An overdrive quad-rotor aircraft experimental platform attitude tracking robust control method

Abstract

The application discloses a kind of overdrive four-rotor aircraft experimental platform attitude tracking robust control methods, belong to the field of aircraft attitude control technology.The application first establishes the mathematical model of four-rotor aircraft, and is converted into linear disturbed double integral model;Proportional-integral-derivative method is used to design nominal controller, to ensure that nominal closed-loop system is asymptotically stable, and adaptive extended state observer is used to estimate the angular velocity and disturbance information of four-rotor aircraft, and a kind of attitude tracking robust controller is designed;By constructing dead zone saturation compensation link, the control influence brought by motor dead zone saturation nonlinear characteristic is weakened.The application can effectively solve the problem brought by motor dead zone saturation characteristic, and transient overshoot and steady-state error performance of closed-loop system are considered simultaneously.

Description

Technical Field

[0001] This invention belongs to the field of aircraft attitude control technology, specifically relating to a robust control method for attitude tracking of an over-driven quadrotor experimental platform. Background Technology

[0002] Unmanned quadcopters, due to their advantages of small size, high stealth, high flexibility, and low cost, are widely used in military and civilian fields for tasks such as search, detection, reconnaissance, photography, and rapid target acquisition. However, during real-world testing, researchers may encounter various risks that could lead to damage to the moving object, resulting in losses. To mitigate such losses, a three-degree-of-freedom quadcopter simulation experimental platform based on quadcopter drones has been developed.

[0003] The quadcopter experimental platform retains the basic characteristics of a real quadcopter, but it still has some problems. For example, the control distribution problem caused by the overdrive structure; the platform is susceptible to unknown and unpredictable disturbances; and the platform can only obtain angle measurement information through the angular position encoder, but not angular velocity measurement information. In practical applications, the motor that drives the rotor blades has nonlinear characteristics such as dead zone saturation, which makes the control law's control effect in practice not meet expectations.

[0004] Currently, a common solution for estimating certain state and disturbance information in quadrotor experimental platform systems is to use an extended state observer (ESO). However, ESOs exhibit large transient overshoot and small steady-state error at high gain parameters, which can easily lead to system instability or even divergence. Conversely, ESOs exhibit small transient overshoot and large steady-state error at low gain parameters. Therefore, it is crucial to select appropriate ESO gain parameters to maintain control system stability. Inappropriate gain parameters can significantly hinder the system from achieving the desired control effect. Summary of the Invention

[0005] To overcome the problems of the aforementioned controllers, this invention proposes a robust control method for attitude tracking of overdriven quadrotors based on an adaptive extended state observer, which takes into account both the transient and steady-state response performance of the closed-loop system.

[0006] The technical solution adopted in this invention is as follows:

[0007] A robust control method for attitude tracking on an over-driven quadrotor experimental platform, the method comprising the following steps:

[0008] Step 1: Establish a three-degree-of-freedom attitude dynamics model of the quadcopter and transform it into a linear disturbed double integral system model;

[0009] Preferably, the three-degree-of-freedom attitude dynamics model of the quadcopter is as follows:

[0010]

[0011]

[0012]

[0013] Where ε, θ, and ψ represent the pitch, roll, and yaw angles of the quadcopter, respectively, all in rad. Let J represent the second derivatives of the pitch, roll, and yaw angles, respectively; ε J θ With J ψ These represent the moments of inertia about the pitch axis, roll axis, and yaw axis, respectively, all in kg·m. 2 ;d ε d θ With d ψ These represent the external disturbances acting on the pitch, roll, and yaw channels, respectively, all in Newtons (N); L represents the average distance from each motor to the center of gravity connecting rod, in meters (m); g represents the acceleration due to gravity, in meters per second (m / s²). 2 ;m f m l m r With m b These represent the masses of the front motor, left motor, right motor, and rear motor, respectively, all in kg; F f F l F r With F b These represent the control input quantities for the front motor, left motor, right motor, and rear motor, respectively, all in N.

