Spacecraft control method and system considering residual vibrations

Abstract

The application discloses a spacecraft control method and system considering residual vibration, and the method comprises the following steps: based on Euler rotation theorem, an Euler axis expression of a spacecraft attitude maneuver process is constructed; a dynamic model of a flexible spacecraft is established; a residual vibration expression of a flexible accessory in the flexible spacecraft is constructed; according to the characteristics and threshold limit of the residual vibration, a trajectory planning is carried out, and a spacecraft angular acceleration trajectory planning curve is generated; and according to the Euler axis expression of the spacecraft attitude maneuver process, the dynamic model of the flexible spacecraft and the spacecraft angular acceleration trajectory planning curve, a control loop is composed. The system comprises an Euler axis calculation module, a dynamic model construction module, a residual vibration construction module, an angular acceleration trajectory planning module and an overall control module. By using the application, the vibration generated in the maneuver process can be inhibited. The application can be widely applied in the field of spacecraft control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of spacecraft control, and particularly relates to a spacecraft control method and system considering residual vibration. BACKGROUND

[0002] In recent years, with the enhancement of spacecraft functions and the increase of payloads, in order to quickly and effectively complete space tasks and maintain long-term on-orbit operation of spacecraft, spacecrafts mostly need to install flexible appendages such as solar panels and moving antennas. Such spacecrafts usually have the dynamic characteristics of large inertia of the star body and large flexibility of the appendages, and thus the concept of flexible spacecraft is generated.

[0003] In the process of attitude rapid maneuvering of a flexible spacecraft, structural vibration of the flexible appendage is inevitably excited. Such vibration seriously affects the normal work of the payload, and is difficult to be attenuated by itself, so effective vibration suppression measures need to be taken to suppress the residual vibration. For the vibration suppression problem of a flexible spacecraft, the input shaping method is currently applied, but the input shaping method only suppresses the residual vibration after maneuvering, and does not consider the vibration suppression during maneuvering. SUMMARY

[0004] In view of this, in order to solve the technical problem that the existing spacecraft control method cannot suppress the vibration generated during maneuvering, thereby leading to unstable control, the present application proposes a spacecraft control method and system considering residual vibration, which comprises the following steps:

[0005] S1, based on the Euler rotation theorem, an Euler axis expression of a spacecraft attitude maneuvering process is constructed;

[0006] S2, a dynamic model of a flexible spacecraft is established;

[0007] S3, a residual vibration expression of a flexible appendage in the flexible spacecraft is constructed;

[0008] S4, trajectory planning is performed according to the characteristics and threshold limit of the residual vibration, and a spacecraft angular acceleration trajectory planning curve is generated;

[0009] S5, a control loop is composed according to the Euler axis expression of the spacecraft attitude maneuvering process, the dynamic model of the flexible spacecraft, and the spacecraft angular acceleration trajectory planning curve.

[0010] In some embodiments, the Euler axis expression of the spacecraft attitude maneuvering process is expressed as follows:

[0011]

[0012] Through the preferred steps, the Euler axis calculation and the determination of the rotation angle are performed for the spacecraft to change from one attitude to another attitude.

[0013] In some embodiments, the dynamics model of the flexible spacecraft is represented as follows:

[0014]

[0015] where I is the inertia matrix of the spacecraft body relative to the body coordinate system; ω is the component of the attitude angular velocity of the spacecraft central rigid body body coordinate system relative to the inertial coordinate system in the body coordinate system; F s is the coupling coefficient matrix of the flexible appendage to the star body; η is a column array composed of each order of vibration mode, η = [η1 η2 … η n ] T , is the first and second order derivative of η relative to time, respectively; T c is the control torque of the system; T d is the environmental disturbance torque of the system; ξ is the modal damping ratio matrix of the flexible appendage, and ξ = diag[ξ1 ξ2 … ξ n ]; κ c is the natural frequency matrix of the flexible appendage, and κ c = diag[κ c1 κ c2 … κ cn ]; n is the number of modes considered.

[0016] Through the preferred step, the spacecraft attitude dynamics model with flexible appendage is established, which provides a model for subsequent spacecraft attitude maneuver trajectory planning, and provides a basis for numerical simulation verification.

