A second-order uncertain sliding mode control method for unmanned helicopters

Abstract

This invention relates to a second-order uncertain sliding mode control method for unmanned helicopters. The design method applies a state observer based on an adaptive RBF neural network for estimating the system state and the extended state of the total disturbance. The observation performance is better than that of the extended state observer of the classical active disturbance rejection controller, reducing the difficulty of tuning the ADRC controller parameters. Furthermore, the estimation of the total disturbance of the second-order uncertain system based on the adaptive RBF neural network reduces the impact of uncertain factors on the performance of the control system. The entire design method overcomes the high-frequency chattering shortcomings of traditional sliding mode controllers, thereby improving the dynamic performance of the controller. It can also effectively overcome the influence of internal and external disturbances faced by unmanned helicopters, improving the disturbance rejection and robustness of the flight control system, and the control performance is superior to that of traditional sliding mode controllers.

Description

Technical Field

[0001] This invention relates to a second-order uncertain sliding mode control method for unmanned helicopters, belonging to the field of second-order uncertain system control technology. Background Technology

[0002] Second-order uncertain systems are prevalent in real-world industrial systems, such as manned / unmanned helicopters / fixed-wing aircraft, inverted pendulums, and autonomous vehicles. The disturbances experienced by second-order uncertain systems are unknown and difficult to calculate and measure. These disturbances fall into two main categories: internal disturbances (structural parameter uncertainties or unmodeled dynamics) and external disturbances (external wind disturbances). They affect the stability of the controlled object, requiring control system design to overcome their impact. Studying the control problems of second-order uncertain systems has significant theoretical and practical implications.

[0003] There are many control design methods for second-order uncertain systems, including linear control, nonlinear control, and intelligent control. In the field of linear control, methods such as Proportional-Integral-Derivative (PID) control and Linear Quadratic Regulator (LQR) control are available. These control methods are simple to design and easy to implement in engineering. However, linear controller design relies excessively on accurate flight dynamics models, while unmanned helicopters face uncertain disturbances, making it difficult for linear controllers to effectively overcome these internal and external disturbances. In the field of nonlinear control, methods such as Backstepping Control, Active Disturbance Rejection Control (ADRC), and Sliding Mode Control (SMC) are available. Among them, sliding mode control and active disturbance rejection control are the most widely used. For example, Ifassiouen et al. designed a sliding mode controller for the flight control of a second-order unmanned helicopter system. They applied Lyapunov stability theory to analyze that the small unmanned helicopter system still has asymptotic stability in the face of internal and external disturbances. Simulation results show that the designed control system has good tracking performance (Journal: International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering; Authors: H. Ifassiouen, M. Guisser, H. Medromi; Publication date: 2007; Article title: Robust nonlinear control of a miniature autonomous helicopter using sliding mode control structure; Pages: 84-89). Ramirez et al. proposed an algorithm that combines integral sliding modes with inversion control. Simulation results showed that the second-order unmanned helicopter system still flew well even under gust interference (Journal of Intelligent and Robotic Systems; Authors: H. Ramirez-Rodriguez, V. Parra-Vega, A. Sanchez-Orta; Publication Date: 2014; Title: Robust backstepping control based on integral sliding modes for tracking of quadrotors; Pages: 51-66).Sliding mode control (SMC) offers advantages such as fast response, insensitivity to parameter changes and disturbances, no need for online system identification, and simple physical implementation. However, once the state trajectory reaches the sliding mode surface, it is difficult to slide strictly along the sliding mode surface to the equilibrium point. Instead, it approaches the equilibrium point by traversing back and forth on both sides, resulting in chattering, which is a major obstacle in the practical application of SMC. Considering the characteristics of internal and external disturbances, Active Disturbance Rejection Control (ADRC) treats internal and external disturbances of the second-order system as the total disturbance. It establishes an Extended State Observer (ESO) through state extension, estimating the total disturbance using the extended state for real-time compensation of system control. ADRC can overcome the influence of internal and external disturbances on system control, giving the system strong robustness. The control system design is not limited by the accuracy of the controlled object model, and this has been verified from both engineering practice and theoretical analysis perspectives. The ADRC controller is a nonlinear controller, and its drawback lies in the large number of controller parameters, making tuning difficult. Meanwhile, the extended state observer's adaptive capability is not strong. Once the internal and external disturbances change significantly, the tuning parameters used for the previous state of the extended state observer may no longer be applicable and need to be readjusted. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a second-order uncertain sliding mode control method for unmanned helicopters, which can not only protect the control of unmanned helicopters from the influence of internal and external disturbances, but also improve the control efficiency for unmanned helicopters.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The present invention designs a second-order uncertain sliding mode control method for unmanned helicopters, which executes the following steps A to C in real time based on real-time target commands to achieve real-time control of unmanned helicopters;

[0006] Step A. Based on the 6-DOF motion characteristics of the unmanned helicopter, construct the kinematic model corresponding to the unmanned helicopter, and then proceed to Step B;

[0007] Step B. Based on the kinematic model of the unmanned helicopter, construct the second-order uncertainty model of the unmanned helicopter attitude and its control loop according to the real-time target command, and obtain the attitude control vector of the unmanned helicopter.

