Rigid spacecraft attitude control method and system based on finite time constraint

Abstract

The invention relates to a rigid spacecraft attitude control method and system based on finite time constraint, and belongs to the technical field of spacecraft attitude control. Comprising the following steps: respectively constructing a spacecraft attitude control system model and a finite time convergence performance function containing a preset time constant; according to the finite time convergence performance function, dynamic attitude constraint is applied to the system state of the spacecraft attitude control system model; converting the attitude constraint into differential homeomorphic mapping of an unconstrained space; obtaining an error conversion variable according to differential homeomorphic mapping; and designing a virtual control law and constructing an error compensation module according to the error conversion variable, and designing an actual control input law according to the virtual control law and the error compensation module. According to the method, rapid convergence of the spacecraft attitude within the preset time is ensured, the dynamic response precision of the spacecraft in the rapid attitude maneuver process is remarkably improved, the control period delay is effectively avoided, and the power consumption is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft attitude control, and in particular to a rigid spacecraft attitude control method and system based on finite time constraints. Background Art

[0002] Existing spacecraft attitude control primarily utilizes proportional-integral-derivative (PID) control. Through the coordinated adjustment of proportional, integral, and derivative (PID) control, it achieves attitude maintenance requirements for basic scenarios such as communication satellite orientation. This method boasts a simple structure, easy engineering implementation, and stable performance in single-satellite steady-state missions, laying a solid technical foundation for the development of the space industry. However, as space missions become increasingly complex, the limitations of traditional control methods are becoming increasingly apparent. During on-orbit servicing missions, the docking process between a spacecraft and a target satellite requires attitude control to achieve fluctuation-free convergence at millisecond-level response speeds. However, parameter tuning for PID control struggles to balance dynamic performance with steady-state accuracy. Furthermore, sudden disturbances in the space environment, such as the solar wind, further challenge the control system's ability to resist interference. Therefore, current spacecraft attitude control technology must address key challenges such as suppressing attitude fluctuations, shortening convergence time, and enhancing interference resistance, providing reliable technical support for future cutting-edge missions such as deep space exploration and on-orbit maintenance.

[0003] Existing PID control methods, with their fixed parameters, struggle to cope with sudden changes in solar pressure and inertia due to fuel consumption. Although the subsequently improved fuzzy adaptive PID method can achieve self-tuning parameters, it still faces the challenge of balancing response speed with steady-state accuracy. Adaptive control, through real-time parameter adjustment, can maintain system stability in situations such as spacecraft inertia changes due to fuel consumption. While sliding mode control achieves precise tracking thanks to its variable structure characteristics, its inherent chattering phenomenon exacerbates propellant consumption and component wear, and even boundary layer technology cannot completely eliminate it. Furthermore, most of these control strategies focus on the steady-state accuracy of the spacecraft's final attitude. However, with the increasing complexity of space missions, the demand for spacecraft attitude control has evolved from simply considering steady-state accuracy to the coordinated control of steady-state accuracy and real-time attitude. In this context, preset performance control effectively suppresses attitude fluctuations and ensures convergence accuracy by introducing a preset performance function to dynamically constrain attitude. However, this type of preset performance control method is usually based on a fixed exponential convergence performance function. Although the preset performance function can limit the attitude error to a specified range, it will take a long time for the actual attitude of the spacecraft to stabilize to the desired attitude, and it cannot guarantee accurate convergence within a certain time. This limitation restricts its application in rapid maneuvering space missions.

[0004] To address these issues, an existing patent (CN118457945A) proposes a variable-performance spacecraft attitude control method that accounts for input saturation. This method first establishes a spacecraft dynamics model with external disturbances and input saturation. A preset attitude performance model is constructed using an error transfer function. Then, an adaptive variable performance function differential equation is designed to dynamically adjust the transient response bounds, thereby suppressing attitude overshoot, optimizing transient response, and ensuring system stability. However, this method's attitude stabilization process is time-consuming and unsuitable for spacecraft performing rapid maneuvers. Another existing patent (CN120029339A) proposes a performance function-based spacecraft attitude tracking control method and system with a preset time and precision. This method first establishes a spacecraft attitude dynamics model. A performance function containing trigonometric functions is designed to dynamically constrain the attitude tracking error and construct a continuous, nonsingular, adaptive attitude tracking controller. This method enables the spacecraft attitude to converge to a preset precision within a preset time, effectively addressing the long attitude stabilization time inherent in traditional methods. However, the trigonometric function calculations in the preset performance function of this method will increase the real-time computing burden of the spacecraft processor, resulting in control cycle delays and increased power consumption, affecting the real-time performance in rapid maneuvering scenarios. Summary of the Invention

[0005] To this end, the technical problem to be solved by the present invention is to overcome the problems in the prior art such as slow convergence speed, long attitude stabilization process, delay in control cycle and significant increase in power consumption.

