Spacecraft attitude fault-tolerant control with actuator saturation and its time estimation method

Abstract

The application discloses a spacecraft attitude fault-tolerant control and a time estimation method considering actuator saturation, and comprises the following steps: S1: a spacecraft attitude kinematics and dynamics model considering actuator failure, saturation and disturbance is established, a non-singular terminal sliding mode variable is designed, and a method for estimating the convergence time of the terminal sliding mode sliding stage is designed; S2: an adaptive fault-tolerant controller for spacecraft attitude maneuver is designed, and a corresponding disturbance adapter and a failure adapter are designed; S3: a method for estimating the time required for the spacecraft attitude to converge to the vicinity of the sliding mode surface is given. The application can guarantee that the spacecraft attitude control system has good precision, rapidness and anti-disturbance ability when the actuator is partially failed and saturated.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology, and in particular to a spacecraft attitude fault-tolerant control considering actuator saturation and its time estimation method. Background Technology

[0002] In modern space missions, we often need to control the thrust direction and magnitude of rocket engines to control spacecraft rendezvous and docking with space stations, or to control astronomical satellites and communication satellites for high-precision pointing. This necessitates frequent attitude maneuvers of the spacecraft. Therefore, how to control spacecraft to perform high-precision attitude maneuvers is a crucial research area in aerospace missions. Currently, there are two main methods for achieving attitude maneuvers in spacecraft: one is to control the spacecraft by expelling a certain mass of air through the jet propulsion system, and the other is to control it by using momentum wheels and control moment gyroscopes to achieve momentum exchange. However, regardless of the method used, it is necessary to know the spacecraft's real-time position state and the desired attitude angle and angular velocity. Only based on this information can the controller output the corresponding control torque using the spacecraft attitude control method.

[0003] Because proportional-integral-derivative (PID) control methods have many advantages such as good stability, easy adjustment, and ease of implementation, they are widely used in traditional spacecraft attitude control. However, in recent times, due to the rapid development of space station construction and manned spaceflight missions, the requirements for spacecraft control have become increasingly stringent, demanding high precision in attitude maneuvering, high maneuvering speed, and strong anti-interference capabilities. To meet these requirements, more and more optimized control methods have been proposed. Examples include a distributed spacecraft attitude cooperative tracking control method disclosed in Chinese patent application CN111752292B, a spacecraft formation attitude cooperative control method based on undirected communication topology disclosed in Chinese patent application CN110687915B, and a spacecraft attitude control method considering flywheel uncertainty disclosed in Chinese patent application CN109164824B.

[0004] The finite-time attitude control methods for spacecraft proposed in the publicly disclosed patents are all based on terminal sliding mode, achieving good results in improving the accuracy, anti-interference capability, and adjustment speed of spacecraft attitude maneuvers. For finite-time control, the most direct and obvious way to prove that the system is finite-time stable is to estimate the convergence time. However, the finite-time controller method designed using terminal sliding mode suffers from the problem of "contradiction between control singularity and estimated convergence time." That is, if the controller is not singular, there is no way to estimate the complete upper bound of the convergence time; if the complete upper bound of the convergence time can be estimated, the control exhibits singularity. Therefore, for spacecraft attitude control methods based on terminal sliding mode, it is of great significance whether a complete upper bound of the convergence time can be given and whether the problem of no controller singularity can be effectively solved. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a design for an attitude controller that enables spacecraft to complete attitude maneuvering tasks quickly and with high precision even in the event of actuator failure or saturation. In addition to being fault-tolerant and disturbance-resistant, it also provides a method for estimating the complete convergence time of the terminal sliding mode variables during the coasting and arrival phases.

[0006] The objective of this invention is achieved through the following technical solutions.

