Post-capture flexible assembly spacecraft negative virtual control method with prescribed time dissipation

Abstract

This application discloses a negative virtual control method for a captured flexible composite spacecraft with a specified time dissipation, relating to the field of spacecraft attitude control. The method includes establishing a rigid-flexible coupled attitude vibration model, constructing a nominal reference model, and determining the matching unknown input term; constructing a deadbeat-free unknown input observer based on the discrete-time control terminal model; determining the predictive sensor output data through the observer, reconstructing the matching unknown input term at the previous sampling time, and calculating the feedforward compensation control quantity; back-calculating the system state vector and determining the trajectory error vector; determining the negative virtual feedback control quantity based on the trajectory error vector, the error reference trajectory, and the preset negative virtual feedback gain, thereby determining the nominal control input; and determining the control input data based on the feedforward compensation control quantity and the nominal control input and applying it to the actuator. This application can synchronously complete the attitude takeover and flexible vibration suppression of the flexible composite spacecraft within a specified time without precisely identifying the complete post-capture parameters.

Description

Technical Field

[0001] This application relates to the field of spacecraft attitude control technology, and in particular to a negative virtual control method for a captured flexible composite spacecraft with a specified time dissipation. Background Technology

[0002] With the development of on-orbit servicing, defunct spacecraft removal, space facility maintenance, and on-orbit assembly missions, attitude takeover control after a servicing spacecraft captures a non-cooperative target has become a crucial step for the smooth execution of subsequent operations. Before capture, non-cooperative targets typically lack accurate information on their inertia, center of mass, structure, and connection configuration. After capture, the resulting combined spacecraft exhibits significant changes in inertia parameters, rigid-flexible coupling relationships, flexible modal characteristics, and body coordinate relationships.

[0003] Large service spacecraft are typically equipped with flexible accessories such as solar panels, antennas, or flexible trusses. Capture impacts and post-capture attitude maneuvers can easily induce flexible modal vibrations, and the reactions generated by these vibrations can affect the rigid body attitude control pathway. Therefore, attitude control of the combined spacecraft after capture cannot only consider rigid body attitude stability but also the suppression of flexible vibrations.

[0004] Traditional post-capture attitude takeover methods include parameter identification, robust adaptive control, perturbation observer control, model-independent control, and data-driven control. Parameter identification methods typically require additional excitation and identification time; robust adaptive methods often require uncertainties or prior upper bounds on their derivatives; traditional perturbation observer methods may rely on linearized small-angle assumptions or asymptotic convergence processes; and general data-driven methods may require lengthy data acquisition, training, or iterative processes. Furthermore, while negative virtual system theory is suitable for vibration control of flexible structures with co-located input-output structures, in post-capture flexible composite spacecraft, strong coupling of attitude dynamics, flexible modes, piezoelectric actuation, nonlinear attitude kinematics, and coordinate mismatch makes it difficult for traditional asymptotic negative virtual control to directly meet the specified time takeover requirements.

[0005] Therefore, there is an urgent need for a negative virtual control method for captured flexible combined spacecraft with a specified time dissipation, in order to solve the technical problem of achieving attitude takeover within a specified time for captured flexible combined spacecraft under conditions of parameter mutation, coordinate mismatch and flexible vibration coupling. Summary of the Invention

[0006] The purpose of this application is to provide a negative virtual control method for a captured flexible combined spacecraft with specified time dissipation, which can achieve specified time attitude takeover and flexible vibration suppression of the captured flexible combined spacecraft without relying on accurate identification of post-capture parameters and unknown input prior upper bounds.

[0007] To achieve the above objectives, this application provides the following solution: This application provides a negative virtual control method for a captured flexible composite spacecraft with a specified time dissipation, including: A rigid-flexible coupled attitude vibration model of a flexible combined spacecraft after the capture of a non-cooperative target is established; the flexible combined spacecraft is formed by a service spacecraft and the captured non-cooperative target rigidly connected; the service spacecraft is equipped with sensors and actuators. A nominal baseline model is constructed based on the known parameters of the service spacecraft prior to capturing the non-cooperative target; Based on the rigid-flexible coupled attitude vibration model and the nominal reference model, the matching unknown input terms are determined; The rigid-flexible coupled attitude vibration model is equivalently transformed into an equivalent control end model represented by the nominal reference model and the matched unknown input terms; The equivalent control terminal model is discretized to obtain a discrete-time control terminal model, and a deadbeat-free unknown input observer is constructed based on the discrete-time control terminal model. Acquire the measured sensor output data at the current sampling time and execute the following control steps: Based on the measured sensor output data at the current sampling time, the predicted sensor output data at the current sampling time is determined by a beatless unknown input observer. Based on the difference between the measured sensor output data and the predicted sensor output data at the current sampling time, the matching unknown input item at the previous sampling time is reconstructed through the beatless unknown input observer; The feedforward compensation control quantity at the current sampling time is calculated based on the matching unknown input terms reconstructed from the previous sampling time. Based on the combination of measured sensor output data and control input data from a preset number of sampling times prior to the current sampling time, and the matching unknown input terms reconstructed from the previous sampling time, the system state vector at the current sampling time is obtained by reverse calculation through the discrete-time control terminal model. The trajectory error vector at the current sampling time is determined based on the expected system state vector and the system state vector at the current sampling time. Based on the trajectory error vector at the current sampling time, an error reference trajectory that returns to zero within a preset time is generated by a time command generator, and the nominal control input at the current sampling time is determined. Based on the difference between the trajectory error vector and the error reference trajectory vector at the current sampling time and the preset negative virtual feedback gain, the negative virtual feedback control quantity at the current sampling time is determined. Based on the nominal control input and negative virtual feedback control quantity at the current sampling time, determine the nominal control input at the current sampling time; Based on the feedforward compensation control quantity and nominal control input at the current sampling time, determine the control input data at the current sampling time, and apply the control input data at the current sampling time to the actuator; The next sampling time is taken as the current sampling time, and the measured sensor output data at the current time is reacquired. The above control steps are repeated until the termination condition is met, so as to realize the attitude control and flexible vibration suppression of the flexible combined spacecraft synchronously within the specified time.

[0008] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a negative virtual control method for a flexible combined spacecraft after capture with a specified time dissipation. By establishing a rigid-flexible coupling attitude vibration model of the flexible combined spacecraft after capture of a non-cooperative target, and constructing a nominal reference model based on the known parameters of the servicing spacecraft before capture, the method unifies the changes in inertia, rigid-flexible coupling, flexible modal parameters, actuator influence matrix, coordinate mismatch, and external disturbances caused by capture into matching unknown input terms. This solves the problem that traditional control methods are difficult to adapt quickly due to sudden changes in parameters and coordinate mismatch of the combined spacecraft after capture. It achieves system modeling and control reference unification without re-identifying the complete inertia and flexible modal parameters after capture. By equivalently transforming the rigid-flexible coupled attitude vibration model into an equivalent control-end model jointly represented by the nominal reference model and the matched unknown input term, and discretizing it to obtain a discrete-time control-end model, a deadbeat-free unknown input observer is constructed based on the discrete-time control-end model. The matched unknown input term from the previous sampling time is reconstructed using the difference between the measured sensor output data and the predicted sensor output data at the current sampling time. This solves the problems of traditional disturbance observer methods relying on linearized small-angle assumptions and asymptotic convergence processes, and robust adaptive methods requiring uncertain prior upper bounds. It achieves one-step delayed accurate reconstruction of the matched unknown input under conditions without prior upper bounds. By calculating the feedforward compensation control quantity based on the matched unknown input term reconstructed from the previous sampling time, the problems of matching uncertainty after acquisition and continuous interference from external disturbances on the system are solved. Feedforward compensation for the comprehensive deviation after acquisition is achieved, transforming the residual term of the compensated system from the matched unknown input itself into the difference between adjacent sampling steps, reducing the system's sensitivity to the amplitude of the unknown input. By combining measured sensor output data and control input data from a preset number of sampling times prior to the current sampling time, along with the matched unknown input terms reconstructed from the previous sampling time, and using a discrete-time control terminal model to inversely calculate the system state vector at the current sampling time, the problem of observer state estimation being contaminated by unknown inputs and thus unable to be directly used for feedback control is solved, achieving accurate state recovery based on historical data. Furthermore, by determining the trajectory error vector at the current sampling time based on the desired system state vector and the system state vector at the current sampling time, and generating an error reference trajectory that returns to zero within a preset time using a specified time command generator based on the trajectory error vector at the current sampling time, the problem of traditional asymptotic negative imaginary control being unable to directly meet the specified time takeover requirements is solved, achieving explicit specified time convergence for attitude takeover.By determining the negative virtual feedback control quantity based on the difference between the trajectory error vector and the error reference trajectory vector at the current sampling time and the preset negative virtual feedback gain, and superimposing the nominal control input and feedforward compensation control quantity to obtain the final control input data, which is then applied to the actuator, the problem of flexible vibration suppression while compensating for uncertainty after acquisition is solved. This ensures that the closed-loop error system still satisfies the strict negative virtual dissipation characteristic of the output when the compensation residual exists, guaranteeing that the attitude control and flexible vibration suppression of the flexible combined spacecraft are completed synchronously within the specified time. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating a negative virtual control method for a captured flexible composite spacecraft with a specified time dissipation, provided as an embodiment of this application.

[0011] Figure 2 This is a flowchart illustrating a negative virtual control method for a captured flexible composite spacecraft with a specified time dissipation, provided as another embodiment of this application.

[0012] Figure 3 This application provides a three-axis attitude angle response curve according to an embodiment of the present application; wherein, Figure 3 (a) is the roll angle response curve; Figure 3 (b) is the pitch angle response curve; Figure 3 (c) is the yaw angle response curve.

[0013] Figure 4 This application provides a triaxial angular velocity response curve according to an embodiment of the present application; wherein, Figure 4 (a) is the x-axis angular velocity response curve; Figure 4 (b) is the y-axis angular velocity response curve; Figure 4 (c) is the z-axis angular velocity response curve.

[0014] Figure 5 This application provides a fourth-order flexible modal displacement response curve according to an embodiment of the present application; wherein, Figure 5 (a) is the displacement response curve for mode 1; Figure 5 (b) is the displacement response curve for mode 2; Figure 5 (c) is the displacement response curve for mode 3; Figure 5 (d) is the displacement response curve for mode 4.

[0015] Figure 6 This application provides a triaxial rigid body control torque response curve according to an embodiment of the present application; wherein, Figure 6 (a) is the rigid body control torque response curve along the x-axis; Figure 6 (b) is the y-axis rigid body control torque response curve; Figure 6 (c) is the z-axis rigid body control torque response curve.

[0016] Figure 7 The four-channel piezoelectric control input response curve provided in one embodiment of this application; wherein, Figure 7 (a) is the control input response curve of piezoelectric 1; Figure 7 (b) is the piezoelectric 2 control input response curve; Figure 7 (c) is the piezoelectric 3 control input response curve; Figure 7 (d) is the piezoelectric 4 control input response curve.

[0017] Figure 8 The control energy and vibration energy response curves provided in one embodiment of this application; wherein, Figure 8 (a) is the control energy response curve; Figure 8 (b) is the vibration energy response curve.

[0018] Figure 9 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] In one exemplary embodiment, such as Figure 1As shown, a negative virtual control method for a captured flexible combined spacecraft with specified time dissipation is provided. This method first establishes a rigid-flexible coupling attitude vibration model of the captured flexible combined spacecraft, retaining the nonlinear attitude kinematic residuals and considering the post-capture coordinate mismatch between the service spacecraft's intrinsic system and the combined system. Then, utilizing the structural characteristics of the post-capture parameter deviations, the inertia changes, rigid-flexible coupling changes, flexible mode changes, actuator influence matrix changes, and external disturbances are uniformly reconstructed into matched unknown inputs in a discrete system. Subsequently, a deadbeat-free unknown input observer is constructed, accurately reconstructing the matched unknown input of the previous sampling step from the current residual signal with a one-step delay, and restoring the current feedback state by combining the output history. Based on this, a specified-time command generator is constructed to ensure that the nominal error reaches zero within a specified number of sampling steps. Finally, a strict negative virtual feedback law is designed to ensure that the closed-loop error system still satisfies the negative virtual dissipation inequality when there are compensating residuals, thereby maintaining negative virtual vibration suppression performance while taking over attitude at a specified time. This application does not require prior accurate identification of the complete inertia, coordinate mismatch, and flexible modal changes of the captured assembly, nor does it require pre-setting unknown inputs and their differential upper bounds. It can achieve attitude takeover, disturbance compensation, and flexible vibration suppression of the captured flexible assembly spacecraft within a specified time. This method is executed by computer equipment, specifically by a terminal or server alone, or by both. In the embodiments of this application, it includes the following steps 101 to 116. Wherein: Step 101: Establish a rigid-flexible coupled attitude vibration model of the flexible combined spacecraft after the non-cooperative target is captured; the flexible combined spacecraft is formed by a service spacecraft and the captured non-cooperative target being rigidly connected; the service spacecraft is equipped with sensors and actuators.

[0022] Step 102: Construct a nominal baseline model based on the known parameters of the service spacecraft before capturing the non-cooperative target.

[0023] Step 103: Based on the rigid-flexible coupled attitude vibration model and the nominal reference model, determine the matching unknown input terms.

[0024] Step 104: The rigid-flexible coupled attitude vibration model is equivalently transformed into an equivalent control end model represented by the nominal reference model and the matched unknown input terms.

[0025] Step 105: Discretize the equivalent control terminal model to obtain the discrete-time control terminal model, and construct a deadbeat-free unknown input observer based on the discrete-time control terminal model.

[0026] Step 106: Obtain the measured sensor output data at the current sampling time and execute the following control steps.

[0027] Step 107: Based on the measured sensor output data at the current sampling time, determine the predicted sensor output data at the current sampling time using a beatless unknown input observer.

[0028] Step 108: Based on the difference between the measured sensor output data and the predicted sensor output data at the current sampling time, reconstruct the matching unknown input item at the previous sampling time using a beatless unknown input observer.

[0029] Step 109: Calculate the feedforward compensation control quantity at the current sampling time based on the matching unknown input terms reconstructed at the previous sampling time.

[0030] Step 110: Based on the combination of measured sensor output data and control input data from a preset number of sampling times prior to the current sampling time, and the matching unknown input terms reconstructed from the previous sampling time, the system state vector at the current sampling time is obtained by reverse calculation through the discrete-time control terminal model.

[0031] Step 111: Determine the trajectory error vector at the current sampling time based on the desired system state vector and the system state vector at the current sampling time.

[0032] Step 112: Based on the trajectory error vector at the current sampling time, generate an error reference trajectory that returns to zero within a preset time using a time command generator, and determine the nominal control input at the current sampling time.

[0033] Step 113: Determine the negative virtual feedback control quantity at the current sampling time based on the difference between the trajectory error vector and the error reference trajectory vector at the current sampling time and the preset negative virtual feedback gain.

[0034] Step 114: Determine the nominal control input at the current sampling time based on the nominal control input and negative virtual feedback control quantity at the current sampling time.

[0035] Step 115: Determine the control input data for the current sampling time based on the feedforward compensation control quantity and nominal control input at the current sampling time, and apply the control input data for the current sampling time to the actuator.

[0036] Step 116: Take the next sampling moment as the current sampling moment, reacquire the measured sensor output data at the current moment, and repeat the above control steps until the termination condition is met, thereby achieving synchronous completion of attitude takeover and flexible vibration suppression of the flexible combined spacecraft within a specified time. The termination condition includes: attitude error condition: the attitude angle error and angular velocity error of the flexible combined spacecraft converge to a preset threshold range; vibration attenuation condition: the flexible modal displacement and modal velocity of the flexible combined spacecraft attenuate to a preset threshold range; time condition: reaching a preset specified takeover time or a preset number of sampling steps; steady-state maintenance condition: within a consecutive preset number of sampling moments, the norm of the trajectory error vector is less than a preset convergence threshold.

[0037] By implementing steps 101 to 116 above, this application can achieve time-limited attitude takeover and flexible vibration suppression under the conditions of simultaneous occurrence of parameter mutations, coordinate mismatches and external disturbances after capture through the collaborative design of matching unknown input reconstruction, beatless observation, time-limited command generation and output strict negative virtual dissipation feedback.

