The paper seeks to study the control system design of a novel unmanned aerial vehicle (UAV). The UAV is capable of vertical takeoff and landing (VTOL), transition flight and cruising via the technique of direct force control. The incremental nonlinear dynamic inversion (INDI) approach is adopted for the 6-DOF nonlinear and nonaffine control of the UAV. Based on the INDI control law, a method of two-layer cascaded optimal control allocation is proposed to handle the redundant and coupled control variables. For the weight selection in optimal control allocation, a dynamic weight strategy is proposed. This strategy can adjust the weight of the objective function according to the flight states and mission requirements, thus determining the optimizing direction and ensuring the rationality of the allocation results. Simulation results indicate that the UAV can track the target trajectory accurately and exhibit continuous maneuverability in transition flight.
UAVs have increasing applications including surveillance, communications, search and rescue operations, and other military tasks. Among different flight conditions of UAVs, the 0–1000 m height area in cities is one of the most significant applications, where complex terrain and significant gusts arising from atmospheric turbulence exist.
This research studies a novel fixed-wing VTOL UAV with thrust vector engines, which can be applied in urban areas. The UAV can get rid of the restrictions imposed by takeoff and landing conditions and be accurately recovered by hover function; the UAV owns a larger combat range and higher flight speed by forward flight capability. A new concept of low-speed cruising is studied in this paper. For the most current VTOL aircrafts, the transition from hover to forward flight is short and stable. However, for low-speed cruising, the transition is prolonged as a normal flight state. The vehicle can maintain transition flight for long time cruising by adopting direct force control and has favorable maneuverability. This flight mode is appropriate for vehicles flying in low-altitude complex conditions. In the meantime, under the low speed of UAV and the inefficient aerodynamic surface control during the transition flight, the incorporated control strategy of vectoring nozzles and aerodynamic surface should be adopted to control the attitude. In view of this, the thrust vector direct force control is of critical significance for transition maneuver. However, large nonlinearities, redundancies, and coupling effects arise when this technique is adopted.
In recent years, the research on VTOL UAVs is increasingly prosperous with the advancements in automatic control and the increasing popularity of UAV platforms [
The INDI method is adopted in this paper to control UAV’s position/attitude during transition maneuver. The INDI method, which originates from the nonlinear dynamic inversion (NDI), solves the incremental form of equations of motion and generates a control law substantially reducing the dependence on aerodynamic model and other vehicle models. INDI was firstly adopted to control UAV’s attitude control by Sieberling et al. [
An INDI control system is designed in this paper to address the 6-DOF nonlinear control of the UAV in transition flight, and the main contributions are listed below:
Given the problems of strong nonlinearities and multiaxis coupling characteristics, a unified 6-DOF nonlinear control strategy is proposed to control position/attitude and there is no need to switch the control logic according to different flight states. The INDI method is introduced to address the model uncertainty and control coupling problem. Different from the work conducted by Lu et al. [ A two-layer cascaded optimal control allocation method is proposed to address the control redundancy based on the INDI control law. The first-layer optimal allocation is conducted to allocate the increment of flight attitude and vectored thrust in the translational dynamics control loop. The solution of the engine thrust, vectoring nozzle deflections, and aerodynamic surface deflections are calculated in the second-layer control allocation A dynamic weight selection strategy is designed for the objective function of the two-layer cascaded optimal control allocation. In dynamic weight selection strategy, a weight generator and a weight regulator are designed, which calculate weight through an analytic hierarchy process (AHP) and adjust weight according to flight states and mission requirement, respectively. The dynamic weight selection strategy can allocate control variables according to mission requirement and ensure the optimal results to be feasible
This paper is constructed as follows: the configuration and aerodynamics characteristics of the VTOL UAV researched in this paper are described in Section
The UAV is designed in a tandem-wing plus lift-body configuration. This aerodynamic configuration can provide more lift under the limitation imposed by wing span, and it makes UAV applicable to fly in low-altitude complex flight condition. The power system consists of a lift fan in the front part of fuselage and two thrust vector engines in each side of the rear part of fuselage, as presented in Figures
UAV aerodynamic and power configurations.
Vectored thrust of power system
UAV power system
Vectored thrust of lift fan
Lift fan
Vectored thrust of engine
Thrust vector engine
In the case of no wind tunnel experiment, the UAV’s aerodynamic coefficients were obtained by the method of aerodynamic estimation and CFD calculation together. In aerodynamic coefficients, the static pitch moment derivative
Prototype basic data.