[0006] In a first aspect, to solve the above technical problems, the present invention provides a method for attitude control of a rigid spacecraft based on finite time constraints, comprising: The spacecraft attitude control system model and the finite time convergence performance function with preset time constants were constructed respectively; According to the finite-time convergence performance function, dynamic attitude constraints are imposed on the system state of the spacecraft attitude control system model; the attitude constraints are converted into a differential homeomorphism mapping in an unconstrained space; according to the differential homeomorphism mapping, an error conversion variable is obtained; according to the error conversion variable, a virtual control law is designed and an error compensation module is constructed, and an actual control input law is obtained according to the virtual control law and the error compensation module.

[0007] In one embodiment of the present invention, the expression of the finite time convergence performance function is: ; in, represents the initial value, represents the final value of the system, represents a constant, Indicates the preset convergence time, Indicates time.

[0008] In one embodiment of the present invention, the steps of applying a dynamic attitude constraint to the system state of the spacecraft attitude control system model according to the finite time convergence performance function; converting the attitude constraint into a differential homeomorphism mapping in an unconstrained space; and obtaining an error conversion variable according to the differential homeomorphism mapping are as follows: Acquiring a system state in the spacecraft attitude control system model; applying a dynamic attitude constraint to the system state according to the finite time convergence performance function; According to the posture constraint, a strictly monotone increasing function is introduced, and a differential homeomorphism mapping relationship is constructed through a hyperbolic tangent function; wherein the strictly monotone increasing function satisfies the following conditions: ; ; The expression for constructing the differential homeomorphism mapping relationship through the hyperbolic tangent function is: ; The differential homeomorphism mapping relationship is inversely solved to obtain an error conversion variable; wherein the expression of the error conversion variable is: ; The time derivative of the error conversion variable is obtained to obtain an unconstrained spatial variable; wherein the expression of the unconstrained spatial variable is: ; in, represents a strictly monotonically increasing function, represents the error conversion variable, and represents the boundary adjustment parameter, Indicates the system status, represents the finite time convergence performance function; represents the gain matrix, represents interference terms, represents the angular velocity vector in the body coordinate system, Represents the pose mapping matrix.

[0009] In one embodiment of the present invention, a dynamic attitude constraint is imposed on the system state according to the finite time convergence performance function, wherein the expression of the attitude constraint is: ; ; in, and represents the boundary adjustment parameter, represents the finite time convergence performance function, Indicates the system status, Represents a constant.

[0010] In one embodiment of the present invention, a virtual control law is designed and an error compensation module is constructed based on the error conversion variable, and the steps of obtaining an actual control input law based on the virtual control law and the error compensation module are as follows: Construct a finite time instruction filter; construct a dynamic error compensation signal according to the finite time instruction filter; wherein the expression of the finite time instruction filter is: ; in, represents the first-level virtual control law; and represents the output signal of the filter; and Indicates adjustable parameters; represents a symbolic function; Represents the intermediate control variable of the command filter; constructing a first error variable according to the error conversion variable; obtaining a first compensated error variable according to the dynamic error compensation signal and the first error variable; Constructing a first-layer virtual control law according to the first compensation error variable; According to the first-layer virtual control law, an output signal of the finite-time command filter is obtained; according to the output signal and the spacecraft attitude control system model, a second error variable is constructed; according to the second error variable, an actual control input law is obtained; wherein the expression of the actual control input law is: ; ; in, represents the error variable, represents a constant, represents the spacecraft moment of inertia matrix; and Indicates the parameters to be designed; 、 and Represents the error variable The weight, Represents the matrix transpose symbol.

[0011] In one embodiment of the present invention, the expression of the first-layer virtual control law is: ; ; in, represents the first-level virtual control law, represents the posture mapping matrix, represents the gain matrix, represents the first error variable, represents the first compensation error variable, represents interference terms, represents a constant, represents a symbolic function; 、 and represents the component of the first compensated error variable, and Indicates the parameters to be designed, Represents the matrix transpose symbol.

[0012] In one embodiment of the present invention, the expression of the dynamic error compensation signal is: ; in, represents the error compensation signal, Indicates the parameters to be designed, represents the gain matrix, represents the posture mapping matrix, represents the output signal of the filter, represents the first-level virtual control law, represents the compensation gain parameter, Represents a symbolic function.

[0013] In one embodiment of the present invention, the compensation gain parameter The satisfied relationship is: ;in, represents the upper bound of the matrix norm, represents the gain matrix, Represents a positive constant.

[0014] In a second aspect, to solve the above technical problems, the present invention provides a rigid spacecraft attitude control system based on finite time constraints, comprising: A construction module is used to construct a spacecraft attitude control system model and a finite time convergence performance function with a preset time constant; a conversion module, configured to impose dynamic attitude constraints on the system state of the spacecraft attitude control system model according to the finite time convergence performance function; convert the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtain an error conversion variable according to the differential homeomorphism mapping; The output module is used to design a virtual control law and construct an error compensation module according to the error conversion variable, and output an actual control input law according to the virtual control law and the error compensation module.

