A spacecraft active disturbance rejection control method with time delay and actuator saturation

Abstract

A spacecraft auto-disturbance rejection control method with time delay and actuator saturation includes the following steps: S1: establishing a spacecraft attitude integrated dynamics model with communication time delay and actuator saturation; S2: designing an outer-loop expansion state observer with a time delay predictor; S3: designing an outer-loop auto-disturbance rejection controller; S4: designing an inner-loop expansion state observer; S5: designing an inner-loop auto-disturbance rejection controller with an anti-saturation strategy. The spacecraft auto-disturbance rejection control method with time delay and actuator saturation described in the present invention can not only effectively avoid the adverse effects of external and internal disturbances on the system, but also has a significant inhibitory effect on communication time delay and actuator saturation phenomena, and can ensure that the position and attitude of the spacecraft are accurately controlled within the controllable range of the actuator, providing sufficient guarantee for the smooth completion of tasks such as spacecraft rendezvous and docking, has good control effect, and is widely used in other spacecraft attitude and orbit control systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft attitude and orbit control, and in particular relates to a spacecraft anti-disturbance control method with time lag and actuator saturation. Background Art

[0002] Spacecraft control has always been a crucial component of space missions. During these missions, spacecraft must complete various tasks under harsh environmental conditions, such as orbit adjustment, target acquisition, docking, and attitude control. However, during these missions, spacecraft are subject to a variety of interferences and disturbances. These interferences can come from the external environment, the spacecraft itself, or errors in sensors and actuators, posing challenges to the performance and stability of control systems.

[0003] In the field of spacecraft control technology, common control methods include classical PID control, model predictive control, sliding mode control, and adaptive control. These methods have been widely used in specific situations, but they also have some drawbacks that limit their performance and reliability in complex tasks. (1) Classical PID controllers usually rely on prior knowledge and manually adjusted parameters. When faced with unknown environments and complex tasks, classical PID control may not be able to provide sufficient robustness and performance; (2) Model predictive control requires the establishment of an accurate dynamic model. Model errors, incomplete modeling, and real-time computational complexity may lead to a decrease in the performance of model predictive control; (3) Sliding mode control usually requires certain prior information and very fast switching control, which may lead to high-frequency actuator motion, thereby increasing mechanical wear and energy consumption; (4) Adaptive control methods perform well in the face of unknown or changing environments, but require more complex parameter estimation and adaptive algorithms, which increases the complexity and computational requirements of the control system.

[0004] As can be seen from the above, while these traditional control methods perform well in some situations, their performance and robustness may be limited when faced with complex and changing aerospace missions. Issues such as time delay and actuator saturation further exacerbate the challenges of these traditional methods.

[0005] To address these technical challenges, active disturbance rejection control (ADRC) has been widely researched and applied. ADRC is an advanced control strategy designed to effectively offset disturbances in a system to maintain performance and stability. The core concept of ADRC is to incorporate disturbance information into the control system, enabling the controller to perceive and offset the effects of disturbances in real time. This helps improve spacecraft control performance and enable better adaptation to complex and changing environments.

[0006] Time delay is a significant issue in spacecraft control, potentially leading to control system instability and degrading performance. Furthermore, actuator saturation is a common problem in spacecraft control. This occurs when the output of an actuator reaches its physical limits, potentially preventing the control system from maintaining the desired trajectory or stability. Summary of the Invention

[0007] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a spacecraft self-disturbance rejection control method with time delay and actuator saturation, which solves the problems of spacecraft attitude and orbit control being affected by time delay, actuator saturation constraints and internal and external disturbances, and ensures that the spacecraft can successfully complete space missions such as rendezvous and docking, formation flying, etc. within its own safety range, and has broad application prospects.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] A spacecraft active disturbance rejection control method with time delay and actuator saturation includes the following steps:

[0010] S1: Establish an integrated dynamic model of spacecraft posture with communication delay and actuator saturation;

[0011] S2: Design an outer-loop extended state observer with a time-delay predictor;

[0012] S3: Design an outer loop ADRC controller;

[0013] S4: Design the inner loop expansion state observer;

[0014] S5: Design an inner-loop ADRC controller with an anti-saturation strategy.

