Fuzzy adaptive sliding mode control method and system suitable for satellite flexible solar wing system

Abstract

The invention discloses a fuzzy adaptive sliding mode control method and system suitable for a satellite flexible solar wing system, and belongs to the technical field of spacecraft control. Aiming at the nonlinear vibration problem caused by structural flexibility, joint gaps and abrasion of a satellite flexible solar wing and the defects of poor trajectory tracking precision and the like caused by insufficient robustness, obvious buffeting and insufficient adaptive capacity of an existing control method, the method comprises the following steps of: constructing a nonlinear dynamic model for accurately representing complex dynamic characteristics of a system; and designing a fuzzy adaptive sliding mode control method to realize high-precision control of the attitude of the flexible solar wing. The method has the strong robustness of sliding mode control and the dynamic adaptation capability of fuzzy self-adaption, the inherent defects of a traditional control method are effectively overcome, the system operation stability and control precision are improved, and technical support is provided for reliable control of spacecraft flexible components.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft control technology, specifically relating to a fuzzy adaptive sliding mode control method and system suitable for satellite flexible solar array systems. Background Technology

[0002] The flexible solar array of a satellite is a core energy supply component for on-orbit operation, and its operational stability and control precision directly determine the satellite's mission execution capability and service life. However, the highly flexible structural characteristics of the solar array make it prone to elastic vibration during movement. Furthermore, gaps inevitably exist at the joints due to manufacturing and assembly errors, long-term on-orbit wear, and other factors. This leads to joint collisions and friction during solar array movement, forming a complex coupled nonlinear characteristic of "flexible deformation - joint gaps - collision friction - wear." This coupling characteristic exacerbates vibration amplitude, increases trajectory tracking errors, severely affects satellite attitude stability, accelerates joint wear and flexible structural fatigue, and further reduces system reliability.

[0003] Existing control strategies for flexible solar panels on satellites all have significant shortcomings and are difficult to meet the comprehensive control requirements in complex coupled scenarios: Traditional PID control is simple in structure and easy to implement, but it has poor adaptability to nonlinear disturbances and cannot effectively suppress coupled vibrations; Simple sliding mode control can cope with certain nonlinear disturbances due to its strong robustness, but switching terms are prone to chattering, which exacerbates joint wear and structural vibration; Single fuzzy control does not require precise modeling, but its control performance depends on empirical rules, lacks dynamic adjustment capabilities, and is insufficiently adaptive; Traditional adaptive control can tune parameters online, but it is highly dependent on the model structure, has a lagging tuning speed, and is difficult to balance dynamic response and steady-state accuracy.

[0004] The core bottleneck of existing technologies lies in the failure to achieve deep synergy between vibration suppression, precision tracking, and adaptive adaptation. The inherent defects of each control method constrain each other, making it impossible to simultaneously meet the requirements for control accuracy, vibration suppression effect, and robustness. Therefore, it is urgent to design a fuzzy adaptive sliding mode control method with both strong robustness and dynamic adaptation capabilities to solve the problems of nonlinear vibration suppression and high-precision trajectory tracking of satellite flexible solar panels. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of insufficient nonlinear vibration, chattering suppression, and lack of adaptive capability in existing technologies for satellite flexible solar array systems, and to provide a fuzzy adaptive sliding mode control method and system suitable for satellite flexible solar array systems.