[0015] On the third aspect, in order to solve the above technical problems, the present invention provides a spacecraft, including the above-mentioned rigid spacecraft attitude control system based on finite time constraints.

[0016] The above technical solution of the present invention has the following beneficial effects compared with the prior art: (1) The present invention discloses a method and system for attitude control of rigid spacecraft based on finite time constraints. By constructing a finite time convergence performance function, the present invention effectively solves the two core problems of traditional attitude constraint control methods: the inability to actively constrain the amplitude of the spacecraft attitude error fluctuation, and the lack of precise control capability of the time required to converge to the preset attitude. This significantly improves the control performance of the spacecraft in rapid maneuvering scenarios. The present invention transforms the attitude constraint into a differential homeomorphism mapping of the unconstrained space, cleverly avoiding the controller design complexity problem caused by directly processing the constraint conditions in traditional attitude constraint control methods. Based on the error conversion variable, a virtual control law is designed, and an error compensation module is constructed, thereby avoiding the computational complexity problem caused by high-order derivatives in traditional methods and significantly improving the computational efficiency of the algorithm. In addition, through the synergistic effect of the finite time convergence performance function and the error compensation module, the estimation process of the virtual control signal and its derivative is synchronized with the attitude error constraint process, further improving the engineering practicality of the algorithm. This not only reduces power consumption, but also avoids control cycle delays and enhances the real-time performance and reliability of the system.

[0017] (2) The present invention organically combines finite-time control theory with instruction filtering technology. While reducing computational complexity, it significantly shortens the convergence time of the filtering process, effectively avoiding the adverse effects of filtering delay or error accumulation on the real-time performance of attitude control, and successfully achieves the coordinated optimization of computational complexity and control real-time performance.

[0018] (3) Based on the Lyapunov function theory, the present invention strictly proves that in the presence of interference, the attitude error can converge to a preset area within a preset time, so that the spacecraft can accurately realize the attitude adjustment process, meeting the needs of complex tasks such as deep space exploration and on-orbit service for fast and high-precision attitude control.

[0019] (4) The present invention can effectively solve the problem that the existing technology is difficult to achieve the specified attitude within the preset time and effectively suppress the interference when the spacecraft faces external space interference and convergence time constraints, thereby meeting the strict requirements for high-precision and high-efficiency attitude control in complex space environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein: Figure 1 This is a flow chart of a rigid spacecraft attitude control method based on finite time constraints in a preferred embodiment of the present invention; Figure 2 A comparison diagram of the finite time convergence performance function and the exponential convergence performance function in a preferred embodiment of the present invention; Figure 3 is a finite time performance function curve diagram under different convergence times in a preferred embodiment of the present invention; Figure 4 This is a convergence curve diagram of the spacecraft attitude and constraint boundary under finite time constraints when the preset convergence time is 8 seconds in the preferred embodiment of the present invention; Figure 5 This is a finite time convergence characteristic curve diagram of the spacecraft angular velocity response when the preset convergence time is 8 seconds in the preferred embodiment of the present invention; Figure 6 This is a graph showing the change of spacecraft control input torque over time when the preset convergence time is 8 seconds in a preferred embodiment of the present invention; Figure 7 This is a graph comparing the attitude responses of the spacecraft using the two control methods when the preset convergence time is 4 seconds in a preferred embodiment of the present invention; Figure 8 This is a comparison graph of spacecraft attitude responses of the two control methods when the preset convergence time is 8 seconds in the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0022] Example 1: Reference Figure 1 As shown, the present invention provides a method for rigid spacecraft attitude control based on finite time constraints, including but not limited to the following steps: S1. Construct a spacecraft attitude control system model and a finite time convergence performance function with a preset time constant respectively; S2. Apply dynamic attitude constraints to the system state of the spacecraft attitude control system model based on the finite time convergence performance function; transform the attitude constraints into a differential homeomorphism mapping in the unconstrained space; and obtain error transformation variables based on the differential homeomorphism mapping; S3. According to the error conversion variable, a virtual control law is designed and an error compensation module is constructed. The actual control input law is obtained according to the virtual control law and the error compensation module.

