A Fixed-Time Control Method for the Transition Phase of a Tilt-Rotor UAV Considering State Constraints

Abstract

The present invention discloses a fixed-time control method for the transition section of a tilt-rotor unmanned aerial vehicle considering state constraints, including: establishing a longitudinal motion switching nonlinear dynamic model of the tilt-rotor unmanned aerial vehicle; designing a calculation method for the tilt corridor in the transition section of the tilt-rotor unmanned aerial vehicle, and constructing an asymmetric time-varying barrier Lyapunov function to solve the state constraint problem; designing a neural network system for estimating the strong modeling uncertainty caused by the complex aerodynamic coupling between the rotors and the wings; designing a fixed-time adaptive flight control law to compensate for the unknown modeling uncertainty using the neural network system signals; constructing a closed-loop multi-Lyapunov function, and designing and analyzing the parameters of the flight control law to ensure that the state of the unmanned aerial vehicle transition section system always remains within the constraint range and can achieve stability within a fixed time. The present invention solves the fixed-time control problem for the longitudinal transition section of the tilt-rotor unmanned aerial vehicle under strong uncertainty and state constraint conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft safety control, and particularly relates to a fixed-time control method for the transition section of a tilt-rotor unmanned aerial vehicle considering state constraints. Background Technique

[0002] With the continuous development of aviation technology, people's requirements for the performance of aircraft are also constantly increasing. Tilt-rotor unmanned aerial vehicles integrate the functions of helicopters and fixed-wing aircraft, can take off and land vertically without a runway and adapt to complex terrains, have the capabilities of precise hovering and high-speed cruising, and are widely used in military, civilian, and commercial fields. Especially, they have great application potential in low-altitude economies such as agricultural monitoring and logistics, and have become the focus of global aviation research in recent years.

[0003] The control strategies for tilt-rotor unmanned aerial vehicles in helicopter and fixed-wing modes are already mature, but due to their special aerodynamic layout during the transition, the control problems are still challenging. Since its transition process mainly occurs in the longitudinal plane, the flight stability of tilt-rotor unmanned aerial vehicles depends to a large extent on the longitudinal flight control law. During the tilt process of the rotor, there is an area called the "tilt corridor", which imposes strict restrictions on the system state of the unmanned aerial vehicle. Once the system state deviates from this area, it will be difficult to ensure the safety of the transition process of the tilt-rotor unmanned aerial vehicle. In addition, the aerodynamic coupling effect between the rotor and the wing not only increases the difficulty of system modeling but also poses higher requirements for the design of the control system. The complexity of aerodynamic coupling leads to modeling uncertainties, which in turn affect the design of control strategies. The control of the tilt process poses extremely high requirements for the convergence of the system. If the convergence of the control system is insufficient, it may cause the unmanned aerial vehicle to swing violently during the transition process, and may even lead to serious consequences such as out-of-control and crashing. Therefore, the existing control methods still have certain limitations in ensuring the smoothness and safety of the transition process. Summary of the Invention

[0004] The technical problem solved by the present invention is: to provide a fixed-time control method for the longitudinal motion transition section of a tilt-rotor unmanned aerial vehicle under strong uncertainties and state constraints. It not only effectively solves the control problem under the tilt corridor restrictions, but also relaxes the accuracy requirements for the aerodynamic coupling modeling between the rotor and the wing, and significantly improves the convergence performance of the system through fixed-time control technology. This method solves the problems of strong modeling uncertainties and state constraints by introducing a neural network system and an asymmetric barrier Lyapunov function, and improves the convergence of the system by designing a fixed-time controller.

[0005] The present invention adopts the following technical solutions to solve the above technical problems: A fixed-time control method for the transition section of a tilt-rotor unmanned aerial vehicle considering state constraints, including the following steps:

[0006] Step 1: Establish a switched nonlinear system model according to the longitudinal motion characteristics of a tilt-rotor unmanned aerial vehicle (UAV).

[0007] Step 2: Establish a tilt corridor for the multi-constraint conditions in the transition section of the tilt-rotor UAV. On this basis, construct an asymmetric barrier Lyapunov function to confine the system state within the range that satisfies the tilt corridor constraints.

[0008] Step 3: Design a neural network system to estimate the unknown modeling uncertainties caused by the aerodynamic coupling between the rotors and the wings, and obtain an approximation of the unknown modeling uncertainties.

[0009] Step 4: Design a flight control law and an adaptive law, and use the output signal of the neural network system obtained in Step 3, that is, the approximation of the unknown modeling uncertainties, to compensate for the unknown modeling uncertainties.

