Unmanned aerial vehicle attitude control method based on adaptive terminal sliding mode

Abstract

The unmanned aerial vehicle attitude control method based on adaptive terminal sliding mode comprises the following steps: 1, establishing an unmanned aerial vehicle attitude stability control system model; 2, designing an improved fast non-singular fixed-time terminal sliding mode surface; 3, according to the designed dynamic sliding mode surface, a non-singular fixed-time terminal sliding mode law is derived; 4, an adaptive law is designed to effectively estimate the upper bound of unknown disturbance; 5, the stability of the closed-loop control system is proved by using the candidate Lyapunov function. The method can ensure that the controller has non-singularity and fast convergence characteristics, and the adaptive law is used to solve the upper bound of unknown disturbance, thereby improving the tracking accuracy of the unmanned aerial vehicle attitude control system under the condition of lumped disturbance.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of unmanned aerial vehicle attitude stabilization control, and particularly relates to an unmanned aerial vehicle attitude control method based on adaptive terminal sliding mode. BACKGROUND

[0002] Unmanned aerial vehicles are widely used in military reconnaissance, disaster rescue and other fields due to their lightness and flexibility. The dynamic system has the characteristics of nonlinearity, strong coupling, modeling uncertainty, etc. In addition, external disturbances also bring great challenges to the attitude stabilization control. The attitude stabilization control system is in the inner loop, and the control bandwidth is high, with a control frequency of up to 200 Hz. Under a high control frequency, the rapid convergence performance of the attitude controller is very important, especially in the case of large disturbance and high dynamics.

[0003] Many scholars have used sliding mode control to solve the attitude stabilization control problem, but the sliding mode tracking control of unmanned aerial vehicles still faces the following difficulties. First, the chattering problem is inevitable, and it can only be weakened to a certain extent within a certain range, which is a major obstacle to the application of sliding mode variable structure control in actual systems. Second, the general sliding mode controller can only guarantee asymptotic stability, but asymptotic stability means that the closed-loop system state can only converge to the equilibrium point as time tends to infinity, which cannot meet the requirement of rapid stability in actual engineering. Third, the singularity problem means that the designed controller will have an infinite value, which is impossible to achieve in actual engineering. Fourth, the time of finite time convergence depends on the initial value of the closed-loop system state, and the convergence time will change with the initial state. If the initial state of the aircraft is far from the equilibrium point, the convergence time will increase exponentially, which is obviously contrary to the control requirements. These difficulties make the attitude stabilization control of unmanned aerial vehicles a challenging research topic.

[0004] Developing the attitude stabilization fixed-time sliding mode control of unmanned aerial vehicles can improve the convergence speed and control accuracy of attitude stabilization control, and provide excellent control performance for the wide application of unmanned aerial vehicles in complex environments such as military reconnaissance, disaster rescue, terrain survey, etc.

[0005] The existing technologies are as follows:

[0006] Application No.: CN201710532250.3, Patent Title: A Finite-Time Adaptive Control Method for Quadrotor UAVs Based on Non-Singular Terminal Sliding Mode, which targets quadrotor UAV systems with inertial uncertainties and external disturbances. Based on the dynamics of the quadrotor UAV system, an adaptive control method for quadrotor UAVs based on non-singular terminal sliding mode control is designed by combining it with adaptive control. The design of non-singular terminal sliding mode ensures the finite-time convergence characteristics of the system and avoids the singularity problem inherent in terminal sliding mode control, effectively reducing chattering. Furthermore, adaptive control is used to handle the inertial uncertainties and external disturbances of the system. This invention provides a control method that can eliminate the singularity problem of the sliding surface and effectively suppress and compensate for the inertial uncertainties and external disturbances of the system, ensuring the finite-time convergence characteristics of the system.

[0007] However, it utilizes a non-singular terminal sliding mode adaptive control method for quadrotor UAVs, which can effectively handle inertial uncertainties and external disturbances. This method guarantees the finite-time convergence characteristics of the system and avoids the singularity problem inherent in terminal sliding mode control, effectively mitigating chattering issues.

[0008] This patent addresses the problem of unknown disturbances in quadcopter UAV trajectory tracking by designing an adaptive law to effectively estimate the upper bound. It also proposes a novel fast non-singular fixed-time terminal sliding surface, thereby designing a non-singular fixed-time terminal sliding mode controller. The closed-loop stability of the control system is proven using candidate Lyapunov functions, improving the tracking accuracy of the UAV attitude control system under lumped disturbances. It is worth noting that the sliding surface used in the comparative patent is...

