Non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method

Abstract

The invention belongs to the technical field of four-rotor unmanned aerial vehicle control systems, and particularly relates to a nonsingular terminal sliding mode and second-order linear active disturbance rejection attitude control method, which comprises the following steps of S1, integrating flight attitude data of a four-rotor unmanned aerial vehicle; s2, establishing a kinetic model for describing the four-rotor unmanned aerial vehicle; s3, designing a nonsingular fast terminal sliding mode controller; s4, adding a second-order linear active disturbance rejection controller; and S5, proving the stability of the Lyapunov. The non-singular terminal sliding mode is combined with the improved second-order linear active-disturbance-rejection controller, it can be guaranteed that a quad-rotor unmanned aerial vehicle control system has the excellent performance such as quick response, robustness and higher tracking precision, and it is convenient for the quad-rotor unmanned aerial vehicle to keep the attitude stable in real time.

Description

Technical Field

[0001] This invention belongs to the technical field of quadcopter unmanned aerial vehicle (UAV) control systems, specifically relating to a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method. Background Technology

[0002] Quadrotor UAVs have broad application prospects in military, civilian, and scientific research fields, and have become one of the research hotspots both domestically and internationally in recent years. A quadrotor UAV is an underactuated, strongly coupled nonlinear system with four inputs and six outputs. Due to the complexity of its dynamic model, the uncertainty of model parameters, and the inaccuracy of modeling, as well as the complexity of the actual flight environment of quadrotor UAVs, higher requirements are placed on the rapid response capability, robustness, and disturbance rejection capability of the quadrotor UAV system.

[0003] Quadrone UAV attitude control often employs methods such as PID attitude control, fuzzy adaptive cascaded PID attitude control, neural network attitude control, and active disturbance rejection attitude control.

[0004] However, current PID attitude control methods cannot achieve asymptotic adjustment when the system has model uncertainties and non-constant external disturbances, and residuals will remain. Applying fuzzy adaptive cascade PID attitude control requires accurate modeling of the UAV's dynamics, including the aircraft's inertial characteristics, torque coupling, and nonlinear effects. Secondly, the fuzzy adaptive cascade PID controller requires adjusting too many parameters, including cascade PID parameters, fuzzy rule weights, and adaptive algorithm parameters. In addition, quadcopter UAV attitude control requires real-time response and high-frequency control commands. The fuzzy adaptive cascade PID control method involves complex calculations and parameter tuning processes, leading to high computational complexity and latency.

[0005] Existing neural network attitude control methods have strong self-organizing and self-learning capabilities, fault tolerance, and robustness, but their stability is poor. High computational complexity and latency lead to slow learning speeds, making it difficult to meet the real-time attitude stability requirements of quadrotor UAVs. Traditional active disturbance rejection attitude control suffers from difficulties in obtaining proportional-derivative gain values ​​and insufficient disturbance compensation when the disturbance frequency increases. Furthermore, traditional active disturbance rejection control algorithms are mainly based on linear control theory and techniques, which have certain limitations for disturbance rejection control of nonlinear systems. Therefore, we propose a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method. Summary of the Invention

[0006] The purpose of this invention is to provide a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method, which combines non-singular terminal sliding mode with an improved second-order linear active disturbance rejection controller. This method can ensure that the quadrotor UAV control system has superior performance such as fast response, robustness, and higher tracking accuracy, and facilitates the quadrotor UAV to maintain attitude stability in real time.

[0007] The specific technical solution adopted by this invention is as follows:

[0008] A non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method includes the following steps:

[0009] S1: Attitude angle data processing and attitude dynamics modeling;

[0010] S2: Design a non-singular fast terminal sliding mode controller;

[0011] S3: Add a second-order linear active disturbance rejection controller;

[0012] S4: Proof of Lyapunov stability.

[0013] The attitude angle data processing and attitude dynamics modeling in step S1 includes the following steps: first, data is collected and integrated using the gyroscope, magnetometer and accelerometer on the quadcopter UAV, and then attitude dynamics modeling is performed.