[0008] Based on the kinematic model of the unmanned helicopter, and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter speed and its control loop are constructed to obtain the speed control vector of the unmanned helicopter.

[0009] Based on the kinematic model of the unmanned helicopter, and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter's position and its control loop are constructed to obtain the position control vector of the unmanned helicopter; then proceed to step C.

[0010] Step C. Control the unmanned helicopter based on its attitude control vector, velocity control vector, and position control vector.

[0011] As a preferred technical solution of the present invention: In step A, based on the 6-DOF motion characteristics of the unmanned helicopter, the kinematic model corresponding to the unmanned helicopter is constructed as follows:

[0012] (1);

[0013] (2);

[0014] (3);

[0015] (4);

[0016] in, T For the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter; T For the unmanned helicopter, the roll rate, pitch rate, and yaw rate are angular velocities. T For the roll Euler angle, pitch Euler angle, and yaw Euler angle of the unmanned helicopter; T Ground coordinates for the unmanned helicopter; The total mass of the unmanned helicopter; , These are the resultant external forces and resultant external moments of all components of the unmanned helicopter. The inertial moment matrix of the unmanned helicopter. The antisymmetric matrix of the three-axis angular rate of the unmanned helicopter. This is the transformation matrix from the body coordinate system to the ground coordinate system. This is the transformation matrix from the angular velocity of the unmanned helicopter to the Euler angular velocity.

[0017] As a preferred technical solution of the present invention: In step B, based on the kinematic model corresponding to the unmanned helicopter, according to the real-time target command, the second-order uncertainty model of the unmanned helicopter attitude and its control loop are constructed as follows to obtain the attitude control vector of the unmanned helicopter.

[0018] Based on equations (2) and (3), the second-order uncertainty model of the attitude of the unmanned helicopter is constructed as follows:

[0019] (5);

[0020] (6);

[0021] in, The external disturbances corresponding to the attitude of the unmanned helicopter. The control vector consists of the pitch, roll, and yaw control parameters of the unmanned helicopter. For about The function, For about The function, For about By combining equations (5) and (6), we obtain the following set of state equations for the second-order attitude system of the unmanned helicopter:

[0022] (7);

[0023] in, ,Will The internal dynamic characteristics, manipulation coupling between channels, and external disturbances are considered as the total disturbance, denoted as the total disturbance. Then equation (7) is updated as follows:

[0024] (8);

[0025] in, The attitude control gain matrix for the unmanned helicopter is the control vector composed of the pitch, roll, and yaw control parameters. With output This constitutes a single-input, single-output relationship;

[0026] Based on definition , , , The second-order nonlinear extended attitude system of the unmanned helicopter is constructed as follows:

[0027] (9);

[0028] Further observation devices for the pitch, roll, and yaw angles of the unmanned helicopter were constructed as follows:

[0029] (10);

[0030] (11);

[0031] (12);

[0032] in, The actual pitch angle, actual roll angle, and actual yaw angle of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For attitude control gains of unmanned helicopters. , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. Indicates a preset constant;

[0033] Further, based on the observations of the unmanned helicopter's pitch angle, roll angle, and yaw angle, the following formula is used:

[0034] (13);

[0035] The control vector is obtained by obtaining the pitch, roll, and yaw control signals of the unmanned helicopter. The attitude control vectors of the unmanned helicopter constitute the attitude control vectors. The target commands for pitch angle, roll angle, and yaw angle of the unmanned helicopter. The control trim values ​​for pitch, roll, and yaw angles of unmanned helicopters. For the output increment of the attitude controller, Let be the sliding membrane function. These are preset parameters.

[0036] As a preferred technical solution of the present invention: In step B, based on the kinematic model corresponding to the unmanned helicopter, according to the real-time target command, the second-order uncertainty model of the unmanned helicopter speed and its control loop are constructed as follows to obtain the speed control vector of the unmanned helicopter.

[0037] Based on equation (1), the second-order uncertainty model of the unmanned helicopter velocity is constructed as follows:

[0038] (14);

[0039] in, Let the external disturbance corresponding to the speed of the unmanned helicopter be defined, and define the disturbance. , For about The function yields the following:

[0040] (15);

[0041] in, For the speed control gain matrix of the unmanned helicopter, Collective pitch control obtained from pitch angle, roll angle, and velocity loop. The virtual control vector formed, along with the forward velocity, lateral velocity, and vertical velocity of the unmanned helicopter, constitutes... This constitutes a one-to-one single-input single-output system;

[0042] Based on definition , , , Then there is The second-order nonlinear extended velocity system of the unmanned helicopter is constructed as follows:

[0043] (16);

[0044] Further observation devices for the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter were constructed as follows:

[0045] (17);

[0046] (18);

[0047] (19);

[0048] in, The actual forward speed, actual lateral speed, and actual vertical speed of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For the speed control gain of unmanned helicopters, , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. Indicates a preset constant;

[0049] Further based on the observations of the unmanned helicopter's forward velocity, lateral velocity, and vertical velocity, the following formula is used:

[0050] (20);

[0051] The control vector consists of the forward velocity channel control, the lateral velocity channel control, and the vertical velocity channel control of the unmanned helicopter. This constitutes the velocity control vector for the unmanned helicopter, enabling control of the drone. The target commands are for the forward speed, lateral speed, and vertical speed of the unmanned helicopter. The control trim values ​​for the forward speed, lateral speed, and vertical speed of the unmanned helicopter. For the output increment of the speed controller, Let be the sliding membrane function. These are preset parameters.