[0017] In some embodiments, in the case where the reference angular acceleration is a r (t), and the maneuver Euler axis is , the residual vibration expression of the flexible appendage in the flexible spacecraft is represented as follows:

[0018]

[0019] where η j represents the j-th order vibration mode, D j represents the j-th element of the column vector , t0 represents the maneuver start time, t f represents the maneuver end time, κ cj represents the j-th order natural frequency of the flexible appendage, ξ j represents the j-th order damping ratio of the flexible appendage, τ represents the time variable, and e represents the natural constant.

[0020] The application also proposes a spacecraft control system considering residual vibration, the system comprising:

[0021] In some embodiments, the spacecraft angular acceleration trajectory planning curve is represented as follows:

[0022]

[0023] Wherein a max represents a threshold value of angular acceleration, T represents a period of a sinusoidal part in the angular acceleration signal, represents a frequency of the sinusoidal part in the angular acceleration signal, t1 represents an end time of the acceleration segment, t2 represents an end time of the constant rolling segment, t mid represents a time of the constant angular acceleration segment, and m represents a power of the selected sinusoidal angular acceleration signal.

[0024] An Euler axis calculation module is configured to construct an Euler axis expression of a spacecraft attitude maneuvering process based on an Euler rotation theorem;

[0025] A dynamics model construction module is configured to establish a dynamics model of the flexible spacecraft;

[0026] A residual vibration construction module is configured to construct a residual vibration expression of a flexible accessory in the flexible spacecraft;

[0027] An angular acceleration trajectory planning module is configured to perform trajectory planning according to characteristics and threshold limits of the residual vibration, and generate a spacecraft angular acceleration trajectory planning curve;

[0028] An overall control module is configured to form a control loop according to the Euler axis expression of the spacecraft attitude maneuvering process, the dynamics model of the flexible spacecraft, and the spacecraft angular acceleration trajectory planning curve.

[0029] Based on the above scheme, the present application provides a spacecraft control method and system considering residual vibration, and provides a control method for fast attitude maneuvering, fast stabilization and soft trajectory of a flexible spacecraft. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a step flowchart of the spacecraft control method considering residual vibration;

[0031] Figure 2 is a structural diagram of the spacecraft;

[0032] Figure 3 is a relationship diagram of υ and λ corresponding to different powers m;

[0033] Figure 4 is an angular acceleration curve diagram of the trajectory planning containing a constant part;

[0034] Figure 5 is a reference angular acceleration design flowchart of trajectory planning;

[0035] Figure 6 is a spacecraft attitude maneuver reference angular acceleration curve chart of trajectory planning;

[0036] Figure 7 is a spacecraft attitude maneuver Euler angle curve chart of trajectory planning;

[0037] Figure 8 、 Figure 9 、 Figure 10 、 Figure 11 is a spacecraft flexible appendage first four order vibration mode variation chart over time;

[0038] Figure 12 、 Figure 13 、 Figure 14 is a spacecraft attitude maneuver expected moment variation chart over time;

[0039] Figure 15 、 Figure 16 、 Figure 17 is a spacecraft attitude angular velocity variation chart over time;

[0040] Figure 18 、 Figure 19 、 Figure 20 、 Figure 21 is a spacecraft attitude quaternion variation chart over time. DETAILED DESCRIPTION

[0041] In view of the technical problem of being unable to suppress the vibration generated in the maneuvering process in the background art, the present application designs a suitable reference trajectory according to a given residual vibration index, and suppresses and controls the flexible vibration excited by the spacecraft in the rapid maneuvering by using a reference angular acceleration trajectory planning technology, so as to overcome the problem that it is difficult to take into account rapidity and stability in the existing conventional attitude maneuvering control.

[0042] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0043] It should be noted that, for the convenience of description, only the parts related to the present application are shown in the drawings. The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0044] It should be understood that the terms "system", "apparatus", "unit" and / or "module" used in the present application are a method for distinguishing different components, elements, parts, sections or assemblies at different levels. However, if other words can achieve the same purpose, the words can be replaced by other expressions.

[0045] As shown in the present application and claims, unless the context clearly indicates otherwise, the words "one", "an", "a", and / or "the" do not specify a singular number, but can also include a plural number. Generally speaking, the terms "comprise" and "include" only indicate the inclusion of the steps and elements explicitly identified, and these steps and elements do not constitute an exclusive list, and the method or device can also include other steps or elements. The element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, product or device comprising the element.

[0046] In the description of embodiments of the present application, "a plurality of" means two or more than two. The following terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features.