[0006] To achieve the above objectives, the present invention employs the following technical solution: On the one hand, this invention provides a fuzzy adaptive sliding mode control method and system suitable for satellite flexible solar array systems, including the following steps: Based on the flexible solar array of a satellite, a nonlinear dynamic model including joint clearance and wear is constructed; the kinematic and dynamic characteristics of the flexible solar array and joint components are comprehensively modeled, and the core control boundary of fuzzy adaptive sliding mode control is clarified. Based on a nonlinear dynamics model, a fuzzy adaptive sliding mode control method is designed. The method includes sliding mode surface design, equivalent control solution, fuzzy inference and adaptive gain tuning, forming a complete closed-loop control logic. Based on the fuzzy adaptive sliding mode control method, the joint position of the satellite's flexible solar array is tracked and controlled, dynamically suppressing nonlinear vibrations caused by the coupling between the gap and the flexible structure, and reducing trajectory tracking errors. The construction of the nonlinear dynamic model, which includes joint clearance and wear, specifically involves: Define the clearance vector as the bearing geometric center. r ob With the geometric center of the bushing r oj The difference eccentricity The gap size satisfies (1); in, R b For the bearing radius, R j Let the bushing radius be and the contact deformation be . The Lankarani-Nikravesh model was used to calculate the joint normal collision force. (2); in, K For contact stiffness, D For the damping term, The response coefficient is set to 0.9. The initial collision velocity at the point of collision, For penetration depth, For relative velocity, For normal force, , ; The tangential friction force is described based on the Stribeck model, and the expression is: (3); in, n =1.5 is the nonlinear coefficient. For contact deformation rate, The static friction coefficient is The coefficient of kinetic friction is . Stribeck speed threshold, It is an empirical constant. The coefficient of viscous friction is... The relative angular velocity of the joint; The total impact force is: (4); The joint wear process is described based on the Archard model, expressed as follows: (5); in, k The wear coefficient is... For normal force, h For wear depth, H Given the material hardness, the above formula quantifies the mapping relationship between joint wear depth, normal force, and sliding distance. An elastic dynamic model of the flexible solar array is established using the Absolute Nodal Coordinates (ANCF) method: Define the generalized coordinates of ANCF beam elements: (6); in, These are the absolute position coordinates of the ANCF link element nodes. The slope component of the absolute position of the beam element node in the global coordinate system; The element displacement field is described by the shape function S matrix: (7); The expression for elastic force is: (8); in, E For elastic modulus, For the strain at the corresponding point on the midline, A For cross-sectional area, Let the moment of inertia of the cross section be... The elongation of this unit ( ); By integrating the collision force model and the ANCF elastic dynamics model, a global nonlinear dynamic equation is established using the Lagrange equation: (9); in, and These are the mass matrix and stiffness matrix. For generalized coordinates, For generalized acceleration, Φ is the constraint matrix, Φ q Jacobian matrix of the constraint matrix, λ Lagrange multipliers For the generalized external force term, For collision force, This is the control force matrix.

[0007] Preferably, the fuzzy adaptive sliding mode control method is specifically as follows: Set trajectory tracking error ( (For the desired generalized coordinates), the sliding surface is defined as: (10); in, K p , K i , K d These are the positive definite proportional, integral, and differential gain matrices, respectively. The error derivative, The second derivative of the error; Differentiating with respect to the sliding surface, we get: (11); Fuzzy adaptive sliding mode control law is based on equivalent control and switching control Composition, the expression is: (12); Among them, the equivalent control torque for: (13); Adjustment terms for fuzzy adaptive sliding mode control The expression is: (14); in, For fuzzy control quantities, For adaptive gain; Fuzzy control quantity and The solution is obtained through fuzzy reasoning, with the reasoning input being... and The input and output are both divided into 7 fuzzy subsets (NB, NM, NS, Z, PS, PM, PB), and triangular membership functions are used, with the expression as follows: (15); in, a , b , c These represent the left boundary, center value, and right boundary of the fuzzy subset, respectively.

[0008] Preferably, it also includes a control system stability verification step, proving the asymptotic stability of the system based on Lyapunov stability theory: Define Lyapunov functions as follows: (16); Its derivative The following equation must be satisfied: (17); Further expansion yields: (18); When using sliding mode control It can be defined as: (19); in, This is the approach control gain related to the upper limit of uncertainty. It is a symbolic function; therefore This satisfies the negative definiteness requirement of the Lyapunov function.

[0009] Preferably, the contact deformation of the joint space δ Satisfy: When δ When the force is less than 0, the joint is in a separated state with no collision contact, and the total collision force is... =0; when δ When the value is ≥0, the joint is in a state of collision contact. δ The collision force is calculated according to the formula in claim 2, and the direction of the collision force is opposite to the direction of the eccentricity vector.

[0010] Preferably, the membership function overlap between fuzzy sliding mode control (FSMC) and fuzzy adaptive sliding mode control (FASMC) is 50%, which ensures a smooth transition of the output variable when the input signal changes continuously and avoids additional disturbances caused by sudden changes in the control quantity.

