Four-rotor unmanned aerial vehicle fractional order PD controller design method based on phase angle margin

Abstract

The invention provides a quad-rotor unmanned aerial vehicle fractional order PD controller design method based on phase margin, and the method employs the concept of phase margin to guide the selection of the parameters of a fractional order PD controller, so as to guarantee that a system has good phase characteristics under different working conditions. Compared with a traditional intelligent algorithm, the phase angle margin method not only reduces the unnecessary calculation amount, but also avoids the problem of premature convergence, thereby improving the efficiency and accuracy of parameter setting. By means of the method, more accurate and efficient fractional order PD controller parameter setting is achieved, and then the overall flight performance of the quad-rotor unmanned aerial vehicle is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle control, and in particular relates to a design method of a fractional-order PD controller for a quad-rotor unmanned aerial vehicle based on phase margin. Background Art

[0002] Quadcopters have been widely used in many fields due to their compact structure and flexible operation. However, due to their inherent nonlinear characteristics and strongly coupled dynamic models, traditional integer-order PID (proportional-integral-differential) controllers are often unable to cope with the complex dynamic behaviors of such systems. Although integer-order PID controllers are easy to implement and perform stably and reliably in many situations, they may not provide sufficient control performance when dealing with nonlinear systems due to their fixed structure. In addition, traditional PID controllers are difficult to effectively solve problems such as model uncertainty or external interference in the system.

[0003] To overcome these limitations, fractional-order PID (proportional-integral-differential) controllers came into being. Fractional-order PID controllers are designed based on fractional-order calculus theory. Compared with traditional integer-order controllers, they provide greater design freedom by introducing fractional orders. This additional degree of freedom enables the controller to better adapt to complex dynamic characteristics, thereby improving the flexibility and robustness of the control system. Fractional-order PID controllers have their advantages. Fractional-order PD controllers simplify the design and tuning process by reducing the number of parameters, and can better optimize the frequency response characteristics of the system, especially in the high-frequency band, which helps to improve the dynamic performance and anti-interference ability of the system. In addition, fractional-order PD controllers can also provide better phase control, which is particularly important for applications that require precise phase adjustment.

[0004] Although fractional-order PD controllers have many advantages, they also face some challenges in practical applications, especially parameter tuning. Compared with integer-order PID controllers, fractional-order PD controllers require more parameters to be tuned, which not only increases the computational complexity but also prolongs the time required for parameter tuning. In addition, traditional parameter tuning methods such as trial and error are often inefficient and it is difficult to find the optimal solution. Summary of the invention

[0005] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to propose a design method for a fractional-order PD controller for a quadrotor drone based on phase margin. This method uses the concept of phase margin to guide the selection of fractional-order PD controller parameters to ensure that the system has good phase characteristics under different working conditions. Compared with traditional intelligent algorithms, the phase margin method not only reduces unnecessary calculations, but also avoids the problem of premature convergence, thereby improving the efficiency and accuracy of parameter setting. Through this method, it is intended to achieve more accurate and efficient fractional-order PD controller parameter setting, thereby improving the overall flight performance of the quadrotor drone.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for designing parameters of a fractional-order PD controller for a quadrotor drone based on a phase margin method, characterized in that it comprises the following steps:

[0008] Step 1, establish the dynamic model of the quadrotor drone;

[0009] Step 2, according to the dynamic model of the quad-rotor drone, obtain the transfer function model of the quad-rotor drone and calculate the transfer function of each channel according to the transfer function model of the quad-rotor drone;

[0010] Step 3, draw a Bode diagram according to the transfer function of each channel, and determine the crossover frequency and phase margin of the controlled vector in the Bode diagram;

[0011] Step 4, calculating the parameters of the PD controller by determining the crossover frequency and phase margin;

[0012] Step 5, input the position error of the quadrotor drone into the fractional-order PD controller of the quadrotor drone position control loop, and calculate the output control quantity of the quadrotor drone position control loop;

[0013] Step 6, the desired attitude angle of the quadrotor drone is calculated by solving the control quantity output by the position control loop of the quadrotor drone and the current attitude angle of the quadrotor drone, and the attitude angle error of the quadrotor drone is obtained;

[0014] Step 7: Observe the output results of the quadrotor drone and evaluate the PD controller parameters.

