Four rotor unmanned aerial vehicle control method based on fractional order PID and fractional order terminal sliding mode

Abstract

The application discloses a kind of based on fractional order PID and fractional order terminal sliding mode quadrotor unmanned aerial vehicle control method, comprising (1) the dynamics model of quadrotor unmanned aerial vehicle is established;(2) construct fractional order PID controller, the desired position of unmanned aerial vehicle and actual position input fractional order PID controller, obtain the control output of unmanned aerial vehicle in X, Y, Z axis direction;(3) according to step (2) control output and current attitude angle are calculated out the desired attitude angle of unmanned aerial vehicle;(4) determine attitude error;(5) construct fractional order terminal sliding surface and obtain the equivalent control law of this fractional order terminal sliding;(6) design fractional order terminal sliding switch control law, combine switch control law and equivalent control law obtain fractional order terminal sliding attitude controller;(7) design Lyapunov function and prove the stability of fractional order terminal sliding attitude controller by Lyapunov theorem.The application guarantees that unmanned aerial vehicle keeps attitude stable when being disturbed by air flow factor.

Description

Technical Field

[0001] This invention relates to the field of control system technology, specifically to a quadcopter unmanned aerial vehicle (UAV) control method based on fractional-order PID and fractional-order terminal sliding mode. Background Technology

[0002] Quadcopter drones have the simplest structure and are the most widely used, playing a crucial role in scientific research both domestically and internationally. While drones were initially developed for military needs, quadcopter drones have expanded into civilian applications through continuous development. For example, quadcopter drones have provided excellent assistance in firefighting and rescue operations, fundamentally improving efficiency due to their small size, simple operation and maintenance, low flight altitude, high maneuverability, and intelligent operation.

[0003] However, quadrotor aircraft, as complex controlled objects characterized by underactuation, strong coupling, multiple variables, and nonlinearity, not only need to solve the problem of attitude control under normal working conditions, but also, in firefighting applications, are affected by various uncertain disturbances, such as airflow effects and mass changes. This places very high demands on the adaptability and robustness of their attitude control algorithms. Currently, traditional control algorithms commonly used in quadrotor UAVs include PID control, sliding mode control, and backstepping control. With PID algorithms, each control parameter is relatively independent, and parameter selection is relatively simple, forming a complete design and parameter tuning method. However, PID controllers are linear controllers, while most controlled objects in reality are nonlinear; using linear approximation for nonlinearity will reduce accuracy. Sliding mode control can overcome system uncertainties and has strong robustness to disturbances and unmodeled dynamics; however, when the state trajectory reaches the sliding mode surface, it is difficult to strictly slide along the sliding mode surface to the equilibrium point, resulting in chattering. Therefore, this type of method often fails to achieve ideal control results when dealing with complex external disturbances. Furthermore, most UAV control systems are limited to the integer order domain. Integer order differential systems characterize the instantaneous changes in object attributes (or states), while fractional order differential systems characterize the changes in object attributes (or states). Therefore, using fractional calculus theory to design control systems can achieve better performance. Summary of the Invention

[0004] Purpose of the invention: To address the above-mentioned technical problems, this invention provides a quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode. By designing a dual-closed-loop control strategy, the outer-loop position control part improves the traditional PID controller from integer to fractional order, weakening the impact of airflow interference through incomplete differentiation and feedforward compensation. The inner-loop attitude control part improves the sliding surface of ordinary sliding mode control to a non-singular terminal sliding surface and introduces fractional-order calculus, allowing the entire UAV control system to reach the equilibrium point faster while possessing time memory and strong robustness. Simultaneously, considering the interference of complex airflow, it ensures that the quadrotor UAV maintains stable attitude even when affected by airflow factors.