[0015] Furthermore, in the above-mentioned spacecraft active disturbance rejection control method with time delay and actuator saturation, step S1 specifically includes the following contents:

[0016] S11: The spacecraft is approximately a rigid body. According to the dual quaternion method, the formula for the relative motion between spacecraft can be expressed as:

[0017]

[0018] in, is the relative pose dual quaternion between the following spacecraft and the target spacecraft, q ct The relative attitude quaternion between the following spacecraft and the target spacecraft is: is the relative position vector between the following spacecraft and the target spacecraft in coordinates, ε is the dual element, and × represents the cross product;

[0019] S12: Accordingly, the formula for the dual quaternion of the relative velocity between spacecraft can be defined as:

[0020]

[0021] in, To follow the relative velocity dual quaternion between the spacecraft and the target spacecraft in the spacecraft coordinates, is the relative velocity vector between the following spacecraft and the target spacecraft in the coordinates;

[0022] S13: The dual quaternion formula for the spacecraft's mass and moment of inertia is defined as:

[0023]

[0024] Among them, m c is the mass matrix, J c is the moment of inertia matrix, I is the identity matrix;

[0025] S14: The dual quaternion method is used to describe the attitude of the spacecraft. According to the above formulas (1), (2) and (3), the relative kinematic and dynamic equations of the spacecraft are obtained as follows:

[0026]

[0027] in, for The first-order differential operation of represents dual quaternion multiplication, for The first-order differential operation of is the velocity dual quaternion of the target spacecraft in the target spacecraft coordinate system, for The conjugate operation of They are gravity (torque) dual quaternion, control force (torque) dual quaternion and perturbation force (torque) dual quaternion respectively;

[0028] S15: Introduce a set of dimensionless variables, the formula is as follows:

[0029]

[0030] Among them, κ is the dimensionless time variable, Ω is the angular velocity of the Earth-Moon system, t is the time variable, ω is the angular velocity, is the dimensionless angular velocity, D is the distance between the Earth and the Moon, is the rotation speed of the sun in the Earth-Moon system, r is the distance, is the dimensionless distance; S16: According to the above formula (5), through dimensionless processing, the formulas of the kinematic and dynamic models are as follows:

[0031]

[0032] Taking into account the communication delay and actuator saturation, according to the above formula (6), the final system equation is written as follows:

[0033]

[0034] Where y(t) is the sensor measurement value after transmission via the communication link, τ is the time delay caused by the communication link, is the actuator saturation function, and its specific expression formula is:

[0035]

[0036]

[0037] in, is the upper limit of the actuator, Represents the symbol of u.

[0038] Furthermore, in the above-mentioned spacecraft active disturbance rejection control method with time delay and actuator saturation, step S2 specifically includes the following contents:

[0039] S21: Rewrite the outer ring system. The formula for rewriting the outer ring system is as follows:

[0040]

[0041] in, is regarded as the virtual control quantity of the next inner loop control. Meanwhile, the rest is considered as the total perturbation of the outer ring system;

[0042] S22: According to the above formula (8), the formula for designing the extended state observer including the time-delay prediction information is as follows:

[0043] e q (t) = η(t) - z 01 (t),

[0044]

[0045]

[0046] Where η(t) is the system posture state including time-delay prediction information The estimated value of q (t) is the extended state observer pair The estimation error is u0(t), which is the virtual control quantity, z 01 (t) is The observed value, z 02 (t) is the observed value of the total disturbance of the outer loop system, β 01 , β 02 These are all corresponding adjustable parameters. The formula of the fal function is as follows:

[0047]

[0048] Where e is the tracking error, sign(e) represents the sign of e, δ represents the length of the linear interval, and ρ is a constant satisfying 0<ρ<1;

[0049] S23: In order to solve the time delay problem caused by communication transmission, the formula for designing the time delay predictor is as follows:

[0050]

[0051] Among them, z1 is Observed value of .

