generated bond graph model are shown in Figure 2
. The main parameters of the gas turbine, as well as the equations used to generate the bond graph model for jet engines, are listed in Table 2
and Table 3
, respectively. The internal control system of the jet engine is an industrial min-max controller to regulate the fuel flow to the combustion chamber in order to follow the required thrust profile precisely. This controller was also discussed and simulated in detail in References [30
]. This strategy is to satisfy all jet engine control modes simultaneously to protect the engine from malfunctions and physical limitations.
shows the complete dynamic model of the gas turbine engine after coupling the bond-graph submodels in which a one-to-one map between the components exists. This figure shows the modular modeling ability of the bond graph approach.
Here, 20-sim software was used to generate the bond graph model for the JQ: 20-sim is a modeling and simulation program for mechatronic systems in which you can enter a model graphically, similarly to drawing an engineering scheme. With these models, you can simulate and analyze the behavior of multidomain dynamic systems and create control systems. Moreover, bond graphs are a network-like description of physical systems in terms of ideal physical processes in which the system characteristics are split up into an (imaginary) set of separate elements. Each element describes an idealized physical process.
For jet engine modeling, the compressor, turbine, and nozzle are considered to be energy dissipater elements (resistance), and the combustion chamber and shaft dynamics are modeled as energy capacitor elements (i.e., capacitor and inertia). These elements are connected together by energy and information bonds, and zero and one junctions.
As can be seen in Table 3
, there are two different types of equations for modeling purposes: algebraic equations and differential equations. It should be noted that combustion chamber, shaft dynamics, and plenum are modeled using differential equations, whereas compressors, turbines, and nozzle models use algebraic equations. The numerical solution starts with the differential equations to calculate inputs for algebraic equations in a predefined ambient condition, and the fuel flow is calculated by the controller. Then, the algebraic equations are solved to complete a time step and to prepare the data for the next step of differential equations. The procedure of the numerical method used for modeling purposes in this paper is shown in Figure 3
Moreover, the jet engines use a DC electric starter motor to operate. The starter motor model comprises electrical and mechanical parts. The electrical part includes stator windings and battery connections to convert the battery electrical energy to mechanical energy on the shaft. The mechanical part, which transfers the produced torque by the electrical part to the shaft, contains the shaft and the ball bearings. This device was also (both the mechanical part and electrical part) modeled in detail in References [14
], and the results were validated against experimental data. The electric starter, its schematic, and the generated bond graph model are shown in Figure 4
. The starter motor characteristics are shown in Table 4
. In addition, Figure 5
confirms the validity of the model by comparing the results to experimental data.
Finally, by combination of modular models of JQ components, the whole model is developed as shown in Figure 6
. Figure 6
a shows the jet engine model with different elements, as discussed earlier. The rigid body motion of the main body is defined by a set of Euler’s equations that are presented in Figure 6
b. The combination of four jet engine models, electric starters, main body, and the controller are shown in Figure 6
c. As shown in this figure, different components of the JetQuad model are combined together using zero and one junctions and by information and energy bonds. Just one of the jet engine models (on the right side of the figure) is expanded, and the three others are masked to keep the figure tidy. The engine control system is also an internal industrial min-max control strategy that regulates fuel flow into the jet engines to satisfy all engine control modes [30
]. This model is able to predict the dynamic behavior of the JQ with any predefined thrust profile. Thus, different scenarios for thrust profiles could be inserted into the model to investigate the dynamics of the JQ.