[0009]

[0010] The sliding surface designed in this patent is...

[0011] ,in

[0012] The two sliding surfaces are completely different, and the comparative patent can only achieve convergence performance over a finite time, while this patent can achieve convergence performance over a fixed time, resulting in superior performance. Therefore, the two patents are completely different in their sliding surface design.

[0013] Application No.: CN 201710823686.8, Patent Name: Dynamic Characteristics Unknown Four-rotor Unmanned Aerial Vehicle Attitude Controller and Method, which assumes that the four-rotor unmanned aerial vehicle model parameters such as moment of inertia, air damping coefficient, etc. are unknown, and the bounded disturbance to the system is time-varying and always exists in the system. For unknown model parameters, the application designs a corresponding differential estimator to estimate the position parameters online. Based on the parameter estimation value, an improved adaptive non-singular terminal sliding mode controller is designed to complete the attitude stable control of the four-rotor unmanned aerial vehicle. In addition, the application also designs an adaptive disturbance compensator to effectively compensate the bounded disturbance. Simulation and experimental results show that the control algorithm can better complete the attitude stable control of the four-rotor unmanned aerial vehicle, and has strong robustness to unknown dynamic characteristics and disturbance of the system.

[0014] It is for unknown model parameters and time-varying bounded disturbance, and a corresponding differential estimator is designed to estimate the position parameters online. Based on the parameter estimation value, an improved adaptive non-singular terminal sliding mode controller is designed to complete the attitude stable control of the four-rotor unmanned aerial vehicle, and has strong robustness to unknown dynamic characteristics and disturbance of the system.

[0015] And the present patent is for the problem of unknown disturbance in the trajectory tracking of the four-rotor unmanned aerial vehicle. An adaptive law is designed to effectively estimate the upper bound value. A novel fast non-singular fixed-time terminal sliding surface is proposed, and a non-singular fixed-time terminal sliding mode controller is designed. The stability of the closed-loop control system is proved by using the candidate Lyapunov function, and the tracking accuracy of the unmanned aerial vehicle attitude control system under the condition of lumped disturbance is improved. It is worth noting that the sliding surface used in the comparison patent is

[0016]

[0017] And the sliding surface designed in the present patent is

[0018] , wherein

[0019] The two sliding surfaces are completely different, and the comparison patent can only achieve finite time convergence performance, while the present patent can achieve fixed time convergence performance, and the performance is better. Therefore, the two patents are completely different in the design of the sliding surface. SUMMARY

[0020] To solve the above problems, the present application proposes an unmanned aerial vehicle attitude control method based on adaptive terminal sliding mode, which can effectively estimate the upper bound value of unknown disturbance, improve the convergence speed and control accuracy of attitude stable control, and improve the stable attitude control performance of unmanned aerial vehicle in complex environment.

[0021] To achieve the above object, the technical scheme adopted by the present application is:

[0022] The present application provides a UAV attitude control method based on adaptive terminal sliding mode, comprising the following steps:

[0023] (1) establishing a UAV attitude stability control system model;

[0024] (2) designing a novel fast non-singular fixed-time terminal sliding mode surface;

[0025] (3) according to the designed dynamic sliding mode surface, a non-singular fixed-time terminal sliding mode law is derived;

[0026] (4) designing an adaptive law to effectively estimate the upper bound value of unknown disturbance;

[0027] (5) using a candidate Lyapunov function to prove the closed-loop stability of the control system.

[0028] As a further improvement of the present application, in step (1), the establishment of the UAV attitude stability control system model comprises the following steps:

[0029] (1.1) establishing a coordinate system;

[0030] establishing an inertial coordinate system and a carrier coordinate system , the position and attitude in the inertial coordinate system are respectively represented as and , the linear velocity and angular velocity in the carrier coordinate system are respectively represented as and , the position rotation matrix from the carrier coordinate system to the inertial coordinate system and the angular velocity transformation matrix are respectively expressed as

[0031] (1)

[0032] (2)

[0033] Here ;

[0034] (1.2) establishing a UAV dynamics model;

[0035] The dynamics model of is expressed as:

[0036] (3)

[0037] Specifically expressed as:

[0038] (4)