[0023] The present invention provides a finite-time constraint-based attitude control method for rigid spacecraft. By constructing a finite-time convergence performance function, this method effectively addresses the inability of traditional attitude constraint control methods to actively constrain the amplitude of spacecraft attitude error fluctuations and the lack of precise control over the time required to converge to a preset attitude. This significantly improves the control performance of spacecraft in rapid maneuvering scenarios. By converting attitude constraints into a differential homeomorphism mapping in an unconstrained space, this method addresses the complex controller design issues inherent in traditional attitude constraint control methods, which arise from directly manipulating the constraints. This method designs a virtual control law based on error conversion variables and constructs an error compensation module, avoiding the computational complexity associated with high-order derivatives in traditional methods and improving the algorithm's computational efficiency. Furthermore, through the synergistic effect of the finite-time convergence performance function and the error compensation module, the estimation process of the virtual control signal and its derivative is synchronized with the attitude error constraint process, further enhancing the algorithm's engineering practicality, reducing power consumption, and avoiding control cycle delays. Therefore, the embodiments of the present invention can effectively solve the problem that when a spacecraft faces external space interference and convergence time constraints, the existing technology is difficult to simultaneously achieve a specified posture within a preset time and effectively suppress interference, thereby meeting the requirements for high-precision and high-efficiency posture control in complex space environments.

[0024] Specifically, for step S1, the dynamic equation of the spacecraft's spatial attitude motion is constructed according to the kinematic law of the rigid body, and its specific expression is: ; in, represents the spacecraft moment of inertia matrix, represents the angular velocity vector in the body coordinate system, represents the control torque, Indicates external interference torque; symbol " " represents the operation from vector to antisymmetric matrix, Represents the matrix transpose symbol.

[0025] Furthermore, the spacecraft moment of inertia matrix and the antisymmetric matrix of the angular velocity vector The specific forms are: , ; in, 、 etc. represent the spacecraft moment of inertia matrix The corresponding component of . Similarly, 、 and The antisymmetric matrix representing the angular velocity vector Corresponding quantity.

[0026] Furthermore, when describing the posture based on the modified Rodriguez parameter, the posture parameter vector is defined as , its kinematic equation is: ; in, is the posture mapping matrix, and its specific expression is: , for The identity matrix, for The antisymmetric matrix of . The modified Rodriguez parameter satisfies the unit vector constraint , used to ensure Reversible and bounded.

[0027] Furthermore, by combining attitude kinematics and dynamics equations, the spacecraft attitude control model is constructed as follows: ; in, is the nonlinear term of angular velocity coupling; is the normalized term of the external disturbance torque. In practical engineering applications, the external disturbance torque satisfy ,in is the upper bound constant of interference, Denotes the norm symbol. Based on the boundedness of the modified Rodriguez parameter and the matrix norm property, it can be deduced that ,in This is a positive upper bound constant for the combined moment of inertia, angular velocity, and disturbance characteristics. This design lays the foundation for stability analysis of spacecraft attitude control systems in actual engineering scenarios.

[0028] Specifically, a finite-time convergence performance function with a preset time constant is constructed, and its mathematical expression is: ; in, represents the initial value, represents the final value of the system, represents a constant, Indicates the preset convergence time. hour, ;when hour, , make sure Convergence is completed within.

[0029] The finite-time convergence performance function constructed in the embodiment of the present invention can ensure that the spacecraft attitude converges rapidly within a predetermined time, while strictly limiting the error fluctuation amplitude and steady-state error within preset boundaries, significantly improving the dynamic response accuracy of the spacecraft during rapid attitude maneuvers.

[0030] Specifically, in step S2, by constructing an attitude error transformation mechanism, the original constraint control problem is transformed into an equivalent problem that ensures the boundedness of the conversion error, which solves the problem of complex controller design caused by directly processing the constraint conditions in traditional attitude constraint control methods.

[0031] Furthermore, the specific steps of step S2 for converting the posture constraint into a differential homeomorphism mapping of the unconstrained space through the error conversion mechanism are as follows: S210, obtain the system status in the spacecraft attitude control system model ; According to the finite time convergence performance function System status Apply dynamic posture constraints (also called boundary constraints), the specific expression is: ; ; in, and represents the boundary adjustment parameter; is a constant used to ensure that the initial error is within the constraint interval.

[0032] S220, in order to transform the bounded constraint problem into the control problem of unconstrained space, a strictly monotonically increasing function is introduced , and construct differential homeomorphism mapping relationship through hyperbolic tangent function. Among them, strictly monotone increasing function The satisfied relationship is: ; .

[0033] The expression for constructing differential homeomorphism mapping relationship of hyperbolic tangent function is: ; in, represents a strictly monotonically increasing function, represents the error transformation variable.

[0034] S230. Inversely solve the differential homeomorphism mapping relationship to obtain the error conversion variable, which is specifically expressed as follows: .

[0035] S240, error conversion variable Calculate the time derivative and simplify it to get the matrix form, the specific expression is: ; Among them, the gain matrix , whose elements ; Interference , its specific elements are expressed as: .

[0036] The embodiment of the present invention constructs an attitude error transformation mechanism and uses a differential homeomorphism mapping to transform the bounded attitude error space into an unconstrained control space, thereby achieving an equivalent transformation of the constraint problem and avoiding the complexity brought by directly processing the inequality constraints, thereby effectively simplifying the controller design process.