[0014] Define the rotational inertia matrix J∈R 3×3 for:

[0015]

[0016] Define the control matrix B∈R 3×4 for:

[0017]

[0018] The values ​​of the control matrix parameters a1 to a4 are set as follows: a1 = Lcosθ, a2 = Lcosε, a3 = Lsinθ·cosε, a4 = Lcosθ·cosε;

[0019] Define the gravity matrix G∈R 3×1 for:

[0020]

[0021] Define the system's control input variables U∈R 4×1 for:

[0022] U = [F f F l F r F b ] T (7)

[0023] Define external perturbation D∈R 3×1 for:

[0024] D = [d ε d θ d ψ ] T (8)

[0025] Define the three-axis attitude angle vector ρ∈R of the system. 3×1 for:

[0026] ρ=[ε θ ψ] T (9)

[0027] By using variable substitution to transform equations (1) to (3), we can obtain the following model:

[0028]

[0029] Moving the moment of inertia to the right side of the equation, we obtain the attitude channel model of the quadcopter:

[0030]

[0031] Define variables (i.e., the controller output of the quadcopter):

[0032] u ρ =J -1 BU+J -1 G (12)

[0033] d ρ =J -1 D (13)

[0034] By transforming equations (1) to (3) using equations (12) and (13), we can obtain the simplified linear disturbed double integral system model:

[0035]

[0036] The linear double integral system mentioned in equation (14) can be further rewritten in the following form:

[0037]

[0038] Where x1 represents the actual attitude angle signal, and x1 = [ε θ ψ] T x2 represents the actual attitude angular rate signal, x3 represents the actual attitude angular acceleration signal, and its value is the actual three-axis disturbance. h(x) represents the rate of change of the disturbance. x represents i The first derivative of , where i = 1, 2, 3, and y represents the actual output signal;

[0039] Step 2: For the linear disturbed double integral model established in Step 1, use AESO to obtain angular velocity estimation information and disturbance estimation information, and design a proportional-integral-derivative (PID) control law.

[0040] An adaptive extended state observer (AESO) takes the actual attitude angle signal as input and outputs an estimated value of the attitude angular rate signal. Attitude angular acceleration signal estimation value And the estimated values ​​of the three-channel perturbation of the actual attitude Specifically, the designed AESO takes the following form:

[0041]

[0042] Where l1(t), l2(t), and l3(t) represent the gain matrices of the three adaptive observers, respectively. and Let x1, x2, and x3 represent the estimated values, respectively. This represents an estimated value of y;

[0043] Design the time-varying gain of the adaptive AESO as follows:

[0044]

[0045] Where ρ1, ρ2, and ρ3 represent the three elements of the three-axis attitude angle vector ρ, ω0 represents the maximum bandwidth diagonal matrix of the three attitude channels, and each diagonal element of ω0 is ω nc (t) represents the maximum AESO bandwidth of the three attitude channels;

[0046] definition

[0047]

[0048] Where, k a It is a positive number less than 1 (default value), T ω For the design change time, and ω ncThe time-varying bandwidth ω(t) is obtained by inputting ω(t) into a Butterworth filter, and the first derivative of ω(t) is also obtained. Second derivative The Butterworth filter takes the following form:

[0049]

[0050] Where s represents the derivative operator of the Butterworth filter, and ξ1 and ξ2 are the design parameters of the Butterworth filter;

[0051] AESO bandwidth can be expressed as:

[0052] ω n (t)=ω0ω(t) (20)

[0053] The intermediate variables are defined as follows:

[0054]

[0055] The specific form of the designed AESO time-varying gain is as follows:

[0056]

[0057] The PID control law can then be expressed as:

[0058]

[0059] in, This represents the desired attitude angular acceleration signal. e represents the desired attitude angular velocity signal. ρ This represents the error between the actual attitude angle signal and the desired attitude angle signal, and e ρ =(ρ-ρ d ), K p K represents the gain matrix of the proportional term coefficients. D K is the gain matrix of the differential coefficients. I Let u be the gain matrix of the integral term coefficients. ρ For controller output;

[0060] Step 3: Compensate for the control performance loss caused by dead zone saturation using an auxiliary system, i.e., design a control law that resists the nonlinearity of motor dead zone saturation:

[0061] The voltage-lift model expression for the dead zone and saturation characteristics of the quadcopter actuator is as follows:

[0062]

[0063] Where, k l and k rd represents the voltage lift coefficients on the left and right sides that are not zero, respectively. l and d r These represent the left and right voltage dead zone boundary points, respectively. l and s r These represent the voltage saturation boundary points on the left and right sides, respectively, and v represents the input voltage;

[0064] The input tension after the system's control commands are distributed via pseudo-inverse matrix control is:

[0065] U = B T (BB T ) -1 u M (25)

[0066] Where U represents the lift distributed to each rotor motor of the quadcopter, and U = [F f F l F r F b ] T u M This indicates a control command that performs control allocation, i.e., a control command that has not passed the dead zone saturation limit;

[0067] The relationship between the input tension and voltage for control distribution is as follows:

[0068] U = k f V (26)

[0069] Where, k f This indicates the lift coefficient of the motor, and V represents the input voltage;

[0070] According to equation (26), the input pulling force of the control distribution is converted into voltage, and the voltage is passed through the dead zone saturation stage to obtain the output voltage V after the dead zone saturation stage. ds (Calculated according to formula (24), the reverse process of the control allocation process is performed to obtain the control command after dead zone saturation limitation:

[0071] U Mc =k f V ds (27)

[0072] The auxiliary system is designed as follows:

[0073]

[0074] Where ΔM represents the difference between the control command after dead-zone saturation limitation and the control command before dead-zone saturation limitation, and ΔM=u M -U Mc , Let c represent the auxiliary system parameter and σ represent the preset threshold.

[0075] The control law requiring compensation can be expressed as:

[0076]

[0077] Where K represents the compensation control law gain parameter matrix;

[0078] The robust control law under input nonlinear compensation (i.e., the control law against motor dead-zone saturation nonlinearity) is then considered as follows:

[0079]

[0080] Step 4: Based on the current input desired attitude angle signal, combined with the robust control law considering input nonlinear compensation obtained in Step 3 and the three-degree-of-freedom attitude dynamics model of the quadcopter constructed in Step 1, the control input quantities of each motor of the quadcopter are obtained and applied to the quadcopter, thereby realizing the tracking control of the three-axis attitude angle to the desired attitude angle signal.

[0081] In this step, u is first obtained based on formula (30). ρ and The value will The value of d ρ Then, based on formula (14), we obtain Then, by combining formulas (1) to (3), the current control input F of each motor (front motor, left motor, right motor, and rear motor) can be obtained. f F l F r With F b To achieve the desired attitude angle signal ρ across three axes. d Tracking and control.

[0082] The technical solution provided by this invention brings at least the following beneficial effects:

[0083] (1) For over-driven quadrotor systems, the present invention provides a state tracking robust control method, which can effectively track and control the attitude angle of over-driven quadrotor under conditions of no angular velocity measurement information, unknown disturbance influence, and dead zone saturation nonlinearity of motor;

[0084] (2) The angle tracking controller provided by the present invention can compensate for the impact of the dead zone saturation nonlinearity of the motor, effectively solve the problems caused by the dead zone saturation of the motor, and improve the robustness of the control system.

[0085] (3) The present invention can effectively estimate unknown disturbances and angular velocity information, and has the characteristics of small transient overshoot and small steady-state error, ensuring the stability of the closed-loop system and improving the transient response performance and steady-state performance of the closed-loop system.

[0086] (4) The controller provided by the present invention is simple in form, easy to calculate and verify, and easy to implement in engineering. Attached Figure Description

[0087] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0088] Figure 1 This is a schematic diagram of a quadcopter experimental platform model.

[0089] Figure 2 The control structure diagram under nonlinear compensation is provided.

[0090] Figure 3 The diagram shows the input and output voltage correspondences for a dead-zone saturation circuit.

[0091] Figure 4 This is a schematic diagram of the three-axis angle tracking error under time-varying perturbations in numerical simulation.

[0092] Figure 5 This is a schematic diagram of the disturbance estimation error under time-varying disturbances in numerical simulation.