[0052] Furthermore, in the above-mentioned spacecraft active disturbance rejection control method with time delay and actuator saturation, step S3 specifically includes the following contents:

[0053] The outer loop ADRC design formula is as follows:

[0054]

[0055] in, For the specified input, e o for The tracking error is α1, and α1 is the gain of the outer loop ADRC controller.

[0056] Furthermore, in the above-mentioned spacecraft ADRC method with time delay and actuator saturation, u0 obtained by formula (10) in step S3 is used to design an inner-loop ADRC controller with an anti-saturation strategy in the subsequent step S5.

[0057] Furthermore, in the above-mentioned spacecraft active disturbance rejection control method with time delay and actuator saturation, step S4 specifically includes the following contents:

[0058] The formula for designing the inner loop extended state observer is as follows:

[0059]

[0060] Among them, e ω is the extended state observer pair The tracking error z1 is The observed value of z2 is the observed value of the total disturbance of the inner loop system, f0 is the known disturbance, β1, β2, Bi All are adjustable parameters.

[0061] Furthermore, in the above-mentioned spacecraft active disturbance rejection control method with time delay and actuator saturation, step S5 specifically includes the following contents:

[0062] Taking actuator saturation into account, the design formula of the inner loop ADRC with anti-saturation strategy is as follows:

[0063]

[0064] Among them, e i is the tracking error of u0, α2 is the gain of the inner loop ADRC, and λ is the adjustable parameter of the anti-saturation strategy.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] (1) The present invention proposes a spacecraft active disturbance rejection control method with time delay and actuator saturation. The dual quaternion method is used to model the kinematics and dynamics of the relative motion between spacecraft. In addition, a set of dimensionless variables is introduced to improve the accuracy and computational efficiency of the model, taking into account the strong coupling relationship and order of magnitude difference between the attitude and orbit of spacecraft in space.

[0067] (2) The present invention discloses a spacecraft active disturbance rejection control method with time delay and actuator saturation. The system is divided into an inner loop system and an outer loop system according to the system structure. An extended state observer based on first-order state information and a nonlinear combination controller are designed in the outer loop system. At the same time, considering the communication time delay problem, a time delay predictor is designed to predict the communication time delay, which effectively predicts and suppresses the impact of the communication time delay on the control system.

[0068] (3) The present invention discloses a spacecraft anti-disturbance control method with time delay and actuator saturation. In the inner-loop control system, an extended state observer based on second-order state information and a nonlinear combination controller are designed. At the same time, considering the actuator saturation problem, an anti-saturation control strategy is designed in the nonlinear combination controller to form a composite controller. This method not only overcomes the adverse effects of uncertainty on the system, but also avoids the actuator saturation phenomenon, effectively improves the robustness of spacecraft attitude and orbit control, and is conducive to achieving spacecraft attitude and orbit control within a safe range.

[0069] (4) The spacecraft self-anti-disturbance control method with time delay and actuator saturation described in the present invention provides sufficient guarantee for the smooth completion of spacecraft rendezvous and docking tasks, has good control effect, and is widely used in other spacecraft attitude and orbit control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 This is a flow chart of a spacecraft active disturbance rejection control method with time delay and actuator saturation according to the present invention;

[0071] Figure 2 Schematic diagram of relative motion modeling of a spacecraft in a libration point orbit according to a spacecraft active disturbance rejection control method with time delay and actuator saturation described in the present invention;

[0072] Figure 3 A block diagram of a spacecraft active disturbance rejection control method with time delay and actuator saturation according to the present invention;

[0073] Figure 4 This is a simulation result diagram of the spacecraft rendezvous and docking relative attitude control using the spacecraft active disturbance rejection control method with time delay and actuator saturation described in the present invention;

[0074] Figure 5 This is a simulation result diagram of the relative position control of spacecraft rendezvous and docking using the spacecraft active disturbance rejection control method with time delay and actuator saturation described in the present invention. DETAILED DESCRIPTION

[0075] The following will be attached Figure 1-5 Example 1 clearly and completely describes the technical solution of the present invention. Obviously, the described embodiment is only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0076] The following embodiment 1 provides a spacecraft active disturbance rejection control method with time delay and actuator saturation.

[0077] Example 1

[0078] The spacecraft self-disturbance rejection control method with time delay and actuator saturation in Example 1 is intended to solve problems such as spacecraft attitude and orbit control being affected by time delay, actuator saturation constraints, and internal and external disturbances, and to ensure that the spacecraft successfully completes space missions such as rendezvous and docking, formation flying, etc. within its own safety range.

[0079] like Figure 1 As shown, the method includes the following steps:

[0080] S1: Establish an integrated dynamic model of spacecraft posture with communication delay and actuator saturation.

[0081] S11: The present invention considers that the spacecraft is approximately a rigid body, such as Figure 2As shown, taking the libration point orbit as an example, according to the dual quaternion method, the formula of the dual quaternion of the spacecraft posture can be written as follows:

[0082]

[0083] in, is the relative pose dual quaternion between the following spacecraft and the target spacecraft, q ct The relative attitude quaternion between the following spacecraft and the target spacecraft is: is the relative position vector between the following spacecraft and the target spacecraft in coordinates, ε is the dual element, and × represents the cross product;

[0084] S12: Accordingly, the formula for the dual quaternion of the relative velocity between spacecraft can be defined as:

[0085]

[0086] in, To follow the relative velocity dual quaternion between the spacecraft and the target spacecraft in the spacecraft coordinates, is the relative velocity vector between the following spacecraft and the target spacecraft in the coordinates;

[0087] S13: The dual quaternion formula for the spacecraft's mass and moment of inertia is defined as:

[0088]

[0089] Among them, m c is the mass matrix, J c is the moment of inertia matrix, I is the identity matrix;

[0090] S14: The dual quaternion method is used to describe the attitude of the spacecraft. According to the above formulas (1), (2) and (3), the relative kinematic and dynamic equations of the spacecraft are obtained as follows:

[0091]

[0092] in, for The first-order differential operation of represents dual quaternion multiplication, for The first-order differential operation of is the velocity dual quaternion of the target spacecraft in the target spacecraft coordinate system, for The conjugate operation of They are gravity (torque) dual quaternion, control force (torque) dual quaternion and perturbation force (torque) dual quaternion respectively;

[0093] S15: Introduce a set of dimensionless variables, the formula is as follows:

[0094]

[0095] Among them, κ is the dimensionless time variable, Ω is the angular velocity of the Earth-Moon system, t is the time variable, ω is the angular velocity, is the dimensionless angular velocity, D is the distance between the Earth and the Moon, is the rotation speed of the sun in the Earth-Moon system, r is the distance, is the dimensionless distance;

[0096] S16: According to the above formula (5), through dimensionless processing, the formulas of the kinematic and dynamic models are obtained as follows:

[0097]

[0098] Taking into account the communication delay and actuator saturation, according to the above formula (6), the final system equation can be written as follows:

[0099]

[0100] Where y(t) is the sensor measurement value after transmission via the communication link, τ is the time delay caused by the communication link, is the actuator saturation function, and its specific expression formula is:

[0101]

[0102]

[0103] in, is the upper limit of the actuator, represents the sign of u. In this embodiment 1, the time delay τ is 1s, The saturation upper limit is 10N control force and 0.1N·m control torque.

[0104] like Figure 2 As shown, in this embodiment 1, the attitude and orbit control of the spacecraft in the libration point orbit in the Earth-Moon system is mainly considered, and the Earth's gravitational perturbation can be expressed as:

[0105]

[0106] in, and are the position vectors of the spacecraft relative to the moon and the earth, G is the gravitational constant, M e and M m are the masses of the moon and the earth respectively. In this embodiment 1, G is taken as 6.67×10-11m3 / kg·s 2 , M e Take 5.974×10 2 4kg, M m Take 7.342×10 22 kg.

[0107] The external disturbance is mainly the solar gravitational perturbation, which can be expressed as:

[0108]

[0109] in, are the position vectors between the Sun and the spacecraft, the Sun and the Earth, and the Sun and the Moon, respectively. s is the mass of the sun, μ is the Earth-Moon system parameter. s Take 1.989×1030kg and μ as 0.012.

[0110] S2: Design an outer-loop extended state observer with a time-delay predictor.

[0111] S21: If Figure 3 As shown, the outer ring system is first rewritten to facilitate subsequent design. The formula for the rewritten outer ring system is as follows:

[0112]

[0113] in, is regarded as the virtual control quantity of the next inner loop control. Meanwhile, the rest is considered as the total perturbation of the outer ring system;

[0114] S22: According to the above formula (8), the formula for designing the extended state observer including the time-delay prediction information is as follows:

[0115] e q (t) = η(t) - z 01 (t),

[0116]

[0117]

[0118] Where η(t) is the system posture state including the time-delay prediction information The estimated value of q (t) is the extended state observer pair The estimation error is u0(t), which is the virtual control quantity, z 01 (t) is The observed value, z 02 (t) is the observed value of the total disturbance of the outer loop system, β01 , β 02 are corresponding adjustable parameters.

[0119] In this embodiment 1, β 01 , β 02 They are and The form of the fal function is as follows:

[0120]

[0121] Where e is the tracking error, sign(e) represents the sign of e, δ represents the length of the linear interval, and ρ is a constant satisfying 0<ρ<1;

[0122] S23: In order to solve the time delay problem caused by communication transmission, the formula for designing the time delay predictor is as follows:

[0123]

[0124] Among them, z1 is Observed value of .

[0125] S3: Design an outer loop ADRC controller.

[0126] like Figure 3 As shown, the outer loop ADRC is designed, and its specific formula is as follows:

[0127]

[0128] in, For the specified input, e o for The tracking error is α1, and α1 is the gain of the outer loop ADRC controller.

[0129] In this embodiment 1, α1 is

[0130] It should be emphasized that u0 obtained in step S3 is used for the subsequent design of the inner-loop ADRC strategy.

[0131] S4: Design the inner loop expansion state observer.

[0132] like Figure 3 As shown, the inner loop expansion state observer is designed, and its specific form is as follows:

[0133]

[0134] Among them, e ω is the extended state observer pair The tracking error z1 is The observed value of z2 is the observed value of the total disturbance of the inner loop system, f0 is the known disturbance, β1, β2, B i All are adjustable parameters.

[0135] In this embodiment 1, β1 is β2 is B i for

[0136] S5: Design an inner-loop ADRC controller with an anti-saturation strategy.

[0137] like Figure 3 As shown, an inner loop ADRC with anti-saturation strategy is designed. The specific formula is as follows:

[0138]

[0139] Among them, e i is the tracking error of u0, α2 is the gain of the inner loop ADRC, and λ is the adjustable parameter of the anti-saturation strategy.

[0140] In this embodiment 1, α2 is λ is

[0141] The simulation results of this embodiment 1 can be found in Figure 4 and Figure 5 .

[0142] The present invention has many specific application paths, and the above is only a preferred embodiment of the present invention. It should be noted that the above embodiments are only used to illustrate the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, several improvements can be made without departing from the principles of the present invention, and these improvements should also be considered as the scope of protection of the present invention.