[0047] In addition, flowcharts are used in the present application to illustrate the operations performed by the system according to the embodiments of the present application. It should be understood that the preceding or subsequent operations are not necessarily performed in sequence. On the contrary, each step can be processed in reverse order or simultaneously. Meanwhile, other operations can be added to these processes, or one or more steps of operation can be removed from these processes.

[0048] Reference Figure 1 The flowchart of an optional example of the spacecraft control method proposed in the present application can be applied to a computer device. The control method proposed in the present embodiment can include but is not limited to the following steps:

[0049] S1, based on Euler's rotation theorem, constructing Euler axis expression of spacecraft attitude maneuver process;

[0050] According to Euler's rotation theorem, the change of the attitude of a rigid body from a given orientation to any other orientation can be achieved by rotating around the Euler axis, and the angle traveled during this process is the shortest. The Euler axis is fixed to the rigid body during the rotation of the rigid body, and is also stationary relative to the inertial space. Therefore, in order to achieve rapid maneuvering and rapid stabilization control of the spacecraft, the spacecraft is required to maneuver along the shortest path in the Euler axis-angle manner. This requires planning a maneuvering path around the Euler axis, and then tracking and controlling it. This step is to calculate the Euler axis and determine the rotation angle when the spacecraft changes from one attitude to another. Specifically as follows:

[0051] Firstly, the attitude quaternion of the spacecraft relative to the reference coordinate system is defined as:

[0052]

[0053] where q0is the scalar parameter in the quaternion, is the vector parameter in the quaternion, and the direction of the Euler axis is represented by the vector part of the quaternion, and the scalar part σ represents the rotation angle of the Euler axis; thus, the Euler axis and angle are calculated by the initial and final attitude quaternions, let the initial attitude quaternion of the spacecraft be and the target attitude quaternion be where q 10 and q t0 are the scalar parameters in the initial attitude quaternion and the target attitude quaternion, and are the vector parameters in the initial attitude quaternion and the target attitude quaternion;

[0054] The characteristic principal axis quaternion Q e of the spacecraft attitude maneuver can be expressed as:

[0055]

[0056] According to formula (2), the angle expression of the rotation along the Euler axis is:

[0057] Φ=2arccos(q e0 ) (3)

[0058] According to formula (2), the Euler axis expression is:

[0059]

[0060] Formula (4) is written in the scalar form, that is, in the spacecraft body coordinate system:

[0061]

[0062] where n ex ,n ey ,n ez are the components of the vector in three directions; q e1 ,q e2 ,q e3 are the three components of the vector .

[0063] Let the planned angular velocity be the angular velocity around the characteristic axis The desired angular velocity trajectory of the spacecraft is represented as:

[0064]

[0065] The desired angular velocity trajectory of the spacecraft is represented as:

[0066]

[0067] The desired angular velocity trajectory of the spacecraft is represented as:

[0068] The initial angle of the spacecraft attitude is considered to be 0°, and the initial angular velocity is 0° / s. The desired attitude angles on the three axes are 60°, 0°, and 0°, respectively. The Euler axis and Euler rotation angle are calculated through the above steps, as follows:

[0069] Φ = 60°,

[0070] S2, Establish the dynamics model of the flexible spacecraft;

[0071] The spacecraft attitude dynamics model with flexible appendages is established, providing a model for spacecraft attitude maneuver trajectory planning and a basis for numerical simulation verification. The specific operations of this step are as follows:

[0072] Ignoring the coupling of the spacecraft orbit and the orbital flexible appendages, the dynamics equation of the flexible spacecraft system can be simplified as:

[0073]

[0074] where I is the moment of inertia matrix of the spacecraft body relative to the body coordinate system; ω is the attitude angular velocity of the spacecraft central rigid body coordinate system relative to the inertial coordinate system in the body coordinate system; F s is the coupling coefficient matrix of the flexible appendages to the spacecraft; η is a column array composed of each order of vibration mode, η = [η1 η2 … η n ] T , are the first and second order derivatives of η with respect to time; T c is the control torque of the system; T d is the environmental disturbance torque of the system; ξ is the modal damping ratio matrix of the flexible appendages, and ξ = diag[ξ1 ξ2 … ξ n ]; κ c is the natural frequency matrix of the flexible appendages, and κ c = diag[κ c1 κ c2 … κ cn ]; n is the number of modes considered.