[0005] Technical Solution: To solve the above problems, this invention discloses a quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode, specifically including the following steps:

[0006] (1) Considering the wind interference factors in the complex external environment, a dynamic model of the quadcopter UAV is established based on the Newton-Euler angle formula;

[0007] (2) Based on fractional-order PID control theory, feedforward compensation theory and incomplete differentiation, construct a fractional-order PID controller; input the desired position and actual position of the quadcopter UAV into the fractional-order PID controller to obtain the control output of the quadcopter UAV in the X, Y and Z axis directions;

[0008] (3) Calculate the desired attitude angle of the quadcopter UAV based on the control output obtained in step (2) and the current attitude angle;

[0009] (4) Determine the attitude error by comparing the expected attitude angle with the actual attitude angle of the quadcopter UAV;

[0010] (5) Construct a fractional-order terminal sliding surface based on the attitude error; differentiate the constructed fractional-order terminal sliding surface and set its derivative to zero, and solve the equivalent control law of the fractional-order terminal sliding surface by combining the dynamic model of the quadcopter UAV.

[0011] (6) Design the fractional-order terminal sliding mode switching control law; combine the fractional-order terminal sliding mode switching control law with the equivalent control law of the fractional-order terminal sliding mode to obtain the fractional-order terminal sliding mode attitude controller.

[0012] (7) Design the Lyapunov function and prove the stability of the fractional-order terminal sliding mode attitude controller using Lyapunov's theorem.

[0013] Furthermore, the dynamic model formula for the quadcopter UAV in step (1) is as follows:

[0014]

[0015] In the formula, (x, y, z) are the position coordinates of the quadcopter UAV in the ground coordinate system. The first derivatives corresponding to x, y, and z are... The corresponding second derivatives are x, y, and z; φ represents the pitch angle of the quadcopter, θ represents the roll angle of the quadcopter, and ψ represents the yaw angle of the quadcopter. These correspond to the first derivatives of φ, θ, and ψ. The corresponding second derivatives are φ, θ, and ψ; m represents the weight of the quadcopter drone; U1, U2, U3, and U4 are the control inputs of the quadcopter drone; k x k y k z All are positional air drag coefficients for quadcopter drones; k Φ k θ k Ψ All are the air drag coefficients of the UAV during flight; I x I y I z All represent the moment of inertia of the quadcopter drone; d1 is the external airflow disturbance on the X-axis during the flight of the quadcopter drone, d2 is the external airflow disturbance on the Y-axis during the flight of the quadcopter drone, and d3 is the external airflow disturbance on the Z-axis during the flight of the quadcopter drone.

[0016] Furthermore, the specific formula for the fractional-order PID controller constructed in step (2) is as follows:

[0017]

[0018] In the formula, U x (s) represents the control output of the quadcopter UAV in the X-axis direction, U y (s) represents the control output of the quadcopter UAV in the Y-axis direction, U z (s) represents the control output of the quadcopter drone in the Y-axis direction; Kp x Kp y Kp z Both represent the proportionality coefficient, Ki x Ki y Ki z Both represent integral coefficients, Kd x Kd y Kd z All represent differential coefficients; λ represents the order of integration, μ is the order of differentiation; T f denoted as filter coefficients; E(s) is the difference between the desired position and the actual position; R(s) is the desired position of the given quadcopter UAV; G(s) is the position model of the quadcopter UAV.

[0019] Furthermore, ignoring air resistance and interference, the output of the fractional-order PID controller is used only as the control output of the quadcopter UAV's coordinate axes; U is obtained according to equation (1). x U y U z The relationship between U1 and attitude angle is shown in equation (3):

[0020]

[0021] The transformation yields:

[0022]

[0023] In the formula, g represents the acceleration due to gravity;

[0024] The desired attitude angle is obtained by solving formulas (1), (3), and (4). The specific formulas are as follows:

[0025]

[0026] In the formula, φ d θ represents the desired pitch angle. d ψ represents the desired roll angle. d This indicates the desired yaw angle.

