A fixed time cross lateral coupling suppression system and method

Abstract

The application discloses a fixed-time lateral coupling suppression system and method, and belongs to the technical field of aircraft control. The system comprises an aircraft lateral coupling fixed-point dynamic model, a fixed-time extended state observer and a fixed-time controller. The state quantity of the system is obtained through the aircraft lateral coupling fixed-point dynamic model, and the fixed-time extended state observer outputs the observation result of the lumped disturbance converging in a fixed time based on the state quantity and the output of the fixed-time controller, so that the feedforward compensation is performed and the disturbance suppression capability of the aircraft is improved. The fixed-time controller is adopted, so that the tracking error of the state quantity of the control system converges in a fixed time. The application improves the guidance control precision of the high-speed aircraft and the suppression capability of the interference and coupling, so that the stability of the flight control system is improved and the response rapidity of the system is considered.

Description

Technical Field

[0001] This invention relates to a fixed-time lateral coupling suppression system and method, belonging to the field of aircraft control technology. Background Technology

[0002] Agile, high-speed aircraft often employ sideslip-turn control, placing demands on maneuverability, overload capacity, and interference suppression capabilities. However, during flight, due to aerodynamic and control coupling, significant cross-coupling exists between the lateral and longitudinal control channels. This coupling characteristic is particularly pronounced during rapid, high-maneuver flight. Coupled with inherent system uncertainties and external disturbances, this severely impacts control quality, guidance accuracy, and even flight safety. Currently, control systems are mostly designed with independent pitch, yaw, and roll channels, treating the coupling between different channels as external disturbances and suppressing and stabilizing them through the robustness of the controller itself. To address the adverse effects of lateral channel coupling, nonlinear dynamics, parameter uncertainties, and external disturbances in high-speed aircraft, a multi-channel integrated control system design is needed to balance system response speed, interference suppression capabilities, and channel decoupling capabilities.

[0003] In the paper "Design of Composite Control for Reentry Attitude of Aerospace Vehicle Considering Dynamic Control Allocation", based on the idea of ​​coordinated branch, a cross-coupled feedback term is introduced in the rolling channel control to stabilize the attitude. However, the nonlinear changes of the flow field of high-speed vehicles are drastic, and even the opposite effect may occur under local conditions. At this time, the fixed feedback term gain may have the opposite effect.

[0004] In the paper "Design of Missile Decoupling Control Based on Incremental Nonlinear Dynamic Inverse", a fast and slow dual-loop tracking controller is designed, and nonlinear inverse and nonlinear function feedback compensation are used to cancel the nonlinear coupling terms of the system. However, the use of incremental dynamic inverse requires the derivatives of the state, especially the derivatives of the angular velocity term, which are not directly measurable quantities on the missile.

[0005] Chinese patent CN112000127B discloses a lateral joint controller for aircraft based on backstepping. It uses backstepping based on inner and outer loop design to decouple channels, but under parameter uncertainty and external interference, the control performance may decline or even become unstable.

[0006] Chinese patent CN111026143B discloses a lateral coupling control method and device for the terminal guidance phase of a lifting body aircraft. It treats the coupling terms between the inner and outer loops as disturbances, observes them using a sliding mode observer, and employs a sliding mode controller to achieve finite-time convergence of the control system. However, its modeling and control only consider the disturbances between the inner and outer loops, and the upper bound of the convergence time depends on the initial conditions of the system. Furthermore, the finite-time sliding mode control of the inner and outer loops also suffers from complex parameter tuning issues. Considering the problems of lateral channel control coupling in high-speed aircraft under modeling uncertainties and external disturbances, existing control methods are still insufficient in improving the system's response speed and robustness. Summary of the Invention

[0007] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a fixed-time lateral coupling suppression system and method, which improves the guidance and control accuracy of high-speed aircraft and the ability to suppress interference and coupling, thereby improving the stability of the flight control system and taking into account the rapid response of the system.