[0052] As a preferred technical solution of the present invention: In step B, based on the kinematic model corresponding to the unmanned helicopter, according to the real-time target command, the second-order uncertainty model of the unmanned helicopter position and its control loop are constructed as follows to obtain the position control vector of the unmanned helicopter.

[0053] Based on equation (4), the second-order uncertainty model of the unmanned helicopter's position is constructed as follows:

[0054] (twenty one);

[0055] in, Define the external disturbance corresponding to the location of the unmanned helicopter, and define the disturbance. , Indicates about The function yields the following:

[0056] (twenty two);

[0057] in, For the position control gain matrix of the unmanned helicopter, for Virtual control variables;

[0058] Based on definition , , , Then there is The second-order nonlinear extended system for the position of the unmanned helicopter is constructed as follows:

[0059] (twenty three);

[0060] The following observation device is further constructed to determine the ground coordinates of the unmanned helicopter's position:

[0061] (twenty four);

[0062] (25);

[0063] (26);

[0064] in, These are the ground coordinates of the actual location of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For position control gain of unmanned helicopters, , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. Indicates a preset constant;

[0065] Further, based on the ground coordinates of the unmanned helicopter's position as observed by the following formula:

[0066] (27);

[0067] The control vector is composed of the ground coordinate manipulation quantities of the unmanned helicopter's forward flight speed and position. This constitutes the position control vector of the unmanned helicopter. The target command is the ground coordinates of the unmanned helicopter's position. The control trim amount represents the ground coordinates of the unmanned helicopter's position. Output increments to the position controller. Let be the sliding membrane function. These are preset parameters.

[0068] The second-order uncertain sliding mode control method for unmanned helicopters described in this invention, compared with existing technologies, has the following technical advantages:

[0069] This invention presents a second-order uncertain sliding mode control method for unmanned helicopters. It establishes a second-order uncertain system model for the unmanned helicopter and designs an adaptive neural network extended state observer. Based on this, a sliding mode control method for the unmanned helicopter is constructed, which can effectively avoid the unmanned helicopter control system being limited by internal and external disturbances. The design method applies a state observer based on an adaptive RBF neural network for estimating the system state and the extended state of the total disturbance. The observation performance is better than that of the classical active disturbance rejection controller extended state observer, reducing the difficulty of ADRC controller parameter tuning. Furthermore, the estimation of the total disturbance of the second-order uncertain system based on the adaptive RBF neural network reduces the impact of uncertain factors on the control system performance. The entire design method overcomes the high-frequency chattering shortcomings of traditional sliding mode controllers, improving the dynamic performance of the controller. It can effectively overcome the influence of internal and external disturbances faced by unmanned helicopters, improving the disturbance rejection and robustness of the flight control system, and the control performance is superior to that of traditional sliding mode controllers. Attached Figure Description

[0070] Figure 1 This is a structural diagram of the sliding mode controller based on the adaptive neural network extended state observer designed in this invention;

[0071] Figure 2 This is a schematic diagram of the attitude control loop for an unmanned helicopter;

[0072] Figure 3 This is a schematic diagram of the speed control loop for an unmanned helicopter;

[0073] Figure 4 This is a schematic diagram of the position control loop for an unmanned helicopter;

[0074] Figure 5 It is the immunity test response curve;

[0075] Figure 6 This is the ESO's estimation curve for the total attitude perturbation;

[0076] Figure 7 It is the robustness test response curve;

[0077] Figure 8 It is the trajectory tracking response along the X, Y, and Z axes;

[0078] Figure 9 It is the ESO's estimation curve for the total perturbation of attitude, velocity, and position;

[0079] Figure 10 It is a figure-eight 3D trajectory response. Detailed Implementation

[0080] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0081] With the increasing application of neural network control methods in the field of intelligent control, Radial Basis Function Neural Networks (RBFNNs), as a commonly used three-layer feedforward network, possess characteristics such as simple structure, fast learning speed, and excellent performance approximation. They can be used for extended state observer design to achieve state extension, better estimate the total disturbance experienced by a second-order system, and improve the disturbance rejection and adaptability of the control system. Sliding mode control law design helps improve the speed of the control system, reduce the difficulty of controller parameter tuning, and enhance controller performance.

[0082] In summary, this invention proposes a second-order uncertain sliding mode control (SMC) method for unmanned helicopters based on the Adaptive Radial Basis Function Neural Network Extended State Observer (ARBFNNESO).

[0083] Determine the nominal model of the second-order uncertain system. The nominal model of the second-order uncertain system considers both internal and external disturbances, namely:

[0084] (1-1);

[0085] Where u and y are the system input and output signals, For the state variables of the system, This is an unknown internal disturbance. The external disturbance is unknown, and b(t) is an unknown compensation coefficient.