[0010] Step 5: Construct a closed-loop multi-Lyapunov function, and design and analyze the parameters of the flight control law to keep the state of the tilt-rotor UAV transition section system within the constraint range all the time, and achieve stability within a fixed time.

[0011] As a preferred solution of the present invention, in Step 1, establish a longitudinal switched nonlinear system dynamic model of the tilt-rotor UAV, including the velocity in the axis direction of the body coordinate system and the velocity in the axis direction, pitch angle pitch angular velocity to form a loop.

[0012] The longitudinal motion dynamic model of the tilt-rotor UAV is as follows:

[0013] ,

[0014] where is the pitch angle, is the velocity vector, is the velocity in the axis direction of the body coordinate system, is the velocity in the axis direction of the body coordinate system, is the pitch angular velocity, , are respectively and the first derivatives, , is the nacelle tilt angle; is the control input, is the thrust generated by the rotor, is the longitudinal cyclic margin angle, is the elevator deflection angle; is the modeling uncertainty function of the aerodynamic coupling between the rotor and the wing, are all unknown nonlinear functions; and are the known nonlinear function for modeling and the control gain respectively, expressed as follows:

[0015] , ,

[0016] where is the gravitational acceleration, is the weight of the tilt-rotor UAV, is the moment of inertia, is the mast height, is a constant coefficient, , are the components of the aerodynamic force coefficient in the body coordinate system axis direction and axis direction respectively, is the pitching moment coefficient generated by the aerodynamic force; is the pitching moment coefficient generated by the elevator deflection angle , , are the components of the elevator deflection angle in the body coordinate system axis direction and axis direction respectively;

[0017] According to the change of the nacelle inclination angle of the tilt-rotor UAV in the transition section, the longitudinal motion model of the transition section is divided into several nonlinear subsystems, and the switched nonlinear system model of the tilt-rotor UAV in the transition section is obtained, expressed as follows:

[0018] ,

[0019] where represents is a right-continuous switching signal, is the total number of subsystems. When , it means that the th subsystem is being activated; , , represent the known nonlinear function for modeling, the control gain, and the modeling unknown uncertainty function corresponding to the system at the moment of the switching signal respectively.

[0020] As a preferred embodiment of the present invention, the calculation method of the tilt corridor for the transition section of the tilt-rotor UAV in step 2 is as follows:

[0021] Determine the constraint conditions for the transition section of the tilt-rotor UAV, including:

[0022] ,

[0023] where and are the resultant external forces in the axis direction and the axis direction in the body coordinate system respectively, is the thrust generated by the rotor, is the nacelle tilt angle, is the weight of the tilt-rotor UAV, is the acceleration due to gravity, is the pitch angle, and are the aerodynamic lift and drag respectively, is the angle of attack of the tilt-rotor UAV, and are the zero-lift angle of attack and the critical stall angle of attack respectively, is the maximum thrust provided by the rotor, is the nacelle tilt angle at time

[0024] By solving the multiple constraint conditions in the above formula, obtain the high-speed segment speed and the low-speed segment speed of the tilt corridor for the transition section; Define the system state constraints as follows:

[0025] ,

[0026] where and are the upper and lower bounds of the system state constraints respectively, is the state of the system;

[0027] As a preferred embodiment of the present invention, construct an asymmetric logarithmic barrier Lyapunov function as follows:

[0028] ,

[0029] where is the tracking error of the system state, is a piecewise function, and are briefly denoted as and respectively, and the expressions are as follows:

[0030] ,

[0031] where is the desired tracking instruction.

[0032] As a preferred embodiment of the present invention, the neural network system described in step 3 is designed as:

[0033] ,

[0034] where is the modeling unknown uncertainty function corresponding to the th subsystem, is a block diagonal matrix, is the ideal weight matrix, is the component of the ideal weight matrix, , is the number of nodes of the neural network, is a vector composed of basis functions, is the vector component, is a Gaussian basis function, is the approximation error of the neural network.

[0035] As a preferred embodiment of the present invention, step 4 designs a fixed-time adaptive flight control law and an adaptation law, and uses the output signal of the neural network system obtained in step 3, that is, the approximation value of the unknown modeling uncertainty, to compensate for the unknown modeling uncertainty. The following error variables are defined:

[0036] ,

[0037] where is the pitch angle tracking error, is the tracking error of the velocity in the axis direction in the body coordinate system, is the tracking error of the velocity in the axis direction in the body coordinate system, is the tracking error of the pitch angular velocity, is the filtering error, is the adaptive parameter tracking error, , , are respectively , , desired tracking instructions, is the virtual control law, is the adaptive parameter, , is The estimated value, is the output of the following first-order non-linear switching filter:

[0038]

[0039] where is the switching filter time constant, and are respectively the parameters to be designed and satisfy , is the virtual control law to be designed, is the first derivative of