[0093] Figure 6 This is a schematic diagram illustrating the angular velocity estimation error under time-varying disturbances in numerical simulation.

[0094] Figure 7 This is the curve showing the change in bandwidth parameter of the adaptive extended state observer in the numerical simulation.

[0095] Figure 8 This is a schematic diagram of the three-axis tracking error under the control law based on AESO design in numerical simulation.

[0096] Figure 9 A schematic diagram of the three-axis angle tracking error under the control law based on ESO when selecting the lower limit value of the bandwidth parameter in numerical simulation.

[0097] Figure 10 A schematic diagram of the three-axis angle tracking error under the ESO-based control law when selecting the upper limit value of the bandwidth parameter in numerical simulation.

[0098] Figure 11This is a schematic diagram of the three-axis angle tracking error in a real-world experiment without dead-zone saturation or auxiliary systems.

[0099] Figure 12 This is a schematic diagram of the voltage distribution for control in a real-world experiment without dead-zone saturation or auxiliary systems.

[0100] Figure 13 This is a schematic diagram of the three-axis angle tracking error in a real-world experiment with a dead zone saturation stage but no auxiliary system.

[0101] Figure 14 This is a schematic diagram of the voltage after the dead-zone saturation stage in a real-world experiment, without an auxiliary system.

[0102] Figure 15 This is a schematic diagram of the three-axis angle tracking error under the conditions of dead zone saturation and auxiliary system in the actual experiment.

[0103] Figure 16 This is a schematic diagram of the voltage after the dead-zone saturation stage in a real-world experiment with an auxiliary system.

[0104] Figure 17 This is a schematic diagram comparing the pitch angle tracking error based on UDE (Uncertainty Disturbance Estimator) and the control law based on AESO and auxiliary system in a real-world experiment.

[0105] Figure 18 This is a schematic diagram comparing the roll angle tracking errors of control laws based on UDE and those based on AESO and auxiliary systems in a real-world experiment.

[0106] Figure 19 This is a schematic diagram comparing the yaw angle tracking errors of control laws based on UDE and those based on AESO and auxiliary systems in a real-world experiment. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0108] This invention proposes a robust attitude tracking control method for an overdriven quadrotor experimental platform. First, a mathematical model of the quadrotor is established and transformed into a linear disturbed double-integral model. A nominal controller is designed using the proportional-integral-derivative (PID) method to ensure asymptotic stability of the nominal closed-loop system. An adaptive extended state observer (AESO) is used to estimate the quadrotor's angular velocity and disturbance information, designing a robust attitude tracking controller. By constructing a dead-zone saturation compensation element, the control influence caused by the motor's dead-zone saturation nonlinearity is mitigated. This invention effectively solves the problem caused by the motor's dead-zone saturation characteristics while simultaneously considering the transient overshoot and steady-state error performance of the closed-loop system.

[0109] See Figure 1 and Figure 2 The present invention provides a robust control method for attitude tracking of an over-driven quadrotor experimental platform, the specific implementation of which includes the following steps:

[0110] Step 1: Establish a three-degree-of-freedom attitude dynamics model of the quadcopter and transform it into a linear disturbed double integral system;

[0111] For over-driven quadcopter systems (such as Figure 1 As shown in the figure), a specific mathematical model is established, as shown in formulas (1) to (3); then it is rewritten as a simplified linear disturbed double integral system model as shown in formula (14).

[0112] Step 2: For the linear disturbed dual-integral system model established in Step 1, use AESO to obtain angular velocity estimation information and disturbance estimation information, and design a proportional-integral-derivative (PID) control law.

[0113] An adaptive extended state observer (AESO) with actual attitude angle signals as input outputs estimated values ​​of attitude angular rate signal, estimated values ​​of attitude angular acceleration signal, and estimated values ​​of actual attitude three-channel disturbance. The specific form of the designed AESO is shown in formula (16).

[0114] The time-varying gain of the adaptive AESO can be designed as shown in formula (22); then the PID control law can be obtained as shown in formula (23).

