A method for stable control of an unmanned aerial vehicle against wind disturbance

Abstract

The present invention discloses a method for stable control of an unmanned aerial vehicle against wind disturbances. Based on the traditional active disturbance rejection control, it is optimized by fusing the Kalman filter KF and the extended state observer ESO to form a composite state observer KFESO. The ESO can ensure the operation of the KF when there are deviations in the system or uncertainties in the model, and the KF can filter the input of the ESO to weaken the influence of noise on the ESO. At the same time, the backstepping method is added to the active disturbance rejection controller, which can improve the response speed of the system, enabling the unmanned aerial vehicle system to respond more quickly when affected by wind disturbances and enhancing the stability of the system. The improved active disturbance rejection controller is adopted in both the position loop and the attitude loop in order to achieve better anti-interference performance and ensure a high response speed of the unmanned aerial vehicle under wind disturbances. The present invention improves the robustness of the algorithm, simplifies the algorithm design, improves the calculation efficiency, enhances the adaptability and generalization ability, and promotes the practical application ability.

Description

Technical Field

[0001] The present invention relates to the field of UAV control, and specifically to a method for stabilizing the control of a UAV against wind disturbance. Background Art

[0002] With the rapid development of UAV technology, UAVs have shown strong application potential in multiple fields such as agriculture, logistics, security, and aerial photography. In the agricultural field, UAVs are used for spraying pesticides and fertilizers, etc., improving agricultural production efficiency; in the logistics field, UAVs can achieve fast and accurate cargo delivery, reducing logistics costs; in the security field, UAVs can perform tasks such as patrol and monitoring, improving social security. However, these application scenarios are often accompanied by complex meteorological conditions, such as strong winds and heavy rains, which pose higher requirements for the flight stability and safety of UAVs. Wind field interference is one of the main challenges faced by UAVs during flight. Changes in the external wind field can cause the attitude and position of the UAV to deviate, thereby affecting its flight stability and accuracy. Under strong wind conditions, the UAV may even crash due to loss of control. Therefore, studying the anti-wind-disturbance stability control algorithm for UAVs and improving the flight stability of UAVs under complex wind field conditions are of great significance for ensuring the safe and efficient completion of tasks by UAVs. With the continuous progress of UAV technology and the expansion of application scenarios, the research and application of anti-wind-disturbance stability control algorithms will have broad market prospects. In the future, UAVs with anti-wind capabilities will be widely used in fields such as express delivery, disaster area rescue, agricultural spraying, and environmental monitoring, bringing greater economic and social benefits to society. At the same time, with the continuous development of artificial intelligence technology, the anti-wind-disturbance stability control algorithm for UAVs will also become more intelligent and autonomous, providing stronger guarantees for the flight safety and stability of UAVs.

[0003] Although the existing anti-wind-disturbance control algorithms for UAVs have improved the stability and safety of UAVs in the wind field to a certain extent, there are still some deficiencies.

[0004] 1. High dependence on the model: Some control algorithms such as Backstepping have high requirements for the accuracy of the UAV's dynamic model. However, during actual flight, due to changes in external factors such as the wind field and air density, it is often difficult to accurately describe the UAV's dynamic model, resulting in limited effects of the algorithm in actual applications.

[0005] 2. Prone to external interference: When some algorithms are affected by external factors such as strong winds and electromagnetic interference, their performance may decline or even fail. This limits the stability and reliability of UAVs in complex environments.

[0006] 3. Complex design steps: For example, in the case of an LQR controller, its design process involves the optimization and adjustment of multiple parameters, requiring high professional knowledge and experience. This increases the difficulty of algorithm development and application.

[0007] 4. Large computational load: Some algorithms consume a large amount of computing resources during operation, which poses a challenge for drones with limited resources. Especially in application scenarios with high real-time requirements, the computational load of the algorithm may become a key factor restricting its performance.

[0008] 5. Lack of real-time performance: Some algorithms are insufficient in real-time performance and cannot respond to changes in the external environment in a timely manner. This may cause delays or out-of-control situations for the drone during flight.