[0086] Treating the sum of internal and external disturbances experienced by the second-order uncertain system as the total disturbance, and expanding the system based on the state expansion principle, we construct a second-order nonlinear extended system as follows:

[0087] (1-2);

[0088] in The new extended state variable contains the total disturbance consisting of internal and external disturbances. Let be a constant, and denote it as... The system (1-2) is a second-order nonlinear extended system with three state variables.

[0089] The Adaptive Neural Network Extended State Observer (ARBFNN-ESO) is established as follows:

[0090] (1-3);

[0091] (1-4);

[0092] (1-5);

[0093] (1-6);

[0094] in, , (i=1,2) are the gain coefficients. With a fixed step size, the output of the radial basis function neural network (RBFNN) is... It is an estimate of the total system disturbance, and the RBFNN input vector is the estimated value of the state variables. , Let be the coordinate vector of the center point of the Gaussian function of the j-th neuron in the hidden layer; Let the width of its Gaussian function be denoted as . It estimates the weights and adjusts them according to the adaptive law (1-6). , .

[0095] The sliding mode controller for the designed second-order nonlinear extended system is:

[0096] (1-7);

[0097] (1-8);

[0098] (1-9);

[0099] (1-10);

[0100] Equation (1-8) is the sliding mode function, and equation (1-9) is the system output versus the target state. The time error is given by equation (1-10), which is the differential error. ,when hour, The results are That is, when At that time, the error The sliding mode function s(t) converges exponentially to 0, and the convergence rate depends on the value of c. That is, the convergence of the sliding mode function s(t) implies that the error e and... It must converge. This can be guaranteed through control law design. The exponential convergence is 0, and the output of the second-order uncertain system can stably track the target state variable.

[0101] Define Lyapunov functions Differentiating with respect to V, we get:

[0102] (1-11);

[0103] Substituting the control law into equation (1-7), we have: It satisfies the Lyapunov stability condition.

[0104] Due to total disturbance Since the problem is unknown, the control law in equation (1-7) is difficult to implement directly and requires solving the total disturbance problem. This invention designs ARBFNN-ESO to estimate the system state variables and the total disturbance variable, thereby obtaining the control law output.

[0105] The ARBFNN-ESO output variable can track the state variables and total disturbance of system (1-2), that is...

[0106] (1-12);

[0107] Equation (1-7) of the sliding mode control law can be rewritten as:

[0108] (1-13);

[0109] (1-14);

[0110] That is, the control law (1-13) is the ARBFNNESO-SMC control law based on the estimate of the unknown total disturbance, such as... Figure 1 As shown, the formula has no switching term, overcoming the shortcomings of traditional sliding mode control chattering. Meanwhile, each system disturbance is estimated using the total disturbance term. As a compensation quantity for the control law, it improves the disturbance rejection, robustness, and adaptability of the control system.

[0111] The present invention proposes a second-order uncertain sliding mode control method for unmanned helicopters. In practical applications, based on real-time target commands, the following steps A to C are executed in real time to achieve real-time control of the unmanned helicopter.

[0112] Step A. Based on the 6-DOF motion characteristics of the unmanned helicopter, construct the kinematic model corresponding to the unmanned helicopter as follows, and then proceed to Step B.

[0113] (1);

[0114] (2);

[0115] (3);

[0116] (4);

[0117] in, T For the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter; T For the unmanned helicopter, the roll rate, pitch rate, and yaw rate are angular velocities. T For the roll Euler angle, pitch Euler angle, and yaw Euler angle of the unmanned helicopter; T Ground coordinates for the unmanned helicopter; The total mass of the unmanned helicopter; , These are the resultant external forces and resultant external moments of all components of the unmanned helicopter. The inertial moment matrix of the unmanned helicopter. The antisymmetric matrix of the three-axis angular rate of the unmanned helicopter. This is the transformation matrix from the body coordinate system to the ground coordinate system. This is the transformation matrix from the angular velocity of the unmanned helicopter to the Euler angular velocity.

[0118] Step B. Based on the kinematic model corresponding to the unmanned helicopter, construct the second-order uncertainty model of the unmanned helicopter attitude and its control loop according to the real-time target command, and obtain the attitude control vector of the unmanned helicopter.

[0119] Based on the kinematic model of the unmanned helicopter, and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter speed and its control loop are constructed to obtain the speed control vector of the unmanned helicopter.

[0120] Based on the kinematic model of the unmanned helicopter, a second-order uncertainty model of the unmanned helicopter's position and its control loop are constructed according to the real-time target command to obtain the position control vector of the unmanned helicopter; then proceed to step C.

[0121] In practical applications, step B above, based on the kinematic model corresponding to the unmanned helicopter, constructs a second-order uncertainty model of the unmanned helicopter attitude and its control loop according to the real-time target command, thereby obtaining the attitude control vector of the unmanned helicopter.