[0011] Preferably, the trajectory tracking control of the joint position and attitude of the satellite's flexible solar array is specifically implemented by: acquiring the generalized coordinates of the satellite's flexible solar array in real time through sensors. Generalized acceleration and joint impact force The signal, after being filtered, is input to the controller; based on the acquired generalized coordinates... With the preset expected generalized coordinates Calculate trajectory tracking error Error change rate and the second derivative of the error ;Will , Substitute into the sliding surface formula to calculate the sliding surface. and its rate of change ;Will , Input to the FSMC module, output fuzzy control quantity ;Will , Input to FASMC module, output adaptive gain ; Calculate equivalent control according to the formula With adjustment items The total control torque is obtained by superposition. ; to control the total torque The output is sent to the actuator to drive the satellite's flexible solar array to move along the desired trajectory, adaptively suppressing nonlinear vibrations caused by gaps and flexible coupling, and achieving high-precision trajectory tracking.

[0012] On the other hand, the present invention provides a fuzzy adaptive sliding mode control system for implementing the above method, comprising: Modeling module: Based on the satellite's flexible solar array, a nonlinear dynamic model is constructed, including joint clearance, collision force, friction force, and wear characteristics. The model covers the ANCF elastic dynamic model, the Lankarani-Nikravesh collision force model, the Stribeck friction force model, the Archard wear model, and the overall nonlinear dynamic equations of the system, and the control boundaries are clearly defined. Control Design Module: Based on the dynamic model output by the modeling module, the module completes the sliding surface design, equivalent control solution, FSMC module design, FASMC module design, and overall control logic integration, forming a closed-loop control structure for fuzzy adaptive sliding mode control, and clarifying the collaborative working logic of each module. Signal acquisition module: The sensor collects the rotation angle of the flexible solar panel in real time, and transmits it to the control calculation module after filtering. Control Calculation Module: Receives the output signal from the signal acquisition module, calculates the trajectory tracking error, sliding surface and its rate of change, and outputs the result through the FSMC and FASMC modules. and Calculate the total control torque according to the control logic; Execution module: Receives the control torque output from the control calculation module, drives the joint motor to move, realizes the attitude adjustment and trajectory tracking of the flexible solar array, and suppresses nonlinear vibration.

[0013] Compared with the prior art, the present invention has the following beneficial effects: This invention overcomes the shortcoming of existing technologies that do not fully consider the coupling characteristics of "flexible deformation-joint clearance-collision friction-wear" of satellite flexible solar arrays. By integrating the ANCF elastic dynamics model, the Lankarani-Nikravesh collision force model, the Stribeck friction force model, and the Archard wear model, a dynamic model that comprehensively characterizes the complex nonlinear characteristics of the system is constructed, providing a reliable foundation for precise control. Compared with the chattering defects of traditional sliding mode control, the rule-fixed problem of single fuzzy control, and the modeling dependence of traditional adaptive control, the FSMC and FASMC cooperative control structure designed in this invention... This invention, through fuzzy inference to dynamically adjust control quantities and adaptive gain to match error states in real time, retains the strong robustness of sliding mode control while effectively suppressing chattering, significantly improving trajectory tracking accuracy and vibration suppression. Simultaneously, by adjusting adaptive gain to reduce joint collision intensity, it alleviates joint wear, extends the on-orbit lifespan of the solar array, and the control method has a clear structure, is easy to implement in engineering and parameter tuning, and can be directly adapted to flexible solar array systems of different specifications. Furthermore, based on Lyapunov stability theory, the asymptotic stability of the system has been rigorously proven, effectively avoiding on-orbit operational risks and improving the reliability of spacecraft mission execution. Attached Figure Description