[0009] 6. Limited generalization ability: Due to the diversity and complexity of the drone flight environment, some algorithms may not be able to provide effective control strategies when facing unknown or untrained wind field conditions. This reduces the autonomy and intelligence level of the drone.

[0010] Therefore, it is necessary to improve such a structure to overcome the above defects. Summary of the Invention

[0011] The purpose of the present invention is to provide a wind disturbance resistant and stable control algorithm for drones that combines a Kalman filter and a backstepping active disturbance rejection controller to solve the problems proposed in the above background technology.

[0012] To achieve the above purpose, the present invention provides the following technical solutions:

[0013] A wind disturbance resistant and stable control method for drones is optimized based on traditional active disturbance rejection control. The Kalman filter KF and the extended state observer ESO are fused to form a composite state observer KFESO; the ESO can ensure that the KF works when there are deviations in the system or uncertainties in the model, and the KF can filter the input of the ESO to weaken the influence of noise on the ESO.

[0014] At the same time, the backstepping method is added to the active disturbance rejection controller, which can improve the response speed of the system, enabling the drone system to respond faster when affected by wind disturbances and improving the stability of the system.

[0015] The improved active disturbance rejection controller is adopted in both the position loop and the attitude loop, aiming to achieve better anti-interference performance and ensure that the drone has higher stability and robustness while having a high response speed under wind disturbances.

[0016] Further, the composite state observer KFESO is specifically:

[0017] To solve the noise problem of the ESO, a Kalman filter KF is used to pre-filter the input signal, and the KF can be given by the following formula:

[0018]

[0019] Where is the estimate x of the system state, is the estimate of the lumped disturbance f, and K s is the AURKF gain matrix.

[0020] For the wind field environment, it is generally considered that the noise of the UAV detected by the Kalman filter under wind disturbance can be regarded as white noise. Therefore, the variance of the noise model can be calculated by the following formula:

[0021]

[0022] Where f s is the simulation frequency. It can be further simplified as:

[0023]

[0024] In the above formula, P is the state estimation error covariance matrix; R is the measurement noise covariance, and in practical applications, R representing the characteristics of the measurement noise can be obtained through white noise testing; Q is the process noise covariance.

[0025] At steady state, it can be considered that At this time, the process noise covariance Q can be replaced by the disturbance estimation error covariance Q d Then there is:

[0026]

[0027] Get the expression of K s :

[0028]

[0029] For the design of the ESO, an extended state observer is constructed as follows:

[0030]

[0031] Where z = [z x z3] T is the estimate of , z x is the estimate of the system state x, and z3 is the estimate of the system disturbance ; L is the gain of the observer. For the value of L, L = [β1 β2 β3] T .

[0032] By designing a reasonable ESO gain matrix, the lumped disturbances existing in the system can be accurately estimated. Define the error as e = x - z, then the derivative of the error can be defined as:

[0033]

[0034] The A e in the above equation has a characteristic equation that can be expressed as:

[0035] λ(s) = s 3 + β1s 2 + β2s + β3

[0036] Analyzing the above characteristic equation, when h is bounded and the roots of λ(s) are all located in the left half-plane, the stability of the state observer can be achieved. Therefore, assume λ0(s) = (s + ω0) 3 , and its solution can be obtained as:

[0037]

[0038] where ω0 is the bandwidth of the state observer. Then the ESO can be designed as:

[0039]

[0040] According to the descriptions of the adaptive robust unscented Kalman filter KF and the extended state observer ESO, the expression of the composite state observer KFESO can be obtained as:

[0041]

[0042] Furthermore, the backstepping method is added to the active disturbance rejection controller. When the backstepping method is added to the active disturbance rejection control of the UAV, since the backstepping method requires the use of second-order differential signals, therefore, the output term of the arranged transition process should include second-order differential signals. To generate second-order differential signals, a third-order differentiator or a cascaded second-order differentiator needs to be used to arrange the transition process.

[0043] Among them, the third-order fast differentiator is a common third-order differentiator, and its expression is:

[0044]

[0045] Among them, the expression of the sat function is:

[0046]

[0047] Since the tracking signal and differential signal generated by the third-order fast differentiator will produce chattering phenomena during convergence, therefore, a cascaded second-order differentiator is used here to obtain the required second-order differential signal.