[0122] like Figure 2 As shown, based on equations (2) and (3), the second-order uncertainty model of the unmanned helicopter attitude is constructed as follows:

[0123] (5);

[0124] (6);

[0125] in, The external disturbances corresponding to the attitude of the unmanned helicopter. The control vector consists of the pitch, roll, and yaw control parameters of the unmanned helicopter. For about The function, For about The function, For about By combining equations (5) and (6), we obtain the following set of state equations for the second-order attitude system of the unmanned helicopter:

[0126] (7);

[0127] in, ,Will The internal dynamic characteristics, manipulation coupling between channels, and external disturbances are considered as the total disturbance, denoted as the total disturbance. Then equation (7) is updated as follows:

[0128] (8);

[0129] in, The attitude control gain matrix for the unmanned helicopter is the control vector composed of the pitch, roll, and yaw control parameters. With output This constitutes a single-input, single-output relationship.

[0130] Based on definition , , , The second-order nonlinear extended attitude system of the unmanned helicopter is constructed as follows:

[0131] (9);

[0132] Further observation devices for the pitch, roll, and yaw angles of the unmanned helicopter were constructed as follows:

[0133] (10);

[0134] (11);

[0135] (12);

[0136] in, The actual pitch angle, actual roll angle, and actual yaw angle of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For attitude control gains of unmanned helicopters. , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. This represents a preset constant.

[0137] Further, based on the observations of the unmanned helicopter's pitch angle, roll angle, and yaw angle, the following formula is used:

[0138] (13);

[0139] The control vector is obtained by obtaining the pitch, roll, and yaw control signals of the unmanned helicopter. The attitude control vectors of the unmanned helicopter, such as Figure 2 As shown, The target commands for pitch angle, roll angle, and yaw angle of the unmanned helicopter. The control trim values ​​for pitch, roll, and yaw angles of unmanned helicopters. For the output increment of the attitude controller, Let be the sliding membrane function. These are preset parameters.

[0140] Regarding the speed of the unmanned helicopter, based on the kinematic model of the unmanned helicopter and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter speed and its control loop are constructed as follows to obtain the speed control vector of the unmanned helicopter.

[0141] like Figure 3 As shown, based on equation (1), the second-order uncertainty model of the unmanned helicopter speed is constructed as follows:

[0142] (14);

[0143] in, Let the external disturbance corresponding to the speed of the unmanned helicopter be defined, and define the disturbance. , For about The function yields the following:

[0144] (15);

[0145] in, For the speed control gain matrix of the unmanned helicopter, Collective pitch control obtained from pitch angle, roll angle, and velocity loop. The virtual control vector formed, along with the forward velocity, lateral velocity, and vertical velocity of the unmanned helicopter, constitutes... This constitutes a one-to-one single-input single-output system.

[0146] Based on definition , , , Then there is The second-order nonlinear extended velocity system of the unmanned helicopter is constructed as follows:

[0147] (16);

[0148] Further observation devices for the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter were constructed as follows:

[0149] (17);

[0150] (18);

[0151] (19);

[0152] in, The actual forward speed, actual lateral speed, and actual vertical speed of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For the speed control gain of unmanned helicopters, , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. This represents a preset constant.

[0153] Further based on the observations of the unmanned helicopter's forward velocity, lateral velocity, and vertical velocity, the following formula is used:

[0154] (20);

[0155] The control vector consists of the forward velocity channel control, the lateral velocity channel control, and the vertical velocity channel control of the unmanned helicopter. This constitutes the speed control vector for unmanned helicopters, enabling control of the drones, such as... Figure 3 As shown, The target commands are for the forward speed, lateral speed, and vertical speed of the unmanned helicopter. The control trim values ​​for the forward speed, lateral speed, and vertical speed of the unmanned helicopter. For the output increment of the speed controller, Let be the sliding membrane function. These are preset parameters.

[0156] Regarding the position of the unmanned helicopter, based on the kinematic model corresponding to the unmanned helicopter, and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter position and its control loop are constructed as follows to obtain the position control vector of the unmanned helicopter.

[0157] like Figure 4 As shown, based on equation (4), the second-order uncertainty model of the unmanned helicopter's position is constructed as follows:

[0158] (twenty one);

[0159] in, Define the external disturbance corresponding to the location of the unmanned helicopter, and define the disturbance. , Indicates about The function yields the following:

[0160] (twenty two);

[0161] in, For the position control gain matrix of the unmanned helicopter, for Virtual control quantity.

[0162] Based on definition , , , Then there is The second-order nonlinear extended system for the position of the unmanned helicopter is constructed as follows:

[0163] (twenty three);

[0164] The following observation device is further constructed to determine the ground coordinates of the unmanned helicopter's position:

[0165] (twenty four);

[0166] (25);

[0167] (26);

[0168] in, These are the ground coordinates of the actual location of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For position control gain of unmanned helicopters, , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. This represents a preset constant.

[0169] Further, based on the ground coordinates of the unmanned helicopter's position as observed by the following formula:

[0170] (27);

[0171] The control vector is composed of the ground coordinate manipulation quantities of the unmanned helicopter's forward flight speed and position. The position control vectors of the unmanned helicopter, such as Figure 4 As shown, The target command is the ground coordinates of the unmanned helicopter's position. The control trim amount represents the ground coordinates of the unmanned helicopter's position. Output increments to the position controller. Let be the sliding membrane function. These are preset parameters.