[0014] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 The flowchart below shows the fuzzy adaptive sliding mode control method applicable to satellite flexible solar array systems of the present invention. Figure 2 This is a schematic diagram of the fuzzy adaptive sliding mode control method applicable to satellite flexible solar array systems of the present invention; Figure 3 This is a schematic diagram of the membership function of a typical fuzzy controller; Figure 4 To express the intent of fuzzy control rules; Figure 5 This is a rendering of the fuzzy adaptive sliding mode control method for satellite flexible solar array systems according to the present invention; Figure 6 Schematic diagram of ANCF beam element modeling; Figure 3 middle: Figure 3 (a) is A diagram illustrating the membership functions; Figure 3(b) is A diagram illustrating the membership functions; Figure 4 middle: Figure 4 (a) is Fuzzy control rules represent intent; Figure 4 (b) is Fuzzy control rules express intent. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0017] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0018] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0019] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0020] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0021] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0022] The present invention will now be described in further detail with reference to the accompanying drawings: Based on the nonlinear dynamic model of a satellite flexible solar array, the relationship between the driving input and the motion of the flexible solar array's end effector was established. However, the structural flexibility, joint clearance nonlinearity, and time-varying nature of the collision force of the flexible solar array can significantly induce control errors. These nonlinear factors prompt the research of corresponding control methods to achieve the required precise motion. To improve control performance, this invention discloses a fuzzy adaptive sliding mode control method suitable for satellite flexible solar array systems, the specific process of which is as follows: Figure 1 As shown: S101, based on the satellite's flexible solar array, constructs a nonlinear dynamic model incorporating joint clearances and wear; models the kinematic and dynamic characteristics of the flexible solar array and joint components, and determines the core control boundary of the fuzzy adaptive sliding mode control; see [link to relevant documentation]. Figure 6 A nonlinear dynamic model of a flexible solar array with gapped joints is constructed, specifically as follows: Joint clearance and collision force modeling: Define the joint clearance vector as the difference between the geometric center of the bearing and the geometric center of the bushing, and the eccentricity. gap size Contact deformation δ = e - c The normal collision force was calculated using the Lankarani-Nikravesh model. The Stribeck model calculates tangential friction. The total collision force is the vector sum of the two forces. ; Flexible solar array modeling: The flexible solar array is modeled using ANCF beam elements, with generalized coordinates for each element. Through the shape function matrix Describe the displacement field and infer missile performance. Element inertia matrix ; Global nonlinear dynamic equations: By incorporating collision forces, friction forces, and gravity through the Lagrange equations, the global dynamic equations are obtained. This equation provides a precise model basis for the design of subsequent control methods.

[0023] S102, based on a nonlinear dynamic model, designs a fuzzy adaptive sliding mode control method. This method includes sliding mode surface design, equivalent control solution, fuzzy inference, and adaptive gain tuning, forming a complete closed-loop control logic; see also... Figure 2 A fuzzy adaptive sliding mode control structure is constructed, specifically as follows: Slip surface design, defining trajectory tracking error Error derivative Second derivative of error Design PID-type sliding surface Calculate the rate of change of the sliding surface By constraining the motion of the sliding surface system, a stable basis is provided for mitigating the effects of vibration. Equivalent control solution, based on sliding surface satisfying The ideal sliding mode conditions are derived, and Substituting into the overall dynamic equation and rearranging, we obtain the equivalent control. ; Fuzzy inference and adaptive gain, see [link to relevant documentation] Figure 3 (a) Figure 4 (a) Constructing fuzzy control quantities and The solution is obtained through fuzzy reasoning, with the reasoning input being... and The input and output are both divided into 7 fuzzy subsets (NB, NM, NS, Z, PS, PM, PB), and triangular membership functions are used, with the expression being: Using fuzzy reasoning and a product inference engine to output... See also Figure 3 (b) Figure 4 (b) Construct the FASMC module to measure trajectory tracking error. and its rate of change As input, it adopts a fuzzy inference structure consistent with FSMC, and outputs adaptive gain. Constructing a fuzzy adaptive adjustment term The total control torque is ; Stability verification: Based on Lyapunov stability theory, Lyapunov functions are defined. Derive its time derivative ,prove The system is asymptotically stable.