[0037] Specifically, in step S3, the backstepping method is used to design a virtual control law and construct an error compensation module, and the actual control input law is designed based on the virtual control law and the error compensation module. The specific steps are: S310. To solve the computational complexity problem caused by high-order derivation in the traditional backstepping method, a finite-time instruction filter is used to replace the complex derivation process through a feedforward compensation mechanism to construct a finite-time instruction filter. The specific expression is: ; in, Represents the input signal of the filter, i.e. the first-layer virtual control law; represents the adjustable parameter that determines the filter convergence speed, and Represents the output signal of the filter, respectively as and its derivative estimated value of; Represents the intermediate control variable of the command filter; represents the symbolic function, which is defined as: ; in, Indicates a variable symbol.

[0038] Furthermore, through nonlinear feedback mechanisms and appropriate Parameter design, the filter can make the estimation error meet the requirements within a limited time. ,in Represents a positive constant.

[0039] Furthermore, in order to eliminate the error caused by filtering, a dynamic error compensation signal is introduced , its specific expression is: ; in, Indicates the parameters to be designed, represents the compensation gain parameter, and ; is the symbolic function vector; 、 、 Indicates the dynamic error compensation signal The weight.

[0040] S320: Obtain the error conversion variable according to step S240 and construct a first error variable , its specific expression is: .

[0041] S330, decoupling the filtering error from the system dynamic error. and the first error variable , defines the error variable after the instruction filter is compensated, that is, the first compensation error variable The first compensation error variable The specific expression is: .

[0042] S340, based on the first compensation error variable , construct the first layer of virtual control law , its specific expression is: ; in, Indicates the parameters to be designed, satisfying ; The expression is: ; in, represents a constant, satisfying ; 、 and Represents the component of the first compensated error variable.

[0043] S350, according to the first layer virtual control law , get the output signal of the finite time command filter; construct the second error variable based on the output signal and the spacecraft attitude control system model , its specific expression is: ; in, is the output signal of the finite time command filter.

[0044] Furthermore, in order to enhance the consistency of variable representation, according to the second error variable , define the error variable as follows: .

[0045] Furthermore, combined with the error variable , design the actual control input law (i.e. control torque) , its specific expression is: ; in, ; 、 and Represents the error variable The weight; are the parameters to be designed.

[0046] The embodiment of the present invention organically combines finite-time control theory with instruction filtering technology, which significantly shortens the convergence time of the filtering process while reducing computational complexity, effectively avoiding the adverse effects of filtering delay or error accumulation on the real-time performance of attitude control, and successfully achieving the coordinated optimization of computational complexity and control real-time performance.

[0047] Specifically, based on the above steps S1 to S3, a Lyapunov function is constructed to prove that the posture error converges to a preset area within a preset time. The specific steps are as follows: S410, construct the first layer Lyapunov function , its mathematical expression is: .

[0048] Furthermore, for the first layer Lyapunov function Taking the derivative, we get: .

[0049] Furthermore, combined with the virtual control law ,get: .

[0050] S420, construct the second layer Lyapunov function , its mathematical expression is: .

[0051] Further, Derivative and introduction of dynamic equations , sorted out to get: ; Among them, the definition According to Young's inequality, the following relationship holds: .

[0052] Furthermore, the actual control input Substitute into the second layer Lyapunov function derivative In the equation, we get: .

[0053] because 、 are all bounded, and their upper bounds are and ,Right now 、 . Using the Young inequality property, we can get: ; (1) .

[0054] because , so Simplifying, we get:

[0055] Further, let , , , Simplifying formula (1) yields:

[0056] S430, when hour, and Available for a limited time Inner convergence, and To ensure the first error variable It can converge in a limited time, thus ensuring Bounded, further proof is needed The finite time convergence of . Therefore, the Lyapunov function of the compensation signal is designed as follows: .

[0057] Further, Taking the derivative we get: .

[0058] According to the design of the command filter, there is a finite time Make , so: ; in is the upper bound of the matrix norm. So, It can be expressed as:

[0059] Further, let ,get: .

[0060] Therefore, as long as the design parameters It can guarantee In a limited time Converges to a small neighborhood near the origin.

[0061] Based on the above steps S410 to S430, the actual total convergence time of the spacecraft attitude control system is: .when When the error variable and are bounded, combined with the error conversion relationship , the attitude error satisfies: That is, the spacecraft attitude is at the preset time The control strategy strictly converges to the dynamic constraint boundary, verifying the finite-time stability of the control strategy.