[0015] In step 1, the interference factors of the external environment during the flight of the quadrotor drone are considered. According to the Euler equation and the inertial-body coordinate system, the dynamic model of the quadrotor drone is established as follows:

[0016]

[0017] In formula (1), x, y, and z are the positions of the quadrotor drone in the inertial coordinate system; The first-order derivative of x, y, and z is used to obtain the speed of the quadrotor drone in the inertial coordinate system; The acceleration of the quadrotor drone in the inertial coordinate system is obtained by taking the second-order derivative of x, y, and z; φ, θ, and ψ represent the attitude angles of the quadrotor drone, namely the roll angle, pitch angle, and yaw angle, respectively; The corresponding first-order derivatives are φ, θ, and ψ; The corresponding second-order derivatives are φ, θ, and ψ; m is the mass of the quadcopter; g is the acceleration due to gravity; U x ,U y ,U z Represents the acceleration of the drone in three orthogonal directions, U 1 Represents the output control quantity of the drone position control loop; I x ,I y ,I z Both represent the moment of inertia of the quadrotor drone.

[0018] In step 2, the LPV method is used to transform the dynamic model of the quadrotor drone into a state space expression, thereby simplifying the controller design process; the state equation after the transformation of formula (1) is

[0019]

[0020] Where A is the coefficient matrix; is the state vector; is the derivative of the state vector in the time domain, B is the input matrix; U = (U 1 ,U x ,U y ,U z ) T S is the input vector; Y = (z, φ, θ, ψ) T is the output vector; C is the output matrix; D is the direct transfer matrix.

[0021] By performing Laplace transform on formula (2), we can get the transfer function model of the quadrotor drone:

[0022]

[0023] Among them, G(s) is the UAV function transfer model, and SI is the frequency domain unit matrix.

[0024] In step 3, based on the obtained transfer function model, use auxiliary analysis software such as MATLAB to draw a Bode diagram. In the Bode diagram, find out the frequency when the phase is -180° as the crossover frequency, and the gain margin at the crossover frequency as the phase margin.

[0025] In step 4, the Ziegler-Nichols law based on frequency response is used to adjust the controller parameters so that the open-loop frequency response of the quadrotor drone has a certain phase margin. By analyzing the Bode diagram of the quadrotor drone transfer function model, the crossover frequency (i.e., the frequency when the open-loop gain is 0dB) is determined, and the parameters of the PD controller are adjusted accordingly to ensure that the quadrotor drone has sufficient stability and dynamic performance.

[0026] In step 5: Based on fractional-order calculus theory and PID control theory, a dual-loop control system for a quadrotor drone based on a fractional-order PD controller is designed, where the inner loop is the quadrotor drone attitude control loop, and the outer loop is the quadrotor drone position control loop. The position error of the quadrotor drone is input into the fractional-order PD controller of the quadrotor drone position control loop, and the output control quantity of the position loop is calculated.

[0027] Furthermore, in vertical take-off and landing, low-speed flight, and hovering, the pitch angle θ and the roll angle φ change very little. In order to simplify the dynamic model of the quadrotor drone, it is assumed that θ=φ≈0, from which U x ,U y ,U z ,U 1 And the relationship between the attitude angle is:

[0028]

[0029] Transformation yields:

[0030]

[0031] In step 6, the output control quantity of the quadrotor position control loop obtained in step (5) is used to calculate the desired attitude angle of the quadrotor. The specific formula is:

[0032]

[0033] In the formula, φ d represents the desired pitch angle, θ d represents the desired roll angle, ψ d represents the desired yaw angle.