[0024] S103, based on the fuzzy adaptive sliding mode control method, performs trajectory tracking control on the joint position and attitude of the satellite's flexible solar array, dynamically suppresses nonlinear vibrations caused by gap and flexible coupling, and reduces trajectory tracking errors; S103.1, Signal Acquisition and Preprocessing; Generalized coordinates of the flexible solar array are acquired using a position sensor. Accelerometer data collection Force sensors collect joint collision forces The sensor signal is input to the controller module after being filtered. S103.2, Error and Sliding Surface Calculation; based on the collected generalized coordinates With the preset expected generalized coordinates Calculate trajectory tracking error Error change rate and the second derivative of the error Substitute into the sliding surface formula to calculate the sliding surface. and its rate of change ; S103.3, Solution and execution of control torque; Input FSMC module output ,Will Input FASMC module output Calculate adjustment items Superimposed equivalent control Obtain the total control torque ,Will The output is sent to the servo motor actuator to drive the flexible solar panel to move along the desired trajectory; S103.4, Control Effect Verification; see [link / reference] Figure 5 Traditional PD control strategies do not adaptively compensate for the coupling disturbances between flexible deformation and joint clearance, resulting in large fluctuations in tracking error and significant influence of nonlinear factors on vibration amplitude. This invention achieves adaptive suppression of coupling disturbances through the coordinated adjustment of FSMC and FASMC, significantly reducing vibration amplitude and fully verifying the superiority of the fuzzy adaptive sliding mode control method.

[0025] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fuzzy adaptive sliding mode control method suitable for satellite flexible solar array systems, characterized in that, Includes the following steps: A nonlinear dynamic model incorporating joint clearances and wear is constructed based on the flexible solar array of a satellite. A comprehensive model of the kinematic and dynamic characteristics of the flexible solar array and its joint components was developed, and the core control boundary of the fuzzy adaptive sliding mode control was defined. Based on a nonlinear dynamics model, a fuzzy adaptive sliding mode control method is designed. The method includes sliding mode surface design, equivalent control solution, fuzzy inference and adaptive gain tuning, forming a complete closed-loop control logic. Based on the fuzzy adaptive sliding mode control method, the joint position and attitude of the satellite's flexible solar array are tracked and controlled. Specifically, the construction of the nonlinear dynamic model including joint clearance and wear is as follows: Define the clearance vector as the bearing geometric center. r ob With the geometric center of the bushing r oj The difference eccentricity The gap size satisfies （1）； in, R b For the bearing radius, R j Let the bushing radius be and the contact deformation be . The Lankarani-Nikravesh model was used to calculate the joint normal collision force. （2）； in, K For contact stiffness, D For the damping term, The response coefficient is set to 0.

9. The initial collision velocity at the point of collision, For penetration depth, Relative velocity, For normal force, , ; The tangential friction force is described based on the Stribeck model, and the expression is: （3）； in, n =1.5 is the nonlinear coefficient. For contact deformation rate, The static friction coefficient is The coefficient of kinetic friction is . Stribeck speed threshold, It is an empirical constant. The coefficient of viscous friction is... The relative angular velocity of the joint; The total collision force is: （4）； The joint wear process is described based on the Archard model, expressed as follows: （5）； in, k The wear coefficient is... For normal force, h For wear depth, H Given the material hardness, the above formula quantifies the mapping relationship between joint wear depth, normal force, and sliding distance. An elastic dynamic model of the flexible solar array is established using the Absolute Nodal Coordinates (ANCF) method: Define the generalized coordinates of ANCF beam elements: （6）； in, These are the absolute position coordinates of the ANCF link element nodes. The slope component of the absolute position of the beam element node in the global coordinate system; The element displacement field is described by the shape function S matrix: （7）； The expression for elastic force is: （8）； in, E For elastic modulus, For the strain at the corresponding point on the midline, A For cross-sectional area, Let the moment of inertia of the cross section be... The elongation of this unit ( ); By integrating the collision force model and the ANCF elastic dynamics model, a global nonlinear dynamic equation is established using the Lagrange equation: （9）； in, and These are the mass matrix and stiffness matrix. For generalized coordinates, For generalized acceleration, Φ is the constraint matrix, Φ q Jacobian matrix of the constraint matrix, λ Lagrange multipliers For the generalized external force term, For collision force, This is the control force matrix.