[0027] Furthermore, step (4) specifically includes:

[0028] To track the desired attitude angle trajectory of the UAV, the attitude error tracking trajectory formula is defined as follows:

[0029] e(t)=r(t)-y(t) (6)

[0030] In the formula, e(t) represents the attitude error tracking trajectory; r(t) represents the trajectory of the quadcopter UAV's desired attitude angle, specifically including φ at each time point. d θ d And given ψ d ;y(t) represents the trajectory of the actual attitude angle of the quadcopter UAV, specifically including φ, θ, and ψ at each moment;

[0031] The attitude error at a certain moment can be expressed as:

[0032]

[0033] In the formula, e φ e represents the error in the pitch angle of a quadcopter drone. θ e represents the error in the roll angle of a quadcopter drone. ψ This indicates the error in the yaw angle of a quadcopter drone.

[0034] Furthermore, the formula for the fractional-order terminal sliding surface constructed in step (5) is:

[0035]

[0036] In the formula, α and β are both positive constants; 0 < α i <1, i takes 1,3...11; 1<α i <2, i takes 2, 4...12.

[0037] Differentiating the constructed fractional-order terminal sliding surface and setting its derivative to zero, and then solving equations (1) and (4) together, we obtain the equivalent control law of the fractional-order terminal sliding surface. The formula is as follows:

[0038]

[0039] In the formula, U φeq U represents the equivalent control output of the pitch angle. θeq U represents the equivalent control output of the roll angle. ψeq The equivalent control output representing the yaw angle; k φ k θ k ψ All of these represent the attitude drag coefficient of a quadcopter drone.

[0040] Furthermore, the specific formula for the fractional-order terminal sliding mode switching control law designed in step (6) is as follows:

[0041]

[0042] In the formula, k φ1 k θ1 k ψ1 η φ η θ η ψ All are positive numbers;

[0043] The specific formula for the fractional-order terminal sliding mode attitude controller, obtained by combining the fractional-order terminal sliding mode switching control law and the equivalent control law of the fractional-order terminal sliding mode, is as follows:

[0044]

[0045] Furthermore, step (7) specifically includes:

[0046] (7.1) Design the Lyapunov function, the formula is as follows:

[0047]

[0048] In the formula, S = [s φ s θ s ψ ]T ;V≥0, and η φ ≥|d1|,η θ ≥|d2|,η ψ ≥|d3|;

[0049] (7.2) Differentiating the Lyapunov function yields:

[0050]

[0051] Proof based on the above formula Negative definiteness, according to Lyapunov's theorem, proves that the fractional-order terminal sliding mode attitude controller is stable.

[0052] Beneficial Effects: Compared with existing technologies, the quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode provides the following significant advantages: 1. By adopting a dual-closed-loop control strategy, different control methods are used for the differences between position control and attitude control of the quadrotor UAV, achieving a certain degree of decoupling between attitude and position and simplifying parameter adjustment; 2. By extending PID control and sliding mode control to the fractional level, the upper limit of system performance is greatly improved, giving the controller the characteristics of time memory and strong robustness; the improved fractional-order PID control enhances the anti-interference ability and control effect of PID control; the fractional-order terminal sliding mode control effectively accelerates the convergence speed of the system on the sliding surface and solves the singularity problem, enabling the quadrotor UAV to quickly respond to commands and adjust its attitude to ensure fuselage stability when facing complex airflow disturbances. Attached Figure Description

[0053] Figure 1 The diagram shown is a schematic representation of the airframe structure and reference coordinate system of the quadcopter UAV described in this invention.

[0054] Figure 2 The diagram shown is a schematic diagram of the overall control principle of the quadcopter UAV described in this invention.

[0055] Figure 3 The diagram shown is a block diagram of the external loop position control system of the quadcopter UAV described in this invention.

[0056] Figure 4 The diagram shown is a block diagram of the internal loop attitude control system of the quadcopter UAV described in this invention.

