An adaptive fuzzy dynamic surface control method for quadrotor aircraft considering time-varying input time delay

Abstract

The application discloses a kind of four-rotor aircraft adaptive fuzzy dynamic surface control methods considering time-varying input delay.The method first establishes the dynamics model of four-rotor aircraft containing time-varying input delay, and on this basis, an adaptive tracking control scheme is designed using dynamic surface control method.For the existence of lumped unknown nonlinear in each subsystem, a fuzzy adaptive system is constructed for approximation and compensation to suppress the influence of unknown disturbance.Further, for the existence of time-varying input delay in the attitude angle subsystem control input, an auxiliary compensation system is introduced to modify the control input, thereby weakening the influence of phase lag caused by time delay on system performance.The application realizes high-precision trajectory tracking of four-rotor aircraft under the condition that unknown nonlinear disturbance and time-varying input delay exist simultaneously.

Description

Technical Field

[0001] This invention belongs to the field of aircraft control technology, specifically relating to an adaptive intelligent tracking control method for quadcopter aircraft. Background Technology

[0002] Quadrotors, due to their simple structure, excellent maneuverability, and low takeoff and landing requirements, have been widely used in military reconnaissance, logistics transportation, and agricultural plant protection. Achieving high-precision trajectory tracking control of quadrotors in complex environments is a key technological foundation for ensuring their safe and stable operation and fully realizing their application value.

[0003] In actual flight, high-precision trajectory tracking heavily relies on the speed and accuracy of the attitude control system. However, due to factors such as the dynamic response delay of the electronic speed controller, the electromechanical time constant of the brushless motor, the computational delay of the airborne control algorithm, and the communication transmission delay in remote-controlled or swarm flight scenarios, the control torque signals acting on the aircraft's roll, pitch, and yaw channels inevitably exhibit time-varying input delays. This type of time-varying input delay directly affects the core input of attitude dynamics, easily causing control command execution lag, resulting in a slower attitude loop response or even oscillations. This further amplifies the position tracking error through the system's strong coupling characteristics, and in severe cases, may lead to flight instability.

[0004] Existing quadrotor trajectory tracking control methods, such as hierarchical control, backstepping control, and dynamic surface control, typically assume that the control torque can be executed precisely without delay. While some studies consider actuator dynamics, they often simplify them to fixed time delays or first-order inertial elements, making it difficult to accurately describe and effectively compensate for the adverse effects of time-varying, bounded, and uncertain-rate-of-change torque input delays on the stability and control performance of the closed-loop system. Furthermore, existing torque input delay compensation control methods are often structurally complex or rely on precise time delay models and parameter information, making it difficult to balance robustness, real-time performance, and implementation complexity in practical engineering applications.

[0005] Therefore, in response to the time-varying input delay problem commonly found in the input torque channel of quadrotor aircraft, it is necessary to study a control method that does not require an accurate delay model, can adapt to delay changes online, and can still guarantee system stability and high-precision trajectory tracking performance under the conditions of model uncertainty and external disturbances, so as to meet the reliability and practicality requirements of engineering applications. Summary of the Invention

[0006] To address the aforementioned problems in the existing technology, this invention proposes an adaptive fuzzy dynamic surface control method for quadrotor aircraft that considers time-varying input delay.

[0007] This invention designs an adaptive fuzzy dynamic surface control method for quadrotor aircraft that considers time-varying input delay. This method ensures that the control signal acting on the aircraft is continuous even when the control signal experiences time-varying delays due to network transmission or actuator dynamics, and achieves high-precision trajectory tracking. Compared with traditional quadrotor trajectory tracking control methods, this invention makes systematic innovations in the following three aspects: 1) Introducing an auxiliary dynamic system to compensate for input delay, improving the system's stability and applicability under time-delay conditions. 2) Integrating fuzzy adaptive and dynamic surface control, using a fuzzy system to approximate and compensate for unknown nonlinearities in each subsystem, and utilizing a dynamic surface filter to generate control commands, balancing disturbance rejection and continuity. 3) Based on the dynamic surface control framework, using its first-order low-pass filter to process virtual control signals, and combining Lyapunov theory to unify the tuning of the controller, adaptive law, and compensator parameters, ensuring that all signals in the closed-loop system are consistent and ultimately bounded, while ensuring continuous control torque output to the actuator.