[0048] Furthermore, backstepping is added to the active disturbance rejection controller;

[0049] The basic idea of backstepping is to decompose a complex nonlinear system into subsystems not exceeding the order of the system, and then design partial Lyapunov functions and intermediate virtual control variables for each subsystem respectively. Keep going backward to the entire system and integrate them to complete the design of the entire control law.

[0050] The dynamic equation of the UAV can be written in the following form:

[0051]

[0052] where X can be expressed as X = [x, y, z, φ, θ, ψ], and U can be expressed as U = [U1 U2 U3 U4] T , and since U1 (defined ) is a control variable related to the position of the UAV, it can be decomposed. Decompose U1 into the X, Y, and Z axis position control components of the UAV, then the decomposed control variable U can be expressed as:

[0053] U = [u x u y u z U2 U3 U4] T

[0054] And f(X) and g(X) in the above formula can be expressed by the following formulas:

[0055]

[0056] Furthermore, backstepping is combined with the active disturbance rejection control principle to design the nonlinear control law of the UAV. Design a single control loop in the control loop. The design steps are as follows:

[0057] S1. Define the desired trajectory of the UAV:

[0058] X d = [x d y d z d φ d θ d ψ d

[0059] S2. According to the desired trajectory defined above, introduce the first tracking error here:

[0060] e1 = X d - X

[0061] S3. Select the first Lyapunov function accordingly and take its derivative:

[0062]

[0063] To make V1(e1) converge, this scheme defines a virtual control quantity Replace Then the derivative of the Lyapunov function can be expressed as:

[0064]

[0065] Also, since k1 is a number greater than 0, so always holds. Therefore, the constructed Lyapunov function converges stably.

[0066] S4. The stability analysis of the first tracking error has been carried out before, and its stable characteristics have been proved. Next, the second tracking error will be introduced and its derivative will be calculated. Since after taking the derivative, At this time, according to the dynamic expression of the above UAV, the expressions of the second tracking error and its derivative can be obtained as:

[0067]

[0068] S5. According to the second tracking error introduced above, a second Lyapunov function applicable to the above formula is selected here and its derivative is calculated:

[0069]

[0070] To make the second Lyapunov function constructed above converge, the second virtual control quantity is defined at this time as:

[0071]

[0072] Then there is This also shows that the constructed second virtual control quantity can make the Lyapunov function stable and enable the controlled object to reach the target state.

[0073] To design the backstepping control law, this scheme further expands the second tracking error, and then it can be deformed into Substitute it into the above formula and combine each item, only retaining e1. Finally, the backstepping control law of the UAV single channel can be obtained as:

[0074]

[0075] Comparing with the standard form of the nonlinear error feedback control law of the active disturbance rejection control, it is not difficult to find that the above control law is consistent with it in form. Therefore, the active disturbance rejection control algorithm is introduced here for combination to form the backstepping active disturbance rejection control. Then the backstepping active disturbance rejection control law can be written as:

[0076] where represents the second-order differential signal output from the third-order fast differentiator, and K d is given according to the design of KFESO above and can be calculated using the formula for calculation.

[0077] Compared with the prior art, the beneficial effects of the present invention are:

[0078] 1. Improve the robustness of the algorithm

[0079] The complementary advantages of the Kalman filter and ESO: The Kalman filter is good at dealing with linear systems and can estimate the state of the system from noisy data. During the flight of the UAV, it can help estimate the state information such as the position and speed of the UAV. The ESO can observe the system state and compensate for the total system disturbance, especially suitable for dealing with nonlinear systems and unknown disturbances. Combining the two can make full use of the linear estimation ability of the Kalman filter and the nonlinear disturbance compensation ability of the ESO to improve the robustness of the algorithm to model errors and external disturbances.

[0080] The disturbance rejection of the backstepping active disturbance rejection control: The backstepping active disturbance rejection control algorithm is based on the backstepping design method and the active disturbance rejection control idea, which can estimate and compensate the disturbance in the system in real time, thereby improving the stability and disturbance rejection of the system. The algorithm realizes high-precision control of the UAV attitude and position by constructing virtual control quantities and state feedback controllers.