[0115] Step 3: Use an auxiliary system to compensate for the control efficiency loss caused by dead zone saturation, and design a control law to resist the nonlinearity of motor dead zone saturation, namely the robust control law under input nonlinearity compensation shown in formula (30).

[0116] Step 4: Introduce the robust control law under input nonlinear compensation from Step 3 into the quadcopter dynamics model to achieve tracking control of the desired attitude angle signal for the three-axis attitude angles.

[0117] In this embodiment of the invention, the physical experimental object is a quadcopter experimental platform. This platform has a typical overacting system with three degrees of freedom and four control inputs, and exhibits the strong nonlinear characteristics of an actual aircraft, which can verify the effectiveness and rationality of the designed control method. A simplified structural diagram of the quadcopter experimental platform is shown below. Figure 1 As shown.

[0118] Experimental Example 1:

[0119] The attitude robust control of a quadcopter system experimental platform was carried out using MATLAB simulation tools to verify the performance of the AESO-based control law in the desired attitude angle tracking control under conditions where the angular velocity measurement information is unknown and disturbances exist.

[0120] Set the desired attitude angle to ε d =0.1sin(0.5t) + 0.3rad, θ d =0.1sin(0.5t)+0.2rad and ψ d =0.1sin(0.5t)+0.1rad, the triaxial controller parameters in step 2 are set to K. p =diag([5 10 5]), K D =diag([4 10 4]) and K I =0 3×3 The maximum bandwidth parameter of AESO is ω0 = 30. The time-varying perturbation information applied to the three axes of the quadcopter experimental platform simulation model is d. ε =d θ =d ψ = 0.2sin(0.25t)rad.

[0121] The effect of three-axis attitude angle tracking error under time-varying perturbation is shown in Figure 4 The effect of estimating the three-axis attitude angle perturbation error under time-varying perturbation is shown in [the figure]. Figure 5 The effect of three-axis attitude angular velocity tracking error under time-varying disturbances is shown in [the figure]. Figure 6 .

[0122] Experimental results show that the tracking errors of the actual angles of the three axes are all within a small range in the simulation environment, and the root mean square error of the three-axis angles is also very small, indicating that the control law designed based on AESO is effective. Under time-varying disturbance simulation conditions, the estimated values ​​of the three-axis disturbances are basically consistent with the actual values. Under constant disturbance simulation conditions, the disturbance estimation error and root mean square error of the three axes are on the order of magnitude, indicating that AESO can accurately estimate various forms of disturbances. The errors and root mean square errors between the estimated and actual angular velocities of the three axes in the simulation are on the order of magnitude, indicating that the estimated angular velocity can be accurately estimated from the actual value, and AESO can accurately estimate angular velocity information.

[0123] Experimental Example 2:

[0124] On a real quadcopter platform, the tracking control performance based on the AESO control law was verified compared to that based on the ESO control law.

[0125] Set the desired attitude angle to ε d = -0.2 + 0.2sin(0.5t)rad, θ d= -0.1 + 0.2sin(0.5t)rad and ψ d =0.1sin(0.5t)+0.1rad, the triaxial controller parameters in step 2 are set to K. p =diag([30 30 30]), K D =diag([17 25 30]) and K I =0 3×3 The upper limit of the bandwidth parameter of AESO is selected as ω. n (t) = diag([3.3 13.36.7]), the lower limit of the bandwidth parameter of AESO is selected as ω. n (t)=diag([2 8 4]), the selected parameters of the Butterworth filter are ξ1=ξ2=2, and the control law design parameters based on the linear ESO are selected as l1(t)=2ω n (t), and

[0126] The AESO bandwidth parameter variation curve is shown below. Figure 7 The effect of triaxial tracking error under the control law based on AESO design is shown in the figure. Figure 8 When selecting the lower limit value of the bandwidth parameter, the effect of three-axis angle tracking error under the control law based on ESO design is shown in [the figure]. Figure 9 When selecting the upper limit value of the bandwidth parameter, the effect of three-axis angle tracking error under the control law based on ESO design is shown in [the figure]. Figure 10 .