[0038] In another exemplary embodiment of this application, the rigid-flexible coupled attitude vibration model is as follows: ; ; in, express The derivative; This represents the system state vector of the flexible combined spacecraft at time t within the flexible combined spacecraft's intrinsic system. This represents the state matrix of the flexible composite spacecraft's intrinsic system. This represents the input matrix within the body of the flexible composite spacecraft. This represents the control input data of the flexible combined spacecraft at time t within the flexible combined spacecraft's main system. The external disturbance moment of the flexible composite spacecraft at time t within the flexible composite spacecraft's own system is represented. This represents the nonlinear residual input matrix of the flexible composite spacecraft system. The nonlinear attitude kinematic residual of the flexible combined spacecraft at time t within the flexible combined spacecraft's intrinsic system is represented. This represents the sensor output data of the flexible composite spacecraft within its main system at time t. This represents the output matrix of the flexible composite spacecraft system.

[0039] In another exemplary embodiment of this application, the nominal baseline model includes a nominal state matrix and a nominal input matrix under the service spacecraft's intrinsic architecture; Based on the rigid-flexible coupled attitude vibration model and the nominal reference model, the unknown input terms for matching are determined, specifically including: The rigid-flexible coupled attitude vibration model is transformed from the flexible combined spacecraft body system to the service spacecraft body system to obtain the control end state matrix and control end input matrix of the rigid-flexible coupled attitude vibration model under the service spacecraft body system. The following formula is used to determine the matching of unknown input items: d ( t )= w ( t )+ N ( t ); ; ; ; Δ A = A - A 0; Δ B = B - B 0; in, d ( t () indicates the matching of an unknown input item at time t; w ( t The figure represents the external disturbance moment of the flexible composite spacecraft at time t within the service spacecraft's main system. N ( t () represents the equivalent matching uncertainty term at time t caused by the parameter deviation after capture; Indicates the construction of a matching matrix for a non-zero block structure; Indicates the deviation of the state matrix; This represents the system state vector of the flexible combined spacecraft at time t within the service spacecraft's intrinsic framework; Indicates the input matrix deviation; This represents the nominal control input of the flexible combined spacecraft at time t within the service spacecraft's main system. A This represents the control end state matrix of the rigid-flexible coupled attitude vibration model under the service spacecraft body system; B This represents the control input matrix of the rigid-flexible coupled attitude vibration model under the service spacecraft body system; This represents the nominal state matrix within the service spacecraft's intrinsic system. This represents the nominal input matrix within the service spacecraft's own system.

[0040] In another exemplary embodiment of this application, the rigid-flexible coupled attitude vibration model is equivalently transformed into an equivalent control end model represented by a nominal reference model and matched unknown input terms, specifically including: The control-end state matrix and control-end input matrix of the transformed rigid-flexible coupled attitude vibration model under the service spacecraft intrinsic system are replaced with the nominal state matrix and nominal input matrix from the nominal baseline model. Matching unknown input terms are then superimposed on the nominal control input. The equivalent control-end model is obtained through the following formula: ; in, express The derivative; This represents the system state vector of the flexible combined spacecraft at time t within the service spacecraft's intrinsic framework; This represents the nominal state matrix within the service spacecraft's intrinsic system. This represents the nominal input matrix within the service spacecraft's own system. This represents the nominal control input of the flexible combined spacecraft at time t within the service spacecraft's main system. This represents the external disturbance moment of the flexible composite spacecraft at time t within the service spacecraft's main system; This represents the equivalent matching uncertainty term at time t caused by the parameter deviation after capture; This represents the nonlinear residual input matrix in the service spacecraft's intrinsic architecture; It represents the nonlinear attitude kinematic residual of the flexible composite spacecraft at time t within the service spacecraft's main system.

[0041] In another exemplary embodiment of this application, the equivalent control terminal model is discretized to obtain a discrete-time control terminal model, and a deadbeat-free unknown input observer is constructed based on the discrete-time control terminal model, specifically including: The discrete-time control terminal model is obtained through the following formula: ; Based on the discrete-time control terminal model, a deadbeat-free unknown input observer is constructed using the following formula: ; in, This represents the system state vector of the flexible combined spacecraft at the (k+1)th sampling time within the service spacecraft's own system. This represents the discrete state matrix within the service spacecraft's intrinsic system. This represents the system state vector of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's intrinsic framework; This represents the discrete input matrix within the service spacecraft's intrinsic architecture. This represents the control input data of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's main system. This represents the unknown input item matched at the k-th sampling time. This represents the discrete nonlinear residual input matrix within the service spacecraft's intrinsic architecture. This represents the nonlinear attitude kinematic residual of the flexible composite spacecraft at the k-th sampling time in the service spacecraft's main system; This represents the sensor output data of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's main system. This represents the discrete output matrix within the service spacecraft's intrinsic architecture. This represents the observer state of the beatless unknown input observer at the (k+1)th sampling time. This represents the control input gain matrix of a deadbeat unknown input observer. This represents the measurement output gain matrix of a beatless unknown input observer. This represents the system state estimation vector of the flexible combined spacecraft at the k-th sampling time under the service spacecraft's own system. This indicates the observer state of the deadbeat-free unknown input observer at the k-th sampling time. This represents the output correction gain matrix of a beatless, unknown input observer. This represents the difference between the measured sensor output data and the predicted sensor output data at the k-th sampling time.

[0042] In another exemplary embodiment of this application, based on the difference between the measured sensor output data and the predicted sensor output data at the current sampling time, the matching unknown input item at the previous sampling time is reconstructed using a beatless unknown input observer, specifically including: The unknown input term from the previous sampling time can be reconstructed using the following formula: ; in, This represents the unknown input item matched at the (k-1)th sampling time during reconstruction; This represents the discrete output matrix within the service spacecraft's intrinsic architecture. This represents the control input gain matrix of a deadbeat unknown input observer. This represents the Moore-Penrose pseudo-inverse operation; This represents the difference between the measured sensor output data and the predicted sensor output data at the k-th sampling time.

[0043] In another exemplary embodiment of this application, the feedforward compensation control quantity for the current sampling time is calculated based on the matching unknown input term reconstructed at the previous sampling time, specifically including: The negative of the matching unknown input term reconstructed at the previous sampling time is used as the feedforward compensation control quantity at the current sampling time.

[0044] In another exemplary embodiment of this application, based on the combination of measured sensor output data and control input data from a preset number of sampling times prior to the current sampling time, and the matching unknown input terms reconstructed from the previous sampling time, the system state vector at the current sampling time is calculated in reverse through a discrete-time control terminal model, specifically including: The system state vector at the current sampling moment can be obtained by reverse calculation using the following formula: ; ; ; ; ; in, This represents the system state vector of the flexible combined spacecraft at the k-th sampling moment obtained by reverse calculation, within the service spacecraft's own system. This represents the discrete state matrix within the service spacecraft's intrinsic system. This represents the system state vector of the flexible combined spacecraft at the (k-1)th sampling moment obtained from the recovery, within the service spacecraft's intrinsic system. This represents the discrete input matrix within the service spacecraft's intrinsic architecture. This represents the control input data of the flexible combined spacecraft under the service spacecraft system at the (k-1)th sampling time. This represents the unknown input item reconstructed at the (k-1)th sampling time; This represents the discrete nonlinear residual input matrix within the service spacecraft's intrinsic architecture. This represents the nonlinear attitude kinematic residual of the flexible combined spacecraft at the (k-1)th sampling time in the service spacecraft's main system. Represents the reconfigurability matrix; Represents the Moore-Penrose pseudoinverse of the reconfigurability matrix; This represents the historical output vector composed of a preset number of sensor output data before the k-th sampling time. The transpose of the discrete output matrix in the service spacecraft's own system; The transpose of the discrete state matrix of the service spacecraft's intrinsic system; Indicates transpose; This represents the corrected output vector after deducting the influence of known input terms at the k-th sampling time. This represents the measured sensor output data of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's main system. This represents the discrete output matrix within the service spacecraft's own system.

[0045] In another exemplary embodiment of this application, the time command generator is specified as: ; ; in, This represents the error reference trajectory vector at the (k+1)th sampling time. Represents the error system matrix; This represents the error reference trajectory vector at the k-th sampling time. Represents the error system input matrix; This represents the nominal control input at the k-th sampling time. This represents the total number of sampling steps corresponding to a preset time period.