[0081] 2. Simplify the algorithm design and improve the calculation efficiency

[0082] The design of the composite observer: By combining the Kalman filter and ESO, a more concise and efficient composite observer can be designed. The observer can simultaneously utilize the advantages of the two algorithms and reduce the complexity in the design process. In addition, by optimizing the algorithm parameters and reducing unnecessary calculation steps, the calculation efficiency of the composite observer can be further improved.

[0083] The simplified implementation of the backstepping active disturbance rejection control: The backstepping active disturbance rejection control algorithm simplifies the design process of the controller by constructing virtual control quantities and state feedback controllers. The algorithm also improves the performance and stability of the controller and reduces the computational complexity by introducing technical means such as nonlinear state error feedback and extended state observer.

[0084] 3. Enhance the adaptability and generalization ability

[0085] Adaptability of the composite observer: The combination of the Kalman filter and ESO enables the composite observer to adapt to different flight environments and wind field conditions. By adjusting the algorithm parameters and observer structure, accurate estimation of the UAV state under different wind field conditions can be achieved. In addition, the composite observer can also handle the nonlinear problems and unknown disturbances during the UAV flight, improving the adaptability and generalization ability of the algorithm.

[0086] Generalization of the backstepping active disturbance rejection control: By introducing the active disturbance rejection control idea, the backstepping active disturbance rejection control algorithm enables the controller to estimate and compensate the disturbances in the system in real time, thus improving the generalization ability of the controller. This algorithm can also handle the uncertainty problems and model errors during the UAV flight, further enhancing the adaptability and robustness of the controller.

[0087] 4. Enhancement of practical application ability

[0088] Real-time performance of the composite observer: The combination of the Kalman filter and ESO enables the composite observer to estimate the state information of the UAV in real time and quickly respond to the changes in the external environment. This improves the flight stability and safety of the UAV in complex environments. In addition, by optimizing the algorithm parameters and reducing the calculation delay, the real-time performance of the composite observer can be further improved.

[0089] Practicality of the backstepping active disturbance rejection control: By constructing the virtual control quantity and the state feedback controller, the backstepping active disturbance rejection control algorithm realizes the high-precision control of the UAV attitude and position. This enables the UAV to maintain a stable flight attitude and position accuracy in complex environments. In addition, this algorithm also considers the nonlinear problems and unknown disturbances during the UAV flight, improving the practicality and reliability of the controller. Description of the drawings

[0090] Figure 1 It is the anti-wind disturbance control framework diagram for the UAV.

[0091] Figure 2 It is the response of the position channel and speed channel under wind disturbance.

[0092] Figure 3 It is the response of the attitude angle channel and attitude angle rate channel under wind disturbance.

[0093] Figure 4 It is the two-dimensional diagram of the trajectory tracking response of the Mars rotorcraft under wind disturbance.

[0094] Figure 5 It is the trajectory tracking response of the position channel and speed channel under wind disturbance.

[0095] Figure 6 It is the trajectory tracking response of the attitude angle channel and attitude angle rate channel under wind disturbance. Detailed implementation manners

[0096] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. Components of the embodiments of the present invention generally described and illustrated in the accompanying drawings here can be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0097] Please refer to Figure 1-4 , a method for anti-wind-disturbance stable control of an unmanned aerial vehicle (UAV). To improve the robustness of the UAV under wind disturbance, it is optimized on the basis of traditional active disturbance rejection control, and a Kalman filter KF and an extended state observer ESO are fused to form a composite state observer KFESO. Compared with the traditional active disturbance rejection extended state observer ESO, the composite state observer KFESO has better performance. The ESO can ensure that the KF works when there are deviations in the system or uncertainties in the model, and the KF can filter the input of the ESO to weaken the influence of noise on the ESO;

[0098] Meanwhile, a backstepping method is added to the active disturbance rejection controller, which can improve the response speed of the system, enabling the UAV system to respond faster when affected by wind disturbance and improving the stability of the system.

[0099] The design framework of the UAV system is as Figure 1 shown.

[0100] Improved active disturbance rejection controllers are adopted in both the position loop and the attitude loop, aiming to achieve better anti-interference performance and ensure that the UAV has higher stability and robustness while having a high response speed under wind disturbance.