[0040] The fixed-time adaptive flight control law and the adaptive law are designed as:

[0041] ,

[0042] ,

[0043] ,

[0044] where and and and and and are respectively positive constants to be designed, , is the state constraint gain, is the pitch angle desired command the first derivative of is the control input, is the inverse matrix of the control gain matrix, is the velocity desired command the first derivative of is the diagonal matrix composed of the adaptive parameters, are the adaptive parameters, is the first derivative of represents the known non-linear function of the subsystem corresponding to the and and are respectively positive definite diagonal matrices to be designed, is the state constraint gain diagonal matrix, is the error variable of the velocity, , , and and and The expression is as follows:

[0045] ,

[0046] where 、 、 are defined as follows: , , 、 are respectively the upper and lower bounds of the state constraint.

[0047] As a preferred embodiment of the present invention, a closed-loop multi-Lyapunov function is constructed as follows:

[0048] When the -th subsystem is activated, the closed-loop multi-Lyapunov function is selected as follows:

[0049] ,

[0050] where 、 、 are respectively the Lyapunov functions constructed considering the error variable pitch angle tracking error , speed tracking error and filtering error , and the expressions are as follows:

[0051] ,

[0052] where 、 are respectively abbreviated as 、 , and are defined as follows: , 、 are respectively the upper and lower bounds of the state constraint, is defined as follows: ;

[0053] The derivative of the multi-Lyapunov function with respect to time is as follows:

[0054] ,

[0055] where , , is the upper bound of the derivative of the desired command, is a positive constant, is the filtering time constant, is the upper bound of the approximation error of the neural network;

[0056] Design the average dwell time , where is a normal value, is any value in the interval, and we obtain:

[0057] ,

[0058] where is the multiple Lyapunov function of the system, is the initial value of the multiple Lyapunov function of the system at time , is the chatter boundary, is a bounded value, that is, the closed-loop switching system is bounded, and at the same time, the system states are all within the safety range of the state constraints.

[0059] As a preferred embodiment of the present invention, considering the system state error variable, design the common Lyapunov function as follows:

[0060] ,

[0061] The common Lyapunov function The derivative with respect to time satisfies the following conditions:

[0062] ,

[0063] where , , , , , that is, the system state error converges to the set at time , and the expression is as follows:

[0064] ,

[0065] where is a positive constant, is the tracking error of the system state;

[0066] By adjusting the control parameters , , , , , , , , control the tracking errors of the attitude angle and speed of the tilt-rotor UAV.

[0067] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0068] (1) The present invention uses a switched non-linear system to describe the longitudinal motion dynamics model of a tilt-rotor UAV. Compared with the traditional single-system model and switched linear system model, the dynamics model proposed by the present invention is more general and has practical application value.

[0069] (2) The present invention uses a neural network system to approximate the complex aerodynamic coupling between the rotors and wings, reducing the constraints on modeling uncertainties and improving the robustness of the control system.

[0070] (3) The present invention uses an asymmetric time-varying barrier Lyapunov function to solve the state constraint problem caused by the tilt corridor, ensuring the smooth transition of the tilt-rotor UAV in the transition section. Description of the drawings

[0071] Figure 1 is the overall flowchart of the method of the present invention.

[0072] Figure 2 is the speed of the tilt-rotor UAV in the embodiment of the present invention simulation curve.

[0073] Figure 3 is the speed of the tilt-rotor UAV in the embodiment of the present invention simulation curve.

[0074] Figure 4 is the pitch angle of the tilt-rotor UAV in the embodiment of the present invention simulation curve.

[0075] Figure 5 is the pitch angular velocity of the tilt-rotor UAV in the embodiment of the present invention simulation curve.

[0076] Figure 6 is the adaptive parameter in the embodiment of the present invention simulation curve.

[0077] Figure 7 is the adaptive parameter in the embodiment of the present invention simulation curve.

[0078] Figure 8 is the adaptive parameter in the embodiment of the present invention simulation curve.

[0079] Figure 9 is the control switching signal diagram. Detailed implementation manners

[0080] The present invention will be further illustrated below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art to the present invention fall within the scope defined by the appended claims of this application.

[0081] A fixed-time control method for the transition section of a tilt-rotor unmanned aerial vehicle considering state constraints according to the present invention has a process as Figure 1 , and includes the following steps:

[0082] (1) First, according to the longitudinal motion characteristics of the tilt-rotor unmanned aerial vehicle, a switched nonlinear system model is established.