[0075] Assuming that the spacecraft body system and the reference system error is small, and ignore the orbital angular velocity related terms, the vibration equation expression can be obtained as follows:

[0076]

[0077] Thus, the flexible accessory vibration equation is approximately:

[0078]

[0079] It can be seen that the essence of vibration suppression is to design a suitable reference angular velocity trajectory a r Under the premise of ensuring the rapid maneuvering of the spacecraft, the excited vibration mode amplitude η is as small as possible.

[0080] In this embodiment, the spacecraft is considered to have two flexible solar panels, such as Figure 2 .

[0081] The spacecraft inertia parameters are as follows:

[0082]

[0083] The environmental disturbance torque of the system is as follows:

[0084]

[0085] The modal damping ratio matrix of the panel is as follows:

[0086]

[0087] The natural frequency matrix of the panel is as follows:

[0088]

[0089] The coupling coefficient matrix of the panel is as follows:

[0090]

[0091] S3, construct the residual vibration expression of the flexible accessory in the flexible spacecraft;

[0092] Deduce the excited residual vibration expression of the spacecraft flexible accessory under the action of the reference angular acceleration trajectory a r (t), the specific operation is as follows:

[0093] For a given arbitrary function a r (t), the expression of the jth mode of the flexible accessory about a r (t) can be obtained as follows:

[0094]

[0095] where D j is the jth element of the column vector , t0 is the maneuver starting time, and t f is the maneuver ending time.

[0096] η δj is the unit step response of the jth mode, which is expressed as

[0097]

[0098] Substituting equation (12) into equation (11) and simplifying, we get

[0099]

[0100] According to the expression (13) of the vibration mode, the residual vibration amplitude at the maneuver ending time t f , i.e., is obtained as

[0101]

[0102] In order to measure the effect of vibration suppression, the residual vibration ratio υ(κ) is defined, which is defined as the ratio of the residual vibration amplitude of the system to the vibration amplitude excited by the maximum angular velocity step input at the frequency point κ, and its mathematical expression is

[0103]

[0104] where η step (κ) is the vibration amplitude excited by the unit step input, and its expression is approximately

[0105]

[0106] At this point, under the condition that the reference angular acceleration is a r (t) and the maneuver Euler axis is , the residual vibration expression of the flexible appendage is given by equation (14), and the residual vibration ratio is given by equation (15). In the angular acceleration trajectory planning process, a r (t) needs to be designed to minimize υ(κ) or V(κ) while ensuring the spacecraft to maneuver quickly and stably, so as to suppress the vibration of the flexible appendage.

[0107] S4, according to the characteristics and threshold limit of the residual vibration, the trajectory planning is carried out, and the spacecraft angular acceleration trajectory planning curve is generated.

[0108] The characteristics of the residual vibration are obtained by substituting the expression of the sinusoidal signal in step S4 into the expression of the residual vibration amplitude in step S3.

[0109] The spacecraft's angular acceleration curve is divided into three segments: acceleration, uniform velocity, and deceleration. Based on the characteristics of residual vibrations excited by trigonometric power functions, and the angular acceleration α of the spacecraft's attitude maneuvering... max and maximum angular velocity ω max To address the limitations, a trajectory planning method based on trigonometric power functions is designed to achieve vibration suppression, as detailed below:

[0110] The general expression for the m-th power function of the sine curve is as follows:

[0111] a m (t)=a max sin m (κt / 2) (17)

[0112] In the formula, a m (t) represents the m-th power function of the sine curve, where m is a positive integer. As m increases, the complexity of the expansion of equation (17) increases.

[0113] For the sake of brevity, only the case where m≤4 is given the specific expansion:

[0114]

[0115] Substituting equation (18) into the analysis of the second-order system, we obtain the expression for the residual vibration amplitude:

[0116]

[0117] Define λ = κ c / κ gives the residual vibration ratio:

[0118]

[0119] Appendix Figure 3 The curves of the residual vibration ratio υ as a function of λ for different powers of m are given when m≤4.

[0120] From equation (20), we can obtain the relationship between υ and λ for different powers of m: when m is the same, υ gradually decreases as the value of λ increases; if the value of λ is large enough, υ and λ... m They are approximately inversely proportional.