[0101] 1. Composite state observer KFESO

[0102] The performance of the traditional extended state observer ESO control depends on the speed and accuracy of the ESO. Usually, high gains are used to achieve fast convergence of the estimation. However, this will lead to the ESO being more sensitive to noise. To solve this problem,

[0103] This solution provides an extended state observer based on a Kalman filter, namely, a composite state observer KFESO.

[0104] To solve the noise problem of ESO, the Kalman filter KF is used to pre-filter the input signal. KF can be given by the following formula:

[0105]

[0106] where is the estimate x of the system state, is the estimate of the lumped disturbance f, and K s is the AURKF gain matrix.

[0107] For the wind field environment, it is generally considered that the noise of the UAV detected by the Kalman filter under wind disturbance can be regarded as white noise. Therefore, the variance of the noise model can be calculated by the following formula:

[0108]

[0109] where f s is the simulation frequency. It can be further simplified as:

[0110]

[0111] In the above formula, P is the state estimation error covariance matrix; R is the measurement noise covariance, and in practical applications, R representing the characteristics of the measurement noise can be obtained through white noise testing; Q is the process noise covariance.

[0112] Generally, it can be considered that the state estimation obtained according to the above KF algorithm is optimal, and the proof process is as follows:

[0113] Proof: For the gain of KF, the gain K in Equation (5.26) can be replaced by the gain K s , then:

[0114]

[0115] The state error of KF can be expressed as then The derivative of can be expressed as Therefore, for the covariance of the noise disturbance, there is:

[0116]

[0117] Now solve the equation for , and its general solution expression can be obtained as:

[0118]

[0119] And because the covariance of the state estimation error can be expressed as then there is:

[0120]

[0121] Taking the derivative of the above formula and simplifying, assuming Φ(t,t)=I, we have:

[0122]

[0123] And in order to obtain the gain K, minimize the trace of , and its cost function can be expressed as:

[0124]

[0125] The necessary condition for minimizing the cost function of the above formula is:

[0126]

[0127] Therefore, we have This proves that the state estimation formula corresponding to the above-selected KF gain vector is optimal.

[0128] At steady state, it can be considered that At this time, the process noise covariance Q can be replaced by the disturbance estimation error covariance Q d to obtain:

[0129]

[0130] According to the above proof process, the expression of K s can be obtained:

[0131]

[0132] For the design of the ESO, construct the following extended state observer:

[0133]

[0134] where z = [z x z3] T is the estimate of , z x is the estimate of the system state x, and z3 is the estimate of the system disturbance ; L is the gain of the observer. For the value of L, L = [β1 β2 β3] T .

[0135] By designing a reasonable ESO gain matrix, the lumped disturbance existing in the system can be accurately estimated. Define the error as e = x - z, then the derivative of the error can be defined as:

[0136]

[0137] A in the above formula e The characteristic equation can be expressed as:

[0138] λ(s) = s 3 +β1s 2 +β2s + β3

[0139] Analyzing the above characteristic equation, when h is bounded and the roots of λ(s) are all located in the left half-plane, the stability of the state observer can be achieved. Therefore, assume λ0(s) = (s + ω0) 3 , and its solution can be obtained as:

[0140]

[0141] where ω0 is the bandwidth of the state observer. Then the ESO can be designed as:

[0142]

[0143] According to the above descriptions of the adaptive robust unscented Kalman filter KF and the extended state observer ESO, the expression of the composite state observer KFESO can be obtained as:

[0144]

[0145] 2. Cascaded second-order tracking differentiator

[0146] When the backstepping method is added to the active disturbance rejection control of the UAV, since the backstepping method requires the use of the second-order differential signal, therefore, the output term of the arranged transition process should include the second-order differential signal, and to generate the second-order differential signal, a third-order differentiator or a cascaded second-order differentiator needs to be used to arrange the transition process.

[0147] Among them, the third-order fast differentiator is a common third-order differentiator, and its expression is:

[0148]

[0149] where the expression of the sat function is:

[0150]

[0151] Since the tracking signal and the differential signal generated by the third-order fast differentiator will produce chattering phenomenon during convergence, therefore, a cascaded second-order differentiator is used here to obtain the required second-order differential signal.