[0007] A spacecraft attitude fault-tolerant control method considering actuator saturation includes the following steps:

[0008] A spacecraft attitude kinematics and dynamics model considering actuator failure, saturation, and disturbances is established. Non-singular terminal sliding mode variables and an adaptive fault-tolerant controller for spacecraft attitude maneuvers are designed. The spacecraft attitude kinematics and dynamics model takes the following form:

[0009] in This represents the spacecraft's angular velocity, which is the projection of the spacecraft's rotational velocity relative to the inertial coordinate system onto its body coordinate system. Indicates the moment of inertia of a spacecraft. This represents the mounting matrix of the reaction wheels used for attitude control, where m represents the number of reaction wheels. Represents the identity matrix; This represents the actuator fault parameter matrix. This represents the fault parameters of the i-th reaction wheel. This indicates that the i-th reaction wheel is completely broken. This indicates that the i-th reaction wheel is functioning correctly and can output control torque normally. This indicates that the i-th reaction wheel has lost some of its effectiveness, but can still output some torque; This indicates the torque deviation effect caused by uncertain factors in the reaction wheel. This represents the output torque of the reaction wheel considering the saturation effect of the actuator, where The output torque of each reaction wheel to be designed is represented by the saturation function. The expression is ,in The saturation function represents the maximum torque that the i-th reaction wheel can output. It can be written as In the form of, The expression is:

[0010]

[0011]

[0012] variable If the value is bounded, then assume there exists a constant. satisfy ; These represent the attitude four elements used to describe the spacecraft's attitude in the coordinate system. Indicates the scalar part. Indicates the vector part; The attitude rotation matrix is ​​expressed as follows: , where the operator Used to represent a skew-symmetric matrix;

[0013] The non-singular terminal sliding mode variable has the following form:

[0014]

[0015] in , Operators are used to control parameters. This indicates the signed exponentiation operation. , express The symbol, when When it is a positive number, ,when When it is negative, ,when When it is 0, If the spacecraft attitude and angular velocity Stable on the sliding surface If the sliding surface is above, it can ensure the spacecraft's attitude. It converges to the equilibrium point within a finite amount of time.

[0016] The adaptive fault-tolerant controller used for spacecraft attitude maneuvers has the following specific structural form:

[0017]

[0018] in , , , , , , , , and All controller gain parameters are in positive constant form and must satisfy the following constraints:

[0019] , ,

[0020] , , , ;

[0021] The interference adaptor structure is as follows:

[0022]

[0023] in The expression is ;

[0024] The fault adaptor structure is as follows:

[0025]

[0026] in Estimated values ​​of fault parameters The relationship is .

[0027] In spacecraft attitude dynamics models that consider actuator failures, saturation, and interference, it is assumed that the actuators do not completely fail. External interference and stuck fault Both are bounded and have unknown constants. and satisfy and Define a function

[0028]

[0029] Based on the above assumptions, it can be concluded that Satisfy the following constraints

[0030]

[0031] in The expression is , It is an unknown positive number.

[0032] A method for estimating the attitude-tolerant control time of a spacecraft considering actuator saturation, specifically a method for estimating the convergence time of the terminal sliding mode coasting phase, referring to the convergence time of the system state on the sliding surface during the coasting phase. Satisfy the following expression:

[0033]

[0034] Where the function and The expressions are respectively and , This indicates the state variable that reaches the sliding surface. The value of .

[0035] Terminal sliding mode variables can be used in a finite time. Converging inward to the neighborhood near the sliding surface Within, and the convergence region and convergence time The expressions are as follows:

[0036]

[0037]

[0038] in Let be any constant between (0,1). Representation function initial value, , and The expression is as follows:

[0039]

[0040]

[0041]

[0042] in , , and The expression is as follows:

[0043]

[0044]

[0045]

[0046]

[0047] in and The expression is as follows:

[0048]

[0049] .

[0050] Compared with existing technologies, the advantages of this invention are: 1. This invention discloses an adaptive fault-tolerant control method for spacecraft attitude maneuver control. Compared with traditional linear control (such as PID control), the method disclosed in this invention is more suitable for ensuring that the spacecraft can successfully and with high quality complete attitude maneuvers even when partial failures are detected in the spacecraft's actuators.

[0051] 2. This invention innovatively discloses a method for estimating the convergence time of the terminal sliding mode variable arrival stage and the sliding stage. Compared with previous methods for estimating non-singular terminal sliding modes, the method disclosed in this invention has the advantages of both controller non-singularity and complete estimation of convergence time.