[0121] According to the definition of λ, it can be seen that high frequency vibration corresponds to a larger λ value, i.e. the angular acceleration signal has a better inhibitory effect on high frequency vibration. Therefore, in the process of designing the angular acceleration trajectory, only the λ value corresponding to the lowest frequency (fundamental frequency) needs to be designed. However, for the same fundamental frequency, the larger the value of λ, the longer the acceleration time of the corresponding angular acceleration curve, so it is desirable to have the smallest value of λ under the premise of meeting the vibration suppression requirement. Table 1 below gives the minimum λ value required for different power sine functions under the same residual vibration ratio υ, denoted as λ min .

[0122] Table 1 Simulation parameters

[0123]

[0124] If the input is an odd power sine signal, the input signal can be written in the following form:

[0125]

[0126] In the formula, α k corresponds to the coefficient of each term in the expansion. Integrating the acceleration signal in the acceleration phase, the angular velocity change curve is as follows:

[0127]

[0128] After the acceleration phase ends, the angular velocity of the spacecraft should reach the maximum angular velocity ω max , i.e.

[0129] ω r (t1)=ω max (23)

[0130] In the formula, t1 represents the end time of the acceleration phase. The relationship between ω max and a max can be derived as follows:

[0131]

[0132] Given that the end time of the acceleration phase t1 is the same as the action time T of the angular acceleration signal, combining formula (22) and substituting κ = 2π / T, the expression of t1 can be derived as follows:

[0133]

[0134] Next, the relationship between the end time of the rolling phase t2 and ω max is determined according to the angle of spacecraft maneuver Φ m . Integrating formula (22), the expression of Euler angle can be obtained as follows:

[0135]

[0136] Then the Euler angle Φ(t1) at time t1 is:

[0137]

[0138] Thus the Euler angle Φ(t2) at time t2 is:

[0139] Φ(t2) = ω max (t2-t1) + Φ(t1) (28)

[0140] Substituting equation (24) into equation (27), the total Euler angle Φ m of the spacecraft maneuver is:

[0141] Φ m = Φ(t2) + Φ(t1) = ω max t2 (29)

[0142] Thus we have:

[0143]

[0144] The total maneuver time t end of the spacecraft is:

[0145]

[0146] While in the case of the same maximum angular acceleration a max and maximum angular velocity ω max , the maneuver time of the step signal is:

[0147]

[0148] Thus the increased maneuver time by using the odd power sine angular acceleration signal is:

[0149]

[0150] If the input is an even power sine signal, the input signal expansion can be written as:

[0151]

[0152] where β k corresponds to the coefficients of each term in the expansion, and β0 is the constant term in the expansion. The same as the derivation of the odd power sine curve, the acceleration time of the even power sine angular acceleration is:

[0153]

[0154] The expression of constant roll end time t2 is:

[0155]

[0156] The expression of total spacecraft maneuver time t is: end

[0157]

[0158] The increased maneuver time Δt is:

[0159]

[0160] A symbol χ is defined to uniformly represent the expression of maneuver time. The definition of χ is as follows:

[0161]

[0162] The χ values corresponding to different power m are shown in Table 2:

[0163] Table 2 χ corresponding to different power m

[0164] m 1 2 3 4 χ 0.6366 0.5 0.4244 0.375

[0165] To simplify the expression, let μ = ω max / a max Equation (33) and equation (38) are uniformly represented as:

[0166]

[0167] The acceleration segment time is uniformly represented as:

[0168] t1 = μ / χ (41)

[0169] Since t1 = 2π / κ, and in combination with λ = κ c / κ, the relationship between λ and μ, χ, κ c can be obtained:

[0170]

[0171] From the above analysis, in the process of designing λ, only the fundamental frequency of the spacecraft needs to be considered. Assuming that the vibration period corresponding to the fundamental frequency of the spacecraft is T base , equation (42) can be written in the following form:

[0172]

[0173] ​In the formula, χ is determined by the acceleration power m, and when m is constant, χ is a constant value. Therefore, the magnitude of μ directly determines the vibration suppression effect. If μ is too small, the value of λ will be too small, and the vibration suppression effect will not be achieved. If μ is too large, it will increase the spacecraft's maneuvering time. Therefore, the value of μ needs to be designed by comprehensively considering the values ​​of λ and Δt.