[0152] 3. Backstepping active disturbance rejection control law

[0153] The basic idea of the backstepping method is to decompose a complex nonlinear system into subsystems not exceeding the order of the system. Then, partial Lyapunov functions and intermediate virtual control variables are designed for each subsystem. This process continues until the entire system is considered, and they are integrated to complete the design of the overall control law. The advantage of the backstepping method is that it can simultaneously design the controller and an adaptive law that can be updated at any time to improve the transient performance of the system. At the same time, the coupling degree of the controlled object is no longer a design issue. According to the design principle of the backstepping method, the dynamic equation of the UAV can be written in the following form:

[0154]

[0155] where X can be expressed as X = [x, y, z, φ, θ, ψ], and U can be expressed as U = [U1 U2 U3 U4] T , and since U1 (defined ) is a control variable related to the position of the UAV, it can be decomposed. Decompose U1 into the X, Y, and Z-axis position control components of the UAV. Then, the decomposed control variable U can be expressed as:

[0156] U = [u x u y u z U2 U3 U4] T

[0157] And f(X) and g(X) in the above equation can be expressed by the following formulas:

[0158]

[0159] Next, the backstepping method is combined with the active disturbance rejection control principle to design the nonlinear control law of the UAV. Design a single control loop in the control loop. The design steps are as follows:

[0160] (1) Define the desired trajectory of the UAV:

[0161] X d = [x d y d z d φ d θ d ψ d

[0162] (2) According to the desired trajectory defined above, introduce the first tracking error here:

[0163] e1 = X d - X

[0164] (3) Select the first Lyapunov function accordingly and take its derivative: ​

[0165]

[0166] To make V1(e1) converge, this scheme defines a virtual control quantity Replace in the above formula with α1 Then the derivative of the Lyapunov function can be expressed as:

[0167]

[0168] Also, since k1 is a number greater than 0, so always holds. Therefore, the constructed Lyapunov function converges stably.

[0169] (4) The stability analysis of the first tracking error has been carried out before, and its stable characteristics have been proved. Next, the second tracking error will be introduced and its derivative will be calculated. Since after the derivative is obtained, At this time, according to the dynamic expression of the above UAV, the expressions of the second tracking error and its derivative can be obtained as:

[0170]

[0171] (5) According to the second tracking error introduced above, a second Lyapunov function applicable to the above formula is selected here and its derivative is calculated:

[0172]

[0173] To make the second Lyapunov function constructed above converge, the second virtual control quantity is defined at this time as:

[0174]

[0175] Then there is This also shows that the constructed second virtual control quantity can make the Lyapunov function stable and enable the controlled object to reach the target state.

[0176] To design the backstepping control law, this scheme further expands the second tracking error, and then it can be deformed into Substitute it into the above formula and combine each item, only retaining e1. Finally, the backstepping control law of the UAV single channel can be obtained as:

[0177]

[0178] Comparing with the standard form of the nonlinear error feedback control law of the active disturbance rejection control, it is not difficult to find that the above control law is consistent with it in form. Therefore, the active disturbance rejection control algorithm is introduced here for combination to form the backstepping active disturbance rejection control. Then the backstepping active disturbance rejection control law can be written as:

[0179]

[0180] where represents the second-order differential signal output from the third-order fast differentiator, and K d is given according to the above design of KFESO and can be calculated using the formula . Thus, the design of the backstepping active disturbance rejection control law is completed.

[0181] Figure 2 and Figure 3 respectively show the responses of the position channel and velocity channel of the position loop and the attitude angle channel and attitude angular velocity channel in the attitude loop of the UAV under hover conditions when it is subjected to wind disturbances. It can be seen from Figure 2 that since the UAV is subjected to stronger horizontal wind disturbances, the UAV deviates farther from the reference hover point in the horizontal direction. Among them, the traditional ADRC benchmark control method has a larger deviation compared with the KFESOBSADRC composite control method. The maximum deviation value of the benchmark control method reaches 0.32 m, while the composite control algorithm only makes the UAV deviate 0.1 m from the reference hover point in the horizontal direction under wind disturbances. This undoubtedly makes the UAV have better stability under horizontal wind disturbances. Looking at the vertical direction, although the wind disturbances in the vertical direction are relatively small, the gap between the two control methods can still be seen. The composite control algorithm still has good stability, making the deviation of the UAV in the vertical direction only 0.04 m, while the deviation of the benchmark control method in the vertical direction reaches 0.15 m. In terms of the velocity channel, it has a similar trend to the position channel. The velocity fluctuation of the composite control algorithm in this scheme is smaller than that of the benchmark control algorithm, and the fluctuation amplitude of the velocity is less than 0.05 m / s.