[0057] Figure 5 The diagram shown is a schematic diagram of the environmental wind interference described in this invention;

[0058] Figure 6 The image shown is a position trajectory tracking diagram of a quadcopter UAV in a specific embodiment; Figure 6 (a) shows the tracking trajectory in the x-axis direction. Figure 6 (b) shows the tracking trajectory in the y-axis direction. Figure 6 (c) shows the tracking trajectory in the z-axis direction;

[0059] Figure 7 The image shown is a trajectory tracking diagram of a quadcopter UAV in a specific embodiment; Figure 7 (a) shows the tracking trajectory at angle φ. Figure 7 (b) is the tracking trajectory at angle θ. Figure 7 (c) is the tracking trajectory with angle ψ. Detailed Implementation

[0060] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0061] like Figure 2 As shown, the present invention provides a quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode, which specifically includes the following steps:

[0062] Step 1: Taking a quadcopter drone as the object, and considering the complex environmental wind interference, establish a dynamic model of the quadcopter drone based on Newton's second law and Euler's equation.

[0063] Specifically, the mainstream form of quadcopter drones is X-shaped. To study their position and attitude information, refer to... Figure 1 The machine structure and reference coordinate system shown are based on the following assumptions:

[0064] (1) The quadcopter UAV is a symmetrical rigid body structure, and the origin of the body coordinate system coincides with the center of mass of the fuselage.

[0065] (2) Without considering the elastic deformation of the quadcopter blades, the position of the quadcopter's center of mass is not affected by the gyro effect;

[0066] (3) The air resistance and gravity experienced during flight are not affected by the flight attitude.

[0067] The specific formula for the dynamic model of a quadcopter drone is as follows:

[0068]

[0069] In the formula, (x, y, z) are the position coordinates of the quadcopter UAV in the ground coordinate system. Let x, y, and z be the first derivatives, respectively. φ represents the second derivatives of x, y, and z, respectively; φ represents the pitch angle of the quadcopter, θ represents the roll angle of the quadcopter, and ψ represents the yaw angle of the quadcopter. φ, θ, and ψ are the first derivatives of φ, θ, and ψ, respectively. φ, θ, and ψ are the second derivatives, respectively; m represents the weight of the quadcopter drone; U1, U2, U3, and U4 are the control inputs of the quadcopter drone; k x k y k z All are positional air drag coefficients for quadcopter drones; k Φ k θ k Ψ All are the attitude drag coefficients of quadcopter UAVs during flight; I x I y I z All represent the moment of inertia of the quadcopter drone; d1, d2, and d3 represent the external airflow disturbances experienced by the quadcopter drone along the X, Y, and Z axes during flight, respectively.

[0070] Step 2: Based on the fractional-order PID control theory, the fractional-order PID controller is improved through feedforward compensation and incomplete differentiation. The improved fractional-order PID controller is used to control the outer ring position subsystem of the quadcopter UAV.

[0071] While introducing a derivative signal into traditional PID control can improve the dynamic performance of a system, it may also amplify the effects of disturbances, especially given the uncertainty and suddenness of environmental winds. Figure 3 As shown, this invention adds a low-pass filter to the derivative stage of the fractional-order PID controller to reduce jitter caused by step signals, while simultaneously compensating for disturbances through a feedforward controller. The controlled object in the outer loop is the three-axis position of a quadcopter UAV. The dynamic model provides the acceleration of the quadcopter UAV relative to the ground coordinate system, and the UAV's position information can be obtained from the acceleration. The specific formula for the constructed fractional-order PID controller is as follows:

[0072]

[0073] In the formula, U x (s) represents the control output of the quadcopter UAV in the X-axis direction, U y (s) represents the control output of the quadcopter UAV in the Y-axis direction, U z (s) represents the control output of the quadcopter drone in the Y-axis direction; Kp x Kp y Kp z Both represent the proportionality coefficient, Ki x Ki y Ki z Both represent integral coefficients, Kd x Kd y Kd z All represent differential coefficients; λ represents the order of integration, μ is the order of differentiation; T fis the filter coefficient; E(s) is the difference between the desired position and the actual position; R(s) is the desired position of the given quadcopter UAV; G(s) is the position model of the quadcopter UAV, that is, the X, Y, Z position output corresponding to formula (14).