[0062] Furthermore, compared with the prior art, the embodiments of the present invention have the following advantages: The finite-time convergence performance function constructed in the embodiments of the present invention ensures rapid convergence of the spacecraft attitude within a predetermined timeframe, while strictly limiting the error fluctuation amplitude and steady-state error to pre-set bounds. This improves the dynamic response accuracy of the spacecraft during rapid attitude maneuvers. By constructing an attitude error transformation mechanism, the constrained attitude error is mapped to an unconstrained space, achieving an equivalent transformation of the constraint problem while avoiding the complexity associated with directly addressing inequality constraints, effectively simplifying the controller design process. A finite-time command filter is introduced, replacing the high-order derivatives used in the backstepping method with a parameterized filter design. This not only reduces computational complexity and avoids singularity issues, but also, through the filter's inherent finite-time convergence properties, synchronizes the estimation process of the virtual control signal and its derivative with the attitude error constraint process, further enhancing the algorithm's engineering practicality. Based on Lyapunov function theory, the present invention rigorously proves that, in the presence of interference, the attitude error can converge to a predetermined region within a predetermined timeframe, enabling the spacecraft to accurately perform attitude adjustments, meeting the requirements for fast, high-precision attitude control for complex missions such as deep space exploration and on-orbit servicing.

[0063] To verify the effectiveness of the method described in the embodiment of the present invention, a simulation experiment was designed and conducted. The following are the specific steps of the simulation experiment.

[0064] Step 1: Construct a spacecraft attitude control system model based on the modified Rodriguez parameters. First, construct the spacecraft attitude dynamics and kinematics model based on the modified Rodriguez parameters as follows: .

[0065] When constructing the above model, the actual setting of the moment of inertia parameters and the external interference assumptions are included. is the spacecraft's moment of inertia matrix, and its specific parameters are: ; is the angular velocity vector of the spacecraft in the body coordinate system; is the control torque; The expression is ; Represents the external interference torque, which comes from external environment such as solar pressure, earth gravity gradient, atmospheric resistance, etc. The specific parameters are set as follows: .

[0066] In the spacecraft attitude kinematics equation, is the nonlinear term related to the angular velocity of the spacecraft; is the normalized term of the external disturbance torque, which represents the impact of the disturbance on the posture. Define the initial modified Rodriguez parameter , which represents the attitude state of the spacecraft at the initial moment; the initial angular velocity , indicating that the spacecraft did not rotate at the initial moment.

[0067] Step 2: Design a finite-time convergence performance function with a preset time constant. First, design a finite-time convergence performance function as follows: ; Among them, set the initial value , system final value ,constant , the preset convergence time Select different values ​​according to the needs of subsequent simulation experiments. Can guarantee hour, ;when hour, To ensure that the system Convergence is completed within the time.

[0068] In order to verify the effectiveness of the finite time performance function designed in the embodiment of the invention, the initial value of the traditional exponential convergence function is set. , terminal value Completely consistent, and conduct comparative simulation, the simulation results refer to Figure 2 Among them, the traditional exponential convergence performance function is expressed as , whose convergence rate is determined by the constant Theoretically, it takes infinite time to approach , and the function of the embodiment of the present invention is Strictly converges to .from Figure 2 It can be seen that when setting When the traditional exponential convergence function At the same time There is a significant deviation, and the curve shows an asymptotic decay trend; while the function of the embodiment of the present invention is It has converged exactly to , and in The convergence slope is steeper within the interval, which fully demonstrates that the finite-time performance function proposed in the embodiment of the present invention has good transient performance.

[0069] Furthermore, in actual engineering applications, it is necessary to independently set the convergence time according to the timing requirements of specific tasks and the performance indicators of the control system. For example, a spacecraft rapid maneuvering mission requires Attitude adjustment is completed within seconds, while conventional orbit maintenance allows Seconds of convergence period. The corresponding finite time performance function curve is shown in Figure 3. This design gives the system significant timing control advantages: on the one hand, by explicitly adjusting It can flexibly match the differentiated requirements of tasks on convergence speed, effectively avoiding the problem of uncontrollable convergence time in traditional methods; on the other hand, based on the preset The control timing can be planned in advance to ensure that the spacecraft can complete attitude convergence within the predetermined time window under complex working conditions, providing a quantitative design basis for system stability and real-time control.

[0070] Step 3: Convert the attitude constraints into a differential homeomorphism mapping in the unconstrained space through the error conversion mechanism, and optimize the parameters .

[0071] Step 4: Use the backstepping method to design the virtual control law and construct the error compensation module, and optimize the parameters In the error compensation signal, select the parameter In the first level of the designed virtual control law , select Parameters In the actual control input law designed, select the parameter .

[0072] Step 5: MATLAB simulations were used to verify the convergence characteristics of the spacecraft attitude controller designed in this embodiment of the present invention within a finite timeframe. Comparisons with traditional constraint methods demonstrated its superiority in transient performance and confirmed the algorithm's effective constraints on overshoot and convergence rate. The following are the simulation results:

[0073] Reference Figure 4 , Figure 4 Showing the spacecraft's attitude Converge to the performance function in finite time The curve of the change over time under the constraint. As can be seen from the figure, the spacecraft attitude is The convergence to the preset stability domain indicates that the method described in the embodiment of the present invention can achieve finite time constrained control of the spacecraft attitude.