[0039] Here the force generated by the motor rotor , the generated torque is , is the lift force generated by the first rotor, and are the thrust and torque coefficients, respectively, is the distance from the center of mass to the rotor center, is the mass, is the moment of inertia matrix. are the aerodynamic moments, is the aerodynamic drag coefficient matrix. is the tension and torque caused by parameter uncertainty and external disturbance in the inertial coordinate system;

[0040] (1.3) Establish a spatial state form dynamics model;

[0041] Convert the dynamics equation into a spatial state form

[0042] (5)

[0043] Here the system state is , and are the parameter uncertainty caused by the system parameters , the nonlinear state function is defined as follows:

[0044] (6)

[0045] The system control gain matrix is , the system control input matrix is expressed as

[0046] (7)

[0047] The external disturbance is defined as follows

[0048] (8)

[0049] Finally, the lumped disturbance containing parameter uncertainty and external disturbance is defined as follows

[0050] (9)

[0051] Assume that the upper bound of the lumped disturbance is known, that is , here An upper bound of the aggregate interference.

[0052] As a further improvement of the application, in the step (2), the novel fast non-singular fixed-time terminal sliding mode surface is designed by the following steps:

[0053] (2.1) defining the system error;

[0054] Let be the desired attitude. The attitude tracking error is defined as the difference between the actual value and the desired value, which is described as

[0055] (10)

[0056] According to this definition, the differential of the tracking error is ;

[0057] (2.2) designing the novel fast non-singular fixed-time terminal sliding mode surface;

[0058] The nonlinear dynamic sliding mode surface is defined as , and the non-singular fast terminal sliding mode surface with fixed-time convergence is designed for a single channel as

[0059] (11)

[0060] where , .

[0061] As a further improvement of the application, in the step (3), the non-singular fixed-time terminal sliding mode law is derived by the following steps:

[0062] (3.1) the derivative of the sliding mode surface is taken:

[0063] (12)

[0064] Here , , . Let , then can be simplified as

[0065] (13)

[0066] (3.2) the designed reaching law ensures that the sliding mode surface converges to zero in fixed time;

[0067] (14)

[0068] where ;

[0069] (3.3) Control law derivation;

[0070] A controller is designed for the following standard second order nonlinear system;

[0071] (15)

[0072] The designed control law is

[0073] (16).

[0074] As a further improvement of the application, in the step (4), the design of the adaptive law comprises the following steps:

[0075] The upper bound of the disturbance is effectively estimated through the design of the adaptive law, and the adaptive switching control law is designed as

[0076] (17)

[0077] (18)

[0078] Here is the estimated value of the lumped disturbance , is a positive constant, and the adaptive nonsingular fixed-time sliding mode control law is designed as

[0079] As a further improvement of the application, in the step (5), the candidate Lyapunov function is used to prove the closed-loop stability of the control system, comprising the following steps:

[0080] (19).

[0081] Consider the following Lyapunov function

[0082] (20)

[0083] Taking the time derivative, we get

[0084] (21)

[0085] Substituting the designed control law , we get

[0086] (22)

[0087] Simplifying equation (22), we get

[0088] (23)

[0089] Since ,get

[0090] (twenty four)

[0091] The designed dynamic sliding surface at a fixed time It converges to the origin. The upper bound of the convergence time to the origin is... , .

[0092] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0093] 1. This method employs a fast non-singular fixed-time sliding mode control design. Compared to traditional sliding mode controllers, the controller designed in this method offers control continuity and further reduces chattering. Furthermore, the proposed algorithm achieves stable convergence within a fixed time, resulting in higher tracking accuracy.

[0094] 2. The fixed-time dynamic sliding surface designed by this method is itself non-singular, and there is no need to set up a critical layer to process the sliding surface in an indirect way to avoid the singularity problem, which further simplifies the design of the sliding surface and reduces the amount of computation.

[0095] 3. The adaptive control law designed in this method is used to effectively estimate the upper bound of the lumped disturbance, further improving the quality of the control input under unknown disturbance conditions. Attached Figure Description

[0096] Figure 1 This is a flowchart of the UAV attitude stabilization control method disclosed in this invention;

[0097] Figure 2 This is a comparison diagram of the effects of the method disclosed in this invention with other traditional methods in the embodiments. Detailed Implementation

[0098] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0099] like Figure 1 As shown, this invention discloses a method for attitude stabilization control of a UAV based on adaptive non-singular fixed-time terminal sliding mode, comprising the following steps:

[0100] (1.1) Establish a coordinate system.