[0034] In step 7, the adjustment time, overshoot, and steady-state error of the quadrotor control system are evaluated to assess whether the PD controller parameters meet the standards. If they do not meet the standards, return to step 4 and fine-tune the PD controller parameters. If the standards are met, the iteration is stopped.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] The present invention uses the LPV method to simplify the UAV dynamics model, and then guides the controller parameter setting through the phase margin, which can ensure that the quadrotor UAV control system has good phase characteristics under different working conditions and improve the stability of the quadrotor UAV control system. At the same time, this method effectively reduces the amount of calculation, speeds up the convergence rate, and is more suitable for computer calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is the body coordinate system and the ground coordinate system of the quad-rotor UAV of the present invention.

[0038] Figure 2 This is a structural diagram of the fractional-order PD control system of the quadrotor drone of the present invention.

[0039] Figure 3 The initial conditions are set according to the embodiment of the present invention, and the Bode diagram of the transfer function for the z-axis is shown.

[0040] Figure 4 It is a vector diagram of the transfer function in the phase margin method of the present invention in the complex plane.

[0041] Figure 5 This is the calculation result of the fractional-order PD controller parameters based on the phase margin method of the present invention.

[0042] Figure 6 It is a Bode diagram of the transfer function after the z-axis transfer function is corrected in the embodiment of the present invention.

[0043] Figure 7 The present invention sets initial conditions according to the embodiment and designs the position tracking result of the quadrotor UAV in the Z-axis direction under the control of the fractional-order PD controller based on the phase margin method.

[0044] Figure 8 The present invention sets initial conditions according to the embodiment, designs the trajectory tracking of the quadrotor UAV in the X-axis direction under the control of the fractional-order PD controller and the traditional integer-order PID controller based on the phase margin method.

[0045] Fig. 9 The present invention sets initial conditions according to the embodiment, designs the trajectory tracking of the quadrotor UAV in the Y-axis direction under the control of the fractional-order PD controller and the traditional integer-order PID controller based on the phase margin method.

[0046] Fig.10 The present invention sets initial conditions according to the embodiment, designs the trajectory tracking of the quadrotor UAV in the Z-axis direction under the control of the fractional-order PD controller and the traditional integer-order PID controller based on the phase margin method.

[0047] Fig.11The present invention sets initial conditions according to the embodiment, designs the attitude results of the roll angle of the quadrotor drone under the control of the fractional-order PD controller and the traditional integer-order PID controller based on the phase margin method.

[0048] Fig.12 The present invention sets initial conditions according to the embodiment, designs fractional-order PD controller based on the phase margin method, and the attitude results of the pitch angle of the quadrotor drone under the control of the traditional integer-order PID controller.

[0049] Fig.13 The present invention sets initial conditions according to the embodiment, designs fractional-order PD controller based on phase margin method and the attitude result of the yaw angle of the quadrotor drone under the control of the traditional integer-order PID controller. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific implementation methods.

[0051] The present invention provides a design method for a quad-rotor UAV fractional-order PD controller based on phase margin, which specifically includes the following steps:

[0052] Step 1: Taking the quadrotor drone as the object, a dynamic model of the quadrotor drone is established based on Newton's second law and Euler's equation.

[0053] Specifically, the mainstream form of quadcopter drones is X-shaped. In order to study its position and attitude information, refer to Figure 1 The body structure and reference coordinate system shown, and the following conditions are assumed to be true;

[0054] 1. The quad-rotor drone is a uniform and symmetrical rigid body. The geometric center, center of gravity, and body coordinate origin of the quad-rotor drone are overlapped for analysis;

[0055] 2. The mass and moment of inertia of the quadcopter drone remain unchanged, and the elastic deformation of the blades is not considered;

[0056] 3. During the flight of a quadrotor drone, the air resistance coefficient remains constant.