[0052] 3. The method disclosed in this invention also considers actuator saturation and the presence of disturbances during the design process, thus making it more practical. Furthermore, the non-smooth control scheme adopted can ensure that the attitude closed-loop system is stable for a finite time. This means that compared with the traditional smooth control method, this scheme has higher stability accuracy, faster response speed, and better anti-disturbance capability. Attached Figure Description

[0053] Figure 1 This is a system block diagram of the spacecraft attitude fault-tolerant control and time estimation method considering actuator saturation disclosed in this invention.

[0054] Figure 2 In the spacecraft attitude fault-tolerant control and time estimation method considering actuator saturation disclosed in this invention, attitude curves corresponding to three control methods for the nominal system are shown (by adjusting parameters to make the convergence time the same).

[0055] Figure 3 In the spacecraft attitude fault-tolerant control and time estimation method considering actuator saturation disclosed in this invention, the angular velocity curves corresponding to the three control methods of the nominal system are shown (by adjusting the parameters to make the convergence time the same).

[0056] Figure 4This invention discloses a spacecraft attitude fault-tolerant control method and time estimation method considering actuator saturation, which includes output torque curves of four reaction wheels corresponding to three control methods of the nominal system.

[0057] Figure 5 In the spacecraft attitude fault-tolerant control and time estimation method considering actuator saturation disclosed in this invention, attitude curves and their partial magnified views are shown for three control methods when the reaction wheel fails.

[0058] Figure 6 In the spacecraft attitude fault-tolerant control and time estimation method considering actuator saturation disclosed in this invention, the angular velocity curves and their partial magnified views are shown for the three control methods when the reaction wheel fails.

[0059] Figure 7 This invention discloses a spacecraft attitude fault-tolerant control method and time estimation method considering actuator saturation, which includes output torque curves of four reaction wheels corresponding to three control methods when a reaction wheel malfunctions. Detailed Implementation

[0060] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0061] Example

[0062] like Figure 1-7 As shown, the present invention includes the following steps:

[0063] S1: Establish a spacecraft attitude kinematics and dynamics model that considers actuator failure, saturation and interference, design a non-singular terminal sliding mode variable, and a method to estimate the convergence time of the terminal sliding mode coasting phase.

[0064] S2: Design an adaptive fault-tolerant controller for spacecraft attitude maneuvering, as well as a corresponding disturbance adaptor and fault adaptor.

[0065] S3: A method is given for estimating the time required for a spacecraft's attitude to converge to the vicinity of the sliding surface.

[0066] The spacecraft attitude kinematics and dynamics model considering actuator failure, saturation, and interference in step S1 is as follows:

[0067]

[0068] in This represents the spacecraft's angular velocity, which is the projection of the spacecraft's rotational velocity relative to the inertial coordinate system onto its body coordinate system. Indicates the moment of inertia of a spacecraft. This represents the mounting matrix of the reaction wheels used for attitude control, where m represents the number of reaction wheels. Represents the identity matrix; This represents the actuator fault parameter matrix. This represents the fault parameters of the i-th reaction wheel. This indicates that the i-th reaction wheel is completely broken. This indicates that the i-th reaction wheel is functioning correctly and can output control torque normally. This indicates that the i-th reaction wheel has lost some of its effectiveness, but can still output some torque; This indicates the torque deviation effect caused by uncertain factors in the reaction wheel. This represents the output torque of the reaction wheel considering the saturation effect of the actuator, where The output torque of each reaction wheel to be designed is represented by the saturation function. The expression is ,in The saturation function represents the maximum torque that the i-th reaction wheel can output. It can be written as In the form of, The expression is:

[0069]

[0070]

[0071] Considering the lack of singularity in control inputs Its value will not tend to infinity, therefore, in a real system, the variable... Since the value is bounded, we can assume that there exists a constant. satisfy ; These represent the attitude four elements used to describe the spacecraft's attitude in the coordinate system. Indicates the scalar part. Indicates the vector part; The attitude rotation matrix is ​​expressed as follows: , where the operator Used to represent a skew-symmetric matrix, such as for a vector ,but The expression is .

[0072] One type of non-singular terminal sliding mode variable in S1 has the following form:

[0073]

[0074] in , Operators are used to control parameters. This represents signed exponentiation, such as , express The symbol, when When it is a positive number, ,when When it is negative, ,when When it is 0, If the spacecraft attitude and angular velocity Stable on the sliding surface If the sliding surface is above, it can ensure the spacecraft's attitude. It converges to the equilibrium point within a finite time; among the sliding mode variables disclosed in this invention, the velocity term uses the spacecraft angular velocity. Instead of traditional The attitude controller based on this design is in No control anomalies will occur nearby.