[0074] By inputting the desired and actual position information of the UAV into a fractional-order PID controller, the control output of the quadcopter UAV in the X, Y, and Z axes is obtained; ignoring air resistance and interference, only the output U of the fractional-order PID controller is considered. x U y U z The control output serves as the coordinate axis of the quadcopter UAV; U is obtained according to equation (14). x U y U z The relationship between U1 and attitude angle is shown in equation (16):

[0075]

[0076] Transforming equation (16) yields:

[0077]

[0078] In the formula, g represents the acceleration due to gravity.

[0079] Step 3: Calculate the desired attitude angles of the quadcopter drone based on its control outputs in the X, Y, and Z axes.

[0080] Specifically, the desired attitude angle is obtained by solving formulas (14), (16), and (17). The formulas are as follows:

[0081]

[0082] In the formula, φ d θ represents the desired pitch angle. d ψ represents the desired roll angle. d This indicates the desired yaw angle.

[0083] Step 4: Determine the attitude error and obtain the attitude error variation law based on the expected attitude angle and the actual attitude angle of the UAV.

[0084] (1) In order to track the desired attitude angle trajectory of the UAV, the attitude error tracking trajectory formula is defined as:

[0085] e(t)=r(t)-y(t) (19)

[0086] In the formula, e(t) represents the attitude error tracking trajectory; r(t) represents the trajectory of the UAV's desired attitude angle, specifically including φ at each time step. d θd And given ψ d ;y(t) represents the trajectory of the UAV's actual attitude angles, specifically including φ, θ, and ψ at each moment;

[0087] The attitude error at a certain moment can be expressed as:

[0088]

[0089] In the formula, e φ e represents the error in the pitch angle of the UAV. θ e represents the error in the roll angle of the drone. ψ This indicates the error in the drone's yaw angle.

[0090] (2) Combining the attitude angle formula in formula (14) with formulas (19) and (20), the attitude error variation law is obtained, and the formula is:

[0091]

[0092] Step 5: Design a fractional-order terminal sliding mode controller based on terminal sliding mode control theory and combined with the attitude error variation law, such as... Figure 4 As shown, attitude control is performed on the inner loop of a quadcopter UAV. To ensure that the UAV attitude control system converges to the equilibrium point in a finite time, a nonlinear sliding surface is used instead of a traditional linear sliding surface to construct a terminal sliding surface. However, terminal sliding control suffers from singularity issues, which can degrade system performance. Therefore, the terminal sliding surface is further improved to become a non-singular terminal sliding surface to resolve the singularity problem. Finally, fractional calculus is combined with the non-singular terminal sliding surface to construct a fractional-order terminal sliding surface.

[0093] (1) A non-singular fractional-order terminal sliding surface was designed, and the specific formula is as follows:

[0094]

[0095] In the formula, α and β both represent positive constants; 0 < α i <1, i takes 1,3...11; 1<α i <2, i takes 2, 4...12.

[0096] (2) Differentiate the constructed fractional-order terminal sliding surface and set its derivative to zero. Combine equations (14) and (17) to obtain the equivalent control law of the fractional-order terminal sliding surface. The formula is:

[0097]

[0098] In the formula, U φeq U represents the equivalent control output of the pitch angle. θeq U represents the equivalent control output of the roll angle.ψeq The equivalent control output representing the yaw angle; k φ k θ k ψ All of these represent the attitude drag coefficient of a quadcopter drone.

[0099] Step 6: Design the fractional-order terminal sliding mode switching control law; combine the fractional-order terminal sliding mode switching control law with the equivalent control law of the fractional-order terminal sliding mode to obtain the fractional-order terminal sliding mode attitude controller.

[0100] (1) A fractional-order terminal sliding mode switching control law is designed by combining fractional calculus with the traditional sliding mode control switching law. The specific formula is as follows:

[0101]

[0102] In the formula, k φ1 k θ1 k ψ1 η φ η θ η ψ All are normal numbers.