[0014] Step S1, attitude angle data processing and attitude dynamics modeling, includes the following steps:

[0015] M1: Define the fixed coordinate system E and the body coordinate system B, where O e Represents the origin of the Earth coordinate system, {x e y e z e} represent the positive directions of the coordinate axes in a fixed coordinate system; O b Let {x} be the origin of the coordinate system of the quadcopter UAV. b y b z b} represent the positive directions of the coordinate axes in the quadcopter drone; where φ represents the rotation angle of the quadcopter drone around the x-axis; θ represents the rotation angle of the quadcopter drone around the y-axis; and ψ represents the rotation angle of the quadcopter drone around the z-axis.

[0016] M2: Transform the attitude angles in the body coordinate system B to the fixed coordinate system E. The rotation matrix is:

[0017]

[0018] M3: Definition Let ω be the attitude angular velocity of the quadcopter UAV in the fixed coordinate system E.B =[p,q,r] represents the attitude angular velocity of the quadcopter drone itself, and the conversion relationship is:

[0019]

[0020] The Euler angular velocity of the quadcopter UAV in the fixed coordinate system E is compared with the angular velocity in the body coordinate system B as follows:

[0021]

[0022] The coordinate position of the quadcopter UAV relative to the fixed coordinate system E is P = [xyz]. T , Let M be the sum of the lift generated by the four motors within the body coordinate system B, k be the thrust coefficient, l be the arm length of the quadcopter drone, and M be the thrust of the four motors. i That is the rotational speed of each motor;

[0023] The torque generated by lift: The counter-torque generated by the propeller: Torque generated by air resistance:

[0024] in It is the anti-torque coefficient, d φ d θ d ψ It is the aerodynamic drag coefficient. The attitude angular acceleration in the body coordinate system of the quadcopter UAV;

[0025] M4: According to the law of angular momentum, the attitude dynamics equations of the quadcopter UAV are as follows:

[0026]

[0027]

[0028]

[0029] Where, τ B =[τ F τ A ] T =[τ Bx τ By τ Bz ] T I B =diag(I x ,I y ,I z ), I x ,I y ,I zThese represent the moments of inertia of the quadcopter drone along the three coordinate axes;

[0030] Combining equation (3) with equation (6), we further obtain:

[0031]

[0032] Introduce virtual control variables (U1, U2, U3, U4), as follows:

[0033]

[0034] The torque τ provided by the four motors B Combining equation (8), we get:

[0035]

[0036] Substituting equation (7) into equation (9), and considering external disturbances [d1 d2 d3]... T The attitude dynamics equations of a quadcopter UAV are as follows:

[0037]

[0038] Step S2, designing a non-singular fast terminal sliding mode controller, includes the following steps:

[0039] N1: Define the roll angle φ tracking error as follows:

[0040] e φ =φ-φ d +K φ ∫(φ-φ d )dt

[0041] Among them, K φ ∫(φ-φ d )dt is the integral term added to the roll angle tracking error, K φ φ is a positive constant. d It is the expected value of the roll angle φ, ∫(·)dt is the integral sign, and the function inside the parentheses is the integrand;

[0042] Define ρ φ To define a custom virtual control variable, the derivative of equation (11) is:

[0043] ;

[0044] N2: Define the Lyapunuov function as follows:

[0045]

[0046] Taking the derivative with respect to V1, we get:

[0047]

[0048] Substituting equation (12) into equation (14), we get:

[0049]

[0050] Define control variable ρ φ for:

[0051]

[0052] Where c1 is a positive parameter, and S is a non-singular fast terminal sliding surface. φ Designed as follows:

[0053]

[0054] Where α, δ, ζ, and λ are positive constants and satisfy... 0 < μ < 1, sgn(·) is the sign function;

[0055] Taking the time derivative of equation (17), we get:

[0056]

[0057] N3: Define Lyapunov functions as follows:

[0058]

[0059] Finding the time derivative of V2, we get:

[0060]

[0061] Substituting equations (15), (16), and (18) into equation (20), we get:

[0062]

[0063] Substituting equation (10) into equation (21), we get:

[0064]

[0065] Step S3, which involves adding a second-order linear active disturbance rejection controller, includes the following steps:

[0066] Q1: The motion equation of the second-order linear active disturbance rejection controller is set as follows:

[0067]

[0068] Where y is the output of the second-order system; u is the control input of the second-order system; ω is the unknown external disturbance of the second-order system; a1 and a2 are the parameters of the second-order system; b is the control gain of the second-order system. Assuming the known part is b0, equation (8) can be transformed into the following equation:

[0069]

[0070] make Equation (25) can be rewritten as:

[0071] ;

[0072] Q2: Let x1 = y, x3 = f, where x3 is the extended state variable of the second-order system. Therefore, the state equation expression for equation (26) is as follows:

[0073]

[0074] Where x1, x2, and x3 are state variables. Equation (27) is transformed into an extended state-space equation:

[0075]

[0076] in, C = [1 0 0];

[0077] The corresponding linearly extended state observer in equation (28) is:

[0078]

[0079] L = [l1 l2 l3] T It is the gain vector of the observer. The gain of the observer can be parameterized by placing all the eigenvalues ​​in the observation bandwidth. The gain of the observer can be expressed by its characteristic equation (30):

[0080] λ(s)=s 3 +l1s 2 +l2s+l3=(s+ω0) 3

[0081] The gain matrix can be obtained as follows:

[0082]

[0083] Equation (29) is simplified to:

[0084]

[0085] In equation (32), z1, z2, and z3 are the estimated values ​​of x1, x2, and x3, respectively, and l1, l2, and l3 are the observer gains. Thus, once the observer gains l1, l2, and l3 are determined, the extended state observer can calculate the various state variables of the original system in real time.

[0086] Q3: The transfer function of the second-order linear active disturbance rejection controller is obtained from equation (32):

[0087] G(s)=l3 / (s 3 +l1s 2 +l2s+l3)

[0088] Equation (33) is a third-order system. After approximating it as a second-order system, we get:

[0089]

[0090] Let l3 = l4(1 + l5s) in equation (32), and after simplification, we obtain the transfer function of the second-order linear active disturbance rejection controller as follows:

[0091] G(S)=l4(1+l5s) / [s 3 +l1s 2 +(l2+l4l5)s+l4]

[0092] Where s is a complex variable, which is the frequency in the Laplace transform domain; l4 and l5 are the observation gains after replacing l3;

[0093] Let the control variable of the system be:

[0094] u=(-z3+u0) / b0

[0095] Ignoring the estimation error of z3 for f, it can be transformed into

[0096] In step Q3, a second-order linear active disturbance rejection controller is designed based on equation (36):

[0097]

[0098] Where u0 is the output of the PD controller, k p k d For the control parameters of the PD circuit, v d This is the expected input.

[0099] Step Q3 involves adjusting parameter k. p and parameter k d The following algorithm is also introduced:

[0100]

[0101] Where r is the fast factor, h1 is the sampling time, fhan(·) is the fastest control synthesis function, v1(t) is the tracking signal of the initial signal, v2(t) is the tracking signal of the derivative of the initial signal, t is a certain state, and t+1 is the next state relative to t.

[0102] The initial signal v d (t) is smooth and bounded, and the tracking error is defined as e = vv d Then the filtering tracking error is defined as:

[0103] χ=[Λ T 1]e

[0104] Where Λ=α1 is a suitable gain vector such that e→0 as χ→0. Taking the derivative with respect to χ, we get:

[0105]

[0106] in,

[0107]

[0108] Approximation is achieved by defining tracking control for the input signal. It's pseudo-control. for Any approximation of can be obtained by adding or subtracting on the right side of equation (38). We get the following formula:

[0109]

[0110] because for The approximate value, so Converging near zero, the pseudo-control input is:

[0111] α=-τ χ +u0-[0 Λ T e

[0112] Where τ is an arbitrarily positive parameter;

[0113] Substituting (37), (42), and (43) into equation (40), we get:

[0114]

[0115] As a control scheme, equation (43) employs the following adaptive law:

[0116]

[0117]

[0118] in, and This is an estimate of the PD gain in LADRC; and It is the estimation error.

[0119] In step S4, the Lyapunov stability proof, the Lyapunov function is defined as follows:

[0120]

[0121] Substituting equation (44) into equation (48) yields equation (49).

[0122]

[0123] Substituting equation (23) into equation (49) and simplifying, we get:

[0124]

[0125] Equation (50) can be rewritten as:

[0126]

[0127] Substituting equations (45) and (46) into equation (51), we get:

[0128]

[0129] Equation (52) is simplified to:

[0130]

[0131] Where c1 and τ are positive parameters, we get:

[0132] .