Item | Data |
---|---|
Running takeoff speed | 15 m/s |
Cruise speed | 20 m/s |
Vehicle length | 1 m |
Rear wing span | 1.57 m |
Vehicle weight | 5 kg |
Maximum engine thrust (single) | 2.6 kg |
Maximum lift fan thrust | 3.8 kg |
Flight range | 6 km |
This section presents the design process of the control system. The trajectory tracking controller, by adopting time-scaled method, is split into four control loops, i.e., translational kinematics (position) control loop, translational dynamics (flight path) control loop, rotational kinematics (attitude) control loop, and rotational dynamics (angular rate) control loop. Given the differences of the inner and outer loops in the time constants, the control laws for inner and outer loops can be designed independently [
The reference flight path vector is calculated in translational kinematic control loop based on the target trajectory. The position vector and flight path vector of the aircraft are defined as
The desired derivatives of position vector can be designed by a classical linear controller according to the reference trajectory and the feedback of the vehicle’s position.
In (
In translational dynamic control loop, the vehicle’s flight path status
In this loop, there are totally 6 control inputs. Among them,
In (
Applying Taylor expansion to
In (
Replace
To simplify the computation process, it is assumed that
In (
In (
However, the filter leads to a delay which should be compensated. In the Taylor expansion shown in (
The model uncertainty stemmed from aerodynamic force in translational dynamic control loop is analyzed in this subsection. The change of aerodynamic coefficients is assumed to be primarily caused by the angle of attack (
In (
The application of INDI in the translational dynamics control loop has two primary advantages. First, INDI control law restrains the model uncertainty caused by aerodynamic force in control matrix
The objective in this control loop is to track
In (
It is noteworthy that
Like aerodynamic force, the aerodynamic coefficients can also be denoted as
In (
The aerodynamic control moments are denoted as
In (
After the calculation of four control loops,
Conceptual block diagram of the control system.
The allocation method of redundant control variables (elements in
The first-layer control allocation is conducted to allocate the increment of flight attitude
In translational dynamics control loop, the control equation is linearized by the INDI method. Accordingly, the dynamic weight pseudoinverse method can be used in control allocation. Based on (
In (
Define
Substitute (
Based on the foregoing deduction, the optimal problem presented in (
On that basis, the minimum norm solution of the control allocation problem is obtained as
In (
The
In the course of control allocation, the weight is adopted to describe the differences of control variables’ significance. On the basis of the significance of control variables changing with flight states and mission requirements, a dynamic weight strategy is proposed to allocate control variables optimally and properly.
The traditional determination of control variable’s weight largely depends on human experience. In this regard, there is no absolute criteria for weight determination. It is commonly difficult to judge a control variable’s significance globally, while the significance between every two control variables can be easily compared. In dynamic weight strategy, the analytic hierarchy process (AHP) is adopted to synthesize comparison results of every two control variables and calculate each control variable’s weight by AHP-judgment matrix. The weight matrixes in the objective function can be denoted as
In (
Based on the subordinations, the sets and control variables are classified into three hierarchies, known as the weight structure, as presented in Figure
Illustration of weight structure.
The weights in different hierarchies are determined, respectively, and they all obey the rules listed below:
Weights in the same set are required to be normalized
Weights in the first and second hierarchies satisfy
In the third hierarchy,
The weight generator is designed to generate the initial value of the weight structure, in every control period before optimization. Its working principle is introduced below:
Establish weight structures which consist of
Artificially design and test several weight structures according to some typical flight states and mission requirements. On this basis, index weight structures with their relative flight states and mission requirements save weight structures into repository.
Acquire weight structure corresponding to the current flight state and mission requirement through traversing the repository.
A simplified repository is established in this paper. For flight states, merely the impact of velocity is factored in, and velocities 5 m/s, 10 m/s, 15 m/s, 20 m/s, and 25 m/s count as typical flight states. In mission requirement, only the impact of direct force control level (
The weight regulator is designed to adjust the weight when control variables exceed their limitation and ensure the rationality of allocation results. The working process of weight regulator is shown below.
Extract control variables saturated in the last control allocation according to the feedback information. The saturated control variable can be single or multiple.
Update saturation counter. Every control variable has a corresponding saturation counter
Adjust the weight structure in accordance with the saturation counter results. For different hierarchies of weight structure, the adjustment strategies are different, as illustrated below:
For
For
For
The range of saturation counter
Working process of first-layer control allocation and dynamic weight strategy.