[0101] Establish an inertial coordinate system and the carrier coordinate system The position and attitude in the inertial coordinate system are respectively represented as: and The linear velocity and angular velocity in the carrier coordinate system are expressed as follows: and Position rotation matrix from body frame to inertial frame and angular velocity transformation matrix are expressed as

[0102] (1)

[0103] (2)

[0104] Here .

[0105] (1.2) Establish the dynamics model of UAV.

[0106] The dynamics model of UAV can be expressed as

[0107] (3)

[0108] Specifically, it is expressed as

[0109] (4)

[0110] Here the force generated by the motor rotor is , and the torque generated is , is the lift force generated by the th rotor, and are the thrust and torque coefficients, respectively, is the distance from the center of mass to the rotor center, is the mass, is the moment of inertia matrix. is the aerodynamic moment, is the aerodynamic drag coefficient matrix. is the tension and torque caused by parameter uncertainty and external disturbance in the inertial coordinate system (e.g. wind, variable load, etc.).

[0111] (1.3) Establish the spatial state form dynamics model.

[0112] Convert the dynamics equation to the spatial state form

[0113] (5)

[0114] Here the system state is . and are parameter uncertainties caused by system parameters . The nonlinear state function is defined as follows

[0115] (6)

[0116] The system control gain matrix is . The system control input matrix is expressed as

[0117] (7)

[0118] The external disturbance is defined as

[0119] (8)

[0120] Finally, the lumped disturbance containing parameter uncertainty and external disturbance is defined as

[0121] (9)

[0122] In general, it is assumed that the upper bound of the lumped disturbance is known, i.e. where is the upper bound value of the lumped disturbance.

[0123] (2.1) Define the system error.

[0124] Let be the desired attitude. The attitude tracking error is defined as the difference between the actual value and the desired value, which is described as

[0125] (10)

[0126] According to this definition, the differential of the tracking error is .

[0127] (2.2) Design a novel fast non-singular fixed-time terminal sliding mode surface.

[0128] Define the nonlinear dynamic sliding mode surface as . For a single channel, the non-singular fast terminal sliding mode surface with fixed-time convergence is designed as

[0129] (11)

[0130] where ,

[0131] (3.1) Differentiate the sliding mode surface .

[0132] (12)

[0133] Here , , . make ,but It can be simplified to

[0134] (13)

[0135] (3.2) The convergence law of the design can guarantee that the sliding surface converges to zero in a fixed time.

[0136] (14)

[0137] in .

[0138] (3.3) Derivation of the control law.

[0139] Design a controller for the following standard second-order nonlinear system.

[0140] (15)

[0141] The designed control law is

[0142] (16)

[0143] (4.1) Design adaptive laws.

[0144] The upper bound of the disturbance is effectively estimated through the design of an adaptive law. The adaptive switching control law is designed as follows:

[0145] (17)

[0146] (18)

[0147] here It is centralized interference The estimated value, It is a positive constant. Design the following adaptive nonsingular fixed-time sliding mode control law:

[0148] (19)

[0149] (5.1) Use candidate Lyapunov functions to prove the closed-loop stability of the control system.

[0150] Consider the following Lyapunov function

[0151] (20)

[0152] Differentiating over time yields the result.

[0153] (21)

[0154] The designed control law is brought into the design , and the following can be obtained

[0155] (22)

[0156] The formula (22) is simplified, and the following can be obtained

[0157] (23)

[0158] Since , the following can be obtained

[0159] (24)

[0160] The designed dynamic sliding mode surface converges to the origin in a fixed time , and the upper bound of the convergence time to the origin is ,

[0161] In order to verify the performance of the unmanned aerial vehicle attitude stabilization control disclosed in the present application, the mass of the unmanned aerial vehicle is , the distance from the rotor to the center of the unmanned aerial vehicle is , the moment of inertia is , the motor moment of inertia is , and the torque damping coefficient matrix is . Compared with the attitude stabilization control system of the traditional sliding mode, the error is shown in Figure 2 , in the figure, “-.” is the traditional sliding mode attitude stabilization curve, “--” is the unmanned aerial vehicle attitude stabilization curve using the present application, and the specific comparison effect is as follows:

[0162] Traditional method The root mean square error of the attitude stabilization control of the three attitude angles is 0.0631, 0.0468, and 0.0438, respectively; the method proposed in the present application The root mean square error of the attitude stabilization control of the three attitude angles is 0.0489, 0.0360, and 0.0344, respectively, and the convergence time is less than 2.1s.