[0133] The technical effects achieved by this invention are as follows:

[0134] This invention presents a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method, which proposes a method combining non-singular terminal sliding mode and an improved second-order linear active disturbance rejection controller. This method can ensure that the quadrotor UAV control system has superior performance such as fast response, robustness, and higher tracking accuracy, and facilitates the quadrotor UAV to maintain attitude stability in real time.

[0135] The present invention provides a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method, which innovatively combines non-singular terminal sliding mode with an improved second-order linear active disturbance rejection controller. This control strategy has excellent anti-disturbance performance against noise disturbances and can greatly reduce the impact of noise disturbances on the control system of quadcopter UAVs.

[0136] The present invention discloses a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method. By using NFTSMC, the convergence speed of the UAV control system is significantly improved, and the singularity problem that may occur in the control system is successfully solved, providing a stable and reliable solution for flight control.

[0137] This invention presents a non-singular terminal sliding mode and second-order linear active disturbance rejection (ADNR) attitude control method. The proposed improved second-order linear ADNR controller can achieve stable UAV attitude with only a few parameter adjustments and can cope with the problem of significant wind disturbance. Comparative analysis shows that the improved second-order linear ADNR controller not only improves the ground stability of the UAV control system but also optimizes the control system model. Attached Figure Description

[0138] Figure 1 This is a flowchart of the non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method of the present invention;

[0139] Figure 2 This is a schematic diagram of the fixed coordinate system E and the body coordinate system B of the present invention. Detailed Implementation

[0140] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0141] like Figure 1-2 As shown, a non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method includes the following steps:

[0142] The first step, in order to establish an accurate dynamic model describing the quadcopter drone, is to define a reference coordinate system. This is done by collecting data from the quadcopter drone's gyroscope, magnetometer, and accelerometer, as follows:

[0143] G1: Determine the fixed coordinate system E and the body coordinate system B. The fixed coordinate system E is a spatial coordinate system used to study the relative position of the quadcopter UAV with respect to the ground during flight. It is used to describe its motion relative to the Earth and determine its own position.

[0144] O e It is the origin of the Earth coordinate system, {x e y e z e} is used to define the positive directions of each coordinate axis in a fixed coordinate system;

[0145] O b It is the origin of the coordinate system of the quadcopter UAV, {xb y b z b} is used to represent the positive directions of each coordinate axis in a quadcopter drone; where {φ θ ψ} are the angles of rotation around each axis, specifically defined as follows: φ is the roll angle, i.e., the angle of rotation of the drone around the x-axis; θ is the pitch angle, i.e., the angle of rotation of the drone around the y-axis; ψ is the yaw angle, i.e., the angle of rotation of the drone around the z-axis;

[0146] G2: Transform the attitude angles in the body coordinate system B to the fixed coordinate system E. The rotation matrix is ​​as follows:

[0147]

[0148] G3: Definition Let ω be the attitude angular velocity of the quadcopter UAV in the fixed coordinate system E. B = [p,q,r] represents the UAV's own attitude angular velocity, and their conversion relationship is as follows:

[0149]

[0150] Based on the above analysis, the Euler angular velocity of the quadcopter UAV in the fixed coordinate system E is approximately equal to the angular velocity in the body coordinate system B.

[0151]

[0152] The coordinate position of the quadcopter UAV relative to the fixed coordinate system E is P = [xyz]. T , Let M be the sum of the lift generated by the four motors within the body coordinate system B, k be the thrust coefficient, l be the arm length of the quadcopter drone, and M be the thrust of the four motors. i That is the rotational speed of each motor;

[0153] The torque generated by lift: The counter-torque generated by the propeller: Torque generated by air resistance:

[0154] in It is the anti-torque coefficient, d φ d θ d ψ It is the aerodynamic drag coefficient. The attitude angular acceleration in the body coordinate system B of the quadrotor UAV;

[0155] G4: According to the law of angular momentum, the attitude dynamics equations of the quadcopter UAV are as follows:

[0156]

[0157]

[0158]

[0159] Where, τ B =[τ F τ A ] T =[τ Bx τ By τ Bz ] T I B =diag(I x ,I y ,I z ), I x ,I y ,I z These represent the moments of inertia of the quadcopter drone along the three coordinate axes.