[0182] It can be seen from Figure 3 that the composite control algorithm is more stable in the control of the angle loop, making the change amplitude of the angle of the UAV smaller compared with the traditional benchmark control algorithm when it is subjected to wind disturbances, especially more significant in the yaw channel (the yaw angle in the yaw channel of the benchmark control method reaches 6.7°, while the maximum yaw angle of the composite control algorithm in this scheme is only 2.5°). At the same time, the change of the angular velocity is faster, which results in the UAV being able to quickly adjust its attitude when encountering wind disturbances, making the UAV have smaller fluctuations in the wind field.

[0183] To further verify the superiority of the composite control algorithm, the trajectory tracking performance analysis of the UAV in a wind disturbance environment is added. The trajectory is designed in the form of an "8" - shaped loop, where the X - axis and Y - axis respectively adopt sine waves with frequencies of 0.5 rad / s and 0.25 rad / s and amplitudes of 3.

[0184] AsFigure 4 The green trajectory line in it is the expected trajectory line of the drone.

[0185] Next, the software-in-the-loop analysis of the trajectory tracking performance of the drone in the wind field environment is carried out by using the benchmark control method and the composite control algorithm respectively. The trajectory tracking effects of the two control algorithms are as Figure 4 shown. The blue trajectory line is the trajectory tracking curve of the drone in the wind field under the composite control algorithm, and the red curve is the trajectory tracking curve of the drone in the wind field under the benchmark control algorithm. It can be seen from the figure that under the composite control algorithm of this scheme, the running trajectory line of the drone in the wind field is closer to the reference trajectory line, and the deviation error is smaller. This also shows that the composite control algorithm makes the closed-loop system of the drone have better anti-disturbance performance.

[0186] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "upper", "lower", "inner", "outer", "left", "right", etc. is based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the invention is usually placed during use, or the orientation or positional relationship commonly understood by those skilled in the art. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance. In the description of the present invention, it should also be noted that unless otherwise clearly specified and limited, terms such as "set", "connected" should be understood in a broad sense. For example, "connected" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