Claims

1. A spacecraft active disturbance rejection control method with time delay and actuator saturation, characterized in that: The steps include: S1: Establish an integrated dynamic model of spacecraft posture with communication delay and actuator saturation; S2: Design an outer-loop extended state observer with a time-delay predictor; S3: Design an outer loop ADRC controller; S4: Design the inner loop expansion state observer; S5: Design an inner-loop ADRC controller with an anti-saturation strategy; The step S1 specifically includes the following contents: S11: According to the dual quaternion method, the formula for the relative motion between spacecraft is expressed as: in, is the relative pose dual quaternion between the following spacecraft and the target spacecraft, q ct The relative attitude quaternion between the following spacecraft and the target spacecraft is: is the relative position vector between the following spacecraft and the target spacecraft in coordinates, ε is the dual element, and × represents the cross product; S12: The formula for the dual quaternion of the relative velocity between spacecraft is defined as: in, To follow the relative velocity dual quaternion between the spacecraft and the target spacecraft in the spacecraft coordinates, is the relative velocity vector between the following spacecraft and the target spacecraft in the coordinates; S13: The dual quaternion formula for the spacecraft's mass and moment of inertia is defined as: Among them, m c is the mass matrix, J c is the moment of inertia matrix, I is the identity matrix; S14: The dual quaternion method is used to describe the attitude of the spacecraft. According to the above formulas (1), (2) and (3), the relative kinematic and dynamic equations of the spacecraft are obtained as follows: in, for The first-order differential operation of represents dual quaternion multiplication, for The first-order differential operation of is the velocity dual quaternion of the target spacecraft in the target spacecraft coordinate system, for The conjugate operation of They are gravity (torque) dual quaternion, control force (torque) dual quaternion and perturbation force (torque) dual quaternion respectively; S15: Introduce a set of dimensionless variables, the formula is as follows: Where k is the dimensionless time variable, Ω is the angular velocity of the Earth-Moon system, t is the time variable, ω is the angular velocity, is the dimensionless angular velocity, D is the distance between the Earth and the Moon, is the rotation speed of the sun in the Earth-Moon system, r is the distance, is the dimensionless distance; S16: According to the above formula (5), through dimensionless processing, the formulas of the kinematic and dynamic models are obtained as follows: Taking into account the communication delay and actuator saturation, according to the above formula (6), the final system equation is written as follows: Where y(t) is the sensor measurement value after transmission via the communication link, τ is the time delay caused by the communication link, is the actuator saturation function, and its specific expression formula is: in, is the upper limit of the actuator, represents the symbol of u; The step S2 specifically includes the following contents: S21: Rewrite the outer ring system. The formula for rewriting the outer ring system is as follows: in, is regarded as the virtual control quantity of the next inner loop control. Meanwhile, the rest is considered as the total perturbation of the outer ring system; S22: According to the above formula (8), the formula for designing the extended state observer including the time-delay prediction information is as follows: Where η(t) is the system posture state including time-delay prediction information The estimated value of q (t) is the extended state observer pair The estimation error is u0(t), which is the virtual control quantity, z 01 (t) is The observed value, z 02 (t) is the observed value of the total disturbance of the outer loop system, β 01 , β 02 These are all corresponding adjustable parameters. The formula of the fal function is as follows: Where e is the tracking error, sign(e) represents the sign of e, δ represents the length of the linear interval, and ρ is a constant satisfying 0<ρ<1; S23: In order to solve the time delay problem caused by communication transmission, the formula for designing the time delay predictor is as follows: Among them, z1 is Observed values ​​of The step S3 specifically includes the following contents: The outer loop ADRC design formula is as follows: in, For the specified input, e o for The tracking error is α1, which is the gain of the outer loop ADRC controller. u0 obtained by formula (10) in step S3 is used in the subsequent step S5; The step S4 specifically includes the following contents: The formula for designing the inner loop extended state observer is as follows: Among them, e ω is the extended state observer pair The tracking error z1 is The observed value of z2 is the observed value of the total disturbance of the inner loop system, f0 is the known disturbance, β1, β2, B i All are adjustable parameters; The step S5 specifically includes the following contents: Taking actuator saturation into account, the design formula of the inner loop ADRC with anti-saturation strategy is as follows: Among them, e i is the tracking error of u0, α2 is the gain of the inner loop ADRC, and λ is the adjustable parameter of the anti-saturation strategy.

Images