[0083] In this embodiment, taking the longitudinal control of the tilt-rotor unmanned aerial vehicle as an example, a longitudinal switched nonlinear system dynamics model of the tilt-rotor unmanned aerial vehicle is established, including the velocity in the axis direction of the body coordinate system and the velocity in the axis direction, pitch angle , pitch angular velocity

[0084] (1),

[0085] where is the pitch angle, is the velocity vector, is the velocity in the axis direction in the body coordinate system, is the velocity in the axis direction in the body coordinate system, is the pitch angular velocity, , are respectively and the first derivatives of, , is the nacelle tilt angle; is the control input (controller), is the thrust generated by the rotor, is the longitudinal cyclic pitch angle, is the elevator deflection angle; is the modeling uncertainty function of the aerodynamic coupling between the rotor and the wing, are all unknown nonlinear functions. and are respectively the modeling known nonlinear function and the control gain, and are expressed as follows:

[0086] , ,

[0087] wherein is the acceleration due to gravity, is the weight of the tiltrotor UAV, is the moment of inertia, is the mast height, is a constant coefficient, and are the component force coefficients of the aerodynamic force coefficients decomposed in the body coordinate system axis direction and axis direction respectively, is the pitch moment coefficient generated by the aerodynamic force; is the pitch moment coefficient generated by the elevator deflection angle , and are the component force coefficients generated by the elevator deflection angle in the body coordinate system axis direction and axis direction respectively.

[0088] According to the change of the nacelle tilt angle of the tiltrotor UAV in the transition section, the longitudinal motion model of the transition section is divided into several nonlinear subsystems, and the switched nonlinear system model of the tiltrotor UAV in the transition section is obtained, which is expressed as follows:

[0089] (2),

[0090] wherein represents is a right - continuous switching signal, is the total number of subsystems. When , it means that the th subsystem is being activated. and and represent the known nonlinear function, control gain and unknown uncertain function of the system corresponding to the switching signal at the moment respectively.

[0091] (2) Establish a tilt corridor for the multi - constraint conditions of the tiltrotor UAV in the transition section. On this basis, construct an asymmetric barrier Lyapunov function to confine the system state within the range that satisfies the tilt corridor constraints.

[0092] During the rotor tilting process, the gravity of the airframe is balanced by the aerodynamic lift and the rotor thrust together. The magnitude of the aerodynamic lift is jointly affected by the speed and angle of attack of the UAV, while the magnitude of the rotor thrust is limited by the nacelle tilt angle and the maximum thrust that the rotor can provide. The constraint conditions of the tiltrotor UAV in the transition section are designed as follows in this embodiment:

[0093] (3),

[0094] where and are the resultant external forces in the -axis direction and -axis direction in the body coordinate system respectively, is the thrust generated by the rotor, is the nacelle tilt angle, is the weight of the tilt-rotor UAV, is the acceleration due to gravity, is the pitch angle, and are the aerodynamic lift and drag respectively, is the angle of attack of the tilt-rotor UAV, and are the angle of attack for zero lift and the critical stall angle of attack respectively, is the maximum thrust provided by the rotor, is the nacelle tilt angle at time and the low-speed segment speed .

[0095] According to the constraints of the high-speed and low-speed segments brought by the tilt corridor, and to ensure that the attitude angle remains within a reasonable range during the tilting process, thus achieving safe flight in the transition segment, the system state needs to be constrained within a reasonable range. Therefore, the system state constraints are defined as follows:

[0096] (4),

[0097] where and are the upper and lower bounds of the system state constraints respectively, is the state of the system.

[0098] Construct an asymmetric logarithmic barrier Lyapunov function as follows:

[0099] (5),

[0100] where is the tracking error of the system state, is a piecewise function, and are briefly denoted as and respectively, and the expressions are as follows:

[0101] (6),

[0102] where is the desired tracking instruction.

[0103] (3) Design a neural network system to estimate the unknown modeling uncertainty caused by the aerodynamic coupling between the rotor and the wing, and obtain an approximation of the unknown modeling uncertainty.

[0104] Lemma 1: For any continuous function defined on the compact set there exists a neural network such that

[0105] (7),

[0106] where is the ideal weight vector of the neural network, is the number of nodes of the neural network, is the basis vector of the neural network, is the approximation error of the neural network satisfying , is an unknown positive constant, usually a Gaussian function is chosen.

[0107] (8),

[0108] where is the center vector, is the width of the Gaussian function.

[0109] According to Lemma 1, the neural network system is designed as:

[0110] (9),

[0111] where is the modeling unknown uncertainty function corresponding to the -th subsystem, is a block - diagonal matrix, is the ideal weight matrix, is the component of the ideal weight matrix, , is the number of nodes of the neural network, is the vector composed of basis functions, is the -th component of the vector is the Gaussian basis function, is the approximation error of the neural network.