[0057] The specific formula of the dynamic model of the quadrotor drone is:

[0058]

[0059] In formula (7), x, y, and z are the positions of the quadrotor drone in the inertial coordinate system; The first-order derivative of x, y, and z is used to obtain the speed of the quadrotor drone in the inertial coordinate system; The acceleration of the quadrotor drone in the inertial coordinate system is obtained by taking the second-order derivative of x, y, and z; φ, θ, and ψ represent the attitude angles of the quadrotor drone, namely the roll angle, pitch angle, and yaw angle, respectively; The corresponding first-order derivatives are φ, θ, and ψ; The corresponding second-order derivatives are φ, θ, and ψ; m is the mass of the quadcopter; g is the acceleration due to gravity; U x ,U y ,U z Represents the acceleration of the drone in three orthogonal directions, U 1 Represents the output control quantity of the drone position control loop; I x ,I y ,I z Both represent the moment of inertia of the quadrotor drone.

[0060] Step 2: According to formula (7), the LPV method of establishing an overall mathematical model is used to solve the dynamic model of the quadrotor drone. Assume that the system state equation is:

[0061]

[0062] Where A is the coefficient matrix; is the state vector; B is the input matrix; U=(U 1 ,U x ,U y ,U z ) T is the input vector; Y = (z, φ, θ, ψ) T is the output vector; C is the output matrix; D is the direct transfer matrix. By performing Laplace transform on formula (8), we can get the transfer function model of the quadrotor drone:

[0063]

[0064] The formulas of each matrix in formula (9) are:

[0065]

[0066]

[0067] In the above formula, SI represents the complex frequency domain matrix transformed from the unit matrix in the transfer function model, φ, θ, ψ represent the attitude angles of the quadrotor drone, namely the roll angle, pitch angle and yaw angle respectively; I x ,I y ,I z Both represent the moment of inertia of the quadrotor drone.

[0068] Furthermore, in vertical take-off and landing, low-speed flight, and hovering, the pitch angle θ and the roll angle φ change very little. In order to simplify the dynamic model of the quadrotor drone, it is assumed that θ = φ ≈ 0;

[0069] Next, we will solve the parameters of the fractional-order PD controller. The solution of the parameters of the fractional-order PD controller is to obtain a correction vector L based on the performance index vector G in the complex plane, so that it can correct the controlled object vector P to reach the required performance index vector G, that is, L·P=G. Then, the controller vector C is used to approximate the correction vector L, and the controller parameter equation can be obtained.

[0070] The steps for solving the parameters of the fractional-order PD controller are as follows:

[0071] (1) Write out the vector form and angular velocity of the controlled object. The controlled object P(s) is written in vector form as:

[0072] P(jω)=|P(jω)|∠P(jω) (14)

[0073] Angular velocity of the controlled object:

[0074]

[0075] (2) In order to ensure that the quadrotor UAV can maintain good dynamic performance and robustness under various conditions, the performance index vector G(jω) should meet the following requirements:

[0076] Stability performance index: According to the open-loop system (drone model without feedback loop, that is, only the dynamic model of the drone and control input) at ω c Phase margin at The stability performance index vector can be obtained as:

[0077]

[0078] Robustness performance index: In order to ensure the robustness of the fractional-order PD controller to gain changes, the robustness condition of gain change is added, that is, the phase of the open-loop transfer function of the quadrotor drone is required to be at the crossover frequency ω c The area nearby is flat.

[0079]

[0080] That is, the performance index vector is required to be at the crossover frequency ω c The angular velocity at is 0.

[0081] (3) According to the stability performance index vector (Equation (16)) and the controlled object vector (Equation (14)), the correction vector can be obtained from L·P=G:

[0082]

[0083] According to the robustness performance index (Equation (17)), L·P=G, we know that at frequency ω c Correction vector angular velocity and the angular velocity of the controlled object The sum is equal to 0, then the angular velocity of the correction vector is:

[0084]

[0085] (4) Use the controller vector to approximate the correction vector, that is, the controller vector and the correction vector have the same modulus, phase angle, and angular velocity. Thus, the equation for solving the controller parameters is obtained. Let and That is, L(jω c )=A∠θ.