[0103] (2) The specific formula for the fractional-order terminal sliding mode attitude controller obtained by combining the fractional-order terminal sliding mode switching control law and the equivalent control law of the fractional-order terminal sliding mode is as follows:

[0104]

[0105] Step 7: Analyze the stability of the quadcopter UAV attitude control model based on Lyapunov's theorem, specifically including:

[0106] (1) Design the Lyapunov function, the formula is as follows:

[0107]

[0108] In the formula, S = [s φ s θ s ψ ] T ;V≥0, and η φ ≥|d1|,η θ ≥|d2|,η ψ ≥|d3|;

[0109] (2) Differentiating the Lyapunov function yields:

[0110]

[0111] Proof based on the above formula Negative definiteness, according to Lyapunov's theorem, proves that the fractional-order terminal sliding mode attitude controller is stable.

[0112] To verify the effectiveness of this invention, the control performance of the quadcopter was verified in the Matlab2020b simulation environment. The parameters of the quadcopter selected in the simulation are shown in Table 1.

[0113] Table 1

[0114]

[0115] Given the expected position of a quadcopter UAV as: x = 10m, y = 10m, z = 10m, ψ = 0.2rad, two strategies are used to track this signal: the fractional-order PID terminal sliding mode control provided in this invention and the traditional PID control. To compare the robustness of the two strategies, the following is introduced: Figure 5 The simulation results shown are for the natural wind disturbance consisting of basic wind, gradual wind, and random wind. Figure 6 , Figure 7 As shown.

[0116] from Figure 6 As can be seen from (a), 6(b), and 6(c), traditional PID control not only exhibits large overshoot after being disturbed, but also has a long settling time. In contrast, the fractional-order PID terminal sliding mode control strategy provided by this invention not only shortens the settling time by more than 25%, but also achieves almost no overshoot. This indicates that under natural wind disturbances, the control strategy proposed in this invention can ensure that the quadcopter UAV can quickly and smoothly reach the predetermined position in a disturbed environment. From Figure 7 As can be seen from (a), 7(b), and 7(c), the fractional-order terminal sliding mode controller designed in this invention can achieve fast and accurate tracking of the desired attitude trajectory obtained after attitude calculation, ensuring the system's fast response and anti-interference capability.

Claims

1. A control method for a quadrotor unmanned aerial vehicle based on fractional-order PID and fractional-order terminal sliding mode, characterized in that, Includes the following steps: (1) Considering the wind interference factors in the complex external environment, a dynamic model of the quadcopter UAV is established based on the Newton-Euler angle formula; (2) Based on fractional-order PID control theory, feedforward compensation theory and incomplete differentiation, construct a fractional-order PID controller; input the desired position and actual position of the quadcopter UAV into the fractional-order PID controller to obtain the control output of the quadcopter UAV in the X, Y and Z axis directions; The specific formula for the fractional-order PID controller constructed in step (2) is as follows: （2） In the formula, This indicates the control output of the quadcopter drone in the X-axis direction. This indicates the control output of the quadcopter drone in the Y-axis direction. This indicates the control output of the quadcopter drone in the Y-axis direction; , , Both represent proportionality coefficients, , , Both represent integral coefficients, , , All represent differential coefficients; Indicates the order of integration. The order of the differential; These are the filter coefficients; This represents the difference between the desired location and the actual location. Given the desired position of a quadcopter drone; A positional model of a quadcopter drone; (3) Calculate the desired attitude angle of the quadcopter UAV based on the control output obtained in step (2) and the current attitude angle; (4) Determine the attitude error by comparing the expected attitude angle with the actual attitude angle of the quadcopter UAV; (5) Construct a fractional-order terminal sliding surface based on the attitude error; differentiate the constructed fractional-order terminal sliding surface and set its derivative to zero, and solve the equivalent control law of the fractional-order terminal sliding surface by combining the dynamic model of the quadcopter UAV. (6) Design the fractional-order terminal sliding mode switching control law; combine the fractional-order terminal sliding mode switching control law with the equivalent control law of the fractional-order terminal sliding mode to obtain the fractional-order terminal sliding mode attitude controller. (7) Design the Lyapunov function and prove the stability of the fractional-order terminal sliding mode attitude controller using Lyapunov's theorem.