[0112] (4) Design the flight control law and adaptive law, and use the output signal of the neural network system obtained in step (3), that is, the approximation value of the unknown modeling uncertainty, to compensate for the unknown modeling uncertainty.

[0113] First, define the following error variables:

[0114] (10),

[0115] where is the pitch angle tracking error, is the tracking error of the velocity in the axis direction of the body coordinate system, is the tracking error of the velocity in the axis direction of the body coordinate system, is the tracking error of the pitch angular velocity, is the filtering error, is the adaptive parameter tracking error, , , are respectively , , of the desired tracking commands, is the virtual control law, is the adaptive parameter, , is 's estimated value, is the output of the following first-order nonlinear switching filter:

[0116] (11),

[0117] where is the switching filtering time constant, , are respectively the parameters to be designed and satisfy , is the virtual control law to be designed, is 's first derivative.

[0118] Considering the error variable , design the following Lyapunov function:

[0119] (12),

[0120] where , are respectively abbreviated as , , and are defined as follows: , 、 are respectively the upper and lower bounds of the state constraint, defined as follows: . .

[0121] According to Eqs. (1) and (10), the derivative of with respect to time is as follows:

[0122] (13),

[0123] where .

[0124] Based on Eq. (13), an adaptive flight control law, i.e., the virtual control law is designed as follows:

[0125] (14),

[0126] where 、 、 are positive constants to be designed, 、 are parameters to be designed and satisfy , is the desired pitch angle command 's first derivative, is the state constraint gain, and its expression is as follows:

[0127] (15),

[0128] where is a parameter to be designed such that ; 、 are respectively 、 's first derivatives.

[0129] Substituting Eq. (14) into Eq. (13), we get:

[0130] (16),

[0131] Secondly, when the th subsystem is activated, considering the error variables 、 , the following Lyapunov function is designed:

[0132] (17),

[0133] According to Equations (1) and (10), the derivative with respect to time is as follows:

[0134] (18),

[0135] Based on Equation (18), a controller and an adaptation law are designed as follows:

[0136] (19),

[0137] (20),

[0138] where is the control input, is the inverse matrix of the control gain matrix, is the desired velocity command 's first derivative, is a diagonal matrix composed of adaptation parameters, represents the known nonlinear function of the th subsystem for modeling, , , are positive definite diagonal matrices to be designed respectively, is the state constraint gain diagonal matrix, is the velocity error variable, , , are positive constants to be designed respectively, , ; is the adaptation parameter, is 's first derivative, , and are positive constants to be designed respectively, , , 's expressions are as follows:

[0139] (21),

[0140] where is a parameter to be designed such that ; , are , 's first derivatives respectively.

[0141] (5) Construct a closed-loop multi-Lyapunov function, design and analyze the parameters of the flight control law, and keep the state of the transition section system of the tilt-rotor UAV within the constraints at all times to ensure the stability of the transition section of the tilt-rotor UAV.

[0142] According to equations (17), (18), (19), and (20), The derivative with respect to time is as follows:

[0143] (22),

[0144] Considering the filter error variable , design the following Lyapunov function:

[0145] (23),

[0146] According to equation (11), and denote the upper bound of as , The derivative with respect to time is as follows:

[0147] (24),

[0148] where is the filter time constant.

[0149] When the th subsystem is activated, design the multi-Lyapunov function of the entire closed-loop system as follows:

[0150] (25),

[0151] where , , are the Lyapunov functions constructed considering the error variables pitch angle tracking error , speed tracking error and filter error respectively.

[0152] Lemma 2: For any positive constant , the following inequality holds:

[0153] ,

[0154] According to Lemma 2, we can obtain:

[0155] (26),

[0156] According to Eqs. (16), (22), (24), and (26), the derivatives with respect to time are as follows: :

[0157] (27),

[0158] where , . is the upper bound of the desired command derivative, is a positive constant, is the filtering time constant, is the upper bound of the neural network approximation error.

[0159] According to Eq. (10), we have , which holds. When the following inequality can be obtained:

[0160] (28),

[0161] where .

[0162] According to Eqs. (25) and (28), the relationship between multiple Lyapunov functions can be obtained as follows:

[0163] (29),

[0164] where .

[0165] Next, it is proved that the switched system is stable. When , and represent the switching instants of the -th subsystem and the -th subsystem, respectively. Integrating Eq. (27) gives the following inequality:

[0166] (30),

[0167] Substituting Eq. (29) into Eq. (30) gives the following inequality:

[0168] (31),

[0169] where denotes the left limit value at , denotes the function value of at time .

[0170] When , for formula (31) from to , denotes the total number of switches that occur in the system within time. By iteration, the following inequality can be obtained:

[0171] (32),

[0172] where is abbreviation.