[0127] Experimental results show that under the control law based on ESO, the actual values ​​of the three-axis attitude angles can track the expected values, verifying the effectiveness of the control law. When selecting the lower limit of the bandwidth, the control effect produced by the control law based on ESO is characterized by small transient overshoot, but large error oscillation amplitude in the subsequent steady state, resulting in good transient control performance. When selecting the upper limit of the bandwidth, the control effect produced by the control law based on ESO is characterized by large transient overshoot, but smaller error oscillation amplitude in the subsequent steady state, resulting in relatively better steady-state control performance. This indicates that the control law based on ESO combines the advantages of the control law based on ESO under two different bandwidth parameters, significantly improving the control effect of the control law based on ESO.

[0128] Experiment Example 3:

[0129] On a real quadcopter platform, the effectiveness of the anti-dead-zone saturation control law designed in conjunction with the auxiliary system was verified using a control law based on a disturbance estimator and an AESO.

[0130] Set the desired attitude angle to ε d = -0.2 + 0.2sin(0.5t)rad, θ d= -0.1 + 0.2sin(0.5t)rad and ψ d =0.2sin(0.25t)rad, the triaxial controller parameters in step 2 are set to K p =diag([30 30 30]), K D =diag([30 30 30]) and K I =0 3×3 The upper limit of the bandwidth parameter of AESO is selected as ω. n (t) = diag([3.5 7.5 7.5]), the selected Butterworth filter parameters are ξ1 = ξ2 = 2, the auxiliary system parameters are designed as c = diag([80 80 80]), K = diag([80 80 80]).

[0131] See the three-axis angle tracking error performance without dead zone saturation and without auxiliary systems. Figure 11 The voltage distribution for control without dead-zone saturation and without auxiliary systems is shown in [reference]. Figure 12 The effect of three-axis angle tracking error with dead zone saturation but no auxiliary system is shown in the figure. Figure 13 The voltage after dead-saturation in a system with dead-saturation but no auxiliary system is shown below. Figure 14 The effect of three-axis angle tracking error with dead zone saturation and auxiliary system is shown in the figure. Figure 15 The voltage after dead-saturation in a system with dead-saturation and an auxiliary system is shown below. Figure 16 The comparison of pitch angle tracking error between UDE-based and AESO+-based control law systems is shown in the figure. Figure 17 The comparison of roll angle tracking error between UDE-based and AESO+-based auxiliary system control laws is shown in the figure. Figure 18 The comparison of yaw angle tracking error between UDE-based and AESO+-based control law systems is shown in the figure. Figure 19 .