2. The quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode according to claim 1, characterized in that, The dynamic model formula for the quadcopter UAV in step (1) is: （1） In the formula, Here are the position coordinates of the quadcopter UAV in the Earth coordinate system. , , Corresponding to The first derivative, , , Corresponding to The second derivative; Indicates the pitch angle of a quadcopter drone. This indicates the roll angle of a quadcopter drone. Indicates the yaw angle of a quadcopter drone; , , Corresponding to , , The first derivative; , , Corresponding to , , The second derivative; Indicates the weight of the quadcopter drone; All are control inputs for quadcopter drones; , , All figures represent the positional air drag coefficients of quadcopter drones. All values ​​represent the air drag coefficients of the drone during flight. Both represent the moment of inertia of a quadcopter drone; The external airflow interference experienced by the X-axis during the flight of a quadcopter drone. The external airflow interference experienced by the Y-axis during the flight of a quadcopter drone. This refers to the external airflow interference experienced by the Z-axis during the flight of a quadcopter drone.

3. The quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode according to claim 2, characterized in that, Step (3) specifically includes: ignoring air resistance and interference, using only the output of the fractional-order PID controller as the control output of the quadcopter UAV's coordinate axes; obtaining the coordinates according to equation (1). and The relationship between the attitude angles is shown in equation (3): （3） The transformation yields: （4） In the formula, Represents gravitational acceleration; The desired attitude angle is obtained by solving formulas (1), (3), and (4). The specific formulas are as follows: （5） In the formula, Indicates the desired pitch angle. Indicates the expected roll angle. This indicates the desired yaw angle.

4. The quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode according to claim 3, characterized in that, Step (4) specifically includes: To track the desired attitude angle trajectory of a quadcopter drone, the attitude error tracking trajectory formula is defined as follows: （6） In the formula, Indicates the attitude error tracking trajectory; This represents the trajectory of the quadcopter drone at the desired attitude angle, specifically including the values ​​at each time step. , And the given ; The trajectory represents the actual attitude angles of the quadcopter drone, specifically including the values ​​at various moments. , , ; The attitude error at a certain moment can be expressed as: （7） In the formula, This indicates the error in the pitch angle of a quadcopter drone. This indicates the error in the roll angle of a quadcopter drone. This indicates the error in the yaw angle of a quadcopter drone.

5. The quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode according to claim 4, characterized in that, The formula for the fractional-order terminal sliding surface constructed in step (5) is: （8） In the formula, , All are positive numbers; , Take 1, 3, ..., 11; , Take 2, 4, ..., 12; Differentiating the constructed fractional-order terminal sliding surface and setting its derivative to zero, and then solving equations (1) and (4) together, we obtain the equivalent control law of the fractional-order terminal sliding surface. The formula is as follows: （9） In the formula, The equivalent control output representing the pitch angle. The equivalent control output representing the roll angle. The equivalent control output representing the yaw angle; , , All of these represent the attitude drag coefficient of a quadcopter drone.

6. The quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode according to claim 5, characterized in that, The specific formula for the fractional-order terminal sliding mode switching control law designed in step (6) is as follows: （10） In the formula, , , , , , All are positive numbers; The specific formula for the fractional-order terminal sliding mode attitude controller, obtained by combining the fractional-order terminal sliding mode switching control law and the equivalent control law of the fractional-order terminal sliding mode, is as follows: （11）。 7. The quadrotor UAV control method based on fractional-order PID and fractional-order terminal sliding mode according to claim 6, characterized in that, Step (7) specifically includes: (7.1) Design the Lyapunov function, the formula is as follows: （12） In the formula, ; ,and , , ; (7.2) Differentiating the Lyapunov function yields: （13） Proof based on the above formula Negative definiteness, according to Lyapunov's theorem, proves that the fractional-order terminal sliding mode attitude controller is stable.

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