[0172] Step C. Control the unmanned helicopter based on its attitude control vector, velocity control vector, and position control vector.

[0173] A simulation experiment was conducted to verify the second-order uncertain sliding mode control method for unmanned helicopters designed in this invention. The simulation verification parameters were set as follows: the initial attitude angles of the unmanned helicopter were all 0°, and the desired target angles were all 5°. The initial values ​​of the unmanned helicopter parameters are shown in Table 1. The controller design verification used an SMC controller and the ESO-SMC controller designed in this invention for comparison. The parameters of the SMC controller and the ESO-SMC controller are shown in Table 2. The RBFNN parameters were selected as Gaussian function parameters. , , , , .

[0174]

[0175]

[0176] (1) Anti-interference simulation and analysis verification: External wind disturbances can interfere with the flight of unmanned helicopters. A rectangular wave signal was used to simulate a sudden wind disturbance during a certain flight period. The parameters of the unmanned helicopter are the initial values ​​in Table 1. At the 5th second, rectangular wave signals with an amplitude of 5 and a time width of 1 second were applied to the outputs of the roll, pitch, and yaw channels, respectively, as external disturbances. The anti-interference ability of the two controllers was verified by simulation. The simulation results are attached. Figure 5 As shown, without external disturbances, the control effects of the SMC controller and the ARBFNNESO-SMC controller are essentially the same, and the unmanned helicopter's attitude can be quickly stabilized to the target attitude angle. However, when external disturbance signals are introduced, the ARBFNNESO-SMC controller exhibits better attitude response stability and smaller fluctuations, indicating that the ARBFNNESO-SMC controller has better anti-interference performance. Figure 6 The graph shows the RBFNN estimation response history curve for the total disturbance expansion state. It can be seen that when no external disturbance is added, the total disturbance value estimated by RBFNN changes slowly. After the external disturbance is added, the total disturbance of the three attitude channels changes abruptly. RBFNN quickly estimates the change in the total disturbance and uses it for control law compensation, so that the ARBFNNNESO-SMC controller has better disturbance rejection capability.

[0177] (2) Robustness Simulation and Analysis Verification: The parameter values ​​of the unmanned helicopter were changed to simulate the uncertainty of the unmanned helicopter system parameters as an internal disturbance. The modified values ​​of the unmanned helicopter parameters are shown in Table 1. Keeping the initial controller parameters in Table 2 unchanged, the attitude control simulation of the unmanned helicopter was performed again using two controllers. The results are as follows: Figure 7As shown, even if the dynamic characteristics of the controlled object change significantly, the ARBFNNESO-SMC controller can still obtain a good dynamic response curve, and the control effect is better than that of the SMC controller.

[0178] The trajectory ARBFNNESO-SMC control system and its simulation verification: three velocity uncertainty models were each constructed using a second-order ARBFNNESO-SMC controller to form a three-axis velocity control loop, as shown in the attached figure. Figure 3 As shown. The speed command is given by the position control loop. The speed control loop is designed with reference to the pitch channel control design method, and the RBFNN is used to handle the total disturbance. Estimate using a state observer , Estimate the control output quantity and superimpose it with the reference quantity to form the control output quantity. This serves as the target input signal for the attitude control loop. As the preceding analysis shows, the controller output calculation formula is similar to equation (3-23), except that the meaning and sign of the physical variables of the control manipulation quantity are changed; the variable is changed from the attitude angle target quantity. and actual quantity Change to speed target quantity This will not be elaborated upon here.

[0179] Each of the three displacement control loops also uses a second-order ARBFNNESO-SMC controller to form a three-axis displacement control loop. Figure 4 The block diagram of the displacement control loop is shown, and the total disturbance is represented by RBFNN. Estimate using a state observer , The estimation is performed, and the displacement command is the pre-set trajectory signal. The control output and the balancing amount are superimposed to form the result. As the input signal for the speed control loop, the specific calculation method for the controller output is similar to that in equation (3-23), except that the meaning and sign of the physical variables of the control manipulation quantity are changed, and the variables are changed from the attitude angle target quantity. and actual quantity Change to location target quantity This will not be elaborated upon here.

[0180] Further flight simulation verification of the control response for the figure-eight climb flight trajectory was conducted. The simulation verification parameters were set as follows: the flight mission objective was set as a figure-eight climb, and simulation verification was performed using both the SMC controller and the ARBFNNESO-SMC controller proposed in this invention. The initial values ​​of the unmanned helicopter parameters are shown in Table 1, and the parameters of the two controllers are shown in Table 3.

[0181]

[0182] The parameters of the attitude inner loop RBFNN are consistent with the parameter values ​​tuned in feature 7. At the 5th second after the simulation begins, a rectangular wave with an amplitude of 5 and a duration of 10 seconds is applied to the outputs of the roll, pitch, yaw, and altitude channel controllers as an external disturbance signal. Keeping the controller parameters unchanged, the unmanned helicopter parameters are changed at the 20th second, as shown in Table 1, to simulate the uncertainty of the unmanned helicopter system parameters as an internal disturbance.