[0008] The technical solution of this invention is: A fixed-time lateral coupling suppression system includes a fixed-point dynamic model of lateral coupling of an aircraft, a fixed-time extended state observer, and a fixed-time controller; The lateral coupling fixed-point dynamics model of the aircraft collects the yaw angle and roll angle, as well as the yaw angular velocity and roll angular velocity output by the navigation system as the state, and collects the yaw channel rudder deflection angle and roll channel rudder deflection angle output by the fixed-time controller as the input. It combines the power coefficient gain matrix and the disturbance matrix to construct a state-space representation of the controlled object model, and transforms it into a standard second-order nonlinear control model. The fixed-time extended state observer treats the unknown disturbance quantities of the yaw channel and the unknown disturbance quantities of the roll channel in the system state equation as lumped disturbances and as extended states. Based on the sideslip angle, roll angle, yaw rate, and roll rate obtained from the aircraft's lateral coupled fixed-point dynamic model, it outputs the observed values ​​of the extended states, so that the observation error of the lumped disturbances converges to zero within a fixed time. The fixed-time controller takes the sideslip angle command and sideslip angle error, and the roll angle command and roll angle error as inputs, and takes the yaw channel rudder deflection angle and the roll channel rudder deflection angle as outputs, so that the tracking error of the attitude angle to the control command converges to zero within a fixed time.

[0009] Furthermore, the lateral coupled fixed-point dynamics model of the aircraft is as follows:

[0010] in, The pitch angle, It is the acceleration due to gravity. For flight speed, For the angle of attack, Sideslip angle, For roll angle, for The first derivative with respect to time for The first derivative with respect to time; Yaw angular velocity, for The first derivative with respect to time; For the roll angular velocity, for The first derivative with respect to time; The rudder deflection angle for the yaw channel. This refers to the rudder deflection angle in the roll channel; The yaw channel dynamic coefficient, The dynamic coefficient of the roll channel; This represents the unknown interference amount in the yaw channel. This represents the unknown interference amount in the roll channel.

[0011] Furthermore, the system state equation is:

[0012] in, , , ;

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] .

[0019] Furthermore, the fixed-time extended state observer is:

[0020] in, , and For the state variables of the observer, System status The observed values, System status The observed values, In an expanding state The observed values, The output of the observer; , and They are respectively , and The first derivative with respect to time System status The observation error, For the observer switching item; , , , For observer gain; power exponent Pick , , , , , , It is a symbolic function.

[0021] Furthermore, in the fixed-time extended state observer, the power exponent , The possible values ​​are: ,

[0022] Observer gain requirements , , Unknown interference in the yaw channel Unknown interference in the roll channel Upper limit of the absolute value after differentiation; Power index , , , The possible values ​​are: , , , , , It is a time constant. .

[0023] Furthermore, the fixed-time controller is obtained by constructing a nonlinear double-power sliding surface and a double-power reaching law, specifically as follows:

[0024] in: ,

[0025]

[0026]

[0027] This is a sideslip angle command. This is the roll angle command. To track errors, For nonlinear sliding surface variables, This is a double power-order approach law. The output of the observer; For sliding surface gain, ; The power exponent of the nonlinear sliding surface. , ; The gain is the double-power-order approaching term. ; and The power exponent. , ; The sign function representing the nonlinear sliding mode variable. This represents the gain of the isokinetic reaching law. .

[0028] Furthermore, in order to avoid , In this case, the control law of the fixed-time controller is:

[0029] in The variable representing the control of sliding surface switching is defined as:

[0030] and To describe the error The size boundary, and .

[0031] Furthermore, nonlinear sliding surface variables It is stable over a fixed time and has an upper bound on its convergence time. ,and Regardless of the initial value of the Lyapunov function:

[0032] Furthermore, when At that time, it exists that:

[0033] Error It is stable over a fixed time and has an upper bound on its convergence time. and Regardless of the initial value of the state error:

[0034] The tracking error of the entire controller will then be within a fixed time. It converges to zero, and the convergence time is independent of the initial state.