[0160] Combining equation (3) with equation (6), we further obtain:

[0161]

[0162] Introduce virtual control variables (U1, U2, U3, U4), as shown below:

[0163]

[0164] The torque τ provided by the four motors B Combining equation (8), we get:

[0165]

[0166] Substituting equation (7) into equation (9), and considering external disturbances [d1 d2 d3]... T The attitude dynamics equations of a quadcopter UAV can be defined as follows:

[0167]

[0168] The second step, in order to enable the quadcopter UAV to stably complete the attitude tracking task, is to design a non-singular fast terminal sliding mode controller, which includes the following steps:

[0169] M1: To clarify the design process of non-singular fast terminal sliding mode controllers, taking the roll angle φ as an example; the tracking error of the roll angle φ is defined as follows:

[0170] e φ =φ-φ d +K φ ∫(φ-φ d )dt (11)

[0171] Among them, K φ ∫(φ-φ d )dt is the integral term added to the roll angle tracking error, K φ φ is a positive constant. d It is the expected value of the roll angle φ; ∫(·)dt is the integral sign, and the function inside the parentheses is the integrand;

[0172] Assume ρ φ To define a custom virtual control variable, the derivative of equation (11) is:

[0173]

[0174] M2: Define the Lyapunuov function as follows:

[0175]

[0176] Taking the derivative with respect to V1, we get:

[0177]

[0178] Substituting equation (12) into equation (14), we get:

[0179]

[0180] The control variable ρ φ Defined as:

[0181]

[0182] Where c1 is a positive parameter, and S is a non-singular fast terminal sliding surface. φ The design is as follows:

[0183]

[0184] Where α, δ, ζ, and λ are positive constants and satisfy... 0 < μ < 1, shn(·) is a sign function;

[0185] Taking the time derivative of (17), we get:

[0186]

[0187] M3: Define Lyapunov functions as follows:

[0188]

[0189] Finding the time derivative of V2, we get:

[0190]

[0191] Substituting equations (15), (16), and (18) into equation (20), we get:

[0192]

[0193] Substituting equation (10) into equation (21), we get:

[0194]

[0195] The third step, in order to improve the anti-interference capability of the quadcopter UAV, involves adding an improved second-order LADRC controller (second-order linear active disturbance rejection controller) to the system. This includes the following steps:

[0196] N1: The second-order linear active disturbance rejection controller has a built-in second-order system (LADRC system). The motion equation of the second-order system can be:

[0197]

[0198] Where: y is the output of the second-order system; u is the control input of the second-order system; ω is the external unknown disturbance of the second-order system; a1 and a2 are system parameters; b is the control gain of the second-order system, which is partially known, let the known part be b0; Equation (8) can be transformed into the following equation:

[0199]

[0200] make Equation (25) can be rewritten as:

[0201]

[0202] N2: Let x1 = y, x3 = f, where x3 is the extended state variable of the second-order system. Therefore, the state equation expression of equation (26) is as follows:

[0203]

[0204] Where x1, x2, and x3 are state variables. Equation (27) is transformed into an extended state-space equation:

[0205]

[0206] in, C = [1 0 0];

[0207] The corresponding linearly extended state observer in equation (28) is:

[0208]

[0209] L = [l1 l2 l3]T It is the gain vector of the observer; the gain of the observer can be parameterized by placing all the eigenvalues ​​in the observation bandwidth, and the gain of the observer can be expressed by its characteristic equation as shown in equation (30):

[0210] λ(s0=s 3 +l1s 2 +l2s+l3=(s+ω0) 3 (30)

[0211] The gain matrix can be obtained as follows:

[0212]

[0213] Equation (29) is simplified to:

[0214]

[0215] In equation (32), z1, z2, and z3 are the estimated values ​​of x1, x2, and x3, respectively, and l1, l2, and l3 are the observer gains. It can be seen that when the appropriate observer gains l1, l2, and l3 are determined, the extended state observer can estimate the various state variables of the original system in real time.

[0216] N3: The transfer function of the second-order linear active disturbance rejection controller is obtained from equation (32):

[0217] G(s)=l3 / (s 3 +l1s 2 +l2s+l3) (33)

[0218] Equation (33) is a third-order system. After approximating it as a second-order system, we get:

[0219]

[0220] To improve the response speed of the second-order system and reduce the amplitude drop and phase lag of the control signal, let l3 = l4(1 + l5s) in equation (32). After simplification, the transfer function of the second-order linear active disturbance rejection controller can be reduced to:

[0221] G(S)=l4(1+l5s) / [s 3 +l1s 2 +(l2+l4l5)s+l4] (35)

[0222] Where s is a complex variable, which is the frequency in the Laplace transform domain; l4 and l5 are the observation gains after replacing l3;

[0223] N4: Let the control variables of the system be as shown in (36):

[0224] u=(-z3+u0) / b0 (36)

[0225] Ignoring the estimation error of z3 for f, the original uncertain system can be transformed into The original nonlinear control system is transformed into a linear integrator series control system, which can be simplified to a mathematical model of the controlled object and improve the control performance of the second-order system.

[0226] N5: In a second-order system, LESO can be used to estimate and compensate for the total disturbance, and a PD controller can be used to meet the control requirements; therefore, a second-order linear active disturbance rejection controller is designed based on equation (36) as shown in equation (37):

[0227]

[0228] Where u0 is the output of the PD controller, k p k d For the control parameters of the PD circuit, v d Expected input;

[0229] N6: To facilitate adjustment of parameter k p and parameter k d An adaptive control method was introduced.

[0230] The algorithm for tracking the differentiator is as follows:

[0231]

[0232] Where r is the fast factor, h1 is the sampling time, fhan(·) is the fastest control synthesis function, v1(t) is the tracking signal of the initial signal, v2(t) is the tracking signal of the derivative of the initial signal, t is a certain state, and t+1 is the next state relative to t.

[0233] N7: Assuming the initial signal v d (t) is smooth and bounded, and the tracking error is defined as e = vv d Then the filtering tracking error is defined as:

[0234] χ=[Λ T 1]e (39)

[0235] Where Λ=a1 is a suitable gain vector such that e→0 when χ→0; taking the derivative with respect to χ, we get:

[0236]

[0237] in,

[0238]

[0239] Approximation is achieved by defining tracking control for the input signal. It's pseudo-control. for Any approximation of can be obtained by adding or subtracting on the right side of equation (38). We get the following formula:

[0240]

[0241] because for The approximate value, so It converges to near zero; the pseudo-control input is designed as follows:

[0242] α=-τχ+u0-[0 Λ T ]e (43)

[0243] Where τ is an arbitrarily positive parameter; substituting (37), (42), and (43) into equation (40) yields:

[0244]

[0245] N8: Assuming that equation (43) is chosen as the control scheme, the following adaptive law is used to make the assumption true:

[0246]

[0247]

[0248] in, and This is an estimate of the PD gain in LADRC; and It represents the estimation error; γ and ε are appropriately chosen parameters.

[0249] Fourth step, define the Lyapunov function as follows:

[0250]

[0251] Differentiating formula (47) yields:

[0252]

[0253] Substituting equation (44) into equation (48) yields equation (49).

[0254]

[0255] Substituting equation (23) into equation (49) and simplifying, we get:

[0256]

[0257] Equation (50) can be rewritten as:

[0258]

[0259] Substituting equations (45) and (46) into equation (51), we get:

[0260]

[0261] Simplifying equation (52) yields:

[0262]

[0263] Where c1 and τ are positive parameters, we get:

[0264]

[0265] because Satisfying Lyapunov's stability theorem, the designed Non-Singular Terminal Sliding Mode (NFTSMC) combined with a second-order Linear Active Disturbance Rejection Controller (LADRC system) can ensure the speed and stability of the quadcopter UAV's attitude.

[0266] In summary, this invention addresses the problem of slow attitude control response in quadrotor UAVs by proposing a method combining an NFTSM and an improved second-order linear active disturbance rejection controller. This control strategy exhibits excellent noise immunity, significantly reducing the impact of noise disturbances on the attitude of the quadrotor UAV. It ensures that the quadrotor UAV control system possesses superior performance such as fast response, robustness, and higher tracking accuracy, facilitating real-time attitude stability maintenance for the quadrotor UAV.

[0267] To address the issue of slow convergence speed in quadcopter drones, the convergence speed of the drone control system was significantly improved by using NFTSMC. At the same time, it successfully solved the singularity problem that may occur in the control system, providing a stable and reliable solution for flight control.