In the second-layer control allocation, the allocation of aerodynamic control surfaces (
The dynamic model of the engine system can be denoted as
Define
In (
The incremental linear allocation method allocates
The increment of aerodynamic control surface is calculated by
The reference value of aerodynamic control surface can be expressed as
On that basis, introduce (
The thrust vector engine model is transformed from a nonlinear system into a linear system, and
The reference thrust vector engine actuators are calculated by (
The range of
The flow chart of the incremental linear allocation is presented in Figure
Second-layer incremental linear allocation method.
In nonlinear allocation, other than calculating
Second-layer normal nonlinear allocation method.
An example is designed in this section to test the control method which is discussed in the previous section. The target trajectory is designed as follows:
The initial state of UAV is static. From 0 to 20 seconds, the vehicle is climbing up and accelerating to 10 m/s in ground
The example involves three different flight states, i.e., VTOL, transition flight, and cruise. These states can adequately show UAV’s longitudinal and lateral maneuverability required for an urban flight vehicle. The controller designed in this paper does not need to switch as flight states change. The trajectory can be tracked merely through adjusting the weights in the controller. As the simulation results prove, the control method can solve nonlinear, nonaffine, and coupled control problems effectively and allocate redundant control variables appropriately.
To show the effectiveness of the two-layer cascaded control allocation for different flight states and mission requirements, two flight strategies are designed. In the first strategy, the UAV will track the trajectory with small attitude angle magnitude and fluctuation. In the second strategy, the vehicle is required to track the target trajectory through employing small direct force control and primarily adopting attitude control. For all strategies, the incremental linear allocation method is adopted in the second-layer control allocation, and 0.01 s is adopted as the calculation step.
For Strategy
The weight structure is generated and regulated all through the trajectory tracking, and at last, the weight changes into (
Additionally, the weight change would be better consecutive for different flight states and mission requirements, since inconsecutive weight change will cause the saltation of flight states. The trajectory tracking result is presented in Figure
Trajectory tracking results.
The flight states of Strategy
Flight states of Strategy
Three-axis velocity
Kinematic angle
Wind angle
Body angle
Control moments
Vectored thrust in body axis
Engine thrust
Vectoring nozzle deflection
Control surface deflection
Percentage of aerodynamic control moments
The wind angle and body angle of the UAV are presented in Figures
Figures
From 20 to 60 seconds, the UAV is in transition flight and making lateral maneuvering, the flight velocity is 10 m/s, and
When
For Strategy
With the generation and regulation of weight structure during trajectory tracking, at the end of simulation, the weight changes into (
The flight states of Strategy
Flight states of Strategy
Wind angle
Body angle
Control moments
Vectored thrust in body axis
Engine thrust
Vectoring nozzle deflection
Due to different weight selections, the tracking maneuver in Strategy
Comparing the change of
The application of the INDI control method has a requirement for the frequency of the control system. High control frequency is especially required for fiercer maneuver. In INDI control, the multiplication of increment caused by coupled control variables counts as a high-order small quantity and is neglected, which will cause large errors under fierce maneuver and large sampling time. Also, in the discrete differentiator, which is used to calculate the derivative of control vectors, the larger sampling time will result in less derivation accuracy. These errors can be restrained through reducing the sampling time, which is equivalent to increase the control frequency. As the simulation results indicate, UAV can track the target trajectory accurately. The application of the INDI method and two-layer cascaded optimal control allocation in a controller of 100 Hz can satisfy the need of maneuver in this case. Furthermore, the simulation validates the effectiveness of the control method developed in this paper.
A trajectory control system is proposed in this paper to solve the nonlinear, nonaffine, redundant, and coupled control problems existing in a UAV, which adopts direct force control technique. The research results are concluded below: (1) as the simulation indicates, the INDI controller is applicable for different flight modes, and the UAV with the INDI controller exhibits continuous maneuverability in transition flight. (2) The two-layer cascaded optimal control allocation is designed based on INDI control law; with rationally designed constraints and cascaded solving strategy, this method transforms the nonlinear coupled allocation problem into an incremental linear-equality constraint optimization problem and largely improves the allocation speed. (3) The dynamic weight strategy can adjust the weights according to different flight states and mission requirements, which ensures the rationality of control allocation. In the future, the control system presented in this paper will be incorporated with the controller of a prototype. A flight test is required to be further conducted to verify the effectiveness of the proposed control system.
The results.mat data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there is no conflict of interest regarding the publication of this paper.
This work is supported by the Aeronautical Science Foundation of China Grant 2016ZA72001 and the National Natural Science Foundation of China Grant 11572036. The authors would like to thank all members of the Microraptor Works, Key Lab of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology.