A rigid spacecraft attitude control method and system based on finite time constraint

Abstract

This invention relates to a rigid spacecraft attitude control method and system based on finite-time constraints, belonging to the field of spacecraft attitude control technology. It includes: constructing a spacecraft attitude control system model and a finite-time convergence performance function containing a preset time constant; applying dynamic attitude constraints to the system state of the spacecraft attitude control system model according to the finite-time convergence performance function; transforming the attitude constraints into a differential homeomorphism mapping in an unconstrained space; obtaining error transformation variables based on the differential homeomorphism mapping; designing a virtual control law and constructing an error compensation module based on the error transformation variables; and designing an actual control input law based on the virtual control law and the error compensation module. This invention ensures rapid convergence of the spacecraft attitude within a predetermined time, significantly improving the dynamic response accuracy of the spacecraft during rapid attitude maneuvers, effectively avoiding control cycle delays, and reducing power consumption.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology, and in particular to a rigid spacecraft attitude control method and system based on finite time constraints. Background Technology

[0002] Current spacecraft attitude control primarily employs Proportional-Integral-Derivative (PID) control. Through the coordinated adjustment of proportional, integral, and derivative components, it achieves attitude maintenance for basic scenarios such as Earth orientation for communication satellites. This method is simple in structure, easy to implement in engineering, and performs stably in single-satellite steady-state operation missions, laying a solid technical foundation for the early development of the space industry. However, as space missions evolve towards greater complexity, the limitations of traditional control methods are becoming increasingly apparent. In on-orbit servicing missions, the docking process between the spacecraft and the target satellite requires attitude control to achieve fluctuation-free convergence with millisecond-level response speeds, while PID control parameter tuning struggles to balance dynamic performance and steady-state accuracy. Furthermore, sudden disturbances in the space environment, such as solar wind, further test the anti-interference capabilities of the control system. Therefore, current spacecraft attitude control technology needs to focus on solving core issues such as suppressing attitude fluctuations, shortening convergence time, and enhancing anti-interference capabilities, 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 handle sudden changes in solar radiation pressure and inertia variations caused by fuel consumption. While improved fuzzy adaptive PID can achieve parameter self-adjustment, it still faces the challenge of balancing response speed and steady-state accuracy. Adaptive control, through real-time parameter adjustment, can maintain system stability even when spacecraft experience inertia changes due to fuel consumption. Sliding mode control achieves precise tracking thanks to its variable structure characteristics, but its inherent chattering phenomenon exacerbates propellant consumption and component wear, which cannot be completely eliminated even with boundary layer technology. Furthermore, most of the aforementioned control strategies focus on the steady-state accuracy of the spacecraft's final attitude. However, as space missions become increasingly complex, the requirements for spacecraft attitude control have evolved from simply considering steady-state accuracy to addressing the issue of coordinated control of steady-state accuracy and real-time attitude. Against this backdrop, preset performance control, by introducing preset performance functions to dynamically constrain attitude, effectively suppresses attitude fluctuations and ensures convergence accuracy. However, such preset performance control methods are usually based on fixed exponential convergence performance functions. Although the attitude error can be limited to a specified range by preset performance functions, it will take a long time for the actual attitude of the spacecraft to stabilize to the desired attitude. It cannot guarantee accurate convergence within a certain time, which limits its application in rapid maneuvering space missions.

[0004] To address the aforementioned issues, an existing patent (CN118457945A) proposes a spacecraft attitude variable performance control method considering input saturation. This method first establishes a spacecraft dynamics model incorporating external disturbances and input saturation; then, it constructs a preset attitude performance model using an error transformation function; finally, it designs an adaptive variable performance function differential equation to dynamically adjust the transient response boundary, thereby suppressing attitude overshoot, optimizing transient response, and ensuring system stability. However, the attitude stabilization process under this method is time-consuming and cannot be applied to scenarios involving rapid maneuvering missions. Another existing patent (CN120029339A) proposes a spacecraft preset time and preset accuracy attitude tracking control method and system based on performance functions. This method first establishes a spacecraft attitude dynamics model; then, it designs a performance function containing trigonometric functions to dynamically constrain the attitude tracking error, and constructs a continuous non-singular adaptive attitude tracking controller. This method can achieve precise convergence of the spacecraft attitude to a preset accuracy within a preset time, effectively solving the problem of long attitude stabilization time in traditional methods. However, the trigonometric function calculations in the preset performance function of this method increase the real-time computational burden on the spacecraft processor, leading to control cycle delays and increased power consumption, which affects real-time performance in rapid maneuvering scenarios. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of slow convergence speed, excessive time consumption in attitude stabilization process, delay in control cycle and significant increase in power consumption in the prior art.

[0006] In a first aspect, to solve the above-mentioned technical problems, the present invention provides a rigid spacecraft attitude control method based on finite time constraints, comprising:

[0007] Construct a spacecraft attitude control system model and a finite-time convergence performance function with a preset time constant, respectively.

[0008] Based on the finite-time convergence performance function, dynamic attitude constraints are applied to the system state of the spacecraft attitude control system model; the attitude constraints are transformed into a differential homeomorphism mapping in an unconstrained space; based on the differential homeomorphism mapping, error transformation variables are obtained; based on the error transformation variables, a virtual control law is designed and an error compensation module is constructed; based on the virtual control law and the error compensation module, the actual control input law is obtained.

[0009] In one embodiment of the present invention, the expression for the finite-time convergence performance function is:

[0010] ;

[0011] in, Indicates the initial value. Represents the system final value. Represents a constant. This indicates the preset convergence time. Indicates time.

[0012] In one embodiment of the present invention, 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, transforming the attitude constraints into a differential homeomorphism in an unconstrained space, and obtaining the error transformation variables according to the differential homeomorphism are as follows:

[0013] Obtain the system state in the spacecraft attitude control system model; apply dynamic attitude constraints to the system state according to the finite-time convergence performance function;

[0014] Based on the attitude constraints, a strictly monotonically increasing function is introduced, and a differential homeomorphism is constructed using the hyperbolic tangent function; wherein, the strictly monotonically increasing function satisfies the following condition:

[0015] ;

[0016] ;

[0017] The expression for constructing the differential homeomorphism mapping relation using the hyperbolic tangent function is as follows:

[0018] ;

[0019] The error transformation variable is obtained by inversely solving the differential homeomorphism mapping relationship; wherein the expression of the error transformation variable is:

[0020] ;

[0021] Taking the time derivative of the error transformation variable yields the unconstrained space variable; wherein, the expression for the unconstrained space variable is:

[0022] ;

[0023] in, This represents a strictly monotonically increasing function. Indicates the error transformation variable. and Indicates the boundary adjustment parameter. Indicates the system status. This represents the finite-time convergence performance function; Represents the gain matrix. Indicates the distractor. This represents the angular velocity vector in the body coordinate system. This represents the attitude mapping matrix.

[0024] In one embodiment of the present invention, dynamic attitude constraints are applied to the system state according to the finite-time convergence performance function, wherein the expression for the attitude constraints is:

[0025] ;

[0026] ;

[0027] in, and Indicates the boundary adjustment parameter. This represents the finite-time convergence performance function. Indicates the system status. Represents a constant.

[0028] In one embodiment of the present invention, the steps of designing a virtual control law and constructing an error compensation module based on the error transformation variable, and obtaining the actual control input law based on the virtual control law and the error compensation module are as follows:

[0029] Construct a finite-time command filter; based on the finite-time command filter, construct a dynamic error compensation signal; wherein, the expression of the finite-time command filter is:

[0030] ;

[0031] in, This represents the first-level virtual control law; and This represents the output signal of the filter; and Indicates an adjustable parameter; Represents a symbolic function; Indicates the intermediate control variables of the instruction filter;

[0032] Based on the error transformation variables, construct the first error variable;

[0033] Based on the dynamic error compensation signal and the first error variable, the first compensation error variable is obtained;

[0034] Based on the first compensation error variable, construct the first-level virtual control law;

[0035] Based on the first-level virtual control law, the output signal of the finite-time command filter is obtained; based on the output signal and the spacecraft attitude control system model, a second error variable is constructed; based on the second error variable, the actual control input law is obtained; wherein the expression of the actual control input law is:

[0036] ;

[0037] ;

[0038] in, Indicates the error variable. Represents a constant. Represents the spacecraft's moment of inertia matrix; and Indicates the parameters to be designed; , and Represents error variable The amount, This represents the matrix transpose symbol.

[0039] In one embodiment of the present invention, the expression of the first-layer virtual control law is:

[0040] ;

[0041] ;

[0042] in, This represents the first-level virtual control law. Represents the attitude mapping matrix. Represents the gain matrix. Indicates the first error variable. Indicates the first compensation error variable. Indicates the distractor. Represents a constant. Represents a symbolic function; , and This represents the components of the first compensation error variable. and Indicates the parameters to be designed. This represents the matrix transpose symbol.

[0043] In one embodiment of the present invention, the expression for the dynamic error compensation signal is:

[0044] ;

[0045] in, This represents the error compensation signal. Indicates the parameters to be designed. Represents the gain matrix. Represents the attitude mapping matrix. This represents the output signal of the filter. This represents the first-level virtual control law. Indicates the compensation gain parameter. Represents a symbolic function.

[0046] In one embodiment of the present invention, the compensation gain parameter The relationship that satisfies this is: ;in, Denotes the upper bound of the matrix norm. Represents the gain matrix. Represents a positive integer.

[0047] Secondly, to solve the above-mentioned technical problems, the present invention provides a rigid spacecraft attitude control system based on finite time constraints, comprising:

[0048] The construction module is used to construct the spacecraft attitude control system model and the finite-time convergence performance function with preset time constants, respectively.

[0049] The transformation module is used to apply dynamic attitude constraints to the system state of the spacecraft attitude control system model according to the finite-time convergence performance function; transform the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtain error transformation variables according to the differential homeomorphism mapping.

[0050] The output module is used to design a virtual control law and construct an error compensation module based on the error transformation variable, and output the actual control input law based on the virtual control law and the error compensation module.

[0051] Thirdly, in order to solve the above-mentioned technical problems, the present invention provides a spacecraft, including the above-mentioned rigid spacecraft attitude control system based on finite time constraints.

[0052] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0053] (1) The rigid spacecraft attitude control method and system based on finite-time constraints described in this invention effectively solves two core problems of traditional attitude constraint control methods by constructing a finite-time convergence performance function: first, the inability to actively constrain the fluctuation amplitude of spacecraft attitude error; and second, the lack of precise control over the time required to converge to the preset attitude. This significantly improves the control performance of spacecraft in rapid maneuvering scenarios. This invention transforms attitude constraints into differential homeomorphisms in unconstrained spaces, cleverly avoiding the controller design complexity problem caused by directly processing constraint conditions in traditional attitude constraint control methods. A virtual control law is designed based on the error transformation variable, 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 constraint process of attitude error, further improving the engineering practicality of the algorithm. This not only reduces power consumption but also avoids control cycle delay, enhancing the real-time performance and reliability of the system.

[0054] (2) This invention organically combines finite-time control theory with command filtering technology, which reduces computational complexity and 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 achieving synergistic optimization of computational complexity and control real-time performance.

[0055] (3) Based on the Lyapunov function theory, this invention rigorously proves that under the presence of disturbance, the attitude error can converge to the preset region within a preset time, enabling the spacecraft to accurately realize the attitude adjustment process and meet the needs of complex missions such as deep space exploration and on-orbit service for fast and high-precision attitude control.

[0056] (4) The present invention can effectively solve the problem that existing technologies are unable to simultaneously achieve the specified attitude within a preset time and effectively suppress interference when spacecraft face external space interference and convergence time constraints, thereby meeting the strict requirements for high-precision and high-efficiency attitude control in complex space environments. Attached Figure Description

[0057] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0058] Figure 1 This is a flowchart of a rigid spacecraft attitude control method based on finite time constraints in a preferred embodiment of the present invention.

[0059] Figure 2This is a comparison chart of the finite-time convergence performance function and the exponential convergence performance function in a preferred embodiment of the present invention;

[0060] Figure 3 This is a graph showing the finite-time performance function curves under different convergence times in a preferred embodiment of the present invention;

[0061] Figure 4 This is a convergence curve of the spacecraft attitude and constraint boundary under finite time constraints when the preset convergence time is 8 seconds in a preferred embodiment of the present invention;

[0062] Figure 5 This is a finite-time convergence characteristic curve of the spacecraft's angular velocity response when the preset convergence time is 8 seconds in a preferred embodiment of the present invention;

[0063] Figure 6 This is a curve 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.

[0064] Figure 7 The graph shows a comparison of the spacecraft attitude response of the two control methods when the preset convergence time is 4 seconds in a preferred embodiment of the present invention.

[0065] Figure 8 The graph shows a comparison of the spacecraft attitude response of the two control methods when the preset convergence time is 8 seconds in a preferred embodiment of the present invention. Detailed Implementation

[0066] 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 and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0067] Example 1:

[0068] Reference Figure 1 As shown, this invention provides a rigid spacecraft attitude control method based on finite time constraints, including but not limited to the following steps:

[0069] S1. Construct the spacecraft attitude control system model and the finite-time convergence performance function with a preset time constant, respectively;

[0070] 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 in an unconstrained space; obtain the error transformation variables based on the differential homeomorphism.

[0071] S3. Based on the error transformation variable, design a virtual control law and construct an error compensation module. Obtain the actual control input law based on the virtual control law and the error compensation module.

[0072] This invention provides a rigid spacecraft attitude control method based on finite-time constraints. By constructing a finite-time convergence performance function, it effectively solves the problems of traditional attitude constraint control methods, such as the inability 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 transforming attitude constraints into differential homeomorphisms in an unconstrained space, it solves the problem of complex controller design caused by directly processing constraint conditions in traditional attitude constraint control methods. This method designs a virtual control law based on error transformation variables and constructs an error compensation module, avoiding the computational complexity caused by high-order derivatives in traditional methods and improving the computational efficiency of the algorithm. 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 derivatives is synchronized with the attitude error constraint process, further improving the engineering practicality of the algorithm, reducing power consumption, and avoiding control cycle delay. Therefore, the embodiments of the present invention can effectively solve the problem that existing technologies cannot simultaneously achieve the specified attitude within a preset time and effectively suppress interference when spacecraft face external space interference and convergence time constraints, thereby meeting the requirements for high-precision and high-efficiency attitude control in complex space environments.

[0073] Specifically, for step S1, based on the kinematic laws of rigid bodies, the dynamic equations for the spacecraft's spatial attitude motion are constructed, and their specific expressions are as follows:

[0074] ;

[0075] in, Represents the spacecraft's moment of inertia matrix. This represents the angular velocity vector in the body coordinate system. Indicates control torque. Indicates external disturbance torque; symbol " " represents the operation from a vector to a skew-symmetric matrix, This represents the matrix transpose symbol.

[0076] Furthermore, the spacecraft's rotational inertia matrix antisymmetric matrix of angular velocity vector The specific forms are as follows:

[0077] , ;

[0078] in, , Equations represent the spacecraft's moment of inertia matrix. The corresponding components. Similarly, , and Antisymmetric matrix representing the angular velocity vector Corresponding components.

[0079] Furthermore, when describing attitude based on the modified Rodriguez parameters, the attitude parameter vector is defined as follows: Its kinematic equations are:

[0080] ;

[0081] in, The attitude mapping matrix is ​​expressed as follows: , for The identity matrix, for The antisymmetric matrix. The modified Rodrigues parameters satisfy the unit vector constraint. , used to ensure It is reversible and bounded.

[0082] Furthermore, combining attitude kinematics and dynamic equations, the spacecraft attitude control model is constructed as follows:

[0083] ;

[0084] in, This represents the nonlinear term of angular velocity coupling; This is the normalized term for the external disturbance torque. In practical engineering applications, the external disturbance torque... satisfy ,in To interfere with the upper bound constant, The norm symbol is used to represent the norm. It can be derived from the boundedness of the modified Rodrigues parameter and the properties of matrix norms. ,in This is a positive upper bound constant that integrates rotational inertia, angular velocity, and disturbance characteristics. This design lays the foundation for stability analysis of spacecraft attitude control systems in practical engineering scenarios.

[0085] Specifically, a finite-time convergence performance function with a preset time constant is constructed, and its mathematical expression is as follows:

[0086] ;

[0087] in, Indicates the initial value. Represents the system final value. Represents a constant. This indicates the preset convergence time. When time... hour, ;when hour, Ensure that The convergence was completed within the timeframe.

[0088] The finite-time convergence performance function constructed in this embodiment of the 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 a preset boundary, thus significantly improving the dynamic response accuracy of the spacecraft during rapid attitude maneuvers.

[0089] 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 transformation error, thus solving the problem of complex controller design caused by directly handling constraint conditions in traditional attitude constraint control methods.

[0090] Furthermore, the specific steps of step S2, which transforms the attitude constraint into a differential homeomorphism of the unconstrained space through an error transformation mechanism, are as follows:

[0091] S210. Obtain the system state from the spacecraft attitude control system model. Based on the finite-time convergence performance function Regarding system status Apply dynamic attitude constraints (also known as boundary constraints), the specific expression of which is:

[0092] ;

[0093] ;

[0094] in, and Indicates boundary adjustment parameters; It is a constant used to ensure that the initial error is within the constraint interval.

[0095] S220. In order to transform the bounded constraint problem into a control problem in an unconstrained space, a strictly monotonically increasing function is introduced. Furthermore, a differential homeomorphism is constructed using the hyperbolic tangent function. Among these, the strictly monotonically increasing function... The relationship that satisfies this is:

[0096] ;

[0097] .

[0098] The expression for constructing the differential homeomorphism relation using the hyperbolic tangent function is as follows:

[0099] ;

[0100] in, This represents a strictly monotonically increasing function. This represents the error transformation variable.

[0101] S230. The error transformation variable is obtained by inversely solving the differential homeomorphism mapping relationship. Its specific expression is as follows:

[0102] .

[0103] S240, Error Transformation Variable Taking the time derivative and simplifying it, we obtain the matrix form, whose specific expression is:

[0104] ;

[0105] Wherein, the gain matrix Its elements Interference items Its specific elements are represented as follows:

[0106] .

[0107] The embodiments of the present invention construct an attitude error transformation mechanism, which uses differential homeomorphism mapping to transform the bounded attitude error space into an unconstrained control space, realizing the equivalent transformation of the constraint problem, while avoiding the complexity caused by directly dealing with inequality constraints, and effectively simplifying the design process of the controller.

[0108] Specifically, in step S3, a virtual control law is designed using the backstepping method and an error compensation module is constructed. Based on the virtual control law and the error compensation module, the actual control input law is designed. The specific steps are as follows:

[0109] S310. To address the computational complexity issue caused by high-order derivatives in the traditional backstepping method, a finite-time instruction filter is employed. This filter replaces the complex derivative process with a feedforward compensation mechanism, and its specific expression is as follows:

[0110] ;

[0111] in, This represents the input signal of the filter, i.e., the first-level virtual control law; This represents an adjustable parameter that determines the convergence speed of the filter. and The output signal of the filter is represented as... and its derivative The estimated value; Indicates the intermediate control variables of the instruction filter; The sign function is defined as follows:

[0112] ;

[0113] in, Indicates variable symbol.

[0114] Furthermore, through a nonlinear feedback mechanism and appropriate Parameter design allows the filter to satisfy the estimation error within a finite time. ,in Represents a positive constant.

[0115] Furthermore, to eliminate errors caused by filtering, a dynamic error compensation signal is introduced. Its specific expression is:

[0116] ;

[0117] in, Indicates the parameters to be designed. This represents the compensation gain parameter, and ; For symbolic function vectors; , , Indicates dynamic error compensation signal The amount.

[0118] S320. Based on the error transformation variable obtained in step S240, construct the first error variable. Its specific expression is:

[0119] .

[0120] S330: Decouple the filtering error from the system dynamic error. Based on the dynamic error compensation signal... and the first error variable Define the error variable after compensation by the instruction filter, i.e., the first compensated error variable. First compensation error variable The specific expression is:

[0121] .

[0122] S340, Based on the first compensation error variable Constructing the first-level virtual control law Its specific expression is:

[0123] ;

[0124] in, Indicates the parameters to be designed, satisfying ; The expression is:

[0125] ;

[0126] in, Denotes a constant that satisfies ; , and This represents the component of the first compensation error variable.

[0127] S350, According to the first-level virtual control law The output signal of the finite-time command filter is obtained; based on the output signal and the spacecraft attitude control system model, a second error variable is constructed. Its specific expression is:

[0128] ;

[0129] in, It is the output signal of the finite-time command filter.

[0130] Furthermore, to enhance the consistency of variable representation, based on the second error variable... Define error variables as follows:

[0131] .

[0132] Furthermore, combining error variables Design the actual control input law (i.e., control torque). Its specific expression is:

[0133] ;

[0134] in, ; , and Represents error variable The amount; These are the parameters to be designed.

[0135] This invention combines finite-time control theory with command filtering technology, which reduces computational complexity and significantly shortens the convergence time of the filtering process. It effectively avoids the adverse effects of filtering delay or error accumulation on the real-time performance of attitude control, and successfully achieves synergistic optimization of computational complexity and control real-time performance.

[0136] Specifically, based on steps S1 to S3 above, a Lyapunov function is constructed to prove that the attitude error converges to a preset region within a preset time. The specific steps are as follows:

[0137] S410. Construct the first-level Lyapunov function. Its mathematical expression is:

[0138] .

[0139] Furthermore, for the first-level Lyapunov function Taking the derivative, we get:

[0140] .

[0141] Furthermore, combined with virtual control laws ,get:

[0142] .

[0143] S420. Construct the second-level Lyapunov function. Its mathematical expression is:

[0144] .

[0145] Furthermore, regarding Differentiate and introduce the dynamic equation The results are as follows:

[0146] ;

[0147] Among them, the definition According to Young's inequality, the following relationship holds:

[0148] .

[0149] Furthermore, the actual control input Substituting into the derivative of the second-level Lyapunov function In the middle, we get:

[0150] .

[0151] because , All are bounded, let their norm upper bounds be respectively and ,Right now , Using the properties of Young's inequality, we can obtain:

[0152] ; (1)

[0153] .

[0154] because Therefore, for After simplification, we get:

[0155]

[0156] Furthermore, let , , , Simplifying formula (1) yields:

[0157]

[0158] S430, when hour, and Can be done in a limited time Convergence, and To ensure the first error variable It can converge in a finite time, thus ensuring Bounded, requires further proof. The Lyapunov function for the compensation signal has finite-time convergence. Therefore, the Lyapunov function for the compensation signal is designed as follows:

[0159] .

[0160] Furthermore, regarding Differentiation yields:

[0161] .

[0162] Based on the design of the instruction filter, there exists a finite time... Make Therefore:

[0163] ;

[0164] in This is the upper bound of the matrix norm. Therefore, It can be represented as:

[0165]

[0166] Furthermore, let ,get:

[0167] .

[0168] Therefore, as long as the design parameters That can guarantee In a limited time It converges inward to a small neighborhood near the origin.

[0169] Combining steps S410 to S430 above, the actual total convergence time of the spacecraft attitude control system is: .when At that time, error variable and Both are bounded, combined with error transformation relationships. The attitude error can be obtained by satisfying: That is, the spacecraft's attitude remains within a preset time. The system converges strictly to the dynamic constraint boundary, verifying the finite-time stability of the control strategy.

[0170] Furthermore, the embodiments of the present invention have the following advantages compared to the prior art:

[0171] The finite-time convergence performance function constructed in this invention ensures that the spacecraft's attitude converges rapidly within a predetermined time and strictly limits the error fluctuation amplitude and steady-state error within preset boundaries, thereby improving 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 constrained problem while avoiding the complexity of directly handling inequality constraints, effectively simplifying the controller design process. A finite-time command filter is introduced, replacing the high-order derivatives in the backstepping method with parameterized filter design. This not only reduces computational complexity and avoids singular problems, but also, through the finite-time convergence characteristics of the filter itself, synchronizes the estimation process of the virtual control signal and its derivative with the constraint process of the attitude error, further improving the engineering practicality of the algorithm. Based on Lyapunov function theory, this invention rigorously proves that, under the presence of disturbances, the attitude error can converge to a preset region within a preset time, enabling the spacecraft to accurately achieve the attitude adjustment process and meeting the requirements of rapid and high-precision attitude control for complex missions such as deep space exploration and on-orbit servicing.

[0172] To verify the effectiveness of the method described in the embodiments of the present invention, a simulation experiment was designed and conducted. The specific steps of the simulation experiment are as follows.

[0173] Step 1: Construct a spacecraft attitude control system model based on modified Rodriguez parameters. First, construct the spacecraft attitude dynamics and kinematics model based on modified Rodriguez parameters as follows:

[0174] .

[0175] The model was constructed based on actual settings of rotational inertia parameters and assumptions about external disturbances. This is the rotational inertia matrix of the spacecraft, with specific parameters as follows:

[0176] ;

[0177] This is the angular velocity vector of the spacecraft in its body coordinate system; It is the control torque; The expression is ; This represents external disturbance torques, which originate from external environmental factors such as solar radiation pressure, Earth's gravitational gradient, and atmospheric drag. The specific parameters are set as follows:

[0178] .

[0179] In the spacecraft attitude kinematics equations This refers to the nonlinear term related to the spacecraft's angular velocity. This is the normalized term for the external disturbance torque, representing the effect of the disturbance on the attitude. The initial corrected Rodriguez parameters are defined. This represents the spacecraft's attitude state at the initial moment; initial angular velocity. This indicates that the spacecraft was not rotating at the initial moment.

[0180] Step 2: Design a finite-time convergence performance function with a preset time constant. First, design the finite-time convergence performance function as follows:

[0181] ;

[0182] Among them, setting initial values System final value ,constant Preset convergence time Different values ​​are selected based on the requirements of subsequent simulation experiments. Therefore, the function... Can guarantee when hour, ;when hour, To ensure the system is Convergence is achieved within a specified time.

[0183] To verify the effectiveness of the finite-time performance function designed in the embodiments of the invention, its initial values ​​are set to be similar to those of the traditional exponential convergence function. Final value Completely identical, and comparative simulations were performed. The simulation results are referenced. Figure 2 The traditional exponential convergent performance function is expressed as follows: Its convergence rate is a constant The decision, in theory, requires an infinite amount of time to approach. The functions in the embodiments of the present invention are Strict convergence to .from Figure 2It can be seen that when setting When the traditional exponential convergence function is in Still with There is a significant deviation, and the curve shows an asymptotic decay trend; while the function in the embodiment of the present invention... The time has converged precisely to And in The steeper convergence slope within the interval fully demonstrates that the finite-time performance function proposed in this embodiment of the invention has good transient performance.

[0184] Furthermore, in practical engineering applications, the convergence time needs to be set independently based on the timing requirements of the specific task and the performance indicators of the control system. For example, rapid maneuvering missions of spacecraft require... Attitude adjustments can be completed within seconds, whereas conventional orbital maintenance allows for... The convergence period is in seconds. Different The corresponding finite-time performance function curve is shown in Figure 3. This design gives the system significant advantages in timing control: on the one hand, through explicit adjustment... It can flexibly match the different convergence speed requirements of tasks, effectively avoiding the problem of uncontrollable convergence time in traditional methods; on the other hand, based on 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 operating conditions, providing a quantitative design basis for system stability and real-time control.

[0185] Step 3: Transform the attitude constraints into a differential homeomorphism in an unconstrained space using an error transformation mechanism, and optimize the parameters. .

[0186] Step 4: In designing the virtual control law and constructing the error compensation module using the backstepping method, the optimal parameters are selected. In the error compensation signal, select parameters. In the first layer of virtual control law design In the middle, select parameters In the actual control input law design, parameters are selected. .

[0187] Step 5: MATLAB simulation was used to verify the convergence characteristics of the spacecraft attitude controller designed in this embodiment of the invention within a finite time. Simultaneously, a comparison with traditional constraint methods demonstrated its advantages in transient performance and verified the algorithm's effective constraints on overshoot and convergence rate. The simulation results are as follows:

[0188] Reference Figure 4 , Figure 4 Demonstrates spacecraft attitude The performance function that converges in finite time The curve showing the change in spacecraft attitude over time under constraints. As can be seen from the figure, the spacecraft attitude changes over a finite time... The convergence to the preset stable region indicates that the method described in this embodiment of the invention can achieve finite-time constraint control of the spacecraft's attitude.

[0189] Reference Figure 5 , Figure 5 Demonstrates the angular velocity of the spacecraft The change over time. As shown in the graph, the angular velocity can... It converges within a finite time, and the angular velocity response curve is smooth without drastic fluctuations.

[0190] Reference Figure 6 , Figure 6 Demonstrates spacecraft control input torque The curve shows the change over time. As can be seen from the graph, the control input torque... It gradually decreases over a finite period of time and eventually tends to stabilize.

[0191] Step 6: To verify the superiority of the finite-time control constraint method described in this embodiment of the invention, a comparative analysis is performed with the traditional constraint control method using an exponential preset performance function. The controller design of the traditional constraint control method is as follows:

[0192] ;

[0193] ;

[0194] .

[0195] Select control parameters that have the same values ​​as the controller designed in the embodiments of the present invention. And the convergence rate of the performance function Consistent with the convergence rate of the finite-time performance function constructed in the embodiments of the present invention, the following simulation results are obtained:

[0196] Reference Figure 7 , Figure 7 It shows the convergence time. Spacecraft attitude The finite-time constraint function designed in the embodiments of the present invention The curves under the influence, and the spacecraft attitude In traditional preset performance functions The curves under the action are shown. The results indicate that, under the same control parameters and convergence rate, both control methods can achieve spacecraft attitude stabilization control, but their dynamic performance differs significantly. The method described in this invention operates under finite-time constraint functions. Under this influence, the time required to enter the preset stable region from the initial error state is shorter, and the slope of the response curve is steeper, indicating a faster error decay rate. Compared to traditional methods, the method of this invention can quickly suppress attitude deviations in the initial stage through a nonlinear feedback mechanism, demonstrating superior transient tracking capability. The convergence speed of traditional constraint control is significantly lagging. Its constraint effect is mainly on attitude... This effect is only noticeable when the error approaches the constraint boundary. The error curve decays slowly in the early stages, and the control variable only has a strong regulating effect when the error value approaches the preset boundary, resulting in a longer overall convergence time.

[0197] Reference Figure 8 , Figure 8 It shows the convergence time. At that time, spacecraft attitude The finite-time constraint function designed in this invention The curves under the influence, and the spacecraft attitude In traditional preset performance functions The curves under the influence of the two methods are shown. Observation and analysis reveal that, from the perspective of the convergence process, both methods achieve constrained control of the spacecraft's attitude, but their convergence characteristics differ significantly. Although the constraint function designed in this invention... In the initial stage of control, attitude The convergence speed is slower than the convergence speed of the traditional preset performance function. However, the pose under the action of the method described in this invention can be clearly seen through the details of the sub-graph. Able to be in the preset time The attitude converges to the preset stability region, while at the same time the traditional performance function is applied. Its error value is still higher than the expected accuracy threshold, and convergence has not yet been completed.

[0198] Furthermore, combined Figure 7 and Figure 8 ,exist and Attitude under two different convergence time settings Both can converge quickly to the target stability region, and the convergence time is similar to... The strict matching of the set values ​​fully demonstrates that the control method designed in this invention achieves 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 precisely adjusted within the pre-set time window, demonstrating the time deterministic advantage that traditional methods do not possess.

[0199] Example 2:

[0200] 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 that of the rigid spacecraft attitude control method based on finite time constraints provided in Embodiment 1, and the repeated parts will not be described again.

[0201] This embodiment provides a rigid spacecraft attitude control system based on finite time constraints, including:

[0202] The construction module is used to construct the spacecraft attitude control system model and the finite-time convergence performance function with preset time constants, respectively.

[0203] The transformation module is used to apply dynamic attitude constraints to the system state of the spacecraft attitude control system model according to the finite-time convergence performance function; transform the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtain the error transformation variables based on the differential homeomorphism mapping.

[0204] The output module is used to design a virtual control law and build an error compensation module based on the error transformation variable, and output the actual control input law based on the virtual control law and the error compensation module.

[0205] Example 3:

[0206] This embodiment provides a spacecraft, including the rigid spacecraft attitude control system based on finite time constraints described in Embodiment 2.

[0207] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0208] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0209] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0210] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0211] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A rigid spacecraft attitude control method based on finite time constraints, characterized in that, include: Construct a spacecraft attitude control system model and a finite-time convergence performance function with a preset time constant, respectively. Based on the finite-time convergence performance function, dynamic attitude constraints are applied to the system state of the spacecraft attitude control system model; the attitude constraints are transformed into a differential homeomorphism in an unconstrained space; and error transformation variables are obtained based on the differential homeomorphism; wherein, the steps for obtaining the error transformation variables are as follows: Obtain the system state in the spacecraft attitude control system model; apply dynamic attitude constraints to the system state according to the finite-time convergence performance function; Based on the attitude constraints, a strictly monotonically increasing function is introduced, and a differential homeomorphism is constructed using the hyperbolic tangent function; wherein, the strictly monotonically increasing function satisfies the following condition: ； ； The expression for constructing the differential homeomorphism mapping relation using the hyperbolic tangent function is as follows: ； The error transformation variable is obtained by inversely solving the differential homeomorphism mapping relationship; wherein the expression of the error transformation variable is: ； Taking the time derivative of the error transformation variable yields the unconstrained space variable; wherein, the expression for the unconstrained space variable is: ； in, This represents a strictly monotonically increasing function. Indicates the error transformation variable. and Indicates the boundary adjustment parameter. Indicates the system status. This represents the finite-time convergence performance function; Represents the gain matrix. Indicates the distractor. This represents the angular velocity vector in the body coordinate system. Represents the attitude mapping matrix; Based on the error transformation variable, a virtual control law is designed and an error compensation module is constructed. The actual control input law is then obtained based on the virtual control law and the error compensation module. The steps for obtaining the actual control input law are as follows: Construct a finite-time command filter; based on the finite-time command filter, construct a dynamic error compensation signal; wherein, the expression of the finite-time command filter is: ； in, This represents the first-level virtual control law; and This represents the output signal of the filter; and Indicates an adjustable parameter; Represents a symbolic function; Indicates the intermediate control variables of the instruction filter; Based on the error transformation variables, construct the first error variable; Based on the dynamic error compensation signal and the first error variable, the first compensation error variable is obtained; Based on the first compensation error variable, construct the first-level virtual control law; Based on the first-level virtual control law, the output signal of the finite-time command filter is obtained; based on the output signal and the spacecraft attitude control system model, a second error variable is constructed; based on the second error variable, the 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's moment of inertia matrix; and Indicates the parameters to be designed; , and Represents error variable The amount, This represents the matrix transpose symbol.

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

3. The rigid spacecraft attitude control method based on finite time constraints according to claim 1, characterized in that, Based on the finite-time convergence performance function, dynamic attitude constraints are applied to the system state, wherein the expression for the attitude constraints is: ； ； in, and Indicates the boundary adjustment parameter. This represents the finite-time convergence performance function. Indicates the system status. Represents a constant.

4. The rigid spacecraft attitude control method based on finite time constraints according to claim 1, characterized in that, The expression for the first-level virtual control law is: ； ； in, This represents the first-level virtual control law. Represents the attitude mapping matrix. Represents the gain matrix. Indicates the first error variable. Indicates the first compensation error variable. Indicates the distractor. Represents a constant. Represents a symbolic function; , and This represents the components of the first compensation error variable. and Indicates the parameters to be designed. This represents the matrix transpose symbol.

5. The rigid spacecraft attitude control method based on finite time constraints according to claim 1, characterized in that, The expression for the dynamic error compensation signal is: ； in, This represents the error compensation signal. Indicates the parameters to be designed. Represents the gain matrix. Represents the attitude mapping matrix. This represents the output signal of the filter. This represents the first-level virtual control law. Indicates the compensation gain parameter. Represents a symbolic function.

6. The rigid spacecraft attitude control method based on finite time constraints according to claim 5, characterized in that, The compensation gain parameter The relationship that satisfies this is: ;in, Denotes the upper bound of the matrix norm. Represents the gain matrix. Represents a positive integer.

7. A rigid spacecraft attitude control system based on finite time constraints, used to implement the rigid spacecraft attitude control method based on finite time constraints as described in any one of claims 1 to 6, characterized in that, include: The construction module is used to construct the spacecraft attitude control system model and the finite-time convergence performance function with preset time constants, respectively. The transformation module is used to apply dynamic attitude constraints to the system state of the spacecraft attitude control system model according to the finite-time convergence performance function; transform the attitude constraints into a differential homeomorphism mapping in an unconstrained space; and obtain error transformation variables according to the differential homeomorphism mapping. The output module is used to design a virtual control law and construct an error compensation module based on the error transformation variable, and output the actual control input law based on the virtual control law and the error compensation module.

8. A spacecraft, characterized in that, Including the rigid spacecraft attitude control system based on finite time constraints as described in claim 7.

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