[0035] A fixed-time lateral coupling suppression method employs a weighted fixed-time lateral coupling suppression system, comprising: The yaw rate and roll rate output by the inertial measurement unit, as well as the yaw angle and roll angle output by the navigation system, are collected. Based on the lateral coupled fixed-point dynamics model of the aircraft, the state variables of the system are obtained. Based on the state variables and the output of the fixed-time controller, the fixed-time extended state observer estimates the external disturbances experienced by the system and outputs the lumped disturbance observation results that converge in a fixed time. By feedforward compensation of lumped interference observation results, the interference suppression capability of the aircraft can be improved; The sideslip angle and roll angle commands calculated by the acquisition and guidance system are combined with the yaw angle and roll angle output by the navigation system. A fixed-time controller is used to make the tracking error of the control system state variables converge within a fixed time. Then, combined with the results after feedforward compensation, the obtained yaw channel rudder deflection angle and roll channel rudder deflection angle are applied to the actuator.

[0036] The advantages of this invention compared to the prior art are: (1) Based on the second-order lateral coupling dynamics model, this invention constructs a high-order fixed-time extended state observer, which can quickly and accurately estimate the lumped disturbances caused by system uncertainties and external disturbances; the controller realizes feedforward compensation for the lumped disturbances, thereby improving the robustness and disturbance suppression capability of the aircraft.

[0037] (2) The controller designed in this invention can ensure that the control system converges within a certain time, and the upper bound of the convergence time is independent of the initial state of the system, thereby effectively improving the response speed of the control system.

[0038] (3) This invention addresses the problem of control law singularity by designing a boundary layer to achieve continuous transformation of the control law and sliding surface, thus ensuring that the controller is non-singular. Attached Figure Description

[0039] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a schematic diagram of the aircraft control system structure of the present invention; Figure 2 This is a simulation diagram of the disturbances and observed values ​​experienced by the yaw and roll channels of the aircraft in this embodiment of the invention. Figure 3 This is a simulation diagram of the sliding surface parameters of the yaw and roll channel of the aircraft in an embodiment of the present invention; Figure 4 This is a simulation diagram of the attitude angle response of the aircraft using the PID channel independent design and the control force yaw and roll channel of the present invention in the embodiment of the present invention; Figure 5 This is a simulation diagram of the attitude angular velocity changes of the aircraft using the PID channel independent design and the control force yaw and roll channel of the present invention in an embodiment of the invention; Figure 6 This is a simulation diagram of the aircraft using PID channel independent design and the control force yaw and roll channel rudder commands of the present invention in an embodiment of the present invention. Detailed Implementation

[0040] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0041] This invention proposes a fixed-time lateral coupling suppression system, comprising a fixed-point dynamic model of lateral coupling of an aircraft, a fixed-time extended state observer, and a fixed-time controller.

[0042] (1) Lateral Coupled Fixed-Point Dynamics Model of the Aircraft Sideslip turning aircraft generate lateral acceleration by establishing sideslip angle and angle of attack, often completing omnidirectional maneuvers quickly without adjusting roll attitude. Lateral coupling often occurs between the normal channel and the roll channel of the main lift, therefore a coupled dynamic model between these two channels needs to be established.

[0043] Based on the structural information of the aircraft, such as the moment of inertia, mass, characteristic length, and characteristic area of ​​each axis about its center of mass, as well as information on aerodynamic forces, thrust, angle of attack, and dynamic pressure output by the navigation system, the dynamic coefficients in the lateral coupled dynamic model of the aircraft are calculated. Combining the sideslip angle, pitch angle, roll angle, velocity, and local gravitational acceleration output by the navigation system, the following lateral coupled fixed-point dynamic model of the aircraft under disturbance is constructed: (1) in, The pitch angle, It is the acceleration due to gravity. For flight speed, For the angle of attack, Sideslip angle, For roll angle; for The first derivative with respect to time for The first derivative with respect to time; Yaw angular velocity, for The first derivative with respect to time; For the roll angular velocity, for The first derivative with respect to time; The rudder deflection angle for the yaw channel. This refers to the rudder deflection angle in the roll channel; The yaw channel dynamic coefficient, This represents the dynamic coefficient for the roll channel. Since the contribution of the rudder to the derivative of the sideslip angle is often small, it can be neglected. . This represents the unknown interference amount in the yaw channel. This represents the unknown interference amount in the roll channel.

