A method for controlling the tilting motion of an aircraft with predetermined time convergence

Abstract

The application belongs to the technical field of aircraft control. The application provides a predetermined time convergence aircraft tilt motion control method. The predetermined time scale function is combined with the sliding mode control in the embodiment of the disclosure, so that the convergence time setting is not dependent on the initial condition and is easy to parameterize, the tilt angle and the tilt angle velocity can converge within the predetermined convergence time, the predetermined time convergence performance and the robustness are good, and the aircraft tilt motion system can be quickly and stably guaranteed. The method is easy to be applied to the aircraft tilt motion stable control under different conditions.

Description

TECHNICAL FIELD

[0001] Embodiments of the present disclosure relate to the technical field of aircraft control, and particularly relate to a pre-determined time convergent aircraft tilt motion control method. BACKGROUND

[0002] Tilt motion stability is crucial for flight stability and maneuverability. By adjusting the tilt angle, precise control of the aircraft attitude can be achieved, enabling it to maintain a stable attitude when performing various flight tasks. For axisymmetric aircraft using Cartesian coordinate control method, tilt motion stability is crucial: on the one hand, the change of tilt angle velocity will cause cross coupling between pitch, yaw and tilt channels, resulting in reduced control efficiency, and even causing uncontrollable high-speed rolling; on the other hand, tilt motion may cause inconsistency in the coordinate system during guidance, causing pitch and yaw channel guidance signals to be disordered, reducing guidance accuracy and affecting flight tasks.

[0003] In summary, fast, stable and robust tilt motion control is an important guarantee for stable flight of the aircraft. However, to achieve fast tilt motion stability control, the traditional control method needs to obtain the desired effect through repeated adjustment of the control parameters.

[0004] Therefore, it is necessary to improve one or more problems in the related technical solutions described above.

[0005] It should be noted that this section aims to provide background or context for the technical solutions of the present disclosure stated in the claims. The description herein is not admitted to be prior art merely because it is included in this section. SUMMARY

[0006] The purpose of the embodiments of the present disclosure is to provide a pre-determined time convergent aircraft tilt motion control method, thereby at least partially overcoming one or more problems caused by the limitations and defects of the related art.

[0007] According to the embodiments of the present disclosure, a pre-determined time convergent aircraft tilt motion control method is provided, which comprises:

[0008] According to the kinematic equation of the aircraft, a small perturbation linearization model of the tilt motion of the aircraft is established;

[0009] According to the small perturbation linearization model of the tilt motion of the aircraft, an aircraft tilt motion system model is established;

[0010] A first predetermined time scale function of the sliding mode convergence section and a second predetermined time scale function of the error convergence section are constructed;

[0011] Based on the aircraft tilt motion system model, the first predetermined time scale function, and the second predetermined time scale function, a predetermined time sliding mode controller is designed.

[0012] The tilting motion of the aircraft is controlled using the predetermined time sliding mode controller.

[0013] Furthermore, the steps for establishing a linearized model of the aircraft's tilt motion with small perturbations, based on the aircraft's kinematic equations, include:

[0014] The kinematic equations of the aircraft are decoupled to obtain a linearized model of the aircraft's tilt motion with small perturbations.

[0015] Furthermore, the expression for the linearized model of the aircraft's tilt motion with small perturbations is as follows:

[0016]

[0017] in, The angle of inclination. for The differential, The tilt angular velocity, for The differential, For rudder deflection, The aerodynamic damping coefficient of the aircraft. For the aileron efficiency of the aircraft.

[0018] Furthermore, the expression for the aircraft tilting motion system model is as follows:

[0019]

[0020] Among them, the first state quantity , For the desired tilt angle, for The differential, the second state quantity , for The derivative, control quantity .

[0021] Furthermore, the expression for the first predetermined time scale function is:

[0022]

[0023] in, For the convergence time of the sliding mode convergence segment, To control startup time, For the desired sliding mode convergence time, For time gain;

[0024] The expression of the second predetermined time scale function is:

[0025]

[0026] wherein, is the expected error convergence time, is the error convergence segment convergence time.