[0173] From , denotes the total number of switches that occur in the system within time, the following can be obtained:

[0174] (33),

[0175] Design the average dwell time , as a normal value, is any value in the interval, the following can be obtained:

[0176] (34),

[0177] where is the chatter boundary, denotes the total number of switches that occur in the system within time, denotes any moment less than the time .

[0178] Substitute formula (34) into formula (33) to obtain:

[0179] (35),

[0180] Similarly, according to the above analysis, the following can be obtained:

[0181] (36),

[0182] where .

[0183] Substitute formulas (35) and (36) into formula (33) to obtain the following inequality relationship:

[0184] (37),

[0185] where is the multi-Lyapunov function of the system, is the multi-Lyapunov function of the system at time The initial value of is the vibration boundary, and is the bounded value. Therefore, when the average dwell time

[0186] When , the following equation can be obtained:

[0187] (38),

[0188] When , similarly, we can get: , .

[0189] In summary, we can get:

[0190] (39),

[0191] Substituting Equation (6) into Equation (39), we can get:

[0192] (40),

[0193] That is, the state variables of the system are all within the constraints, and the proof is completed.

[0194] Next, it is proved that the system state tracking error can achieve fixed-time convergence. Consider the error variable , and design the Lyapunov function as follows:

[0195] (41),

[0196] Substituting Equations (14) and (26) into Equation (41), the following inequality can be obtained:

[0197] (42),

[0198] Consider the error variable , and design the Lyapunov function as follows:

[0199] (43),

[0200] Substituting Equations (19) and (20) into Equation (43), the following inequality can be obtained:

[0201] (44),

[0202] According to Equation (26), let and , , and , the following inequality can be obtained:

[0203] (45),

[0204] In summary, the system state error will be at time converge to the set inside.

[0205] (46),

[0206] where is a positive constant, is the tracking error of the system state.

[0207] Adjust the control parameters , , , , , , , to reduce the tracking errors of the attitude angle and speed of the tilt-rotor UAV.

[0208] To verify the fixed-time control method for the transition section of the tilt-rotor UAV considering state constraints in the present invention, numerical simulation is carried out based on the controlled object (Equation (2)) and the simulation results are given.

[0209] According to Equation (4), select the system state constraints as follows:

[0210] ,

[0211] where , are respectively the upper and lower bounds of the pitch angle constraint, , are respectively the upper and lower bounds of the pitch angular velocity constraint, , are respectively the upper and lower bounds of the velocity in the axis direction in the body coordinate system, , are respectively the upper and lower bounds of the velocity in the axis direction in the body coordinate system.

[0212] According to the virtual control law (Equation (14)), select the control parameters as: , , , , .

[0213] According to the controller (Equation (19)), the control parameters are selected as follows: , , .

[0214] According to the adaptation law (Equation (20)), the control parameters are selected as follows: , , .

[0215] Regarding the neural network system, design

[0216] , ,

[0217] ;

[0218] The simulation results are as Figures 2 to 9 . As Figure 2 and Figure 3 show, during the entire tilt transition section of the UAV, the flight speed and of the UAV can well track the desired commands and always remain within the boundaries of the state constraints, meeting the flight speed under the tilt corridor constraints. Figure 4 and Figure 5 show that the pitch angle and pitch angular velocity of the UAV can well track the desired commands and always remain within the boundaries of the state constraints, ensuring that the attitude of the UAV can be well maintained stable during the entire tilt transition section. Figures 6 - 8 shows the response curve of the adaptation parameter. Figure 9 is the curve of the switching signal .

[0219] It can be seen from the simulation results that in the presence of state constraints and strong modeling uncertainties, a fixed-time control method for the transition section of a tilt-rotor UAV considering state constraints proposed by the present invention can still effectively guarantee the speed and attitude tracking performance of the UAV, so that the tilt-rotor UAV can smoothly complete the transition from the helicopter mode to the fixed-wing mode.