[0044] Assumption and Both are continuous and bounded disturbances; both are differentiable and their first derivatives are also bounded. , , , ,in This represents the upper limit of the absolute value of the interference. This represents the upper limit of the absolute value of the first derivative of the disturbance. , All numbers must be positive integers. Let , , Then the original controlled object model can be rewritten as: (2) in, ,

[0045]

[0046]

[0047]

[0048]

[0049] .

[0050] It should be noted that, strictly speaking, for the system state equation (2), and This is not the state of the system. However, regarding the missile itself, the angular velocity is a value directly measured by the inertial measurement unit, therefore it can be... and State variables in Replaced with angular velocity value.

[0051] From the above, it can be seen that when hour, It is a non-singular matrix.

[0052] The goal of control is to manage bounded disturbances whose derivatives are bounded. and Under this effect, the coupling effect between different channels in the lateral direction is suppressed, thereby improving the quality of the control system.

[0053] (2) Fixed-time extended state observer For the system state equation (2), the uncertainties in the system parameters and external disturbances are considered as a lumped disturbance and treated as the extended state of the system. Based on the system's input and output data, the unmeasurable disturbance signal is estimated online. Based on fixed-time control theory, a fixed-time extended state observer is designed to observe this lumped disturbance to ensure that the observation error of the disturbance converges to zero within a fixed time.

[0054] The design of a fixed-time extended state observer is shown below: (3) in, , and Let be the state variables of the observer, where System status The observed values, System status The observed values, In an expanding state The observed values, This is the output of the observer. for The first derivative with respect to time System status The observation error, For the observer switching item; , , , For observer gain; Its power exponent Take values ​​respectively ,in This is a symbolic function. In By adding the first term to the formula, the stability of the system can be further guaranteed and the convergence speed of the observer can be improved.

[0055] Design parameters for a fixed-time extended state observer: For the fixed-time extended state observer as shown in formula (3), the corresponding parameters are designed as follows: power exponent and Value requirements , Observer gain requirements , power exponent , , , Values , , , . This is the observer switching option, and its value is either 0 or 1. Its values ​​are: (4) in It is a time constant, determined based on actual working conditions.

[0056] By designing the above observer and its parameters, the state of the system under observation can be made to converge to the origin within an upper bound time, which is independent of the initial state of the observation error.

[0057] (3) Fixed time controller Design a fixed-time controller based on the observer output: 1) Acquire the yaw rate output from the inertial measurement unit. and roll angular velocity and the sideslip angle calculated by the navigation system. and roll angle These constitute the state variables of the system; the sideslip angle command calculated by the acquisition and guidance system is also included. and roll angle command These constitute the expected instructions of the system.

[0058] 2) Define the tracking error as follows: (5) Calculate the first and second derivatives of the error: , ,in and These are the first and second derivatives of the yaw angle command, respectively. and These are the first and second derivatives of the roll angle command, respectively. and These are the second derivatives of the yaw angle and the roll angle, respectively.

[0059] 3) Based on the error and its derivative, design a sliding mode control method, where the nonlinear sliding surface is shown below: (6) in, For nonlinear sliding surface gain, ; For a nonlinear sliding surface, the power exponent is required. , Taking its derivative, we get: (7) 4) Assume the observer's output satisfies , This is the upper bound of the absolute value of the observation error. The double power-order reaching law is designed as follows: (8) in, For the gain of the double power-approaching term, it is required that ; and To represent the power exponent, it is required that... , ; To express the gain of the isotropic reaching law, we need to... Based on the observer's output, the controller is designed as follows: (9) 5) Define the Lyapunov function: (10) Substituting formula (9) into the equation, the first derivative of the above equation is: (11) because Therefore, (12) Note that the design should be based on the aforementioned parameters. , Based on the fixed-time stability theory, the sliding surface variable... It is stable over a fixed time and has an upper bound on its convergence time. ,and It is independent of the initial value of the Lyapunov function.