2. The fuzzy adaptive sliding mode control method for satellite flexible solar array systems according to claim 1, characterized in that, The aforementioned fuzzy adaptive sliding mode control method is specifically as follows: Define trajectory tracking error ( (For the desired generalized coordinates), the sliding surface is defined as: （10）； in, K p , K i , K d These are the positive definite proportional, integral, and differential gain matrices, respectively. The error derivative, The second derivative of the error; Differentiating with respect to the sliding surface, we get: （11）； Fuzzy adaptive sliding mode control law is based on equivalent control and switching control Composition, the expression is: （12）； Among them, the equivalent control torque for: （13）； Adjustment terms for fuzzy adaptive sliding mode control The expression is: （14）； in, For fuzzy control quantities, For adaptive gain; Fuzzy control quantity and The solution is obtained through fuzzy reasoning, with the reasoning input being... and The input and output are both divided into 7 fuzzy subsets (NB, NM, NS, Z, PS, PM, PB), and triangular membership functions are used, with the expression as follows: （15）； in, a , b , c These represent the left boundary, center value, and right boundary of the fuzzy subset, respectively.

3. The fuzzy adaptive sliding mode control method for satellite flexible solar array systems according to claim 1, characterized in that, This includes steps for verifying the stability of the control system, and proving the asymptotic stability of the system based on Lyapunov stability theory: Define Lyapunov functions as follows: （16）； Its derivative The following equation must be satisfied: （17）； Further expansion yields: （18）； When using sliding mode control It can be defined as: （19）； in, It is the approach control gain related to the upper limit. It is a symbolic function; therefore This satisfies the negative definiteness requirement of the Lyapunov function.

4. The fuzzy adaptive sliding mode control method for satellite flexible solar array systems according to claim 1, characterized in that, Contact deformation of joint space δ Satisfy: When δ When the force is less than 0, the joint is in a separated state with no collision contact, and the total collision force is... =0; when δ When ≥0, the joint is in a state of collision contact. δ The collision force is calculated using the formula of the nonlinear dynamics model, and the direction of the collision force is opposite to the direction of the eccentricity vector.

5. The fuzzy adaptive sliding mode control method for satellite flexible solar array systems according to claim 1, characterized in that, The membership functions of fuzzy sliding mode control (FSMC) and fuzzy adaptive sliding mode control (FASMC) overlap by 50%.

6. The fuzzy adaptive sliding mode control method for satellite flexible solar array systems according to claim 1, characterized in that, The specific process for trajectory tracking control of the joint position and attitude of the satellite's flexible solar array is as follows: The generalized coordinates of the satellite's flexible solar array are collected in real time by sensors. Generalized acceleration and joint impact force The signal is input to the controller after being filtered. Based on the collected generalized coordinates With the preset expected generalized coordinates Calculate trajectory tracking error Error change rate and the second derivative of the error ;Will , Substitute into the sliding surface formula to calculate the sliding surface. and its rate of change ;Will , Input to the FSMC module, output fuzzy control quantity ;Will , Input to FASMC module, output adaptive gain ; Calculate the equivalent control using the formula. With adjustment items The total control torque is obtained by superposition. ; to control the total torque The output is sent to the actuator to drive the satellite's flexible solar array to move along the desired trajectory.

7. A fuzzy adaptive sliding mode control system for implementing the method of any one of claims 1-6, comprising: Modeling module: Based on the satellite's flexible solar array, a nonlinear dynamic model is constructed, including joint clearance, collision force, friction force, and wear characteristics. The model covers the ANCF elastic dynamic model, the Lankarani-Nikravesh collision force model, the Stribeck friction force model, the Archard wear model, and the overall nonlinear dynamic equations of the system, and the control boundaries are clearly defined. Control Design Module: Based on the dynamic model output by the modeling module, it completes the sliding surface design, equivalent control solution, FSMC module design, FASMC module design and overall control logic integration to form a closed-loop control structure for fuzzy adaptive sliding mode control. Signal acquisition module: The sensor collects the rotation angle of the flexible solar panel in real time, and transmits it to the control calculation module after filtering. Control Calculation Module: Receives the output signal from the signal acquisition module, calculates the trajectory tracking error, sliding surface and its rate of change, and outputs the result through the FSMC and FASMC modules. and Calculate the total control torque according to the control logic; Execution module: Receives the control torque output from the control calculation module, drives the joint motor to move, realizes the attitude adjustment and trajectory tracking of the flexible solar array, and suppresses nonlinear vibration.

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