[0174] To ensure that the residual vibration meets certain specifications, λ needs to be greater than a certain value. min ,Right now

[0175] λ≥λ min (44)

[0176] Substituting equation (44) into equation (43), we obtain the constraints regarding μ:

[0177] μ≥χλ min T base (45)

[0178] Since the value of μ is proportional to the increase in maneuver time, it is desirable to design μ to be as small as possible, i.e., λ = λ min If this is established, the additional maneuver time is:

[0179] Δt=(1-χ)λ min T base (46)

[0180] In reality, μ is determined by system performance and is rarely strictly equal to χλ. min T base .

[0181] To minimize the increased maneuver time while meeting vibration suppression requirements, the following measures were taken:

[0182] μ<χλ min T base With μ>χλ min T base We will analyze two scenarios:

[0183] 1) μ<χλ min T base

[0184] In this case, the residual vibration cannot meet the design requirements, and the maximum angular acceleration a needs to be increased. max The value of is designed to be more conservative, as shown in the following expression:

[0185]

[0186] The increase in maneuver time is the shortest at this point, and the expression is the same as that in equation (40).

[0187] 2) μ>χλmin T base

[0188] In this case, the spacecraft's increased maneuver time is too long. At this time, consider adding a constant acceleration segment at the peak of the angular acceleration signal, as shown in Fig. 6. Figure 4 .

[0189] According to the symmetry of the angular acceleration shown in the figure, the expression for t2 is the same as that without the constant acceleration segment. Since the angular velocity after the end of the acceleration segment is ω max , the area enclosed by the angular acceleration of the acceleration segment is equal to ω max , thus the relationship is derived as follows:

[0190] ω max = a max χT + a max t mid (48)

[0191] In the formula, t mid is the time of the constant angular acceleration segment. In this case, the increased maneuver time is:

[0192] Δt = (t2 + T + t mid ) - (t2 + μ) = (1 - χ)T (49)

[0193] The effect of vibration suppression depends on λ = T / T base . If λ is taken as the minimum value allowed λ min , according to the definition of μ, the required t mid value can be obtained:

[0194] t mid = μ - χλ min T base (50)

[0195] At this time, Δt takes the minimum value, which is the same as that in formula (49). From the above analysis, the expression of the minimum value of Δt is the same as formula (49) in different cases. Table 3 gives the minimum value of Δt corresponding to different m and υ.

[0196] Table 3 Minimum value of Δt corresponding to different m and υ

[0197]

[0198] Finally, the condition for the spacecraft to have a constant rolling phase is t2≥t1, that is, the following inequality needs to be satisfied:

[0199] Φ m / ω max ≥ μ + (1 - χ)λ min Tbase (51)

[0200] If the designed parameters cannot satisfy the inequality, a max and ω max are reduced by the same multiple to make the equality of equation (51) hold. At this time, the corresponding ω max is solved, and its expression is as follows:

[0201]

[0202] In summary, the design process of the spacecraft angular acceleration trajectory is as shown in the attached Figure 5 .

[0203] According to the design process of the spacecraft angular acceleration trajectory, the spacecraft angular acceleration trajectory in this embodiment is designed as follows:

[0204] The estimated ω max = 2° / s = 0.0349 rad / s, a max = 0.4° / s 2 = 0.0070 rad / s 2 , and μ = ω max / a max = 5 is calculated; the maximum vibration period of the spacecraft is defined as the period corresponding to the first-order natural frequency of the attachment, i.e.

[0205] Usually, the maximum residual vibration ratio υ max = 0.05 is taken, and table 3 is found to make m = 3 to minimize Δt; combined with m, υ, table 1 and table 2 are found to correspond to λ min = 2.79 and χ = 0.4244.

[0206] Since χλ min T base = 0.4244 × 2.79 × 22.0463 = 26.1045, the above condition μ < χλ min T base is satisfied, a max is reduced to a max = ω max / χλ min T base = 0.0349 / 26.1045 = 0.0013 rad / s 2 , and the value of μ is updated to μ = 26.8462 at this time; the condition μ ≥ χλ min T base is satisfied, and the next step of the design process is performed.

[0207] Since Φ m / ω max= 60 / 2 = 30s, μ + (1 - χ)λ min T base = 26.8462 + (1 - 0.4244) x 2.79 x 22.0463 = 62.2509s, which satisfies the condition Φ m / ω max < μ + (1 - χ)λ min T base , so ω max is reduced to ω max = Φ m / (μ + (1 - χ))λ min T base ) = 60 / 62.2509 = 0.9638° / s = 1.6822 x 10 -2 rad / s, correspondingly, a max is reduced to a max = ω max / μ = 1.6822 x 10 -2 / 26.8462 = 6.2661 x 10 -4 rad / s 2 ; at this time, it can be obtained by calculation that Φ m / ω max = 60 / 0.9638 = 62.2536s, which satisfies the condition Φ m / ω max ≥ μ + (1 - χ)λ min T base , the next step of the design process is performed.

[0208] After the above calculation, the main parameters of the reference angular acceleration trajectory are obtained: the maximum angular acceleration a max = 6.2661 x 10 -4 rad / s 2 , the acceleration segment time t1 = 62.2509s, the constant angular acceleration segment time t mid = 0.7417s, and the rolling segment end time t2 = 62.2536s.

[0209] Up to now, the design process of the spacecraft angular acceleration trajectory in this embodiment is completed.

[0210] S5, according to the Euler axis expression of the spacecraft attitude maneuver process, the dynamics model of the flexible spacecraft, and the spacecraft angular acceleration trajectory planning curve, a control loop is formed;

[0211] The Euler axis and Euler angle around which the spacecraft attitude maneuver is calculated in step S1, the attitude angular acceleration trajectory planning curve designed in step S4, and the spacecraft attitude dynamics model derived in step S2 are collectively used to form a complete loop of the spacecraft attitude control system.

[0212] According to this complete loop, by using numerical simulation software to build the spacecraft attitude control system, the simulation running time is set to 200s, the initial maneuver time is set to 0s, the reference angular acceleration trajectory of the maneuver is as shown by the solid line in Figure 6 , the Euler angle change in the maneuver process is as shown by the solid line in Figure 7 , the first four vibration modes of the flexible accessory can be simulated respectively as shown by the solid line in Figure 8 , 9 , 10, 11, the expected torque curve of the spacecraft attitude maneuver is as shown by the solid line in Figure 12 , 13 , 14, the spacecraft attitude angular velocity curve is as shown by the solid line in Figure 15 , 16 , 17, the spacecraft attitude quaternion change curve is as shown by the solid line in Figure 18 , 19 , 20, 21.

[0213] From the spacecraft attitude angle curve and the spacecraft attitude angular velocity curve, it is known that the time for the spacecraft attitude angle to change from the initial zero value to the expected value is 125s, the maximum attitude angle deviation after reaching stability is 0.004°, and the attitude stability is 0.0006° / s.

[0214] In order to reflect the advantages of the spacecraft trajectory soft vibration suppression method according to the residual vibration index design described in the patent, the spacecraft attitude maneuver control effect without using the vibration suppression method proposed in the patent is compared. By using the same simulation environment, the spacecraft attitude control system is built, the traditional bang-off-bang maneuver method is used, the reference angular acceleration trajectory of the maneuver is as shown by the dashed line in Figure 6 , the Euler angle change in the maneuver process is as shown by the dashed line in Figure 6 , the first four vibration modes of the flexible accessory can be simulated respectively as shown by the dashed line in Figure 8 , 9 , 10, 11, the expected torque curve of the spacecraft attitude maneuver is as shown by the dashed line in Figure 12 , 13 , 14, the spacecraft attitude angular velocity curve is as shown by the dashed line in Figure 15 , 16 , 17, the spacecraft attitude quaternion change curve is as shown by the dashed line in Figure 18 , 19 , 20, 21.

[0215] By comparing with the result obtained in step five, it can be obtained that the time for the spacecraft attitude angle from the initial zero value to the desired value is 90s, the maximum attitude angle deviation after reaching the stable state is 0.02°, and the attitude stability is 0.001° / s. By using the flexible spacecraft rapid attitude maneuver vibration suppression method described in the patent, the reference angular velocity trajectory designed is soft, the dispersion has little influence on the trajectory shape, the output torque of the spacecraft attitude control actuator does not exist mutation, and the spacecraft attitude angular velocity curve obtained is soft. Compared with the traditional bang-off-bang maneuver mode, this method will not lose some key vibration suppression information and make the vibration suppression effect worse.

[0216] A spacecraft control system considering residual vibration, comprising:

[0217] An Euler axis calculation module, which is based on the Euler rotation theorem to construct an Euler axis expression of a spacecraft attitude maneuver process;

[0218] A dynamics model construction module, which is used to establish a dynamics model of a flexible spacecraft;

[0219] A residual vibration construction module, which is used to construct a residual vibration expression of a flexible accessory in the flexible spacecraft;

[0220] An angular acceleration trajectory planning module, which is used to plan a trajectory according to the characteristics and threshold limits of the residual vibration, and generate a spacecraft angular acceleration trajectory planning curve;

[0221] An overall control module, which is used to form a control loop according to the Euler axis expression of the spacecraft attitude maneuver process, the dynamics model of the flexible spacecraft, and the spacecraft angular acceleration trajectory planning curve.