[0046] In another exemplary embodiment of this application, the negative virtual feedback control quantity at the current sampling time is determined based on the difference between the trajectory error vector and the error reference trajectory vector at the current sampling time and a preset negative virtual feedback gain, specifically including: The negative virtual feedback control quantity at the current sampling time is determined by the following formula: ; ; in, This represents the negative virtual feedback control quantity at the k-th sampling time. This represents the nominal control input at the k-th sampling time. This indicates the preset negative virtual feedback gain; This represents the relative error at the k-th sampling time. This represents the trajectory error vector at the k-th sampling time. This represents the error reference trajectory vector at the k-th sampling time.

[0047] The following example illustrates this application using a specific time-dissipated capture-after-capture flexible composite spacecraft negative virtual control process.

[0048] In one exemplary embodiment, such as Figure 2As shown, a negative virtual control method for a captured flexible combined spacecraft with specified time dissipation is provided. This method uses a known model of the servicing spacecraft before capture as a nominal reference model. It reconstructs post-capture parameter mutations, coordinate mismatches, and external disturbances into matched unknown input terms in the nominal input channel, and reconstructs these matched unknown input terms with a one-step delay using a deadbeat unknown input observer. After unknown input compensation, this application restores the current feedback state by outputting the history and reconstructed unknown inputs. Then, it performs coordinate transformation and error decomposition on the compensated discrete-time system, constructing a specified-time command generator to ensure the nominal error reaches zero within a given number of sampling steps. Simultaneously, it designs a strictly negative virtual feedback gain to ensure that the relative error system with compensation residuals still satisfies the strictly negative virtual dissipation inequality. Specifically, it includes the following steps.

[0049] S1. Establish a rigid-flexible coupled attitude vibration model for the flexible combined spacecraft after the capture of the non-cooperative target. The flexible combined spacecraft is formed by a rigid connection between the service spacecraft and the captured non-cooperative target. The rigid-flexible coupled attitude vibration model simultaneously includes the rigid body attitude motion of the combined spacecraft, the modal vibration of the flexible appendages, the control torque of the rigid body actuator, the piezoelectric actuation input, external disturbances, and nonlinear attitude kinematic residuals. The flexible combined spacecraft's own system is introduced during the modeling process. F c Serving the spacecraft system F s and orbital reference frame F o First, in the flexible combined spacecraft system F c A continuous-time composite model is established, and then... F c arrive F s The unknown coordinate transformation converts the continuous-time composite model into a service spacecraft system. F s The control terminal model is used to obtain the control terminal state matrix. A , Control terminal input matrix B and nonlinear attitude kinematic residual input matrix E .

[0050] As an optional implementation, in step S1, the flexible composite spacecraft system... F c Used to describe flexible composite spacecraft formed after the capture of a non-cooperative target, serving the spacecraft's core system. F s Orbital reference frame used to describe the service spacecraft in which sensors and actuators reside. F o Let be a locally vertical and locally horizontal reference system; Θ =[ ,θ,ψ] T This indicates the main system of the flexible combined spacecraft. F c Relative orbital reference frame F o The attitude angle vector, where θ and ψ are the roll angle, pitch angle, and yaw angle, respectively; let ω =[ ω x , ω y , ω z ] T This indicates the main system of the flexible combined spacecraft. F c The angular velocity vector below, where ω x , ω y ,and ω z These are the three-axis angular velocity components; let η ∈ R m Represents the modal coordinate vector of the flexible attachment. m To preserve the flexible modal order; let express η Regarding time t The first derivative of , i.e., the flexible modal velocity vector; let express η Regarding time t The second derivative of is the flexible modal acceleration vector; let T c ∈ R 3 This represents the control torque of a rigid body actuator. T d ∈ R 3 Indicates the external disturbance torque. u p ∈ R r Indicates piezoelectric actuation input. r Let be the number of piezoelectric actuation channels; J ∈ R 3×3 This represents the moment of inertia matrix of the combined spacecraft. δ ∈ R m×3 Represents the rigid-flexible coupling matrix. C ∈ R m×m Represents the modal damping matrix. K ∈ Rm×m Denotes the modal stiffness matrix, Δ p ∈ R m×r This represents the piezoelectric actuation effect matrix; the superscript T indicates the transpose operation of the matrix or vector. R m Let m represent the m-dimensional real vector space.

[0051] As an optional implementation, in step S1, the attitude kinematics of the combined spacecraft retains the nonlinear attitude kinematic residuals, written as: ; in, express Θ Regarding time t The derivative of f c ( t ) represents the nonlinear attitude kinematic residual; if ω 0 represents the orbital angular velocity. R 1( Θ )and R 2( Θ ) indicates the attitude angle Θ Given a defined attitude kinematics matrix, then f c ( t The design is as follows: ; The rigid-flexible coupling dynamics of the combined spacecraft can be written as: ; ; in, express ω Regarding time t The derivative of Indicates by ω The generated antisymmetric matrix is ​​produced by the vector cross product operation.

[0052] As an optional implementation, the rigid-flexible coupling dynamics of the combined spacecraft are eliminated. Then, design the equivalent inertia matrix. And design lumped nonlinear disturbance torque ,in, It is a non-singular matrix; the flexible composite spacecraft system is selected. F c The state vector under x c ( t ), control input u c ( t and lumped disturbancew c (t) are respectively: ; ; ; in, 0 r for r Zero-dimensional vector.

[0053] Flexible composite spacecraft system F c The continuous-time combination model is written as follows: ; in, express The derivative with respect to time t, A c For the flexible combined spacecraft system F c The state matrix below, B c For the flexible combined spacecraft system F c The input matrix below, E c For the flexible combined spacecraft system F c The nonlinear attitude kinematic residual input matrix, and A c , B c , E c Designed as follows: ; ; ; in, I 3 is a three-dimensional identity matrix. I m It is an m-dimensional identity matrix. express The inverse matrix of . Therefore, A c , B c , E c All of these are obtained by organizing the dynamics of the captured combined body in step S1, and serve as the basis matrix for the subsequent transformation of the control terminal model of the service spacecraft.

[0054] As an optional implementation, in step S1, the flexible composite spacecraft system is introduced. F c To serve the spacecraft system F s Unknown orthogonal transformation matrix R sc , R sc satisfy Design the first diagonal transformation matrix. Second diagonal transformation matrix Where diag(·) denotes a block diagonal matrix consisting of the matrices within the brackets. I r for r A 3D identity matrix; transformed as follows: , , , The flexible combined spacecraft system F c The continuous-time combined model is converted into the service spacecraft system. F c The control terminal model below: ; in, x ( t To serve the spacecraft system F s The control terminal state vector below, u ( t To serve the spacecraft system F s The control input vector below, w ( t To serve the spacecraft system F s The control end disturbance vector below, f ( t To serve the spacecraft system F s Nonlinear attitude kinematic residuals express x ( t ) on time t The derivative; the control terminal state matrix A , Control terminal input matrix B and the nonlinear attitude kinematic residual input matrix of the control end E They are designed as follows: , , The A , B andE This is the final service spacecraft control terminal model matrix obtained in step S1; since the sensors and actuators are installed on the service spacecraft, subsequent steps S2 to S5 are all based on the service spacecraft's own system. F s The control terminal model is designed based on this.

[0055] S2, the service spacecraft system obtained in step S1 F s Based on the lower control model, a nominal baseline model is constructed using the known dynamic parameters of the servicing spacecraft before non-cooperative target acquisition, and the nominal state matrix is ​​obtained. A 0 and nominal input matrix B 0; Change the control terminal state matrix in step S1. A With the nominal state matrix A The difference of 0 is denoted as the state matrix deviation Δ. A The control input matrix in step S1 is then transferred. B With the nominal input matrix B The difference of 0 is denoted as the input matrix deviation Δ. B According to Δ A and Δ B Structure construction matching matrix B N This allows the changes in inertia caused by capture, changes in rigid-flexible coupling, changes in flexible modal parameters, changes in piezoelectric actuation effects, coordinate mismatch, and external disturbances to be uniformly represented as actions acting on the nominal input channel. B Matching 0 with unknown input.