Claims

1. A method for stable control of an unmanned aerial vehicle against wind disturbances, characterized in that, Based on the traditional active disturbance rejection control, an optimization is carried out. The Kalman filter KF and the extended state observer ESO are fused to form a composite state observer KFESO; the ESO ensures that the KF works when there are deviations in the system or uncertainties in the model, and the KF filters the input of the ESO to weaken the influence of noise on the ESO; At the same time, the backstepping method is added to the active disturbance rejection controller; the response speed of the system is improved, so that the UAV system can respond faster when affected by wind disturbances and the stability of the system is improved; The improved active disturbance rejection controllers are adopted in both the position loop and the attitude loop; in order to achieve better anti-interference performance, ensure that the UAV has a higher response speed under wind disturbances, and has higher stability and robustness; The specific form of the composite state observer KFESO is as follows: To solve the noise problem of the ESO, the Kalman filter KF is used to pre-filter the input signal, and the KF is given by the following formula: where is the estimated system state x, is the estimated lumped disturbance f, and K s is the AURKF gain matrix; For the wind field environment, it is generally considered that the noise of the UAV detected by the Kalman filter under wind disturbances is regarded as white noise. Therefore, the variance of the noise model is calculated by the following formula: where f s is the simulation frequency; further simplification is as follows: In the above formula, P is the state estimation error covariance matrix; R is the measurement noise covariance, and in practical applications, R representing the characteristics of the measurement noise is obtained through white noise testing; Q is the process noise covariance; At steady state, it is considered that At this time, the process noise covariance Q is replaced by the perturbation estimation error covariance Q d to obtain: Obtain K s The expression of: For the design of the ESO, the following extended state observer is constructed: where z = [z x z3] T is an estimate of, z x is an estimate of the system state x, and z3 is an estimate of the system disturbance ; L is the gain of the observer, and for the value of L, L = [β1 β2 β3] T ; By designing a reasonable ESO gain matrix, the lumped disturbances existing in the system are accurately estimated; define the error as e = x - z, then the derivative of the error is defined as: A in the above formula e The characteristic equation is expressed as: λ(s) = s 3 + β1s 2 + β2s + β3 Analyze the above characteristic equation. When h is bounded and the roots of λ(s) are all located in the left half plane, the state observer is stable. Therefore, assume that λ0(s) = (s + ω0) 3 , and its solution is obtained as follows: where ω0 is the bandwidth of the state observer; then the ESO is designed as: According to the descriptions of the adaptive robust unscented Kalman filter KF and the extended state observer ESO, the expression of the composite state observer KFESO is obtained as: The backstepping method is added to the active disturbance rejection controller. When the backstepping method is added to the active disturbance rejection control of the UAV, since the backstepping method requires the use of second-order differential signals, therefore, the output term of the arranged transient process should include second-order differential signals. To generate second-order differential signals, a third-order differentiator or a cascaded second-order differentiator needs to be used to arrange the transient process; where the expression of the third-order fast differentiator is: where the expression of the sat function is: A cascaded second-order differentiator is used to obtain the required second-order differential signal; The backstepping method is added to the active disturbance rejection controller; The basic idea of the backstepping method is to decompose a complex nonlinear system into subsystems not exceeding the order of the system, and then design partial Lyapunov functions and intermediate virtual control quantities for each subsystem respectively. Keep going back to the whole system and integrate them to complete the design of the entire control law; The dynamic equation of the UAV is written in the following form: where X is represented as X = [x, y, z, φ, θ, ψ], and U is represented as U = [U1 U2 U3 U4] T , and since U1 is a control quantity related to the position of the drone, it is defined that decompose it, decompose U1 into the X, Y, and Z axis position control components of the drone, then the decomposed control variable U is represented as: U = [u x u y u z U2 U3 U4] T And f(X) and g(X) in the above formula are represented by the following formula: The backstepping method is combined with the active disturbance rejection control principle to design the nonlinear control law of the UAV. The design of a single control loop in the control loop is as follows: S1. Define the desired trajectory of the UAV: X d = [x d y d z d φ d θ d ψ d ​ S2. According to the desired trajectory defined above, the first tracking error is introduced here: e1 = X d -X S3. Thus, the first Lyapunov function is selected and its derivative is calculated: To make V1(e1) converge, a virtual control quantity is defined Replace in the above formula with α1, then the derivative of the Lyapunov function is expressed as: Also, since k1 is a number greater than 0, so always holds. Therefore, the constructed Lyapunov function converges stably; S4. The stability analysis of the first tracking error has been carried out previously, and its stable characteristics have been proven. Next, the second tracking error will be introduced and differentiated. Since is obtained at this time, the expressions of the second tracking error and its derivative are obtained according to the dynamic expression of the above UAV as follows: S5. According to the second tracking error introduced above, the second Lyapunov function applicable to the above formula is selected here and its derivative is calculated: In order to make the second Lyapunov function constructed above converge, the second virtual control quantity is defined at this time as: Then there is This also shows that the second virtual control quantity constructed makes the Lyapunov function stable and enables the controlled object to reach the target state; If the second tracking error is further expanded, it is transformed into Substitute it into the above formula and combine each term, only retaining e1, and finally obtain the backstepping control law for the single channel of the UAV as follows: Comparing with the standard form of the nonlinear error feedback control law of the active disturbance rejection control, the active disturbance rejection control algorithm is introduced for combination to form the backstepping active disturbance rejection control. Then the backstepping active disturbance rejection control law is written as: wherein represents the second-order differential signal output from the third-order fast differentiator, and K d is given according to the above design of KFESO and is calculated using the formula for calculation.

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