This paper presents a flight control system for an organic flight array (OFA) with a new configuration consisting of multimodularized ductedfan unmanned aerial vehicles. The OFA has a distinguished advantage of assembling or separating with respect to its missions or operational conditions because of its reconfigurable structure. Therefore, designing a controller that can be flexibly applied in each situation is necessary. First, a dynamic modeling of the OFA based on a single ductedfan vehicle is performed. Second, the inner loop for attitude control is designed through dynamic model inversion and a PD controller. However, an adaptive control component is needed to flexibly cope with the uncertainty because the operating environment of the OFA is varied, and uncertainty exists depending on the number of modules to be assembled and disturbances. In addition, the performance of the neural network adaptive controller is verified through a numerical simulation according to two scenarios.
Unmanned aerial vehicles (UAVs) with many types, sizes, and ways of flight have been used in various fields during the past decades. Interest in vertical takeoff and landing (VTOL) vehicles, in particular, greatly increased because having a space for a runway is not necessary, and hovering is easier than in fixedwing UAVs. These features have recently been used for military purposes, such as surveillance of urban warfare and nearfield reconnaissance. In addition, performing missions (e.g., communication relay, widearea reconnaissance, and radar jamming) is possible because the field of application is diversified and because of the growth of technology. The VTOL UAVs are also utilized in the civil field for image photographing and in the aviation transport industry because of their advantages. Moreover, the VTOL UAVs have also been actively utilized for hobby and leisure and are classified into multirotor [
Although various VTOL UAVs are capable of hovering, their operation is restricted in the environment, where gusts or strong winds are constantly blown. Moreover, a disadvantage of having the thrusttoweight ratio lower than that of a fixedwing also exists. Therefore, many studies were conducted to overcome the disadvantages of the VTOL UAVs. Accordingly, studies have also been recently conducted to overcome the instability of the vehicle by using a controller that can more robustly cope with gusts and disturbances [
Operational concept of the OFA.
Figure
Simulation model.
Control surface sign conventions.
Definition  Sense  Flaps  Effect 

The acceleration and angular acceleration can generally be defined based on the coordinate system of Figure
The moment variables of (
Rotor:
In (
Fuselage: the fuselage generates a drag force proportional to the area along each axis. The force and the moment by the fuselage are defined as follows:
Here,
Duct: the duct has a circular symmetrical shape around the
The force and the drag per unit angle generated by the airfoil using (
The lip moment induced by the lift imbalance phenomenon and the momentum drag generated by the reaction of the duct during the translational motion are included in the duct component.
Each component can be expressed as follows:
The
Control surfaces: the control surfaces, which change the attitude of the vehicle by adjusting the direction of the wake generated by the rotor, are located directly below the duct. They perform the roles of an aileron, elevator, and rudder. The forces and moments generated by the control surfaces are defined as follows:
Gravity: the gravity generates a force based on the bodyfixed coordinate system whenever the attitude of the vehicle changes. The forces generated by the roll and pitch motion of the vehicle are defined as follows:
Gyroscopic moment: the gyroscopic moment is defined as a moment that is incidentally induced to the vehicle by the rotating rotor. Each component can be expressed as follows:
The gyroscopic moment is a value proportional to the angular velocity and the RPM of the rotor. In (
Coefficients of the rotor component by DFDC.
Component  Parameter  Value 