[0222] The contents in the above method embodiments are all applicable to the system embodiments, the system embodiments specifically realize the same functions as the above method embodiments, and achieve the same beneficial effects as the above method embodiments.

[0223] The above is a specific description of the preferred implementation of the present application, but the present application is not limited to the above embodiments, and those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the present application, and these equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A spacecraft control method considering residual vibration, characterized in that, Includes the following steps: S1. Based on Euler's rotation theorem, construct the Euler axis expression for the spacecraft's attitude maneuvering process; S2. Establish a dynamic model of the flexible spacecraft; S3. Construct the residual vibration expression for the flexible attachments in a flexible spacecraft; S4. Based on the characteristics and threshold limitations of residual vibration, perform trajectory planning and generate the spacecraft angular acceleration trajectory planning curve; S5. Based on the Euler axis expression of the spacecraft's attitude maneuvering process, the dynamic model of the flexible spacecraft, and the spacecraft's angular acceleration trajectory planning curve, a control loop is formed; The spacecraft's angular acceleration trajectory planning curve is shown below: Where a max The threshold value represents the angular acceleration, and T represents the period of the sinusoidal component of the angular acceleration signal. t represents the frequency of the sinusoidal component of the angular acceleration signal, t1 represents the end time of the acceleration phase, t2 represents the end time of the constant rolling phase, and t mid This represents the time interval of the constant angular acceleration segment, and m represents the power of the selected sinusoidal angular acceleration signal.

2. The spacecraft control method considering residual vibration according to claim 1, characterized in that, The Euler axis expression for the spacecraft's attitude maneuvering process is as follows: Where Φ represents the angle of rotation along the Euler axis, The vector part representing the attitude quaternion.

3. The spacecraft control method considering residual vibration according to claim 2, characterized in that, The dynamic model of the flexible spacecraft is represented as follows: Where I is the moment of inertia matrix of the spacecraft body relative to the body coordinate system; ω is the component of the attitude angular velocity of the spacecraft's central rigid body coordinate system relative to the inertial coordinate system in the body coordinate system; F s η is the coupling coefficient matrix of the flexible attachment to the celestial body; η is the array of vibration modes of each order, η=[η1η2…η n ] T , These are the first and second derivatives of η with respect to time, respectively; T c T is the control torque of the system. d Let ξ be the environmental disturbance torque of the system; ξ be the modal damping ratio matrix of the flexible attachment, and ξ = diag[ξ1ξ2…ξ] n ];κ c Let be the natural frequency matrix of the flexible attachment, and κ c =diag[κ c1 κ c2 …κ cn ]; n is the modal order under consideration.

4. The spacecraft control method considering residual vibration according to claim 2, characterized in that, With reference angular acceleration a r (t), the motorized Euler axis is In the case of flexible spacecraft, the residual vibration expression of the flexible attachments is as follows: Where, η j Let D represent the j-th vibration mode. j Represents column vectors The j-th element, t0 represents the start time of the maneuver, t f Indicates the end time of the maneuver, κ cj Let ξ represent the j-th natural frequency of the flexible attachment. j Let represent the j-th order damping ratio of the flexible attachment, τ represent the time variable, and e represent the natural constant.

5. A spacecraft control system that considers residual vibration, characterized in that, For performing the control method as described in claim 1, comprising: The Euler axis calculation module, based on Euler's rotation theorem, constructs the Euler axis expression for the spacecraft's attitude maneuvering process; The dynamics model building module is used to build dynamics models of flexible spacecraft; The residual vibration construction module is used to construct the residual vibration expressions for flexible attachments in flexible spacecraft; The angular acceleration trajectory planning module is used to plan the trajectory based on the characteristics of residual vibration and threshold constraints, and generate the spacecraft's angular acceleration trajectory planning curve. The overall control module is used to form a control loop based on the Euler axis expression of the spacecraft's attitude maneuvering process, the dynamic model of the flexible spacecraft, and the spacecraft's angular acceleration trajectory planning curve.

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