[0060] (13) when At that time, it can be seen from formula (6) that, (14) Therefore, the error amount It is stable over a fixed time and has an upper bound on its convergence time. and It is independent of the initial value of the state error.

[0061] (15) Therefore, the tracking error of the entire controller will be within a fixed time. It converges to zero, and the convergence time is independent of the initial state.

[0062] 6) To avoid in , At this point, a singularity problem will occur in the control law, therefore the control law is modified as follows: (16) in The variable representing the control of sliding surface switching is defined as: (17) in and To describe the error Size boundaries, requirements , The value is determined according to the actual working conditions.

[0063] Fixed-time lateral coupling suppression methods, such as Figure 1 As shown, a lateral coupled fixed-point dynamic model of the aforementioned aircraft is first established. The system's state variables are obtained by acquiring the yaw and roll angular velocities output from the inertial measurement unit, as well as the sideslip and roll angles calculated by navigation. Based on these state variables and the controller output, a high-order extended state observer is designed to estimate the external disturbances experienced by the system. The system's state variables are then analyzed using the fixed-time convergent lumped disturbance observation results from the observer output. Perform feedforward compensation to improve the aircraft's interference suppression capability. Acquire the sideslip angle command calculated by the guidance system. and roll angle command By combining the state variables output by the navigation system, a nonlinear sliding surface and a double power-law approaching law are designed to form a fixed-time controller, which ensures that the tracking error of the control system's state variables converges within a fixed time.

[0064] like Figure 2 The present invention provides simulation curves of the estimated value of the disturbance and the actual value of the disturbance by the fixed-time extended state observer when disturbance is added to the yaw channel and the roll channel in the embodiment of the present invention. The curves show that the estimated value of the observer can converge to the actual value within a fixed time.

[0065] like Figure 3 Simulation curves of the sliding mode variables of the yaw and roll channels of the aircraft in the embodiments of the present invention are given. The curves show that the fixed-time controller can ensure that the system sliding surface converges to zero.

[0066] like Figure 4 The paper presents the attitude angle response curves of the yaw and roll channels of the aircraft when the PID channel independent design is adopted and the control method of the present invention is adopted. The curves show that the aircraft in the embodiment of the present invention responds to attitude angle commands faster and the roll angle overshoot is significantly reduced compared with the PID channel independent design, and the state tracking error converges to zero.

[0067] like Figure 5 The paper presents the attitude angular velocity response curves of the yaw and roll channels of the aircraft when the PID channel is independently designed and the control of the present invention is adopted. The curves show that the number of angular velocity oscillations in the embodiment of the present invention is less than that in the PID channel independently designed.

[0068] like Figure 6 The paper presents the yaw and roll rudder command curves of the aircraft using the PID channel independent design and the control of the present invention in the embodiment of the invention. The curves show that the rudder commands output by the embodiment of the present invention are more stable than those of the PID channel independent design.

[0069] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A fixed-time lateral coupling suppression system, characterized in that, This includes a lateral coupled fixed-point dynamics model of the aircraft, a fixed-time extended state observer, and a fixed-time controller; The lateral coupling fixed-point dynamics model of the aircraft collects the yaw angle and roll angle, as well as the yaw angular velocity and roll angular velocity output by the navigation system as the state, and collects the yaw channel rudder deflection angle and roll channel rudder deflection angle output by the fixed-time controller as the input. It combines the power coefficient gain matrix and the disturbance matrix to construct a state-space representation of the controlled object model, and transforms it into a standard second-order nonlinear control model. The fixed-time extended state observer treats the unknown disturbance quantities of the yaw channel and the unknown disturbance quantities of the roll channel in the system state equation as lumped disturbances and as extended states. Based on the sideslip angle, roll angle, yaw rate, and roll rate obtained from the aircraft's lateral coupled fixed-point dynamic model, it outputs the observed values ​​of the extended states, so that the observation error of the lumped disturbances converges to zero within a fixed time. The fixed-time controller takes the sideslip angle command and sideslip angle error, and the roll angle command and roll angle error as inputs, and takes the yaw channel rudder deflection angle and the roll channel rudder deflection angle as outputs, so that the tracking error of the attitude angle to the control command converges to zero within a fixed time.