[0056] As an optional implementation, in step S2, a nominal reference matrix is ​​constructed using the known parameters of the pre-service spacecraft. A 0 and B 0; the A 0 and B 0 and A and B They have the same block structure, but A 0 and B 0 is obtained from the known inertia, known rigid-flexible coupling parameters, known modal parameters, and known piezoelectric actuation influence matrix of the pre-capture servicing spacecraft, and the coordinate transformation matrix is ​​taken as the identity matrix; based on the control end model obtained in step S1, the control end model is rewritten as: ; Design state matrix deviation Δ A = A - A 0, input matrix deviation Δ B = B - B 0, where ΔA and Δ B These represent the equivalent matrix deviations in the servicing spacecraft control terminal model for changes in inertia, rigid-flexible coupling, flexible mode parameters, piezoelectric actuation effects, and coordinate mismatch after capture, respectively. Therefore, step S2 is not about rebuilding a new model, but rather using the control terminal model obtained in step S1. A , B , E Based on this, a nominal benchmark model is introduced. A 0、 B 0 and separate the post-capture deviation Δ A , ΔB .

[0057] As an optional implementation, in step S2, according to Δ A and Δ B Constructing a matching matrix using a non-zero block structure B N , so that: , ,in B N To project the captured parameter deviation onto the nominal input channel B The matching matrix on 0; B 0 B N It has the following block structure: ; in," " represents any block matrix compatible with the matrix dimension. I 3 represents the three-dimensional identity matrix. I m Represent an m-dimensional identity matrix; design matching uncertainties. N (t) is And design a continuous-time matching unknown input d(t) as d ( t )= w ( t )+ N ( t Therefore, the control-end model is equivalently rewritten as: ; in, d ( t It also includes external disturbances. w ( t And the equivalent matching uncertainty caused by post-capture parameter deviation and coordinate mismatch. N ( t ).

[0058] S3. Perform zero-order hold discretization on the control terminal model obtained in step S2 to obtain a discrete-time control terminal model; construct a deadbeat-free unknown input observer for the discrete-time control terminal model, and reconstruct the matching unknown input of the previous sampling step from the current measurement residual by one-step delay; then use the output history, control input history, nonlinear attitude kinematic residual, and the reconstructed value of the matching unknown input to restore the current feedback state; and design a feedforward compensation control input based on the reconstructed value of the matching unknown input, so that the residual terms in the compensated system are transformed from the matching unknown input itself into the difference terms of the matching unknown input in adjacent sampling steps.

[0059] As an optional implementation, in step S3, the continuous-time control terminal model matching the unknown input form is sampled with a period of... T s By performing zero-order hold discretization, we obtain the discrete-time control terminal model: ; in, k For discrete sampling times, x ( k ) is the first k The control terminal status at each sampling time u ( k ) is the first k Control input at each sampling time, d ( k ) is the first k Matching unknown input at each sampling time. f ( k ) is the first k Nonlinear attitude kinematic residuals at each sampling time, y ( k ) is the first k Measurement output at each sampling time, C d Measurement matrix; Discrete state matrix A d Discrete input matrix B d and discrete nonlinear residual input matrix E d They are respectively: , , ,in e (·) This represents a matrix exponential function, where τ is the integration variable. T s The sampling period is used to determine the discrete-time control terminal model, which is directly discretized from the continuous-time matched unknown input model in step S2. This model is the target for the subsequent design of the deadbeat-free unknown input observer and the specified-time negative virtual controller.

[0060] As an optional implementation, the deadbeat-free unknown input observer in step S3 is constructed as follows: ; in, s ( k ) represents the observer state. The observer state estimate, r ( k To measure the residual, , and Let be the observer matrix to be designed; the observer matrix satisfies: , , ;in I The identity matrix has the same dimension as the corresponding matrix; when the above conditions hold, the measurement residuals satisfy: ,when When the column is full rank, the reconstructed value of the unknown input matched in the previous sampling step is: ,in express d ( k The reconstructed value of -1), (·) + This indicates the calculation of the Moore-Penrose inverse; the differenceless unknown input observer reconstructs the matching unknown input using algebraic residual relations after a one-sampling-step delay, without requiring pre-defined parameters. d ( k )or d ( k )- d ( k The upper bound of -1).

[0061] As an optional implementation, in step S3, the observer state estimate... It is not directly used as the feedback state; the feedback state is recovered by matching the unknown input reconstruction value with the output history and the previous sampling step, specifically including: Design correction output for ; Design historical output vector Y ( k )for: ; And design a reconfigurability matrix Π for ; like Π rank is n ,in n =6+2m is the state x ( kIf the dimension of the variable is m, and the modal order of the flexible attachment is m, then the state of the previous sampling step can be uniquely recovered by the following formula: ; The current feedback state is restored by the following formula: ; in, To restore the feedback state of the previous sampling step, To restore the current feedback state; when and Π rank is n Sometimes, That is, the current feedback state is equal to the actual state.

[0062] As an optional implementation, the feedforward compensation control input in step S3 is designed as follows: ; in, u ( k () represents the actual discrete control input applied. For the nominal control input to be designed, The reconstructed value of the unknown input from the previous sampling step is used to match the input; after substituting it into the discrete-time control terminal model, the compensated system satisfies... Among them, the compensation residual Δ d ( k The design is as follows: ;when At that time, there is Δ d ( k )= d ( k )- d ( k -1), that is, the residual terms in the compensated system are transformed from matching the unknown input itself into the difference terms matching the unknown input in adjacent sampling steps.

[0063] S4. Perform coordinate transformation and error decomposition on the compensated discrete-time control terminal model from step S3, decomposing the system error into a first sub-error and a second sub-error, and construct a specified time command generator so that the error reference trajectory generated by the specified time command generator is within a specified number of sampling steps. N p The interior reaches zero; where N p Let be a pre-given positive integer, and N p ≥2, specified takeover time (preset specified time) T p satisfy T p = N pT s , T s The sampling period.

[0064] As an optional implementation, in step S4, the... B d Write it in blocks according to state as follows ,in, B d1 ∈ R (3+m)×(3+r) The first block input matrix is ​​related to the attitude angle and the flexible modal coordinates. B d2 ∈ R (3 +m)×(3+r) The second block input matrix is ​​related to the angular velocity and the flexible modal velocity; when B d2 When the row is full rank, construct the coordinate transformation matrix. , for B d2 Find the Moore-Penrose inverse matrix and design the transformed state. ζ ( k )for ζ ( k )= Gx ( k )=[ ζ 1( k ) T , ζ 2( k ) T ] T ,in, ζ 1( k ) is the first substate. ζ 2( k ) is the second sub-state; the coordinate transformation makes This concentrates the control input channels into the second sub-state equation.

[0065] In implementing this method, the transformed system matrix is ​​designed. A z = GA d G -1 and will A z Divided into blocks ,in A 11 , A 12 , A 21and A 22 All are with ζ 1( k ), ζ 2( k Dimensionally compatible block matrices; design the transformed residual input matrix. E z = GE d and will E z Divided into blocks E z =[ E 1; E 2]; Under the system structure described above, E If 2 is a zero matrix or can be incorporated into the compensation residual term, then the compensated system can be written as: ; Design reference trajectory ζ 1( k )and ζ 2( k ), and design error: ; in, e 1( k ) represents the first sub-error. e 2( k ) represents the second sub-error; when A 12 When non-singular, choose ζ 2d ( k )satisfy: Thus, the error relationship is obtained: .

[0066] As an optional implementation method, nominal control input Designed as follows: ,in u eq ( k ) is the auxiliary control input (negative virtual feedback control quantity); the total design error e ( k )=[ e 1( k ) T , e 2( k ) T ] T The error system is obtained as follows: ,in, , , ,in, Ae Here is the state matrix of the error system. B e The input matrix for the error system, w r ( k ) is due to the compensation residual Δ d ( k The residual compensation input caused by ).

[0067] As an optional implementation, the time command generator in step S4 is: , e d ( k )=0, where e d ( k ( ) is the error reference trajectory generated by the time command generator. u d ( k () is the input to the command generator; for the specified number of sampling steps N p Construct the reachability matrix C Np and stacked input vectors U d : , ;choose: ,make e d ( N p )=0, and make e d ( k )=0 for all k ≥ N p Established; among them, Representation matrix A e of N p Power of 1 express C Np Moore-Penrose inverse.