[0163] The above is only a preferred embodiment of the present application, and is not intended to limit the present application in any other form, and any modification or equivalent change made according to the technical essence of the present application still falls within the scope of the present application.

Claims

1. A UAV attitude control method based on adaptive terminal sliding mode, comprising the following steps, characterized in that: (1) establishing a UAV attitude stability control system model; (2) designing an improved fast non-singular fixed-time terminal sliding surface; In step (2), the design of the improved fast non-singular fixed-time terminal sliding surface includes the following steps: (2.1) define the system error; Let For the desired pose, the pose tracking error is defined as the difference between the actual and desired values, which is described as （10） According to this definition, the derivative of the tracking error is ; (2.2) design an improved fast non-singular fixed-time terminal sliding surface; The nonlinear dynamic sliding surface is defined as For a single channel, a nonsingular fast terminal sliding surface with fixed-time convergence is designed as （11） wherein , ; (3) According to the designed dynamic sliding surface, a non-singular fixed-time terminal sliding law is derived; (4) Design an adaptive law to effectively estimate the upper bound of unknown disturbance; (5) Use the candidate Lyapunov function to prove the closed-loop stability of the control system.

2. The UAV attitude control method based on adaptive terminal sliding mode according to claim 1, characterized in that: In step (1), establishing a UAV attitude stability control system model includes the following steps: (1.1) Establish a coordinate system; Establish the inertial coordinate system and the body coordinate system The position and pose in the inertial coordinate system are respectively denoted as and The linear velocity and angular velocity in the body coordinate system are respectively denoted as and The position rotation matrix from the body coordinate system to the inertial coordinate system and the angular velocity transformation matrix are respectively expressed as （1） （2） Here ; (1.2) Establish a UAV dynamics model; The dynamics model is expressed as: （3） Specifically expressed as: （4） Here the force generated by the motor rotor , the generated torque is , the lift generated by the first rotor, and are the thrust and torque coefficients respectively, is the distance from the center of mass to the rotor center, is the mass, is the moment of inertia matrix, are the aerodynamic moments, is the aerodynamic drag coefficient matrix, is the tension and torque caused by parameter uncertainty and external disturbance in the inertial coordinate system; (1.3) Establish a spatial state form dynamics model; Convert the dynamics equation to a spatial state form （5） Here the system state is , and is the parameter uncertainty caused by the system parameter , the nonlinear state function is defined as follows: （6） The system control gain matrix is , the system control input matrix is expressed as （7） External interference Is defined as follows （8） Finally, the lumped disturbance including parameter uncertainty and external disturbance is defined as follows （9） Suppose the upper bound of the aggregate interference is known, i.e. where is the upper bound of the aggregate interference.

3. The UAV attitude control method based on adaptive terminal sliding mode according to claim 2, characterized in that: In step (3), the derivation of the non-singular fixed-time terminal sliding law includes the following steps: (3.1) Derivation of the sliding surface Taking the derivative: （12） Here , , . Let then can be simplified to （13） (3.2) Design the reaching law to ensure that the sliding surface converges to zero in a fixed time; （14） wherein ; (3.3) Control law derivation; The following standard second-order nonlinear system is designed to design a controller; (15) The designed control law is (16)。 4. The UAV attitude control method based on adaptive terminal sliding mode according to claim 3, characterized in that: In step (4), the design of the adaptive law includes the following steps: Through the design of the adaptive law, the upper bound of the disturbance is effectively estimated, and the adaptive switching control law is designed as （17） （18） Here is the estimate of the lumped disturbance , is a positive constant, and the adaptive nonsingular fixed-time sliding mode control law is designed as （19）。 5. The UAV attitude control method based on adaptive terminal sliding mode according to claim 4, characterized in that: In step (5), the use of candidate Lyapunov function to prove the closed-loop stability of the control system includes the following steps: Consider the following Lyapunov function （20） Take the time derivative to get; （21） Control law incorporated into design , resulting in （22） Simplify equation (22) to get （23） Due to , obtain （24） The designed dynamic sliding mode surface converges to the origin in fixed time The upper bound of the convergence time to the origin is , .

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