2. The fixed-time lateral coupling suppression system according to claim 1, characterized in that, The lateral coupled fixed-point dynamics model of the aircraft is as follows: in, The pitch angle, It is the acceleration due to gravity. For flight speed, For the angle of attack, Sideslip angle, For roll angle, for The first derivative with respect to time for The first derivative with respect to time; Yaw angular velocity, for The first derivative with respect to time; For the roll angular velocity, for The first derivative with respect to time; The rudder deflection angle for the yaw channel. This refers to the rudder deflection angle in the roll channel; The yaw channel dynamic coefficient, The dynamic coefficient of the roll channel; This represents the unknown interference amount in the yaw channel. This represents the unknown interference amount in the roll channel.

3. The fixed-time lateral coupling suppression system according to claim 2, characterized in that, The system state equation is: in, , , ; 。 4. The fixed-time lateral coupling suppression system according to claim 3, characterized in that, The fixed-time extended state observer is: in, , and For the state variables of the observer, System status The observed values, System status The observed values, In an expanding state The observed values, The output of the observer; , and They are respectively , and The first derivative with respect to time System status The observation error, For the observer's switching option; , , , For observer gain; power exponent Pick , , , , , , It is a symbolic function.

5. A fixed-time lateral coupling suppression system according to claim 4, characterized in that, Power exponent in a fixed-time extended state observer , The value can be: ， Observer gain requirements , , Unknown interference in the yaw channel Unknown interference in the roll channel Upper limit of the absolute value after differentiation; Power index , , , The value can be: , , , , , It is a time constant. .

6. A fixed-time lateral coupling suppression system according to claim 4, characterized in that, The fixed-time controller is obtained by constructing a nonlinear double-power sliding surface and a double-power reaching law, specifically as follows: in: ， This is a sideslip angle command. This is the roll angle command. To track errors, For nonlinear sliding surface variables, This is a double power-order approach law. The output of the observer; For sliding surface gain, ; The power exponent of the nonlinear sliding surface. , ; The gain is the double-power-order approaching term. ; and The power exponent, , ; The sign function representing the nonlinear sliding mode variable. This represents the gain of the constant-rate reaching law. .

7. A fixed-time lateral coupling suppression system according to claim 6, characterized in that, To avoid , In this case, the control law of the fixed-time controller is: in The variable representing the control of sliding surface switching is defined as: and To describe the error The size boundary, and .

8. A fixed-time lateral coupling suppression system according to claim 7, characterized in that, Nonlinear sliding surface variables It is stable over a fixed time and has an upper bound on its convergence time. ,and Regardless of the initial value of the Lyapunov function: 。 9. A fixed-time lateral coupling suppression system according to claim 8, characterized in that, when At that time, it exists that: Error It is stable over a fixed time and has an upper bound on its convergence time. and Regardless of the initial value of the state error: The tracking error of the entire controller will then be within a fixed time. It converges to zero, and the convergence time is independent of the initial state.

10. A fixed-time lateral coupling suppression method, employing the fixed-time lateral coupling suppression system of claim 1, characterized in that, include: The yaw rate and roll rate output by the inertial measurement unit, as well as the yaw angle and roll angle output by the navigation system, are collected. Based on the lateral coupled fixed-point dynamics model of the aircraft, the state variables of the system are obtained. Based on the state variables and the output of the fixed-time controller, the fixed-time extended state observer estimates the external disturbances experienced by the system and outputs the lumped disturbance observation results that converge in a fixed time. By feedforward compensation of lumped interference observation results, the interference suppression capability of the aircraft can be improved; The sideslip angle and roll angle commands calculated by the acquisition and guidance system are combined with the yaw angle and roll angle output by the navigation system. A fixed-time controller is used to make the tracking error of the control system state variables converge within a fixed time. Then, combined with the results after feedforward compensation, the obtained yaw channel rudder deflection angle and roll channel rudder deflection angle are applied to the actuator.

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