[0068] S5. The design outputs a strictly negative virtual feedback gain, ensuring that the nominal error system, without compensating residuals, operates within a specified number of sampling steps. N p The system converges internally and ensures that the relative error system with compensation residuals satisfies the strictly negative virtual dissipation inequality of the output. Finally, it implements the attitude vibration cooperative control law composed of the unknown input feedforward compensation term and the strictly negative virtual feedback term of the output at a specified time, so as to realize the attitude takeover and flexible vibration suppression of the flexible combined spacecraft at a specified time after capture.

[0069] As an optional implementation, in step S5, a relative error is designed. for And design auxiliary control input ,in K To output strictly negative imaginary feedback gain; construct K =[ K 1, K 2], K 1 represents the first block gain of the feedback gain matrix distributed column-wise. K 2 represents the second block gain of the feedback gain matrix distributed in columns, and selects... , Then the closed-loop relative error matrix A cl satisfy Therefore, when the residual compensation input w r ( k When )=0, the relative error It becomes zero within a finite number of sampling steps; combined with a specified time command generator, the total error can be guaranteed. e ( k ) within the specified number of sampling steps N p It reaches zero.

[0070] As an optional implementation, in step S5, when there is residual compensation input... w r ( k When ), the relative error system is written as: ;make ,in and These are the first and second components of the relative error, respectively; design intermediate quantities. P ( k )for And design a positive definite energy storage function. V ( k )for Design virtual adjustment output z ( k )for ; in, z ( k This is used for outputting strictly negative virtual dissipation analysis rather than direct sensor measurement; if A 12 If it is not singular, then there exists an output strictness coefficient. γ >0, ensuring that the relative error system satisfies the strictly negative virtual dissipation inequality. Where ||·|| denotes the vector 2 norm,z ( k +1)- z ( k ) represents the forward differential of the virtual adjustment output. The dissipation inequality is used to ensure that the closed-loop error system still has strictly negative virtual dissipation characteristics when the compensation residual exists.

[0071] As an optional implementation, the output strictness coefficient γ is selected as... ,in λ max (·) represents the largest eigenvalue of the matrix; since A 12 Non-singular, Since it is a positive definite matrix, γ is a positive number.

[0072] As an optional implementation, the discrete control input ultimately applied to the captured flexible composite spacecraft is: ,in u ( k Decomposed by channel , T c ( k () represents the control torque of the rigid body actuator. u p ( k () is the piezoelectric actuation input; Match the unknown input to the previous sampling step for reconstruction of the deadbeat unknown input observer; ζ 1( k ), ζ 2( k The current recovery feedback state Obtained through coordinate transformation; From actual error e ( k Error reference trajectory between the specified time command generator and the target time. e d ( k Subtract from each other to get the result.

[0073] In one exemplary embodiment, this application does not require prior accurate identification of the complete inertia matrix after the non-cooperative target has been captured. J Coordinate mismatch matrix R sc The changes in the rigid-flexible coupling matrix, the flexible modal frequency, the flexible modal damping, or the piezoelectric actuation influence matrix do not require pre-given matching unknown inputs. d ( k ) and its adjacent sampling step difference d ( k )- d ( k-1) upper bound; This application achieves the capture of a flexible combined spacecraft within a specified takeover time by using a series design of post-capture deviation matching reconstruction, deadbeat-free unknown input observation, output historical state recovery, specified time command generation, and output strictly negative virtual dissipation feedback. T p Internal attitude error elimination and flexible vibration suppression.

[0074] Example 1 I. Establish the control terminal model of the captured combined body.

[0075] Firstly, in the flexible composite spacecraft system F c A rigid-flexible coupled attitude vibration model is established below. Attitude angle Θ Describe the basic structure of the flexible composite spacecraft F c Relative to the orbital reference frame F o attitude, angular velocity ω exist F c The Chinese character represents this. Posture kinematics is written as... ,in f c ( t ) represents the retained nonlinear attitude kinematic residuals.

[0076] Based on rigid-flexible coupling dynamics, the flexible modal acceleration is eliminated. The equivalent inertia matrix is ​​then obtained. and lumped nonlinear disturbance torque Select state ,enter and disturbance A continuous-time composite model can be obtained. .

[0077] Since the sensors and actuators remain mounted on the servicing spacecraft after capture, the servicing spacecraft's intrinsic system F_s is introduced into the flexible combined spacecraft's intrinsic system. F c Unknown orthogonal transformation R sc .pass , , and The combined model is converted into a control terminal model within the service spacecraft's core system. .

[0078] II. Reconstruction of unknown inputs by matching biases after capture.

[0079] Construct the nominal reference matrix from the known model of the pre-capture servicing spacecraft. A0 and B 0, and capture the control matrix. A , B The difference between the matrix and the nominal matrix is ​​denoted as Δ. A = A - A 0 and Δ B = B - B 0.

[0080] According to Δ A and Δ B Constructing a matching matrix using a block structure B N ,make and .design and d ( t )= w ( t )+ N ( t This allows the captured parameter deviation and external disturbances to be uniformly written into the nominal input channel, thus obtaining... .

[0081] This step explicitly connects the actual control model with the nominal model before capture: giving the actual A , B , E ,exist A , B , E Based on separation A 0、 B 0 and the deviation term, then project the deviation term onto B Channel 0 is used to match unknown inputs.

[0082] III. Discretization, deadbeat-free unknown input observation and state recovery.

[0083] By performing zero-order preserved discretization on a continuous-time matched unknown input model, we obtain: .

[0084] Construct a deadbeat-free unknown input observer: .

[0085] When the observer matrix satisfies the corresponding algebraic elimination condition, we have .like If the column is full, then it can be... We obtain the reconstructed value of the unknown input from the previous sampling step.

[0086] Since the observer state estimation error is driven by unknown inputs, this application does not directly... Instead of using the feedback state, it utilizes the output history, control input history, nonlinear residuals, and recover x ( k When the reconfigurability matrix When the column rank is full, the state of the previous sampling step can be restored and the current feedback state can be further restored.

[0087] IV. Strict negative virtual feedback design for the generation and output of commands at specified times.

[0088] use The system is subjected to feedforward compensation, and the residual input after compensation is: When the deadbeat reconstruction is accurate, Δ d ( k )= d ( k )- d ( k -1), that is, the residual term is reduced from the unknown input itself to the difference of adjacent sampling steps.

[0089] Will B d Write it in blocks according to state as follows ,exist B d2 Constructing coordinate transformations under full rank conditions G This ensures that the control input only enters the second sub-state equation. Define the error. e 1( k ), e 2( k And select a reference trajectory ζ 2d ( k ), thus obtaining the error system .

[0090] Construct a time-defined command generator Through the reachability matrix C Np Obtain the input sequence U d ,make e d ( k At a given number of sampling steps N p The value becomes zero afterward. Relative error is defined. and design ,in K make A cl satisfy .

[0091] In the presence of compensated residuals w r (k When selecting the energy storage function... V ( k and virtual regulation output z ( k ), so that the relative error system satisfies This allows the strictly negative virtual dissipation property of the output to be maintained while taking over at the specified time.

[0092] To further illustrate the feasibility of this application, a simulation embodiment of attitude control for a flexible combined spacecraft after capture is provided. In this embodiment, the actual parameters after capture are only used to generate a nonlinear closed-loop simulation object. The controller synthesis is based on the nominal parameters before capture and a matching unknown input reconstruction mechanism. The simulation parameters of the flexible combined spacecraft after capture are shown in Table 1 below.

[0093] Table 1 Simulation parameters of the flexible combined spacecraft after capture

[0094] The external disturbance torque uses a multi-frequency sine and cosine combination signal, with an order of magnitude of 10. -3 N·m is used to verify the robustness of the deadbeat-free unknown input observer and the strictly negative imaginary control law with specified time output in the presence of external disturbances. Simulation comparisons include the method of this application, the asymptotically stable negative imaginary control method, and dynamic... H The output feedback control method, all three methods are applied to the same nonlinear capture-after flexible combined spacecraft model.