[0220] The above embodiments are only used to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A fixed-time control method for the transition section of a tilt-rotor UAV considering state constraints, characterized in that It includes the following steps: Step 1: Establish a switched nonlinear system model according to the longitudinal motion characteristics of the tilt-rotor UAV; Establish the longitudinal switched nonlinear system dynamics model of the tilt-rotor UAV, including the loop composed of the velocity u in the x-axis direction and the velocity w in the z-axis direction, the pitch angle θ, and the pitch angular velocity q in the body coordinate system; The longitudinal motion dynamics model of the tilt-rotor UAV is as follows: where x1 = θ is the pitch angle, X2 = [x 21 , x 22 , x 23 T is the velocity vector, x 21 = u is the velocity in the x-axis direction in the body frame, x 22 = w is the velocity in the z-axis direction in the body frame, x 23 = q is the pitch angular velocity, are the first-order derivatives of x1 and X2 respectively, β m is the nacelle inclination angle; U = [T r , T r θ a , δ e T is the control input, T r is the thrust generated by the rotor, θ a is the longitudinal cyclic pitch angle, δ e is the elevator deflection angle; is the modeling uncertainty function of the aerodynamic coupling between the rotor and the wing, and △f1, △f2, △f3 are all unknown nonlinear functions; and are the known nonlinear functions in the modeling and the control gain respectively, and are expressed as follows:​​ where g is the acceleration due to gravity, M is the weight of the tilt-rotor UAV, I y0 is the moment of inertia, l r is the mast height, k y is a constant coefficient, C xc and C zc are the component force coefficients of the aerodynamic force coefficient resolved in the x-axis direction and z-axis direction of the body coordinate system respectively, and C mc is the pitching moment coefficient generated by the aerodynamic force; is the pitching moment coefficient generated by the elevator deflection angle δ e , are the component force coefficients generated by the elevator deflection angle δ e in the x-axis direction and z-axis direction of the body coordinate system respectively; According to the nacelle inclination angle β of the tilt-rotor UAV in the transition section m Based on the change of β, the longitudinal motion model of the transition section is divided into several nonlinear subsystems, and the switched nonlinear system model of the tilt-rotor UAV in the transition section is obtained, which is expressed as follows: where $\sigma(t):[0,\infty)\to\mathcal{N}$ represents that $\sigma(t)$ is a right - continuous switching signal, $\mathcal{N}$ is the total number of subsystems. When $\sigma(t)=k$, it means that the $k$-th subsystem is being activated; respectively represent the known nonlinear function, control gain, and unknown uncertain function corresponding to the system at time $t$ of the switching signal $\sigma(t)$; Step 2: Establish a tilt corridor for the multi-constraint conditions in the transition section of the tilt-rotor UAV. On this basis, construct an asymmetric barrier Lyapunov function to confine the system state within the range that satisfies the tilt corridor constraints; Step 3: Design a neural network system to estimate the unknown modeling uncertainty caused by the aerodynamic coupling between the rotor and the wing and obtain an approximation of the unknown modeling uncertainty; The neural network system is designed as: wherein is the modeling unknown and uncertain function corresponding to the k-th subsystem, is a block diagonal matrix, is the ideal weight matrix, is the component of the ideal weight matrix, j = 1, 2, 3, l>1 is the number of nodes of the neural network, is a vector composed of basis functions, is the vector component of, is a Gaussian basis function, ε * is the approximation error of the neural network; Step 4: Design a flight control law and an adaptation law, and use the output signal of the neural network system obtained in Step 3, that is, the approximation of the unknown modeling uncertainty, to compensate for the unknown modeling uncertainty; Step 5: Construct a closed-loop multi-Lyapunov function, and design and analyze the parameters of the flight control law to keep the state of the tilt-rotor UAV transition section system always within the constraint range and achieve stability within a fixed time; Construct a closed-loop multi-Lyapunov function as follows: When the k-th subsystem is activated, a closed-loop multi-Lyapunov function V is selected k as follows: where V1, V 2,k , are the pitch angle tracking error z1 and velocity tracking error Z2 = [z 21 , z 22 , z 23 considering the error variables respectively, T and the filtering error ε f to construct the Lyapunov function, and the expression is as follows: where k a1 (t), k b1 (t) are respectively abbreviated as k a1 , k b1 , and are defined as follows: are respectively the upper and lower bounds of the state x1 constraint, k aij (t), k bij (t) are respectively abbreviated as k aij , k bij , h(z ij ) is a piecewise function, and the expression is as follows: where are respectively the upper and lower bounds of the system state constraint, x ijd is the desired tracking instruction, z ij is the tracking error of the system state; is the adaptive parameter tracking error, d 2j is a positive constant to be designed, j = 1, 2, 3; Multiple Lyapunov functions V k Derivative with respect to time Is as follows: where △ x is the upper bound of the desired command derivative, a2 is a positive constant, and τ k is the filtering time constant, and ε is the upper bound of the neural network approximation error; Design average dwell time where μ > 2 is the normal value, and δ is any value in the interval (0, λ), obtaining: where V(t) σ(t) is the multi - Lyapunov function of the system, V σ(t) (0) is the initial value of the multi - Lyapunov function of the system at time t = 0, N0 is the chatter boundary, W′ is a bounded value, that is, the closed - loop switching system is bounded, and at the same time, the system states are all within the safe range of the state constraints.