[0183] Simulation results are as follows Figure 8-9 As shown, the ARBFNNESO-SMC controller exhibits higher trajectory tracking accuracy than the SMC controller. After a rectangular wave disturbance is applied at the 5th second, the SMC controller's trajectory tracking response fluctuates significantly, with a marked increase in tracking control response errors in all three directions. Furthermore, even after the disturbance disappears, the SMC controller's tracking control response error does not decrease rapidly, leading to a large deviation in the tracking trajectory. In contrast, the ARBFNNESO-SMC controller can quickly estimate and compensate for the disturbance, maintaining a good match between its tracking trajectory and the predetermined trajectory. After changing the unmanned helicopter parameters at the 20th second, the SMC controller exhibits an even larger tracking control response error. These simulation results demonstrate that the ARBFNNESO-SMC controller possesses excellent disturbance rejection and robustness, effectively overcoming internal and external disturbances faced by the unmanned helicopter and ensuring high-precision trajectory tracking.

[0184] The aforementioned technical solution proposes a second-order uncertain sliding mode control method for unmanned helicopters. It establishes a second-order uncertain system model for the unmanned helicopter and designs an adaptive neural network extended state observer. Based on this, a sliding mode control method for the unmanned helicopter is constructed, effectively avoiding the unmanned helicopter control system from being limited by internal and external disturbances. The design method applies a state observer based on an adaptive RBF neural network for estimating the system state and the extended state of the total disturbance. The observation performance is better than that of the classical active disturbance rejection controller extended state observer, reducing the difficulty of ADRC controller parameter tuning. Furthermore, the estimation of the total disturbance of the second-order uncertain system based on the adaptive RBF neural network reduces the impact of uncertain factors on the performance of the control system. The entire design method overcomes the high-frequency chattering shortcomings of traditional sliding mode controllers, improving the dynamic performance of the controller. It can effectively overcome the influence of internal and external disturbances faced by unmanned helicopters, improving the disturbance rejection and robustness of the flight control system, and its control performance is superior to that of traditional sliding mode controllers.

[0185] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A second order uncertain sliding mode control method for unmanned helicopter based on adaptive neural network extended state observer, characterized in that: Based on real-time target commands, steps A to C are executed in real time to achieve real-time control of the unmanned helicopter; Step A. Based on the 6-DOF motion characteristics of the unmanned helicopter, construct the kinematic model corresponding to the unmanned helicopter, and then proceed to Step B; Step B. Based on the kinematic model of the unmanned helicopter, construct the second-order uncertainty model of the unmanned helicopter attitude and its control loop according to the real-time target command, and obtain the attitude control vector of the unmanned helicopter. Based on the kinematic model of the unmanned helicopter, and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter speed and its control loop are constructed to obtain the speed control vector of the unmanned helicopter. Based on the kinematic model of the unmanned helicopter, and according to the real-time target command, a second-order uncertainty model of the unmanned helicopter's position and its control loop are constructed to obtain the position control vector of the unmanned helicopter; then proceed to step C. Step C. Control the unmanned helicopter based on its attitude control vector, velocity control vector, and position control vector; In step A, based on the 6-DOF motion characteristics of the unmanned helicopter, the kinematic model corresponding to the unmanned helicopter is constructed as follows: （1）； （2）； （3）； （4）； in, T For the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter; T For the unmanned helicopter, the roll rate, pitch rate, and yaw rate are angular velocities. T For the roll Euler angle, pitch Euler angle, and yaw Euler angle of the unmanned helicopter; T Ground coordinates for the unmanned helicopter; The total mass of the unmanned helicopter; , These are the resultant external forces and resultant external moments of all components of the unmanned helicopter. The inertial moment matrix of the unmanned helicopter. The antisymmetric matrix of the three-axis angular rate of the unmanned helicopter. This is the transformation matrix from the body coordinate system to the ground coordinate system. This is the transformation matrix from the angular velocity of the unmanned helicopter to the Euler angular velocity.