[0095] To verify the effectiveness of the method proposed in this application, numerical simulation was performed using a captured flexible combined spacecraft model. The sampling period was taken as... T s =0.25s, simulation duration is set to 200s, and the specified number of sampling steps is... N p =50, therefore the takeover time is stipulated as T p =12.5s. The nominal model retains the fourth-order flexible mode. The actual controlled object is subject to parametric perturbations relative to the nominal model. The actual moment of inertia is taken as 1.2 times the nominal value, the actual rigid-flexible coupling matrix is ​​taken as 1.1 times the nominal value, the actual modal natural frequency is taken as 0.9 times the nominal value, the actual damping ratio is taken as 0.95 times the nominal value, and the actual piezoelectric actuation influence matrix is ​​taken as 0.8 times the nominal value. The initial attitude angle is set to [-20.21°, 18.60°, -10.72°], the initial angular velocity is set to [5.01, -4.20, 2.34]° / s, the initial flexible modal displacement is set to [-0.018, -0.021, 0.024, 0.022], and the initial modal velocity is zero. No limiting is applied to the rigid body control torque and the piezoelectric input voltage during the simulation. Figure 6 and Figure 7 This demonstrates the unlimited control input obtained directly from the control law calculation.

[0096] Depend on Figure 3 It can be seen that under large initial attitude deviation conditions, the roll angle, pitch angle and yaw angle can all decay rapidly and approach zero under control. Attitude take-off is basically completed near the specified take-off time, indicating that the method of this application can achieve rapid stabilization of the attitude of the combined body after capture.

[0097] Depend on Figure 4 It can be seen that the angular velocities of all three axes decay rapidly and gradually converge to near zero. The response process is stable, without continuous divergence or large oscillations, indicating that the designed control law can effectively suppress the attitude angular velocity deviation of the combined body after capture.

[0098] Depend on Figure 5 It can be seen that the displacements of the fourth-order flexible modes all exhibit gradually decaying oscillation characteristics, eventually converging to near zero. This indicates that while completing attitude control, the flexible vibration is also effectively suppressed, verifying the effectiveness of the negative virtual control structure of this application in suppressing flexible vibration.

[0099] Depend on Figure 6 It can be seen that the three-axis rigid body control torque is rapidly established in the initial stage of control based on the attitude error and the compensation term for the unknown input, and then gradually decays as the attitude error and angular velocity error decrease. Since no limit is applied to the control torque in the simulation, this curve reflects the actual torque requirement of the control law under the current parameter conditions.

[0100] Depend on Figure 7 It can be seen that the four piezoelectric control inputs have a regulating effect in the initial stage, and then gradually decrease, indicating that the piezoelectric actuation channels participate in the suppression of flexible vibration. Since no limit was applied to the piezoelectric voltage in the simulation, the curve reflects the actual voltage requirement of the control law under the current parameter conditions.

[0101] Depend on Figure 8 It can be seen that both control energy and vibration energy remain bounded during the system evolution process. Control energy gradually accumulates and then tends to level off, while vibration energy gradually stabilizes as the flexible mode decays. This indicates that the method of the present invention has good energy utilization and vibration suppression effects while achieving posture takeover at a specified time.

[0102] In summary, Figures 3 to 8 Simulation results show that the specified time dissipation negative virtual control method proposed in this application can still achieve rapid attitude takeover, flexible vibration suppression, and quantitative assessment of control input requirements of the combined spacecraft under conditions of post-capture parameter uncertainty, rigid-flexible coupling changes, coordinate mismatch, and external disturbances, by relying on the collaborative design of deadbeat unknown input observation and specified time negative virtual control.

[0103] In summary, the beneficial effects of this application are as follows: First, the changes in inertia, rigid-flexible coupling, modal changes, piezoelectric actuation effects, coordinate mismatch, and external disturbances after capture are unified as unknown inputs for matching, thus avoiding the need to re-identify complete parameters.

[0104] Second, the deadbeat unknown input observer does not require prior upper bounds on the unknown input and its difference.

[0105] Third, the feedback state is accurately recovered by outputting history, avoiding the direct use of observer state estimates that are contaminated by unknown inputs.

[0106] Fourth, the time command generator specifies the takeover time.

[0107] Fifth, the strict negative virtual dissipation constraint output preserves the ability to suppress flexible vibrations.

[0108] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 9 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores negative virtual control processing data for a captured flexible combined spacecraft with a specified time dissipation. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a negative virtual control method for a captured flexible combined spacecraft with a specified time dissipation.

[0109] Those skilled in the art will understand that Figure 9 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer equipment to which the present application is applied. Specific computer equipment may include, for example, [the following is a list of possible additional structures]. Figure 9The embodiments show more or fewer components, combinations of certain components, or different component arrangements. In one exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, which the processor executes to implement the steps in the above-described method embodiments.

[0110] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0111] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0112] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0113] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0114] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0115] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for negative virtual control of a captured flexible composite spacecraft with a specified time dissipation, characterized in that, include: A rigid-flexible coupled attitude vibration model of a flexible combined spacecraft after the capture of a non-cooperative target is established; the flexible combined spacecraft is formed by a service spacecraft and the captured non-cooperative target rigidly connected; the service spacecraft is equipped with sensors and actuators. A nominal baseline model is constructed based on the known parameters of the service spacecraft prior to capturing the non-cooperative target; Based on the rigid-flexible coupled attitude vibration model and the nominal reference model, the matching unknown input terms are determined; The rigid-flexible coupled attitude vibration model is equivalently transformed into an equivalent control end model represented by the nominal reference model and the matched unknown input terms; The equivalent control terminal model is discretized to obtain a discrete-time control terminal model, and a deadbeat-free unknown input observer is constructed based on the discrete-time control terminal model. Acquire the measured sensor output data at the current sampling time and execute the following control steps: Based on the measured sensor output data at the current sampling time, the predicted sensor output data at the current sampling time is determined by a beatless unknown input observer. Based on the difference between the measured sensor output data and the predicted sensor output data at the current sampling time, the matching unknown input item at the previous sampling time is reconstructed through the beatless unknown input observer; The feedforward compensation control quantity at the current sampling time is calculated based on the matching unknown input terms reconstructed from the previous sampling time. Based on the combination of measured sensor output data and control input data from a preset number of sampling times prior to the current sampling time, and the matching unknown input terms reconstructed from the previous sampling time, the system state vector at the current sampling time is obtained by reverse calculation through the discrete-time control terminal model. The trajectory error vector at the current sampling time is determined based on the expected system state vector and the system state vector at the current sampling time. Based on the trajectory error vector at the current sampling time, an error reference trajectory that returns to zero within a preset time is generated by a time command generator, and the nominal control input at the current sampling time is determined. Based on the difference between the trajectory error vector and the error reference trajectory vector at the current sampling time and the preset negative virtual feedback gain, the negative virtual feedback control quantity at the current sampling time is determined. Based on the nominal control input and negative virtual feedback control quantity at the current sampling time, determine the nominal control input at the current sampling time; Based on the feedforward compensation control quantity and nominal control input at the current sampling time, determine the control input data at the current sampling time, and apply the control input data at the current sampling time to the actuator; The next sampling time is taken as the current sampling time, and the measured sensor output data at the current time is reacquired. The above control steps are repeated until the termination condition is met, so as to realize the attitude control and flexible vibration suppression of the flexible combined spacecraft synchronously within the specified time.

2. The negative virtual control method for a captured flexible composite spacecraft with dissipated data over a specified time, as described in claim 1, is characterized in that... The rigid-flexible coupled attitude vibration model is as follows: ； ； in, express The derivative; This represents the system state vector of the flexible combined spacecraft at time t within the flexible combined spacecraft's intrinsic system. This represents the state matrix of the flexible composite spacecraft's intrinsic system. This represents the input matrix within the body of the flexible composite spacecraft. This represents the control input data of the flexible combined spacecraft at time t within the flexible combined spacecraft's main system. The external disturbance moment of the flexible composite spacecraft at time t within the flexible composite spacecraft's own system is represented. This represents the nonlinear residual input matrix of the flexible composite spacecraft system. The nonlinear attitude kinematic residual of the flexible combined spacecraft at time t within the flexible combined spacecraft's intrinsic system is represented. This represents the sensor output data of the flexible composite spacecraft within its main system at time t. This represents the output matrix of the flexible composite spacecraft system.