[0086] Where A is the magnitude of the correction vector, and θ is the phase angle of the correction vector. By solving the control parameter step (4), the correction vector is approximated by the fractional-order PD controller vector. The controller vector is equal to the magnitude and phase angle of the correction vector, which means that the stability performance index is met. Figure 4 and three The law of cosines of angles gives:

[0087]

[0088] from Figure 4 The geometric relationship can be seen in:

[0089]

[0090] Combining equation (22) and equation (23), we can get:

[0091]

[0092] Finally, the parameter K can be obtained by combining equations (20), (21), and (24): P , K d , μ.

[0093] Example:

[0094] In order to verify the effectiveness of the present invention, the control performance of the quadrotor drone is verified in the simulation environment of Matlab2022b. The parameters of the quadrotor drone selected in the simulation are shown in Table 1:

[0095] Table 1

[0096]

[0097] Substituting the data in Table 1 into formula (9), the transfer function matrix G(s) is obtained as follows:

[0098]

[0099] In formula (25), the first row represents the transfer function of the z-axis; the second row represents the transfer function of the roll angle φ channel; the third row represents the transfer function of the pitch angle θ channel; and the fourth row represents the transfer function of the yaw angle ψ channel. When simulating a quadrotor drone, since the quadrotor drone is driven by a motor, the transfer function in formula (25) cannot represent the transfer function of each channel. In this case, the original transfer function is multiplied by the first-order inertial link. The new transfer function obtained is:

[0100]

[0101] Furthermore, the Bode diagrams of the four channel transfer functions are plotted to determine the crossover frequency and phase margin. Taking the z-axis channel as an example, the Bode diagram is as follows: Figure 3 As shown;

[0102] from Figure 3 It can be seen that when the crossover frequency is given to be 60 rad / s, the amplitude of the z-axis channel is -63.1 dB and the phase is -261°.

[0103] Next, we will solve the parameters of the fractional-order PD controller. The solution of the parameters of the fractional-order PD controller is to obtain a correction vector L based on the performance index vector G in the complex plane, so that it can correct the controlled object vector P to reach the required performance index vector G, that is, L·P=G. Then, the controller vector C is used to approximate the correction vector L, and the controller parameter equation can be obtained.

[0104] The steps for solving the parameters of the fractional-order PD controller are as follows:

[0105] (1) Write out the vector form and angular velocity of the controlled object. The controlled object P(s) is written in vector form as:

[0106] P(jω)=|P(jω)|∠P(jω) (27)

[0107] Angular velocity of the controlled object:

[0108]

[0109] (2) According to the system requirements, write the performance indicator vector G(jω).

[0110] Stability performance index: According to the open-loop system at ω c Phase margin at The stability performance index vector can be obtained as:

[0111]

[0112] Robustness performance index: In order to ensure the robustness of the system to gain changes, the robustness condition of gain change is added, that is, the phase of the system open-loop transfer function is required to be at the crossover frequency ω c The area nearby is flat.

[0113]

[0114] That is, the performance index vector is required to be at the crossover frequency ω c The angular velocity at is 0.

[0115] (3) The correction vector L is obtained according to L·P=G.

[0116] According to the stability performance index vector (Equation (29)) and the controlled object vector (Equation (26)), the correction vector can be obtained by L·P=G:

[0117]

[0118] According to the robustness performance index (Equation (30)), L·P=G, we know that at frequency ω c Correction vector angular velocity and the angular velocity of the controlled object The sum is equal to 0, then the angular velocity of the correction vector is:

[0119]

[0120] (4) Use the controller vector to approximate the correction vector, that is, the controller vector and the correction vector have the same modulus, phase angle and angular velocity. Thus, the equation for solving the controller parameters is obtained.

[0121] make and That is, L(jω c )=A∠θ.