Thrust  
Torque  
The OFA generally means a combined vehicle of two or more single ductedfan modules. In this research, each ductedfan vehicle was assembled to have the same control surface direction for the simplification of the dynamic modeling. In addition, all modules were located on the same plane, so as not to consider the
Arrangement of the control surfaces in the assembling mode.
The control matrix
The model dynamic inversion technique can linearly convert nonlinear dynamic equations to cancel the nonlinearities. Applying a linear controller to such nonlinear engineering models is not easy because most engineering models have nonlinearities. The dynamic equation can be expressed as follows if the state variables of the dynamic model are measurable [
The nonlinearity of the system can be canceled, and the system can be controlled in a stable state if the pseudo control input can be appropriately designed. Furthermore, the system can be controlled using a linear controller if the nonlinearity is removed by applying the model inversion technique to a nonlinear system. However, perfectly implementing the same model as that of the actual aircraft is impossible because the aircraft model can be changed due to the mission environment or arbitrary influence even in actual flight situations. Therefore, a complete model cannot be implemented, and an error occurs when applying the DMI technique. This process is called the model inversion error. The dynamic model considering the model error can be expressed as follows:
As a result, the error equations can now be defined by (
The objective of the adaptive control input is to design
The adaptive control input was designed to compensate for the model error, which changes in real time. A model error can generally be implemented by the neural network with a finite number of basis functions as follows:
In this case, a value can be defined as follows if it is obtained by the weight that can generate an optimal adaptive control input on
The absolute difference between the estimated and actual values of the model error is given by (
On the compact domain, it is possible to assume that
There is a fixed point
As a result, the model error can be canceled through the adaptive input and can be defined as
The weights designed in (
The
Figure
Schematic of the radial basis function neural network.
Gaussian function used as basis.
Input variables of the neural network.
Channel  Input variables 

Phi ( 

Theta ( 

Psi ( 
A PD controller was used, and the DMI method was applied herein as an inner loop for attitude control. A controller structure with an adaptive control input based on the neural network was additionally considered in a situation where a model error occurs. Figure
Controller structure of the adaptive neural network.
A numerical simulation was performed herein by applying the dynamic model inversion technique and the PD controller. The simulation result was analyzed according to the presence or absence of the NN by defining the scenario in which the uncertainty or the disturbance occurred. Each of the scenarios simulated the attitude control assuming a situation, in which an arbitrary model uncertainty is given, and simulated the path control in the situation where the strong disturbance continuously influences. Figure
Simulation model consisting of three single modules.
The first scenario assumed that the model uncertainty increases as the number of ductedfan vehicles increases. It is assumed that 0 to 30% model uncertainty is generated in real time when two modules are added to the existing module. A simulation was performed to verify the control performance according to the application of the neural network. Figure
Euler angle response in scenario 1.
RPM control input in scenario 1.
Control surface deflection angle in scenario 1.
Weight value of the neural network in scenario 1.
The second scenario presented a situation where the OFA consisting of three modules performed path control to combine with the other arrays in a strong disturbance environment. The attitude controller of the inner loop was generally classified according to whether the neural network was applied.
The outer loop for the path control adopted the PID controller. The disturbance was also assumed to be a uniform wind of 1.5 m/s along the
Position of the OFA in scenario 2.
However, when the neural network controller is applied, it is observed that the position command is slightly slower but follows normally. Figure
Attitude response when considering the neural network in scenario 2.
RPM control input when considering the neural network in scenario 2.
Control surface deflection angle when considering the neural network in scenario 2.
Since harsh disturbance is injected from the beginning of the simulation, such oscillation may be observed until the weights between the neural network layers are adjusted with sufficient samples of the system inputs/outputs. Furthermore, we considered the HS5070MH servo motor as the control surface actuator that can deflect 60 deg for 0.12 sec at no load condition. Even if the full actuator performance cannot be guaranteed due to the aerodynamic load to the servo during the flight, there is still a sufficient margin to accommodate the maximum angular velocity (200 deg/s) observed in the simulation results. Figure
Weight value of the neural network in scenario 2.
This study presented a concept of the organic flight array that can simultaneously perform various missions with a single ductedfan vehicle through the assembling, separation, and cooperation modes. First, this study proposed a dynamic model for a single ductedfan vehicle and defined the OFA dynamic model of the affine form, which is specified by the number of assembling modules. A control system was designed based on this through a dynamic model inversion and a PD controller. The adaptive controller based on the radial basis function neural network was also designed for the control system that can avoid model uncertainty or disturbance. Subsequently, the integrated simulation environment was constructed to verify the controller performance. The simulation results confirmed that the control performance was improved when the adaptive controller using the radial basis function neural network was considered in the case of model uncertainty or disturbance. Consequently, the control stability can be guaranteed when the neural network is used as an adaptive controller in a situation where the model uncertainty is large or the disturbance is strong.
The authors declare that they have no conflicts of interest.
This work is partly supported by the research project (no. 10062497) funded by the Ministry of Trade, Industry & Energy, Korean Government.