[0074] Reference Figure 5 , Figure 5 Shows the spacecraft angular velocity As can be seen from the figure, the angular velocity can be The convergence is within a limited time, and the angular velocity response curve is smooth without sharp fluctuations.

[0075] Reference Figure 6 , Figure 6 Shows the spacecraft control input torque The curve of change over time. As can be seen from the figure, the control input torque It gradually decreases within a limited time and finally stabilizes.

[0076] Step 6: To verify the superiority of the finite time control constraint control method described in the embodiment of the present invention, a comparative analysis is conducted with a traditional constraint control method using an exponential preset performance function. The controller design of the traditional constraint control method is as follows: ; ; .

[0077] Select the same control parameters as those of the controller designed in the embodiment of the present invention , and the performance function convergence rate The convergence rate of the finite time performance function constructed in accordance with the embodiment of the present invention is consistent with the following simulation results:

[0078] Reference Figure 7 , Figure 7 Shows the convergence time Spacecraft attitude The finite time constraint function designed in the embodiment of the present invention Curve diagram under action, and spacecraft attitude In traditional preset performance function The results show that under the same control parameters and convergence rate conditions, both control methods can achieve spacecraft attitude stability control, but there are significant differences in dynamic performance. The method of the present invention is in the finite time constraint function Under the action of the constraint control, the time required from the initial error state to entering the preset stable domain is shorter, and the slope of the response curve is larger, indicating that the error decays faster. Compared with the traditional method, the method of the present invention can quickly suppress the posture deviation through the nonlinear feedback mechanism in the initial stage, showing better transient tracking ability. The convergence speed of the traditional constraint control is obviously lagging. Its constraint effect is mainly in the posture It is only significant when approaching the constraint boundary, which is manifested as the error curve decaying slowly in the early stage. Only when the error value approaches the preset boundary, the control amount will have a strong regulatory effect, resulting in a longer overall convergence time.

[0079] Reference Figure 8 , Figure 8 Shows the convergence time When the spacecraft attitude The finite time constraint function designed in this invention Curve diagram under action, and spacecraft attitude In traditional preset performance function Through observation and analysis, we can see that: from the perspective of the convergence process, both methods have achieved the constraint control of the spacecraft attitude, but there are obvious differences in the convergence characteristics. Although the constraint function designed by the present invention In the early stage of control, posture The convergence speed is slower than the traditional preset performance function convergence speed posture , but it can be clearly seen from the details of the sub-graph that the posture under the action of the method of the present invention Ability to set time Converges to the preset stable domain, while at the same time the posture under the action of the traditional performance function , its error value is still higher than the desired accuracy threshold and has not yet completed convergence.

[0080] Further, combined with Figure 7 and Figure 8 ,exist and Under two different convergence time settings, the posture can quickly converge to the target stable domain, and the convergence time is The set value of is strictly matched, which fully demonstrates that the control method designed by the present invention realizes strict time constraints on the attitude error convergence process through the construction and parameter design of the finite time performance function, ensuring that the spacecraft attitude can be accurately adjusted within the pre-set time window, reflecting the time certainty advantage that traditional methods do not have.

[0081] Example 2: Based on the same inventive concept, this embodiment provides a rigid spacecraft attitude control system based on finite time constraints. The principle of solving the problem is similar to the rigid spacecraft attitude control method based on finite time constraints provided in Example 1, and the repeated parts will not be repeated.

[0082] This embodiment provides a rigid spacecraft attitude control system based on finite time constraints, including: A construction module is used to construct a spacecraft attitude control system model and a finite time convergence performance function with a preset time constant; A conversion module is used to impose dynamic attitude constraints on the system state of the spacecraft attitude control system model according to a finite time convergence performance function; convert the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtain error conversion variables based on the differential homeomorphism mapping; The output module is used to design a virtual control law and construct an error compensation module according to the error conversion variable, and output the actual control input law according to the virtual control law and the error compensation module.

[0083] Example 3: This embodiment provides a spacecraft, including the rigid spacecraft attitude control system based on finite time constraints described in the second embodiment.

[0084] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0085] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0086] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0087] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0088] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for attitude control of a rigid spacecraft based on finite time constraints, characterized in that: include: The spacecraft attitude control system model and the finite time convergence performance function with preset time constants were constructed respectively; applying a dynamic attitude constraint to a system state of the spacecraft attitude control system model according to the finite time convergence performance function; converting the attitude constraint into a differential homeomorphism mapping in an unconstrained space; and obtaining an error transformation variable according to the differential homeomorphism mapping; According to the error conversion variable, a virtual control law is designed and an error compensation module is constructed, and an actual control input law is obtained according to the virtual control law and the error compensation module.

2. A method for rigid spacecraft attitude control based on finite time constraints according to claim 1, characterized in that: The expression of the finite time convergence performance function is: ； in, represents the initial value, represents the final value of the system, represents a constant, Indicates the preset convergence time, Indicates time.

3. The method for rigid spacecraft attitude control based on finite time constraints according to claim 1, characterized in that: The steps of applying dynamic attitude constraints to the system state of the spacecraft attitude control system model according to the finite time convergence performance function; converting the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtaining an error conversion variable according to the differential homeomorphism mapping are as follows: Acquiring a system state in the spacecraft attitude control system model; applying a dynamic attitude constraint to the system state according to the finite time convergence performance function; According to the posture constraint, a strictly monotone increasing function is introduced, and a differential homeomorphism mapping relationship is constructed through a hyperbolic tangent function; wherein the strictly monotone increasing function satisfies the following conditions: ； ； The expression for constructing the differential homeomorphism mapping relationship through the hyperbolic tangent function is: ； The differential homeomorphism mapping relationship is inversely solved to obtain an error conversion variable; wherein the expression of the error conversion variable is: ； The time derivative of the error conversion variable is obtained to obtain an unconstrained spatial variable; wherein the expression of the unconstrained spatial variable is: ； in, represents a strictly monotonically increasing function, represents the error conversion variable, and represents the boundary adjustment parameter, Indicates the system status, represents the finite time convergence performance function; represents the gain matrix, represents interference terms, represents the angular velocity vector in the body coordinate system, Represents the pose mapping matrix.

4. The method for rigid spacecraft attitude control based on finite time constraints according to claim 3, characterized in that: According to the finite time convergence performance function, a dynamic attitude constraint is imposed on the system state, wherein the expression of the attitude constraint is: ； ； in, and represents the boundary adjustment parameter, represents the finite time convergence performance function, Indicates the system status, Represents a constant.

5. The method for rigid spacecraft attitude control based on finite time constraints according to claim 1, characterized in that: According to the error conversion variable, a virtual control law is designed and an error compensation module is constructed. The steps of obtaining the actual control input law according to the virtual control law and the error compensation module are as follows: Construct a finite time instruction filter; construct a dynamic error compensation signal according to the finite time instruction filter; wherein the expression of the finite time instruction filter is: ； in, represents the first-level virtual control law; and represents the output signal of the filter; and Indicates adjustable parameters; represents a symbolic function; Represents the intermediate control variable of the command filter; constructing a first error variable according to the error conversion variable; obtaining a first compensated error variable according to the dynamic error compensation signal and the first error variable; Constructing a first-layer virtual control law according to the first compensation error variable; According to the first-layer virtual control law, an output signal of the finite-time command filter is obtained; according to the output signal and the spacecraft attitude control system model, a second error variable is constructed; according to the second error variable, an actual control input law is obtained; wherein the expression of the actual control input law is: ； ； in, represents the error variable, represents a constant, represents the spacecraft moment of inertia matrix; and Indicates the parameters to be designed; 、 and Represents the error variable The weight, Represents the matrix transpose symbol.

6. The method for rigid spacecraft attitude control based on finite time constraints according to claim 5, characterized in that: The expression of the first-layer virtual control law is: ； ； in, represents the first-level virtual control law, represents the posture mapping matrix, represents the gain matrix, represents the first error variable, represents the first compensation error variable, represents interference terms, represents a constant, represents a symbolic function; 、 and represents the component of the first compensated error variable, and Indicates the parameters to be designed, Represents the matrix transpose symbol.

7. The method for rigid spacecraft attitude control based on finite time constraints according to claim 5, characterized in that: The expression of the dynamic error compensation signal is: ； in, represents the error compensation signal, Indicates the parameters to be designed, represents the gain matrix, represents the posture mapping matrix, represents the output signal of the filter, represents the first-level virtual control law, represents the compensation gain parameter, Represents a symbolic function.

8. The method for rigid spacecraft attitude control based on finite time constraints according to claim 7, characterized in that: The compensation gain parameter The satisfied relationship is: ;in, represents the upper bound of the matrix norm, represents the gain matrix, Represents a positive constant.

9. A rigid spacecraft attitude control system based on finite time constraints, characterized in that: include: A construction module is used to construct a spacecraft attitude control system model and a finite time convergence performance function with a preset time constant; a conversion module, configured to impose dynamic attitude constraints on the system state of the spacecraft attitude control system model according to the finite time convergence performance function; convert the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtain an error conversion variable according to the differential homeomorphism mapping; The output module is used to design a virtual control law and construct an error compensation module according to the error conversion variable, and output an actual control input law according to the virtual control law and the error compensation module.

10. A spacecraft, characterized in that: Including a rigid spacecraft attitude control system based on finite time constraints as described in claim 9.

Images