[0027] Further, according to the aircraft tilting motion system model, the first predetermined time scale function and the second predetermined time scale function, in the step of designing a predetermined time sliding mode controller, comprising:

[0028] designing a predetermined time sliding mode surface according to the second predetermined time scale function;

[0029] designing a predetermined time sliding mode reaching law according to the first predetermined time scale function;

[0030] designing the predetermined time sliding mode controller according to the aircraft tilting motion system model, the predetermined time sliding mode surface and the predetermined time sliding mode reaching law.

[0031] Further, the expression of the predetermined time sliding mode surface is:

[0032]

[0033] wherein, is a first control parameter, is a second control parameter, and , , , is the differential of .

[0034] The expression of the predetermined time sliding mode reaching law is:

[0035]

[0036] wherein, is a third control parameter, is a fourth control parameter, is a fifth control parameter, is a sixth control parameter, , , , , , is the differential of .

[0037] The expression of the predetermined time sliding mode controller is:

[0038]

[0039] wherein, .

[0040] The technical scheme provided by the embodiments of the present disclosure can include the following beneficial effects:

[0041] In the embodiments of the present disclosure, by using the above-mentioned aircraft tilt motion control method with predetermined time convergence, on the one hand, the predetermined time scale function is combined with the sliding mode control, so that the convergence time setting is not dependent on the initial conditions and is easy to parameterize, the tilt angle and the tilt angle velocity can converge within the predetermined convergence time, and the method has good predetermined time convergence performance and robustness, and can ensure the rapid stability of the aircraft tilt motion system. On the other hand, the method is easy to apply to the tilt motion stability control of the aircraft under different conditions. BRIEF DESCRIPTION OF DRAWINGS

[0042] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate embodiments consistent with the present disclosure and, together with the description, further serve to explain the principles of the present disclosure. It is to be understood that the drawings are designed solely for purposes of illustration to be used in conjunction with the description. It is to be understood that the drawings are designed solely for purposes of illustration and are not intended to limit the scope of the disclosure in any way.

[0043] Figure 1 A step diagram of a predetermined time convergence aircraft tilt motion control method in an exemplary embodiment of the present disclosure is shown;

[0044] Figure 2 A structure diagram of a predetermined time sliding mode controller based aircraft tilt motion stability control in an exemplary embodiment of the present disclosure is shown;

[0045] Figure 3 A tilt angle change curve in an exemplary embodiment of the present disclosure is shown;

[0046] Figure 4 A tilt angle velocity change curve in an exemplary embodiment of the present disclosure is shown;

[0047] Figure 5 A rudder deflection angle change curve in an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0048] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the implementations set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the inventive concept to those skilled in the art. The described features, structures, or characteristics can be combined in one or more implementations.

[0049] In addition, the accompanying drawings are merely schematic and are not intended to be drawn to scale. Identical reference numerals denote like or similar parts throughout the several views, so that repeated description is omitted. Some of the block diagrams shown in the drawings are functional entities, which do not necessarily correspond to physically or logically independent entities.

[0050] A predetermined time convergent aircraft tilting motion control method is provided in the example embodiment. Referring to FIG. 1, the predetermined time convergent aircraft tilting motion control method can include steps S101-S105. Figure 1

[0051] Step S101: establishing an aircraft tilting motion small perturbation linearization model according to an aircraft kinematics equation;

[0052] Step S102: establishing an aircraft tilting motion system model according to the aircraft tilting motion small perturbation linearization model;

[0053] Step S103: constructing a first predetermined time scale function of a sliding mode convergence section and a second predetermined time scale function of an error convergence section;

[0054] Step S104: designing a predetermined time sliding mode controller according to the aircraft tilting motion system model, the first predetermined time scale function and the second predetermined time scale function;

[0055] Step S105: controlling the tilting motion of the aircraft by using the predetermined time sliding mode controller.