[0268] To address the challenges of parameter tuning and the need to adjust excessive parameters during flight testing of quadcopter UAVs, an improved second-order linear active disturbance rejection controller (ADRC) is proposed. This controller can achieve stable UAV attitude with minimal parameter adjustments and effectively handles the impact of wind disturbances. Comparative analysis demonstrates that the improved ADRC not only enhances the stability of the UAV control system but also optimizes the control system model.

[0269] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method, characterized in that: Includes the following steps: S1: Attitude angle data processing and attitude dynamics modeling; S2: Design a non-singular fast terminal sliding mode controller; S3: Add a second-order linear active disturbance rejection controller; S4: Proof of Lyapunov stability.

2. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 1, characterized in that: The attitude angle data processing and attitude dynamics modeling in step S1 includes the following steps: first, data is collected and integrated using the gyroscope, magnetometer and accelerometer on the quadcopter UAV, and then attitude dynamics modeling is performed.

3. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 1, characterized in that: The attitude dynamics modeling in step S2 includes the following steps: M1: Define the fixed coordinate system E and the body coordinate system B, where O e Represents the origin of the Earth coordinate system, {x e y e z e } represent the positive directions of the coordinate axes in a fixed coordinate system; O b Let {x} be the origin of the coordinate system of the quadcopter UAV. b y b z b } represent the positive directions of the coordinate axes in the quadcopter drone; where φ represents the rotation angle of the quadcopter drone around the x-axis; θ represents the rotation angle of the quadcopter drone around the y-axis; and ψ represents the rotation angle of the quadcopter drone around the z-axis. M2: Transform the attitude angles in the body coordinate system B to the fixed coordinate system E. The rotation matrix is: M3: Definition Let ω be the attitude angular velocity of the quadcopter UAV in the fixed coordinate system E. B =[p,q,r] represents the attitude angular velocity of the quadcopter drone itself, and the conversion relationship is: The relationship between the Euler angular velocity of the quadcopter UAV in the fixed coordinate system E and the angular velocity in the body coordinate system is as follows: The coordinate position of the quadcopter UAV relative to the fixed coordinate system E is P = [xyz]. T , Let M be the sum of the lift generated by the four motors within the body coordinate system B, k be the thrust coefficient, l be the arm length of the quadcopter drone, and M be the thrust of the four motors. i That is the rotational speed of each motor; The torque generated by lift: The counter-torque generated by the propeller: Torque generated by air resistance: in It is the anti-torque coefficient, d φ d θ d ψ It is the aerodynamic drag coefficient. The attitude angular acceleration in the body coordinate system of the quadcopter UAV; M4: According to the law of angular momentum, the attitude dynamics equations of the quadcopter UAV are as follows: Where, τ B =[τ F τ A ] T =[τ Bx τ By τ Bz ] T I B =diag(I x ,I y ,I z ), I x ,I y ,I z These represent the moments of inertia of the quadcopter drone along the three coordinate axes; Combining equation (3) with equation (6), we further obtain: Introduce virtual control variables (U1, U2, U3, U4), as follows: The torque τ provided by the four motors B Combining equation (8), we get: Substituting equation (7) into equation (9), and considering external disturbances [d1 d2 d3]... T The attitude dynamics equations of a quadcopter UAV are as follows:

4. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 1, characterized in that: The design of the non-singular fast terminal sliding mode controller in step S2 includes the following steps: N1: Define the roll angle φ tracking error as follows: e φ =φ-φ d +K φ ∫(φ-φ d )dt (11) Among them, K φ ∫(φ-φ d )dt is the integral term added to the roll angle tracking error, K φ φ is a positive constant. d It is the expected value of the roll angle φ, ∫(·)dt is the integral sign, and the function inside the parentheses is the integrand; Define ρ φ To define a custom virtual control variable, the derivative of equation (11) is: N2: Define the Lyapunuov function as follows: Taking the derivative with respect to V1, we get: Substituting equation (12) into equation (14), we get: Define control variable ρ φ for: Where c1 is a positive parameter, and S is a non-singular fast terminal sliding surface. φ Designed as follows: Where α, δ, ζ, and λ are positive constants and satisfy... sgn(·) is a sign function; Taking the time derivative of equation (17), we get: N3: Define Lyapunov functions as follows: Finding the time derivative of V2, we get: Substituting equations (15), (16), and (18) into equation (20), we get: Substituting equation (10) into equation (21), we get:

5. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 4, characterized in that: The addition of a second-order linear active disturbance rejection controller in step S3 includes the following steps: Q1: The motion equation of the second-order linear active disturbance rejection controller is set as follows: Where y is the output of the second-order system; u is the control input of the second-order system; ω is the unknown external disturbance of the second-order system; a1 and a2 are the parameters of the second-order system; b is the control gain of the second-order system. Assuming the known part is b0, equation (8) can be transformed into the following equation: make Equation (25) can be rewritten as: Q2: Let x1 = y, x3 = f, where x3 is the extended state variable of the second-order system. Therefore, the state equation expression for equation (26) is as follows: Where x1, x2, and x3 are state variables. Equation (27) is transformed into an extended state-space equation: in, C = [1 0 0]; The corresponding linearly extended state observer in equation (28) is: Where L = [l1 l2 l3] T It is the gain vector of the observer. The gain of the observer can be parameterized by placing all the eigenvalues ​​in the observation bandwidth. The gain of the observer can be expressed by its characteristic equation (30): λ(s)=s 3 +l1s 2 +l2s+l3=(s+ω0) 3 (30) The gain matrix can be obtained as follows: Equation (29) is simplified to: In equation (32), z1, z2, and z3 are the estimated values ​​of x1, x2, and x3, respectively, and l1, l2, and l3 are the observer gains. Thus, once the observer gains l1, l2, and l3 are determined, the extended state observer can calculate the various state variables of the original system in real time. Q3: The transfer function of the second-order linear active disturbance rejection controller is obtained from equation (32): G(s)=l3 / (s 3 +l1s 2 +l2s+l3) (33) Equation (33) is a third-order system. After approximating it as a second-order system, we get: Let l3 = l4(1 + l5s) in equation (32), and after simplification, we obtain the transfer function of the second-order linear active disturbance rejection controller as follows: G(S)=l4(1+l5s) / [s 3 +l1s 2 +(l2+l4l5)s+l4] (35) Where s is a complex variable, which is the frequency in the Laplace transform domain; l4 and l5 are the observation gains after replacing l3; Let the control variable of the system be: u=(-z3+u0) / b0 (36) Ignoring the estimation error of z3 for f, it can be transformed into 6. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 5, characterized in that: In step Q3, a second-order linear active disturbance rejection controller is designed based on equation (36): Where u0 is the output of the PD controller, k p k d For the control parameters of the PD circuit, v d This is the expected input.

7. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 6, characterized in that: Step Q3 involves adjusting parameter k. p and parameter k d The following algorithm is also introduced: Where r is the fast factor, h1 is the sampling time, fhan(·) is the fastest control synthesis function, v1(t) is the tracking signal of the initial signal, v2(t) is the tracking signal of the derivative of the initial signal, t is a certain state, and t+1 is the next state relative to t.

8. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 7, characterized in that: The initial signal v d (t) is smooth and bounded, and the tracking error is defined as e = vv d Then the filtering tracking error is defined as: x=[Λ T 1]e (39) Where Λ=a1 is a suitable gain vector such that e→0 when χ→0. Taking the derivative with respect to χ, we get: in, Approximation is achieved by defining tracking control for the input signal. It's pseudo-control. for Any approximation of can be obtained by adding or subtracting on the right side of equation (38). We get the following formula: because for The approximate value, so Converging near zero, the pseudo-control input is: α=-τχ+u0-[0 Λ T ]e (43) Where τ is an arbitrarily positive parameter; Substituting (37), (42), and (43) into equation (40), we get:

9. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 8, characterized in that: As a control scheme, equation (43) employs the following adaptive law: in, and This is an estimate of the PD gain in LADRC; and It is the estimation error.

10. The non-singular terminal sliding mode and second-order linear active disturbance rejection attitude control method according to claim 9, characterized in that: The Lyapunov stability proof in step S4 is as follows: Define the Lyapunov function: Substituting equation (44) into equation (48) yields equation (49). Substituting equation (23) into equation (49) and simplifying, we get: Equation (50) can be rewritten as: Substituting equations (45) and (46) into equation (51), we get: Equation (52) is simplified to: Where c1 and τ are positive parameters, we get:

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