[0122] Where A is the magnitude of the correction vector, and θ is the phase angle of the correction vector. By solving the control parameter step (4), the correction vector is approximated by the fractional-order PD controller vector. The controller vector is equal to the magnitude and phase angle of the correction vector, which means that the stability performance index is met. Figure 4 and three The law of cosines of angles gives:

[0123]

[0124] from Figure 4 The geometric relationship can be seen in:

[0125]

[0126] Combining equation (35) and equation (36), we can get:

[0127]

[0128] Finally, the parameter K can be obtained by combining equations (33), (34), and (37): P , K d , μ.

[0129] Next, we bring in the amplitude and phase of the z-axis channel, and we get the following result: Figure 5 Shown: From Figure 5 As can be seen in K P =226.623, μ=1.62307, substituting the result into formula (33), we get K d =2.0947, bring in the fractional-order PD controller parameters, and set the crossover frequency ω c =60 phase margin The Bode diagram of the corrected transfer function G = L·P is: Figure 6 :exist Figure 6 In the figure, we can see that at the crossover frequency ω c = 60, the amplitude is almost 0, and the phase also satisfies the phase margin The design of the controller proves that it is a success.

[0130] For further verification, the fractional-order PD controller is connected to the model of the quadrotor drone and the simulation waveform is observed. d =sint, its simulation waveform is as follows Figure 7 As shown:

[0131] As you can see from the picture, the z-axis tracks the set value perfectly.

[0132] Furthermore, given the expected position of the quadcopter, x d = sint,y d = cost, z d =2t, The fractional-order PD controller provided by the present invention is used to track this signal. The simulation results are shown in Figure 8 , Fig. 9 , Fig.10 shown.

[0133] from Figure 8 , Fig. 9 , Fig.10It can be seen that the traditional PID control not only has a large overshoot in the process of tracking the target signal, but also has a long adjustment time. Compared with the fractional-order PD controller provided by the present invention, not only the adjustment time is shortened by more than 25%, but also almost no overshoot is achieved. This shows that the control strategy proposed by the present invention can ensure that the quadcopter drone reaches the desired position quickly and smoothly. Fig.11 , Fig.12 and Fig.13 is the change of attitude angle of the quadrotor drone during movement, from Fig.11 and Fig.12 and Fig.13 It can be seen that the fractional-order PD controller designed in the present invention can realize fast and accurate tracking of the desired attitude trajectory obtained after attitude solution, ensuring the rapid response and anti-interference ability of the system.

Claims

1. A design method for a fractional-order PD controller for a quadrotor drone based on phase margin, characterized in that: The steps include: Step 1, establish the dynamic model of the quadrotor drone; Step 2, according to the dynamic model of the quad-rotor drone, obtain the transfer function model of the quad-rotor drone and calculate the transfer function of each channel according to the transfer function model of the quad-rotor drone; Step 3, draw a Bode diagram according to the transfer function of each channel, and determine the crossover frequency and phase margin of the controlled vector in the Bode diagram; Step 4, calculating the parameters of the PD controller by determining the crossover frequency and phase margin; Step 5, input the position error of the quadrotor drone into the fractional-order PD controller of the quadrotor drone position control loop, and calculate the output control quantity of the quadrotor drone position control loop; Step 6, the desired attitude angle of the quadrotor drone is calculated by solving the control quantity output by the position control loop of the quadrotor drone and the current attitude angle of the quadrotor drone, and the attitude angle error of the quadrotor drone is obtained; Step 7: Observe the output results of the quadrotor drone and evaluate the PD controller parameters.