[0056] By the above-described predetermined time convergent aircraft tilting motion control method, on the one hand, the predetermined time scale function is combined with the sliding mode control, so that the convergence time setting is not dependent on the initial conditions and is easy to parameterize, the tilting angle and the tilting angular velocity can converge within a predetermined convergence time, and the predetermined time convergence performance and robustness are good, so that the aircraft tilting motion system can be quickly and stably guaranteed. On the other hand, the method is easy to apply to the aircraft tilting motion stable control under different conditions.

[0057] In the following, the steps of the above-described predetermined time convergent aircraft tilting motion control method in the example embodiment will be described in more detail. Figures 1 to 5

[0058] In step S101, an aircraft tilting motion small perturbation linearization model is established according to an aircraft kinematics equation.

[0059] Specifically, the axisymmetric aircraft kinematics equation is decoupled to obtain the aircraft tilting motion small perturbation linearization model: ​​

[0060] (1)

[0061] wherein, is the tilt angle, is the tilt angle velocity, is the rudder angle, the power coefficient is the air vehicle aerodynamic damping coefficient, is the air vehicle aileron efficiency.

[0062] In step S102, the air vehicle tilt motion system model is established according to the air vehicle tilt motion small perturbation linearization model.

[0063] Specifically, the air vehicle tilt motion system model is further established according to the air vehicle tilt motion small perturbation linearization model, and the expected tilt angle is , the state quantity , , the control quantity , and the air vehicle tilt motion system model is as follows:

[0064] (2)

[0065] In step S103, the first predetermined time scale function of the sliding mode convergence section and the second predetermined time scale function of the error convergence section are constructed.

[0066] The two-section predetermined time scale function is constructed, and the predetermined time gain needs to satisfy .

[0067] Specifically, the first stage is the sliding mode convergence section. is the control start time, is the expected sliding mode convergence time, is the sliding mode convergence section convergence time, and the predetermined time scale function is designed as:

[0068] (3)

[0069] The second stage is the error convergence section. is the expected error convergence time, is the error convergence section convergence time, and the predetermined time scale function is designed as:

[0070] (4)

[0071] Let , , for a continuously differentiable function if it satisfies

[0072] (5)

[0073] wherein , the first stage , , the second stage , .

[0074] for any

[0075] (6)

[0076] then:

[0077] (7)

[0078] therefore,

[0079] (8)

[0080] that is:

[0081] (9)

[0082] guaranteeing the predetermined time adjustment to the current stage.

[0083] In step S104, a predetermined time sliding mode controller is designed according to the aircraft tilting movement system model, the first predetermined time scale function and the second predetermined time scale function.

[0084] Specifically, the predetermined time sliding mode controller is designed, and control parameters are set , , , , , , and the predetermined time stability of the controller is analyzed.

[0085] Firstly, a predetermined time sliding mode surface is established:

[0086] (10)

[0087] Secondly, a predetermined time sliding mode reaching law is designed:

[0088] (11)

[0089] The predetermined time sliding mode controller is expressed as follows:

[0090] (12)

[0091] The predetermined time stability of the predetermined time sliding mode controller is analyzed, and a function of the sliding mode convergence section is constructed:

[0092] (13)

[0093] Taking derivative, we have:

[0094] (14)

[0095] That is, the system can converge to the sliding mode surface at the predetermined time, and at this time, the condition is satisfied: That is:

[0096] (15)

[0097] The function of the error convergence segment is constructed as:

[0098] (16)

[0099] Taking derivative, we have:

[0100] (17)

[0101] That is, the system error can converge to 0 at the predetermined time, the aircraft tilt angle can converge as expected, and the aircraft tilt motion is stable.

[0102] In step S105, the tilt motion of the aircraft is controlled by using the predetermined time sliding mode controller.

[0103] Specifically, the predetermined time sliding mode controller is designed and brought into the aircraft tilt motion system, the rudder deflection angle command is generated according to the tilt angle and the tilt angle velocity measured and fed back by the inertial component, and the actuator changes the attitude of the aircraft according to the command to realize stable control.