2. The unmanned helicopter second-order uncertain sliding mode control method based on adaptive neural network extended state observer according to claim 1, characterized in that: In step B, based on the kinematic model corresponding to the unmanned helicopter, and according to the real-time target command, the second-order uncertainty model of the unmanned helicopter attitude and its control loop are constructed as follows to obtain the attitude control vector of the unmanned helicopter. Based on equations (2) and (3), the second-order uncertainty model of the attitude of the unmanned helicopter is constructed as follows: （5）； （6）； in, The external disturbances corresponding to the attitude of the unmanned helicopter. The control vector consists of the pitch, roll, and yaw control parameters of the unmanned helicopter. For about The function, For about The function, For about By combining equations (5) and (6), we obtain the following set of state equations for the second-order attitude system of the unmanned helicopter: （7）； in, ,Will The internal dynamic characteristics, manipulation coupling between channels, and external disturbances are considered as the total disturbance, denoted as the total disturbance. Then equation (7) is updated as follows: （8）； wherein, is a gain matrix for attitude control of the unmanned helicopter, a control vector composed of a pitch channel manipulation quantity, a roll channel manipulation quantity, and a yaw channel manipulation quantity of the unmanned helicopter and an output quantity constitute a single-input-single-output relationship; Based on the definition , , , , the second-order nonlinear extended system of the unmanned helicopter attitude is constructed as follows: （9）； Further observation devices for the pitch, roll, and yaw angles of the unmanned helicopter were constructed as follows: （10）； （11）； （12）； in, The actual pitch angle, actual roll angle, and actual yaw angle of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For attitude control gains of unmanned helicopters. , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. Indicates a preset constant; Further, based on the observations of the unmanned helicopter's pitch angle, roll angle, and yaw angle, the following formula is used: （13）； The control vector is obtained by obtaining the pitch, roll, and yaw control signals of the unmanned helicopter. The attitude control vectors of the unmanned helicopter constitute the attitude control vectors. The target commands for pitch angle, roll angle, and yaw angle of the unmanned helicopter. The control trim values ​​for pitch, roll, and yaw angles of unmanned helicopters. For the output increment of the attitude controller, Let be the sliding membrane function. These are preset parameters.

3. The unmanned helicopter second order uncertain sliding mode control method based on adaptive neural network extended state observer according to claim 1, characterized in that: In step B, based on the kinematic model corresponding to the unmanned helicopter, and according to the real-time target command, the second-order uncertainty model of the unmanned helicopter speed and its control loop are constructed as follows to obtain the speed control vector of the unmanned helicopter. Based on equation (1), the second-order uncertainty model of the unmanned helicopter velocity is constructed as follows: （14）； in, Let the external disturbance corresponding to the speed of the unmanned helicopter be defined, and define the disturbance. , For about The function yields the following: （15）； in, For the speed control gain matrix of the unmanned helicopter, Collective pitch control obtained from pitch angle, roll angle, and velocity loop. The virtual control vector formed, along with the forward velocity, lateral velocity, and vertical velocity of the unmanned helicopter, constitutes... This constitutes a one-to-one single-input single-output system; Based on definition , , , Then there is The second-order nonlinear extended velocity system of the unmanned helicopter is constructed as follows: （16）； Further observation devices for the forward flight speed, lateral speed, and vertical speed of the unmanned helicopter were constructed as follows: （17）； （18）； （19）； in, The actual forward speed, actual lateral speed, and actual vertical speed of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For the speed control gain of unmanned helicopters, , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. Indicates a preset constant; Further based on the observations of the unmanned helicopter's forward velocity, lateral velocity, and vertical velocity, the following formula is used: （20）； The control vector consists of the forward velocity channel control, the lateral velocity channel control, and the vertical velocity channel control of the unmanned helicopter. This constitutes the velocity control vector for the unmanned helicopter, enabling control of the drone. The target commands are for the forward speed, lateral speed, and vertical speed of the unmanned helicopter. The control trim values ​​for the forward speed, lateral speed, and vertical speed of the unmanned helicopter. For the output increment of the speed controller, Let be the sliding membrane function. These are preset parameters.

4. The second-order uncertain sliding mode control method for unmanned helicopters based on an adaptive neural network extended state observer according to claim 1, characterized in that: In step B, based on the kinematic model corresponding to the unmanned helicopter, and according to the real-time target command, the second-order uncertainty model of the unmanned helicopter position and its control loop are constructed as follows to obtain the position control vector of the unmanned helicopter. Based on equation (4), the second-order uncertainty model of the unmanned helicopter's position is constructed as follows: （21）； in, Define the external disturbance corresponding to the location of the unmanned helicopter, and define the disturbance. , Indicates about The function yields the following: （22）； in, For the position control gain matrix of the unmanned helicopter, for Virtual control variables; Based on definition , , , Then there is The second-order nonlinear extended system for the position of the unmanned helicopter is constructed as follows: （23）； The following observation device is further constructed to determine the ground coordinates of the unmanned helicopter's position: （24）； （25）； （26）； in, These are the ground coordinates of the actual location of the unmanned helicopter. , , This is the gain coefficient. To maintain a fixed step size, It is a radial basis function neural network (RBFNN). , For the hidden layer of a radial basis function neural network (RBFNN) The coordinate vector of the center point of the Gaussian function of the node neuron. For the hidden layer of a radial basis function neural network (RBFNN) The width of the Gaussian function of the node neuron. For position control gain of unmanned helicopters, , Indicates the estimated weights. , The default parameter is greater than 0. Indicates about numbers The sign function, Returns 1 if the value is greater than 0. Returns -1 if the value is less than 0. Returns 0 if the value is 0. Represented by natural constant An exponential function with base 0. Indicates a preset constant; Further, based on the ground coordinates of the unmanned helicopter's position as observed by the following formula: （27）； The control vector is composed of the ground coordinate manipulation quantities of the unmanned helicopter's forward flight speed and position. This constitutes the position control vector of the unmanned helicopter. The target command is the ground coordinates of the unmanned helicopter's position. The control trim amount represents the ground coordinates of the unmanned helicopter's position. Output increments to the position controller. Let be the sliding membrane function. These are preset parameters.

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