[0075] The method for estimating the convergence time of the terminal sliding mode in S1 specifically refers to the convergence time of the system state during the sliding mode phase on the sliding surface. Satisfy the following expression:

[0076]

[0077] Where the function and The expressions are respectively and , This indicates the state variable that reaches the sliding surface. The value of .

[0078] The following theoretical proof demonstrates the rationality of the above analysis. If the spacecraft's attitude state variables can stabilize on the sliding surface... Based on the spacecraft kinematic model and the sliding surface, we have the equation... Valid. The candidate Lyapunov function is defined as follows: Taking its derivative, we get

[0079]

[0080] because Therefore, attitude state It can asymptotically converge to the origin, while It converges asymptotically to 1. The proof will be presented in two cases below. and They can converge to their respective equilibrium points within a finite amount of time.

[0081] Scenario 1: When exist When the interval is reached. At that time, Substitute into From this, we can obtain:

[0082]

[0083] According to the following finite-time stability lemma:

[0084] Lemma: Consider the following continuous system:

[0085]

[0086] If a Lyapunov function exists and positive numbers and , making the inequality If it is established, then the system For finite-time stability, and for convergence time satisfying The constraints, among which express The initial value.

[0087] The spacecraft attitude state variables can be obtained. In a limited time It becomes internally stable at the equilibrium point, and The following constraints must be satisfied:

[0088]

[0089] in Indicates at time Time variable The value of .

[0090] Scenario 2: When exist When the interval is reached. hour, Will first From within a time period Converging to 0, and then It converges from 0 to 1 within time. The following calculations are performed respectively. and The mathematical expression. Selection of candidate Lyapunov functions. Differentiating it, we get:

[0091]

[0092] Integrating both sides of the above equation will calculate the convergence time. The following constraints must be satisfied:

[0093]

[0094] in Indicates at time Time variable The value of , the formula shows It will be at time From the inside It converges to 0. (Regarding...) Both sides are in the interval Integral yields

[0095]

[0096] so The convergence time is and The sum is given by the following formula:

[0097]

[0098] In summary and ,according to Depending on the location, the estimated time for the sliding phase of the sliding mode variable can be obtained as follows:

[0099]

[0100] The proof is complete.

[0101] The adaptive fault-tolerant controller for spacecraft attitude maneuvering in step S2 has the following specific structural form:

[0102]

[0103] Among them , , , , , , , , and All controller gain parameters are in positive constant form and must satisfy the following constraints:

[0104] , ,

[0105] , , , ;

[0106] One type of interference adaptive structure in S2 is:

[0107]

[0108] in The expression is .

[0109] One type of fault adaptor structure in S2 is:

[0110]

[0111] middle Estimated values ​​of fault parameters The relationship is .

[0112] Step S3, one method for estimating the time required for the spacecraft attitude to converge to the vicinity of the sliding surface, refers to the ability of the terminal sliding mode variable to converge within a finite time. Converging inward to the neighborhood near the sliding surface Within, and the convergence region Convergence time of sliding mode variables in the arrival phase The expressions are as follows:

[0113]

[0114]

[0115] in Let be any constant between (0,1). Representation function initial value, , and The expression is as follows:

[0116]

[0117]

[0118]

[0119] in , , and The expression is as follows:

[0120]

[0121]

[0122]

[0123]

[0124] in and The expression is as follows:

[0125]

[0126] .

[0127] The following theoretical proof demonstrates the rationality of the above analysis. This is achieved through the definition... Then the sliding mode variable It can be written in the following form:

[0128]

[0129] As can be seen from the above formula, Equivalent to The Lyapunov candidate functions are defined as follows:

[0130]

[0131] in and The definition has been given above. Regarding... Differentiation yields:

[0132]

[0133] in

[0134]

[0135] Notice Therefore, there is Then for Further simplification yields

[0136]

[0137] Using the relevant lemmas, we can obtain the following inequality:

[0138]

[0139] Further transformation of the above equation yields the following form:

[0140]

[0141] in Substituting the above formula into... From this, we can obtain:

[0142]

[0143] definition And then The following simplification yields:

[0144]

[0145] Substituting the above equation into... From the middle

[0146]

[0147] If you choose The following conditions must be met:

[0148]

[0149] Then the above The expression can be further simplified to:

[0150]

[0151] in Using the relevant lemmas, we can see that in the above equation... The following constraints can be satisfied:

[0152]

[0153] Notice Therefore, we can obtain:

[0154]

[0155] Substitute the above results into From this, we can obtain:

[0156]

[0157] Substituting the control design and the two adaptives described above into the above equation, we can obtain:

[0158]

[0159] For any and The following equation holds true.

[0160]

[0161]

[0162] Substitute the results of the two equations above into From the middle

[0163]

[0164] Scenario 1: When Sometimes, .

[0165] Scenario 2: When Sometimes,

[0166] in, and .

[0167] Combining the two situations above, we can conclude that: .

[0168] Similarly, we can also obtain: .

[0169] Substituting the two inequalities above into... From this, we can obtain:

[0170]

[0171] in and The expression for has been defined above. To illustrate that the above formula reflects the finite-time stability of the system, the following practical finite-time stability theorem is introduced:

[0172] Lemma: Consider the following continuous system:

[0173]

[0174] If a Lyapunov function exists and positive numbers , and , making the inequality If it is established, then the system This indicates that the system state can be stabilized in a practically finite-time manner. Converging inward to near the equilibrium point Within its neighborhood, express initial value, It is an arbitrary constant between 0 and 1.

[0175] Based on the above lemma and It can be seen that the sliding mode variable converges in actual finite time, which indicates that In a limited time It converges inward to the neighborhood of the following equilibrium point:

[0176]

[0177] And convergence time The following constraints must be satisfied:

[0178]

[0179] The proof is complete.

[0180] The effectiveness of the algorithm disclosed in this application is verified using simulation software. Let the moment of inertia of the spacecraft be... Install matrix The structural formula is as follows:

[0181]

[0182] Let the expression for the interference be: The initial values ​​of the spacecraft's attitude and angular velocity are and rad / s, control parameters set to , , , , , , and , The control task is to control the attitude. Towards Convergence, controlling angular velocity Towards The convergence occurs at rad / s.

[0183] This simulation compares the control algorithm disclosed in this invention with the traditional PID control method and the control method in reference 1 (K. Lu, and Y. Xia, “Finite-time fault-tolerant control for rigid spacecraft with actuator saturations,” IET Control Theory and Applications, vol. 7, No. 11, pp. 1529-1539, 2018.). For fairness, we conducted two sets of simulations. In the first set, we assumed no actuator malfunction and adjusted the other two controllers so that the convergence times of the attitude curves and angular velocity curves corresponding to the three controllers were the same. In the second set of simulations, we assumed a sudden malfunction of the reaction wheel, with the malfunction type shown in the following formula:

[0184] , , ,

[0185] , .

[0186] Then observe the state response curves of the three controllers when the spacecraft's reaction wheel fails.

[0187] The relevant simulations for the first group of actuators without faults are as follows: Figures 2-4 As shown in the figure, (a) is a simulation diagram of the PID control method, (b) is the control method in reference 1, and (c) is the finite-time control method based on terminal sliding mode disclosed in this invention. Figure 2 and Figure 3 It can be seen that the convergence time for the spacecraft's attitude and angular velocity driven by the three controllers is 35s. Figure 3 The output torques of the three control methods shown are all roughly the same, thus achieving the expected results. In the second set of simulations, it is assumed that the reaction wheel suddenly malfunctions; the relevant simulation results can be seen... Figures 5-7 .from Figure 5 It can be seen that the stability accuracy of the attitude system controlled by PID is approximately 0.01, while the control accuracy of Reference 1 is 0.0025, which is an order of magnitude higher than that of PID. The control accuracy of the method disclosed in this invention is 0.00025, which is also an order of magnitude higher than that of Reference 1. Furthermore, the convergence time of the method disclosed in this invention is significantly faster than the other two methods. Figure 6 It can be seen that the stability accuracy of the spacecraft's angular velocity under PID control is approximately 0.0003 rad / s, the stability accuracy of the control method in Reference 1 is 0.00002 rad / s, while the stability accuracy of the method disclosed in this invention is approximately 0.000001 rad / s, significantly higher than the other two control methods. Furthermore, the convergence time of the method disclosed in this invention is also significantly faster than the other two methods. Figure 7 As can be seen from the output torque curves of the four reaction flywheels for the three control methods, the maximum output torque is the same for all three methods. Based on the simulation results above, the adaptive fault-tolerant finite-time attitude control method disclosed in this invention still possesses advantages such as fast convergence speed, high control accuracy, and good anti-disturbance capability, even when facing actuator failures, saturation, and considering external disturbances.