[0008] The technical solution adopted in this invention is an adaptive fuzzy dynamic surface control method for quadrotor aircraft that considers time-varying input delay, comprising the following steps:

[0009] S1. Establish a dynamic model of a quadcopter with time-varying time delay;

[0010] The acceleration vector of the aircraft in the inertial coordinate system is According to Newton's second law:

[0011]

[0012] in The total mass of the aircraft , , For the aircraft along , , The acceleration of the shaft, The total thrust generated by the four rotors of the aircraft. , They represent trigonometric functions respectively. , ,in Corresponding attitude angle: For roll angle, For pitch angle, Yaw angle , , for , , Shaft air damping coefficient, , , for , , The linear velocity of the shaft, It is the acceleration due to gravity. This is the lumped unknown nonlinear term of the position subsystem, which includes disturbances such as external disturbances and uncertainties in system parameters;

[0013] Substituting and rearranging, we obtain the state equation form of the position dynamic subsystem:

[0014]

[0015] in and These are the aircraft's position vector and linear velocity vector, respectively. and The expression is as follows:

[0016]

[0017]

[0018] For Euler angles, the kinematic formula is:

[0019]

[0020] in , , Let be the angular velocities of the aircraft about the roll, pitch, and yaw axes in the body coordinate system. , , The rate of change of the aircraft's roll angle, pitch angle, and yaw angle;

[0021] Let the above transformation matrix be... Both sides simultaneously multiply by left The inverse matrix is ​​obtained as follows:

[0022]

[0023] calculate ,get:

[0024]

[0025] Considering external disturbances and system uncertainties, a lumped unknown nonlinear term is introduced. The attitude angle vector in the attitude angle subsystem is obtained. Equations of state:

[0026]

[0027] in and These are the aircraft's attitude angle vector and angular velocity vector, respectively. The expression is as follows:

[0028]

[0029] For the rotation of a rigid body about the body coordinate system, Euler's equations are:

[0030]

[0031] in Here is the rotational inertia matrix. , This refers to the total torque acting on the aircraft.

[0032] get:

[0033]

[0034] Substituting the moment of inertia matrix and each torque term into the Euler equation, we obtain the angular rate vector in the attitude angle subsystem. Equations of state:

[0035]

[0036] in Input the torque vector into the organism. For lumped unknown nonlinear terms, , The expression is as follows:

[0037]

[0038]

[0039] Based on the principles of rigid body dynamics and Euler angle kinematics, a quadrotor aircraft is dynamically modeled. Through systematic derivation, a dynamic model of the quadrotor aircraft consisting of a position subsystem and an attitude subsystem is established. The control input of the attitude angle subsystem incorporates a time-varying input delay, which is a bounded delay function with a limited rate of change. Its mathematical model is expressed as follows:

[0040]

[0041] S2. To address the lumped unknown nonlinearities in the position and attitude angle subsystems, an adaptive fuzzy system is constructed to approximate and compensate for these lumped unknown nonlinearities. If a centrally averaged defuzzifier, product inference engine, and single-valued defuzzifier method are used, the output... for:

[0042]

[0043] in For the fuzzy system input vector, This is the fuzzy rule consequent parameter estimation vector. To determine the number of fuzzy rules, For fuzzy basis function vectors;

[0044] S3. Based on the desired trajectory and the actual trajectory of the quadcopter, define the position subsystem error vector and design the target control law for the position subsystem. ;

[0045] Based on the position subsystem error, a virtual control signal for the position subsystem is generated. During the generation process, the fuzzy system is used to compensate for the unknown nonlinearities in the position subsystem, and a first-order low-pass filter is introduced into the virtual control signal of the position subsystem for filtering.

[0046]

[0047]

[0048]

[0049] S4. Based on the desired attitude angle trajectory and the actual attitude angle state of the quadcopter, define the attitude angle subsystem error vector and design the virtual control input;

[0050] Based on the attitude angle subsystem error, a virtual control signal for the attitude angle subsystem is generated. During the generation process, the fuzzy system is used to compensate for the unknown nonlinearities in the attitude angle subsystem, and a first-order low-pass filter is introduced into the virtual control signal of the attitude angle subsystem for filtering.