2. The design method of a quadrotor UAV fractional-order PD controller based on phase margin according to claim 1 is characterized in that: In step 1, the interference factors of the external environment during the flight of the quadrotor drone are considered. According to the Euler equation and the inertial-body coordinate system, the dynamic model of the quadrotor drone is established as follows: In formula (1), x, y, and z are the positions of the quadrotor drone in the inertial coordinate system; The first-order derivative of x, y, and z is used to obtain the speed of the quadrotor drone in the inertial coordinate system; The acceleration of the quadrotor drone in the inertial coordinate system is obtained by taking the second-order derivative of x, y, and z; φ, θ, and ψ represent the attitude angles of the quadrotor drone, namely the roll angle, pitch angle, and yaw angle, respectively; The corresponding first-order derivatives are φ, θ, and ψ; The corresponding second-order derivatives are φ, θ, and ψ; m is the mass of the quadcopter; g is the acceleration due to gravity; U x ,U y ,U z It represents the acceleration of the UAV in three orthogonal directions, and U1 represents the output control value of the UAV position control loop; I x ,I y ,I z Both represent the moment of inertia of the quadrotor drone.

3. The design method of a quadrotor UAV fractional-order PD controller based on phase margin according to claim 1 is characterized in that: In step 2, the dynamic model of the quadrotor drone is converted into a state space expression through the LPV method, thereby simplifying the controller design process; the dynamic model of the quadrotor drone in step 1 is converted into the following state equation: Where A is the coefficient matrix; is the state vector; is the derivative of the state vector in the time domain, B is the input matrix; U = (U1, U2, U3, U4) T is the input vector; Y = (z, φ, θ, ψ) T is the output vector; C is the output matrix; D is the direct transfer matrix.

4. The design method of a quadrotor UAV fractional-order PD controller based on phase margin according to claim 3 is characterized in that: Performing Laplace transform on the state equation (2) of the quadrotor drone, we get the transfer function model of the quadrotor drone: Among them, G(s) is the UAV function transfer model, and SI is the frequency domain unit matrix.

5. The design method of a quadrotor UAV fractional-order PD controller based on phase margin according to claim 1 is characterized in that: In step 3, according to the obtained transfer function model, the Bode diagram is drawn using MATLAB auxiliary analysis software. In the Bode diagram, the frequency when the phase is -180° is found as the crossover frequency, and the gain margin at the crossover frequency is the phase margin.

6. The design method of a quadrotor UAV fractional-order PD controller based on phase margin according to claim 1 is characterized in that: In step 4, the Ziegler-Nichols phase margin law is used to determine the parameters of the PD controller based on the crossover frequency and the phase margin.

7. The design method of a quadrotor drone fractional-order PD controller based on phase margin according to claim 1 is characterized in that: In step 5: Based on fractional-order calculus theory and PD control theory, a dual-loop control system for a quadrotor drone based on a fractional-order PD controller is designed, where the inner loop is the quadrotor drone attitude control loop, and the outer loop is the quadrotor drone position control loop. The position error of the quadrotor drone is input into the fractional-order PD controller of the quadrotor drone position control loop, and the output control quantity of the position loop is calculated.

8. The method for designing a quadrotor UAV fractional-order PD controller based on phase margin according to claim 2 is characterized in that: In vertical takeoff and landing, low-speed flight, and hovering, the pitch angle θ and roll angle φ change little. In order to simplify the dynamic model of the quadrotor drone, it is assumed that θ=φ≈0. According to step 1, U x ,U y ,U z , the relationship between U1 and attitude angle is: Transformation yields:

9. The quadrotor UAV fractional-order PD controller design method based on phase margin according to claim 1 is characterized in that: In step 6, the output control quantity of the quadrotor position control loop obtained in step (5) is used to calculate the desired attitude angle of the quadrotor. The specific formula is: In the formula, φ d represents the desired pitch angle, θ d represents the desired roll angle, ψ d represents the desired yaw angle.

10. The quadrotor UAV fractional-order PD controller design method based on phase margin according to claim 1 is characterized in that: In step 7, the adjustment time, overshoot, and steady-state error of the quadrotor control system are evaluated to assess whether the PD controller parameters meet the standards. If they do not meet the standards, return to step 4 and fine-tune the PD controller parameters. If the standards are met, the iteration is stopped.

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