3. The negative virtual control method for a captured flexible composite spacecraft with dissipated time according to claim 1, characterized in that, The nominal baseline model includes the nominal state matrix and nominal input matrix under the service spacecraft's intrinsic architecture; Based on the rigid-flexible coupled attitude vibration model and the nominal reference model, the unknown input terms for matching are determined, specifically including: The rigid-flexible coupled attitude vibration model is transformed from the flexible combined spacecraft body system to the service spacecraft body system to obtain the control end state matrix and control end input matrix of the rigid-flexible coupled attitude vibration model under the service spacecraft body system. The following formula is used to determine the matching of unknown input items: d ( t )= w ( t )+ N ( t )； ； ； ； D A = A - A 0; D B = B - B 0; in, d ( t () represents the matching of unknown input items at time t; w ( t The figure represents the external disturbance moment of the flexible composite spacecraft at time t within the service spacecraft's main system. N ( t () represents the equivalent matching uncertainty term at time t caused by the parameter deviation after capture; This indicates the construction of a matching matrix for a non-zero block structure; Indicates the deviation of the state matrix; This represents the system state vector of the flexible combined spacecraft at time t within the service spacecraft's intrinsic framework; Indicates the input matrix deviation; This represents the nominal control input of the flexible combined spacecraft at time t within the service spacecraft's main system. A This represents the control end state matrix of the rigid-flexible coupled attitude vibration model under the service spacecraft body system; B This represents the control input matrix of the rigid-flexible coupled attitude vibration model under the service spacecraft body system. This represents the nominal state matrix within the service spacecraft's intrinsic system. This represents the nominal input matrix within the service spacecraft's own system.

4. The negative virtual control method for a captured flexible composite spacecraft with dissipated data over a specified time, as described in claim 3, is characterized in that... The rigid-flexible coupled attitude vibration model is equivalently transformed into an equivalent control end model represented by the nominal reference model and the matched unknown input terms, specifically including: The control-end state matrix and control-end input matrix of the transformed rigid-flexible coupled attitude vibration model under the service spacecraft intrinsic system are replaced with the nominal state matrix and nominal input matrix from the nominal baseline model. Matching unknown input terms are then superimposed on the nominal control input. The equivalent control-end model is obtained through the following formula: ； in, express The derivative; This represents the system state vector of the flexible combined spacecraft at time t within the service spacecraft's intrinsic framework; This represents the nominal state matrix within the service spacecraft's intrinsic system. This represents the nominal input matrix within the service spacecraft's own system. This represents the nominal control input of the flexible combined spacecraft at time t within the service spacecraft's main system. This represents the external disturbance moment of the flexible composite spacecraft at time t within the service spacecraft's main system; This represents the equivalent matching uncertainty term at time t caused by the parameter deviation after capture; This represents the nonlinear residual input matrix in the service spacecraft's intrinsic architecture; It represents the nonlinear attitude kinematic residual of the flexible composite spacecraft at time t within the service spacecraft's main system.

5. The negative virtual control method for a captured flexible composite spacecraft with dissipated data over a specified time, as described in claim 1, is characterized in that... The equivalent control terminal model is discretized to obtain a discrete-time control terminal model. Based on this discrete-time control terminal model, a deadbeat-free unknown input observer is constructed, specifically including: The discrete-time control terminal model is obtained through the following formula: ； Based on the discrete-time control terminal model, a deadbeat-free unknown input observer is constructed using the following formula: ； in, This represents the system state vector of the flexible combined spacecraft at the (k+1)th sampling time within the service spacecraft's own system. This represents the discrete state matrix within the service spacecraft's intrinsic system. This represents the system state vector of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's intrinsic framework; This represents the discrete input matrix within the service spacecraft's intrinsic architecture. This represents the control input data of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's main system. This represents the unknown input item matched at the k-th sampling time. This represents the discrete nonlinear residual input matrix within the service spacecraft's intrinsic architecture. This represents the nonlinear attitude kinematic residual of the flexible composite spacecraft at the k-th sampling time in the service spacecraft's main system; This represents the sensor output data of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's main system. This represents the discrete output matrix within the service spacecraft's intrinsic architecture. This represents the observer state of the beatless unknown input observer at the (k+1)th sampling time. This represents the control input gain matrix of a deadbeat unknown input observer. This represents the measurement output gain matrix of a beatless unknown input observer. This represents the system state estimation vector of the flexible combined spacecraft at the k-th sampling time under the service spacecraft's own system. This indicates the observer state of the deadbeat-free unknown input observer at the k-th sampling time. This represents the output correction gain matrix of a beatless, unknown input observer. This represents the difference between the measured sensor output data and the predicted sensor output data at the k-th sampling time.

6. The negative virtual control method for a captured flexible composite spacecraft with dissipated data over a specified time, as described in claim 5, is characterized in that... Based on the difference between the measured sensor output data and the predicted sensor output data at the current sampling time, the matching unknown input term at the previous sampling time is reconstructed using a beatless unknown input observer, specifically including: The unknown input term from the previous sampling time can be reconstructed using the following formula: ； in, This represents the unknown input item matched at the (k-1)th sampling time during reconstruction; This represents the discrete output matrix within the service spacecraft's intrinsic architecture. This represents the control input gain matrix of a deadbeat unknown input observer. This represents the Moore-Penrose pseudo-inverse operation; This represents the difference between the measured sensor output data and the predicted sensor output data at the k-th sampling time.

7. The negative virtual control method for a captured flexible composite spacecraft with dissipated time according to claim 1, characterized in that, The feedforward compensation control quantity for the current sampling time is calculated based on the reconstructed matching unknown input term from the previous sampling time, specifically including: The negative of the matching unknown input term reconstructed at the previous sampling time is used as the feedforward compensation control quantity at the current sampling time.

8. The negative virtual control method for a captured flexible composite spacecraft with dissipated time according to claim 1, characterized in that, Based on the combination of measured sensor output data and control input data from a preset number of sampling times prior to the current sampling time, and the matching unknown input terms reconstructed from the previous sampling time, the system state vector at the current sampling time is calculated in reverse through the discrete-time control terminal model. Specifically, it includes: The system state vector at the current sampling moment can be obtained by reverse calculation using the following formula: ； ； ； ； ； in, This represents the system state vector of the flexible combined spacecraft at the k-th sampling moment obtained by reverse calculation, within the service spacecraft's own system. This represents the discrete state matrix within the service spacecraft's intrinsic system. This represents the system state vector of the flexible combined spacecraft at the (k-1)th sampling moment obtained from the recovery, within the service spacecraft's intrinsic system. This represents the discrete input matrix within the service spacecraft's intrinsic architecture. This represents the control input data of the flexible combined spacecraft under the service spacecraft system at the (k-1)th sampling time. This represents the unknown input item reconstructed at the (k-1)th sampling time; This represents the discrete nonlinear residual input matrix within the service spacecraft's intrinsic architecture. This represents the nonlinear attitude kinematic residual of the flexible combined spacecraft at the (k-1)th sampling time in the service spacecraft's main system. Represents the reconfigurability matrix; Represents the Moore-Penrose pseudoinverse of the reconfigurability matrix; This represents the historical output vector composed of a preset number of sensor output data before the k-th sampling time. The transpose of the discrete output matrix in the service spacecraft's own system; The transpose of the discrete state matrix of the service spacecraft's intrinsic system; Indicates transpose; This represents the corrected output vector after deducting the influence of known input terms at the k-th sampling time. This represents the measured sensor output data of the flexible combined spacecraft at the k-th sampling time within the service spacecraft's main system. This represents the discrete output matrix within the service spacecraft's own system.

9. The negative virtual control method for a captured flexible composite spacecraft with dissipated data over a specified time, as described in claim 1, is characterized in that... The specified time command generator is: ； ； in, This represents the error reference trajectory vector at the (k+1)th sampling time. Represents the error system matrix; This represents the error reference trajectory vector at the k-th sampling time. Represents the error system input matrix; This represents the nominal control input at the k-th sampling time. This represents the total number of sampling steps corresponding to a preset time period.

10. The method for negative virtual control of a captured flexible composite spacecraft with dissipated time according to claim 9, characterized in that, Based on the difference between the trajectory error vector and the error reference trajectory vector at the current sampling time, and the preset negative virtual feedback gain, the negative virtual feedback control quantity at the current sampling time is determined, specifically including: The negative virtual feedback control quantity at the current sampling time is determined by the following formula: ； ； in, This represents the negative virtual feedback control quantity at the k-th sampling time. This represents the nominal control input at the k-th sampling time. This indicates the preset negative virtual feedback gain; This represents the relative error at the k-th sampling time. This represents the trajectory error vector at the k-th sampling time. This represents the error reference trajectory vector at the k-th sampling time.

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