[0132] Experimental results show that without applying dead-zone saturation, the voltage after control distribution exhibits a large peak value instantaneously. With only dead-zone saturation applied, the overshoot of the pitch and roll axes is significantly reduced, the maximum and minimum steady-state errors are smaller, the mean error is smaller, and the root mean square error is smaller. The tracking effect of the yaw axis remains largely consistent, although the mean steady-state error is slightly larger. This indicates that when the input voltage of the experimental platform is entirely within the dead-zone saturation voltage range, the control law's performance can be improved. When both dead-zone saturation and the auxiliary system are applied, the steady-state error range, mean, and root mean square error values ​​of the three axes are largely consistent. The overshoot of pitch and yaw axis angle tracking is significantly reduced, and the maximum steady-state error of the yaw axis decreases, indicating a reduction in the yaw axis tracking fluctuation amplitude. This verifies the effectiveness of the control law designed considering nonlinear compensation. Compared to the control law designed based on UDE, the control law designed based on AESO and the auxiliary system has the characteristics of smaller transient overshoot and smaller steady-state error, weakening the impact of dead-zone saturation nonlinearity and improving the control performance.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0134] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A robust control method for attitude tracking of an over-driven quadrotor experimental platform, characterized in that, Includes the following steps: Step 1: Establish a three-degree-of-freedom attitude dynamics model of the quadcopter and transform it into a linear perturbed double integral system; Step 2: For the constructed linear disturbed dual-integral system, and based on the angular velocity estimation information and disturbance estimation information obtained by the adaptive extended state observer, design a proportional-integral-derivative control law; Step 3: Use an auxiliary system to compensate for the control performance loss caused by dead zone saturation, and obtain a robust control law considering input nonlinearity compensation. Step 4: Based on the current input desired attitude angle signal, combined with the robust control law considering input nonlinear compensation and the three-degree-of-freedom attitude dynamics model of the quadcopter constructed in Step 1, the control input quantities of each motor of the quadcopter are obtained and applied to the quadcopter. Step 2 is as follows: With actual attitude angle signals As input to the Adaptive Extended State Observer (AESO), its output includes: an estimated value of the attitude angular rate signal. Attitude angular acceleration signal estimation value And the estimated values ​​of the three-channel perturbation of the actual attitude ; , , These represent the pitch angle, roll angle, and yaw angle of a quadcopter, respectively. The specific form of the AESO is as follows: in, , and They represent , and The estimated value, This represents the actual attitude angular rate signal. This represents the actual attitude angular acceleration signal. The value is the actual three-axis disturbance. This represents an estimate of the actual output signal; , and These represent the three gain matrices of AESO, and their specific expressions are as follows: Three intermediate variables , and The specific calculation formula is as follows: in, , and These represent the three-axis attitude angle vectors respectively. The three elements, and , Represents the imaginary unit. Let represent the diagonal matrix of the maximum bandwidth of AESO for the three attitude channels, and Each diagonal element for: , This represents a pre-defined positive number less than 1. Indicates the preset change time; Indicates will Time-varying bandwidth obtained by inputting into Butterworth filter , , They represent time-varying bandwidths respectively. The first and second derivatives; Specifically, the Butterworth filter is: in, Describes the derivative operator of the Butterworth filter. and These are the design parameters for the Butterworth filter; The design proportional-integral-derivative control law is as follows: in, This represents the desired attitude angular acceleration signal. This represents the desired attitude angular velocity signal. Indicates the actual attitude angle signal With the desired attitude angle signal The error between them This represents the gain matrix of the proportional term coefficients. This represents the gain matrix of the differential coefficients. This represents the gain matrix of the integral term coefficients; Step 3 specifically involves: Configure the auxiliary system as follows: in, This indicates the control command after dead-zone saturation limitation. Control commands that have not undergone dead zone saturation limitation The difference, Represents intermediate variables of the auxiliary system. express The first derivative, Indicates auxiliary system parameters, This indicates the preset threshold value for the auxiliary system; The robust control law considering input nonlinear compensation is specifically set as follows: Among them, the control law that needs compensation , This represents the gain parameter matrix of the compensation control law.

2. The method as described in claim 1, characterized in that, In step 1, the three-degree-of-freedom attitude dynamics model is specifically as follows: in, , , These represent the second derivatives of the pitch, roll, and yaw angles, respectively. , and These represent the moments of inertia about the pitch axis, roll axis, and yaw axis, respectively. , and These represent the external disturbance terms acting on the pitch, roll, and yaw channels, respectively. This represents the average distance from each motor to the center of gravity of the connecting rod; Represents gravitational acceleration; , , and These represent the masses of the front motor, left motor, right motor, and rear motor, respectively. , , and These represent the control input quantities for the front motor, left motor, right motor, and rear motor, respectively.

3. The method as described in claim 2, characterized in that, The model of the linear disturbed double integral system is as follows: Among them, the controller output The lumped interference of the system ; rotational inertia matrix Control Matrix Gravity matrix External disturbances ; Control input variables ; Among them, control matrix parameters ~ The values ​​are set as follows: , , , .

4. The method as described in claim 1, characterized in that, Control commands The process involves converting the input force allocated by the control into voltage, and then passing it through a dead-zone saturation stage to obtain the output voltage after the dead-zone saturation stage. Based on Perform the reverse process of control allocation to obtain the control command after dead-zone saturation limitation. : ,in This indicates the lift coefficient of the motor.

5. The method as described in claim 4, characterized in that, Voltage The calculation formula is: in, and These represent the non-zero voltage lift coefficients for the left and right motors, respectively. and These represent the voltage dead zone boundary points of the left and right motors, respectively. and These represent the voltage saturation boundary points of the left and right motors, respectively. This indicates the input voltage.

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