Claims

1. A spacecraft attitude fault-tolerant control method considering actuator saturation, characterized in that, Includes the following steps: A spacecraft attitude kinematics and dynamics model considering actuator failure, saturation, and disturbances is established. Non-singular terminal sliding mode variables and an adaptive fault-tolerant controller for spacecraft attitude maneuvers are designed. The spacecraft attitude kinematics and dynamics model takes the following form: ; in This represents the spacecraft's angular velocity, which is the projection of the spacecraft's rotational velocity relative to the inertial coordinate system onto its body coordinate system. Indicates the moment of inertia of a spacecraft. This represents the mounting matrix of the reaction wheels used for attitude control, where m represents the number of reaction wheels. Represents the identity matrix; This represents the actuator fault parameter matrix. This represents the fault parameters of the i-th reaction wheel. This indicates that the i-th reaction wheel is completely broken. This indicates that the i-th reaction wheel is functioning correctly and can output control torque normally. This indicates that the i-th reaction wheel has lost some of its effectiveness, but can still output some torque; This indicates the torque deviation effect caused by uncertain factors in the reaction wheel. This represents the output torque of the reaction wheel considering the saturation effect of the actuator, where The output torque of each reaction wheel to be designed is represented by the saturation function. The expression is ,in The saturation function represents the maximum torque that the i-th reaction wheel can output. It can be written as In the form of, The expression is: ； ； variable If the value is bounded, then assume there exists a constant. satisfy ; These represent the attitude four elements used to describe the spacecraft's attitude in the coordinate system. Indicates the scalar part. Indicates the vector part; The attitude rotation matrix is ​​expressed as follows: , where the operator Used to represent a skew-symmetric matrix; The non-singular terminal sliding mode variable has the following form: ； in , Operators are used to control parameters. This indicates the signed exponentiation operation. , express The symbol, when When it is a positive number, ,when When it is negative, ,when When it is 0, If the spacecraft attitude and angular velocity Stable on the sliding surface If the sliding surface is above, it can ensure the spacecraft's attitude. It converges to the equilibrium point within a finite time. The adaptive fault-tolerant controller used for spacecraft attitude maneuvers has the following specific structural form: in , , , , , , , , and All controller gain parameters are in positive constant form and must satisfy the following constraints: ， ， ； ， ， ， ； The interference adaptor structure is as follows: ； in The expression is ; The fault adaptor structure is as follows: ； in Estimated values ​​of fault parameters The relationship is ; This includes methods for estimating the convergence time of the terminal sliding mode phase, specifically referring to the convergence time of the system state during the sliding phase on the sliding surface. Satisfy the following expression: ； Where the function and The expressions are respectively and , This indicates the state variable that reaches the sliding surface. The value; The method for estimating the time required for a spacecraft's attitude to converge to the vicinity of the sliding surface is to use the terminal sliding mode variable energy in a finite time. Converging inward to the neighborhood near the sliding surface Within, and the convergence region Convergence time of sliding mode variables in the arrival phase The expressions are as follows: ； ； in Let be any constant between (0,1). Representation function initial value, , and The expression is as follows: ； ； ； in , , and The expression is as follows: ； ； ； ； in and The expression is as follows: ； 。 2. The spacecraft attitude fault-tolerant control method considering actuator saturation according to claim 1, characterized in that, In spacecraft attitude dynamics models that consider actuator failures, saturation, and interference, it is assumed that the actuators do not completely fail. External interference and stuck fault Both are bounded and have unknown constants. and satisfy and Define a function ； Based on the above assumptions, it can be concluded that Satisfy the following constraints ； in The expression is , It is an unknown positive number.

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