[0104] In one specific embodiment, the kinematics equation of the decoupled axisymmetric aircraft is solved to obtain a small perturbation linearization model of the tilt motion of the aircraft:

[0105] (1)

[0106] wherein the current tilt angle is , the tilt angle velocity is , the rudder deflection angle is , the aerodynamic damping coefficient of the tilt direction of the aircraft , and the aileron efficiency of the aircraft .

[0107] According to the small perturbation linearization model of the tilt motion of the aircraft, a tilt motion system model of the aircraft is established.

[0108] ​​Specifically, the aircraft tilting motion system model is further established according to a small perturbation linearization model of the aircraft tilting motion, and the desired tilting angle is , the state variable is , , the control variable is , and the aircraft tilting motion system model is as follows:

[0109] (2)

[0110] To ensure system stability, the desired tilting angle is , and .

[0111] Two predetermined time scale functions are constructed, and the predetermined time gain =4.

[0112] The first stage is the sliding mode convergence stage. is the control start time, is the desired sliding mode convergence time, is the sliding mode convergence stage convergence time, and the values of 1.5s, 1.0s and 0.5s are taken respectively, and the predetermined time scale function is designed as:

[0113] (3)

[0114] The second stage is the error convergence stage. is the desired error convergence time, is the error convergence stage convergence time, and the values of 0.5s, 1.0s and 0.5s are taken respectively, and the predetermined time scale function is designed as:

[0115] (4)

[0116] Let , , for a continuously differentiable function , if the following conditions are met:

[0117] (5)

[0118] where , the first stage , , the second stage , .

[0119] For any

[0120] (6)

[0121] then:

[0122] (7)

[0123] Therefore,

[0124] (8)

[0125] That is,

[0126] (9)

[0127] The predetermined time adjustment to the current stage can be ensured.

[0128] The predetermined time sliding mode controller is designed, and the control parameters are set , , , , , The predetermined time stability of the controller is analyzed.

[0129] Firstly, the predetermined time sliding mode surface is established:

[0130] (10)

[0131] Secondly, the predetermined time sliding mode reaching law is designed:

[0132] (11)

[0133] The predetermined time sliding mode controller is represented as follows:

[0134] (12)

[0135] The predetermined time stability of the predetermined time sliding mode controller is analyzed, and the function of the sliding mode convergence section is constructed:

[0136] (13)

[0137] Derivation is as follows:

[0138] (14)

[0139] That is, the system can converge to the sliding mode surface according to the predetermined time at , at which time is satisfied, that is:

[0140] (15)

[0141] The function of the error convergence section is constructed:

[0142] (16)

[0143] Derivation is as follows:

[0144] (17)

[0145] That is, the system error can be resolved within a predetermined time. When the tilt angle converges to 0, the tilt angle of the aircraft can converge as expected, and the tilt motion of the aircraft is stable.

[0146] like Figure 2 The diagram shows the structure of a vehicle tilt motion stabilization control system based on a predetermined time sliding mode controller. By incorporating the designed predetermined time sliding mode controller into the vehicle's tilt motion system, a rudder deflection command is generated based on the tilt angle and tilt angular velocity measured and fed back by the inertial components. The actuators then change the vehicle's attitude according to the command, achieving stable control.

[0147] In one specific embodiment, algorithm simulation is performed to verify the effectiveness of this application.

[0148] Figures 3 to 5 The black dashed line in the middle represents , The simulation results are shown in black lines. , The simulation results are shown in black dashed lines. , The simulation results.

[0149] Figure 3 The curve shows the change in tilt angle. Simulation results show that, under the predetermined time convergence aircraft tilt motion control method of this application, the predetermined time... and Both can be preset, and the tilt angle can converge at the desired predetermined time. , and , Both simulations were in Convergence , Simulation can be Time convergence, meaning this method guarantees that the tilt angle from Fast convergence to This enables stable control of the aircraft's tilting motion.