[0051]

[0052]

[0053]

[0054] S5. To address the time-varying input delay in the attitude angle subsystem control input, an auxiliary compensation system is introduced and the final control law is designed:

[0055]

[0056]

[0057] Attached Figure Description

[0058] Figure 1 This is a flowchart of the invention;

[0059] Figure 2 This is a control framework diagram according to an embodiment of the present invention;

[0060] Figure 3 These are simulation results of the three-dimensional trajectory tracking control according to an embodiment of the present invention;

[0061] Figure 4 These are simulation results of the position tracking control according to an embodiment of the present invention;

[0062] Figure 5 These are simulation results of attitude tracking control according to an embodiment of the present invention;

[0063] Figure 6 These are simulation results of the control input and position tracking error variation curves according to an embodiment of the present invention;

[0064] Figure 7 These are simulation results of unknown nonlinearities in embodiments of the present invention. Detailed Implementation

[0065] Existing quadrotor trajectory tracking control methods often assume that the control input can be executed accurately without delay, or simplify the actuator dynamics to a known fixed input delay model. This makes it difficult to effectively address the common problems of unknown time-varying and bounded input delays in real-world systems. Furthermore, existing delay compensation methods typically rely on accurate system models or known delay information, or require the introduction of complex predictive compensation mechanisms. These methods are difficult to directly apply to quadrotor systems with strong nonlinearity, underactuated characteristics, and uncertain disturbances, thus limiting their engineering practicality.

[0066] To address the above problems, the present invention provides the following approach:

[0067] 1) An auxiliary dynamic system is introduced to compensate for the time-varying input delay in the attitude angle subsystem, thereby correcting the delayed control input. Without relying on an accurate system model and time delay information, the phase lag and performance degradation caused by the input delay are reduced, and the stability of the system under time-varying delay conditions is improved.

[0068] 2) Combining fuzzy adaptive and dynamic surface control methods, the fuzzy system is used to perform online compensation for the unknown nonlinearities of each subsystem. A first-order low-pass filter is designed to process the virtual control signal to avoid the differentiation of the virtual control signal, thereby achieving decoupling of iterative design and ensuring the continuity of control input.

[0069] 3) Based on the dynamic surface control framework and combined with Lyapunov theory, the parameters of the controller, adaptive law and compensator are uniformly tuned. While ensuring that all signals of the closed-loop system are consistent and eventually bounded, the control torque output to the actuator is continuous.

[0070] Based on the above research ideas, the structural block diagram of the adaptive fuzzy dynamic surface control method for quadrotor aircraft considering time-varying input delay is as follows: Figure 2 As shown, the controller design steps include the following:

[0071] 1) The dynamic model of the quadcopter with time-varying time delay is determined as follows:

[0072]

[0073]

[0074] 2) Based on the approximation requirement of the lumped unknown nonlinearity of each subsystem, a fuzzy system is constructed to approximate them separately. , , Output It can be written as:

[0075]

[0076] if For an unknown continuous function, there exists an approximation:

[0077]

[0078] in It is the approximation error;

[0079] 3) Consider the desired trajectory In conjunction with the dynamic subsystem, the following position error vector is defined:

[0080]

[0081] Differentiating equation (29) yields:

[0082]

[0083] The virtual control input is represented by the following expression:

[0084]

[0085] in ;

[0086] for The output of the following first-order low-pass filter:

[0087]

[0088] in The filter time constant;

[0089] Define the following linear rate error vector and filter error vector:

[0090]

[0091]

[0092] Differentiating equation (33) yields:

[0093]

[0094] Define the following unknown continuous function:

[0095]

[0096] The target control law and fuzzy rule consequent estimation parameter matrix of the position dynamic subsystem are designed as follows:

[0097]

[0098]

[0099] in , , , ;

[0100] 4) Construct the Lyapunov function for the position subsystem:

[0101]

[0102] By combining the designed virtual control law and fuzzy adaptive law, it is proved that the position tracking error signal is uniformly and ultimately bounded:

[0103]

[0104] 5) Consider the desired attitude angle In conjunction with the attitude angle dynamic subsystem, the attitude angle error vector is defined as follows:

[0105]

[0106] Differentiating equation (41) yields:

[0107]

[0108] Define the following unknown continuous function:

[0109]

[0110] The virtual control input is represented by the following expression:

[0111]

[0112] in , ;

[0113] for The output of the following first-order low-pass filter:

[0114]

[0115] in The filter time constant;

[0116] The parameter matrix for estimating the consequent of fuzzy rules is:

[0117]

[0118] in , , ;

[0119] Define the following angular rate error vector and filter error vector:

[0120]

[0121]

[0122] Differentiating equation (47) yields:

[0123]

[0124] definition:

[0125]

[0126] use An auxiliary dynamic system was designed to compensate for input delay:

[0127]

[0128] in , ;

[0129] Define the following unknown continuous function:

[0130]

[0131] The final control law and fuzzy rule consequent estimation parameter matrix of the attitude subsystem are designed as follows:

[0132]

[0133]

[0134] in , , , ;

[0135] 6) For the attitude subsystem, design the Lyapunov-Krasovskii functional and construct the Lyapunov function:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141] By combining the designed virtual control law, final control law, and corresponding fuzzy adaptive law, it is proven that the attitude angle tracking error signal is uniformly and ultimately bounded, thus theoretically guaranteeing the global stability and trajectory tracking performance of the entire closed-loop system.

[0142] (60)

[0143] To verify the effectiveness of the proposed adaptive fuzzy dynamic surface control method for quadrotors that considers time-varying input delay, the trajectory tracking control process of a quadrotor was simulated and verified.

[0144] Reference trajectory set , , , External interference is set to ,in For random disturbance components. The time-varying input delay is set to... The main parameters of the quadcopter are shown in Table 1.

[0145] Table 1: Main Parameters of Quadrotor Aircraft

[0146]

[0147] Figures 3-7 The stability and tracking performance of the quadcopter system (15) with time-varying delay are shown under the control framework and control scheme proposed in this invention. It can be seen that this invention can still achieve high-precision trajectory tracking of quadcopter under the conditions of time-varying input delay, model uncertainty and external disturbance.

[0148] The present invention has been described above by way of examples. Those skilled in the art should understand that the present disclosure is not limited to the examples described above, and various changes, modifications and substitutions can be made without departing from the scope of the present invention.

Claims

1. An adaptive fuzzy dynamic surface control method for a quadrotor aircraft considering time-varying input delay, characterized in that: Specifically, the following steps are included: S1. Establish a dynamic model of a quadcopter with time-varying time delay; A dynamic model of a quadrotor aircraft is established, comprising a position subsystem and an attitude angle subsystem. The control input of the attitude angle subsystem includes a time-varying input delay, which is a bounded delay with a limited rate of change. The model is as follows: （1） In the formula and Let these represent the aircraft's position vector and linear velocity vector, respectively. and These represent the aircraft's attitude angle vector and angular rate vector, respectively. It is system output. This represents the aircraft's attitude angle and total thrust. The lift vector determined by both This represents the machine's input torque vector, which is the control input in this paper. , , , Given the system's dynamic functions and matrices, , , This represents the lumped unknown nonlinearity in each subsystem; S2. For the lumped unknown nonlinearity existing in the position subsystem and attitude angle subsystem, a fuzzy system is constructed to approximate and compensate for the lumped unknown nonlinearity. S3. Based on the desired trajectory and the actual trajectory of the quadcopter, define the position subsystem error vector and design the target control law for the position subsystem. By combining the target control law and the dynamics of the quadrotor, the desired attitude angle is calculated. , ; S4. Based on the desired attitude angle trajectory and the actual attitude angle state of the quadcopter, define the attitude angle subsystem error vector and design the virtual control input; S5. To address the time-varying input delay in the attitude angle subsystem control input, an auxiliary compensation system is introduced and the final control law is designed: 。 2. The adaptive fuzzy dynamic surface control method for quadrotor aircraft considering time-varying input delay as described in claim 1, characterized in that: A dynamic surface control method is adopted to design a first-order low-pass filter, avoiding the need to differentiate the virtual control variables and achieving decoupling of the iterative design.

3. The adaptive fuzzy dynamic surface control method for quadrotor aircraft considering time-varying input delay as described in claim 1, characterized in that: To address the time-varying input delay in the attitude angle subsystem, an auxiliary tracking error is constructed and an auxiliary compensation system is introduced to correct the attitude angle control input. Simultaneously, stability analysis is performed using a constructed Lyapunov–Krasovskii functional. This solves the controller design problem caused by time-varying input delay and input discontinuity without requiring differentiation of the control input or the application of the integral mean value theorem, thereby improving stability and trajectory tracking performance under conditions of input delay.

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