2. A fixed-time control method for the transition section of a tilt-rotor UAV considering state constraints according to claim 1, characterized in that The calculation method of the tilt corridor for the transition section of the tilt-rotor UAV designed in Step 2 is as follows: Determine that the constraint conditions for the transition section of the tilt-rotor UAV include: where f x and f z are the resultant external forces in the x-axis and z-axis directions in the body coordinate system, T r is the pulling force generated by the rotor, β m is the nacelle inclination angle, M is the weight of the tilt-rotor UAV, g is the acceleration due to gravity, θ is the pitch angle, L and D are the aerodynamic lift and drag respectively, α is the angle of attack of the tilt-rotor UAV, α0 and α s are the zero-lift angle of attack and the critical stall angle of attack respectively, T rmax is the maximum pulling force provided by the rotor, β m (t) is the nacelle inclination angle at time t; By solving the multiple constraints in the above equation, the high-speed section speed and low-speed section speed of the transition section tilt corridor are obtained; the system state constraints are defined as follows: and the low-speed section speed V (t); wherein are the upper and lower bounds of the system state constraint, respectively, and x ij is the state of the system.

3. A fixed-time control method for the transition section of a tilt-rotor UAV considering state constraints according to claim 2, characterized in that Constructing an Asymmetric Logarithmic Barrier Lyapunov Function As follows: where z ij is the tracking error of the system state, h(z ij ) is a piecewise function, k aij (t), k bij (t) are respectively abbreviated as k aij , k bij , and the expressions are as follows: where x ijd is the desired tracking instruction.

4. A fixed-time control method for the transition section of a tilt-rotor UAV considering state constraints according to claim 3, characterized in that, The fixed-time adaptive flight control law and adaptation law designed in Step 4 use the output signal of the neural network system obtained in Step 3, that is, the approximation of the unknown modeling uncertainty, to compensate for the unknown modeling uncertainty, and define the following error variables: where z1 is the pitch angle tracking error, z 21 is the tracking error of the velocity u in the x-axis direction in the body coordinate system, z 22 is the tracking error of the velocity w in the z-axis direction in the body coordinate system, z 23 is the tracking error of the pitch angular velocity, ε f is the filtering error, is the adaptive parameter tracking error, x 1d 、x 21d 、x 22d are the desired tracking commands of x1, x 21 、x 22 respectively, x 23d is the virtual control law, is the adaptive parameter, j = 1, 2, 3, is the estimated value of θ 2j,k x 23c is the output of the following first-order nonlinear switching filter: where τ σ(t) is the switching filter time constant, a and b are design parameters to be determined and satisfy 0 < a < 1, b > 1, x 23d is the virtual control law to be designed, is the first derivative of x 23c ; The fixed-time adaptive flight control law and adaptation law are designed as: where k1, c1, c2, a2, c 5j and d 2j are respectively positive constants to be designed, j = 1, 2, 3, is the state constraint gain, is the desired pitch angle command x 1d 's first derivative; U is the control input, is the inverse matrix of the control gain matrix, is the desired velocity command X 2d 's first derivative, is the diagonal matrix composed of adaptive parameters, is the adaptive parameter, is 's first derivative, represents the known nonlinear function of the k-th subsystem for modeling, K2 = diag{k 21 , k 22 , k 23}, C3 = diag{c 31 , c 32 , c 33}, C4 = diag{c 41 , c 42 , c 43} are respectively positive definite diagonal matrices to be designed, is the state constraint gain diagonal matrix, Z2 = [z 21 , z 22 , z 23 T is the error variable of velocity, Z1 = [z1, 0, 0] T , Z β = [β 21 z 21 , β 22 z 22 , β 23 z 23 T , β1, β2, β 2j and 's expressions are as follows:​​ where k a1 and k b1 and h(z1) are defined as follows: are the upper and lower bounds of the constraint on state x1, respectively.

5. A fixed-time control method for the transition section of a tilt-rotor UAV considering state constraints according to claim 4, characterized in that, Considering the system state error variables, design a common Lyapunov function as follows: Common Lyapunov function Derivative with respect to time Satisfies the following conditions: where ι1 = min{c1, c 31 , c 32 , c 33}, ι2 = min{c2, c 41 , c 42 , c 43}, that is, the system state error converges to the set Γ at time T z as follows: where κ is a positive constant and z ij is the tracking error of the system state; By adjusting the control parameters k1, c1, c2, K2 = diag{k 21 , k 22 , k 23}, C3 = diag{c 31 , c 32 , c 33}, C4 = diag{c 41 , c 42 , c 43}, c 5j > 0, d 2j > 0, j = 1, 2, 3, to control the tracking errors of the attitude angle and velocity of the tilt-rotor UAV.

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