[0150] Figure 4 The curve shows the change in tilt angular velocity. Simulation results show that, under the predetermined time convergence aircraft tilt motion control method of this application, the predetermined time... and Both can be preset, and the tilt angular velocity can converge according to the desired predetermined time. , and , Both simulations were in Convergence , Simulation can be Convergence occurs when the tilt angular velocity is less than 100°C throughout the entire process. This method ensures rapid convergence of the tilt angular velocity, thereby achieving stable control of the aircraft's tilt motion.

[0151] Figure 5 The curve shows the change in the rudder deflection angle. Simulation results show that, under the aircraft tilt motion control method with predetermined convergence time proposed in this application, the rudder deflection angle remains constant throughout the entire trajectory. Within a certain range, the tilt angle can be effectively controlled, achieving stable control of the aircraft's tilting motion.

[0152] The aforementioned aircraft tilt motion control method with predetermined time convergence achieves two advantages. First, by combining a predetermined time scale function with sliding mode control, the convergence time setting becomes independent of initial conditions and is easy to tune parameters. The tilt angle and tilt angular velocity converge within the predetermined convergence time, exhibiting excellent predetermined time convergence performance and robustness, thus ensuring rapid stabilization of the aircraft tilt motion system. Second, this method is easily applicable to the stable control of aircraft tilt motion under different conditions.

[0153] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0154] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0155] Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the features disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.

Claims

1. A method for controlling the tilt motion of an aircraft with convergence over a predetermined time, characterized in that, The method includes: Based on the kinematic equations of the aircraft, a linearized model of the aircraft's tilt motion with small perturbations is established; Based on the linearized model of small disturbances in the tilt motion of the aircraft, a model of the tilt motion system of the aircraft is established. Construct a first predetermined time scale function for the sliding mode convergence segment and a second predetermined time scale function for the error convergence segment; Based on the aircraft tilting motion system model, the first predetermined time scale function, and the second predetermined time scale function, a predetermined time sliding mode controller is designed; specifically, the step of designing the predetermined time sliding mode controller based on the aircraft tilting motion system model, the first predetermined time scale function, and the second predetermined time scale function includes: Design a predetermined time sliding surface based on the second predetermined time scale function; Based on the first predetermined time scale function, design a predetermined time sliding mode approach law; Based on the aircraft tilt motion system model, the predetermined time sliding surface, and the predetermined time sliding mode approach law, the predetermined time sliding mode controller is designed. The tilting motion of the aircraft is controlled using the predetermined time sliding mode controller; wherein... The expression for the first predetermined time scale function is: in, For the convergence time of the sliding mode convergence segment, To control startup time, For the desired sliding mode convergence time, For time gain; The expression for the second predetermined time scale function is: in, Let the expected error convergence time be... The time required for the convergence of the error convergence segment; The expression for the predetermined time sliding surface is: in, This is the first state variable. For the second state quantity, The first control parameter, It is the second control parameter, and , , , for The differential; The expression for the predetermined time sliding mode reaching law is: in, This is the third control parameter. This is the fourth control parameter. This is the fifth control parameter. This is the sixth control parameter. , , , , , for The differential; The expression for the predetermined time sliding mode controller is: in, For symbolic functions, The aerodynamic damping coefficient of the aircraft. For the aileron efficiency of the aircraft.

2. The aircraft tilt motion control method with predetermined time convergence according to claim 1, characterized in that, The steps for establishing a linearized model of the aircraft's tilt motion with small perturbations, based on the aircraft's kinematic equations, include: The kinematic equations of the aircraft are decoupled to obtain a linearized model of the aircraft's tilt motion with small perturbations.

3. The aircraft tilt motion control method with predetermined time convergence according to claim 2, characterized in that, The expression for the linearized model of the aircraft's tilt motion with small perturbations is as follows: in, The angle of inclination. for The differential, The tilt angular velocity, for The differential, For rudder deflection, The aerodynamic damping coefficient of the aircraft. For the aileron efficiency of the aircraft.

4. The aircraft tilt motion control method with predetermined time convergence according to claim 3, characterized in that, The expression for the aircraft tilting motion system model is as follows: Among them, the first state quantity , For the desired tilt angle, for The differential, the second state quantity , for The derivative, control quantity .

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