A distributed SAR satellite specified time attitude cooperative anti-saturation control method

Abstract

This invention discloses a distributed satellite attitude cooperative anti-saturation control method at a predetermined time. First, a SAR satellite formation model considering saturation constraints is established. Then, a preset performance boundary function that converges within a specified time is designed. Next, problems such as external interference and actuator saturation constraints in the satellite formation flight system are addressed. Finally, a SAR satellite attitude cooperative control law at a predetermined time is designed based on an anti-saturation compensator, an interference observer, and sliding mode control. This invention enables the formation satellites to achieve convergence of attitude cooperative errors within a specified time under actuator saturation constraints, while remaining within the preset performance boundary. It also features high control accuracy, good control performance, and fast convergence speed.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft control technology, specifically relating to a distributed SAR satellite attitude cooperative anti-saturation control method at a specified time. Background Technology

[0002] In Earth observation, SAR satellite formations are not limited by lighting and weather conditions because they synthesize images by emitting electromagnetic waves and receiving reflected waves. They can take high-resolution microwave photos around the clock and in all weather conditions. They can even obtain information that is hidden through shallow ground or sparse vegetation. Therefore, they have irreplaceable uniqueness in fields such as disaster assessment, mineral exploration and military reconnaissance, and are a current research hotspot in the field of aerospace applications.

[0003] With the increasing number of Earth observation missions, SAR satellite formations often need to observe multiple target points on the ground within a single orbital period. Each target point can only be observed by the satellite within its visible time window. Therefore, how to select and prioritize observation tasks within this limited time window is crucial for improving the efficiency of observation missions. Satellite agility is also a mainstream development direction in current SAR satellite technology. Utilizing high-torque attitude control mechanisms, remote sensing satellite platforms possess capabilities such as rapid, wide-range attitude maneuvers and multiple imaging modes. The formation and agility of SAR satellites increase the flexibility of observation missions, but also make mission planning more complex. Researching efficient mission planning techniques can help fully utilize the maneuverability of agile satellites and improve the observation benefits of SAR satellite formations.

[0004] When satellite formations observe ground targets, they need to meet the target's visibility time window constraint. According to the observation mission planning, the attitude transfer time between two adjacent targets is finite. How to complete the attitude transfer between targets within this limited time and achieve the specified observation duration is a key factor in successfully completing the observation mission planning. Therefore, studying the high-precision, time-specific SAR satellite formation attitude cooperative control problem can effectively improve the formation's observation performance. Simultaneously, considering the various interferences in the space environment and the saturation phenomenon of satellite attitude actuators, it is necessary to study satellite formation attitude cooperative control under external disturbances and actuator saturation constraints. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a pre-defined time attitude cooperative anti-saturation control method for distributed SAR (Synthetic Aperture Radar) satellites. First, a SAR satellite formation model considering saturation constraints is established. Then, a preset performance boundary function that converges within a specified time is designed. Next, problems such as external interference and actuator saturation constraints in the satellite formation flight system are addressed. Finally, based on an anti-saturation compensator, an interference observer, and sliding mode control, a pre-defined time attitude cooperative control law for SAR satellites is designed. This invention enables formation satellites to achieve convergence of attitude cooperative errors within a specified time under actuator saturation constraints, while remaining within the preset performance boundary, exhibiting high control accuracy, good control performance, and fast convergence speed.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] Step 1: Establish a SAR satellite formation model that considers saturation constraints;

[0008] Step 2: Design a preset performance boundary function that can converge within a specified time;

[0009] Step 3: Design a coordinated control law for the attitude of the SAR satellite at a predetermined time based on the anti-saturation compensator, interference observer, and sliding mode control.

[0010] Preferably, step 1 specifically comprises:

[0011] Step 1-1: The kinematic equations of the formation satellite attitude described by quaternions are as follows:

[0012]

[0013] Where, q 0,i and q v,i Let ω represent the scalar and vector parts of the attitude quaternion of satellite i in the formation, respectively. i This represents the attitude angular velocity of the formation satellite i relative to the inertial frame.

[0014] Step 1-2: For any vector Define the cross product operator ζ × for:

[0015]

[0016] The satellite attitude dynamics equations are then obtained as follows:

[0017]

[0018] Among them, J i U represents the moment of inertia of satellite i in the formation. i ∈R 3d represents the control torque. i ∈R 3 This indicates the external interference experienced by satellite i in the formation;

[0019] Steps 1-3: Let Let ω represent the expected attitude quaternion of satellite i in the formation. d,i Let i represent the desired angular velocity of satellite i in the formation; define the attitude error quaternion between the body coordinate system and the desired coordinate system as: The attitude angular velocity error is ω e,i Then we have:

[0020]

[0021] ω e,i =ω i -C i ω d,i (7)

[0022] Among them, C i Let be the attitude transfer matrix between the body coordinate system and the desired coordinate system of satellite i in the formation, and satisfy:

[0023]

[0024] The kinematic equation for the attitude error of satellite i in the formation is:

[0025]

[0026] The dynamic equation for the attitude error of satellite i in the formation is:

[0027]

[0028] Steps 1-4: Convert the kinematic and dynamic equations of the satellite formation attitude error into Eulerian-Lagrange system form. The dynamic equation of the attitude error of satellite i in the formation is then expressed as:

[0029]

[0030] in:

[0031] M a,i =P i T J i P i (13)

[0032] P i =T i -1 (14)

[0033]

[0034] us,i =P i T u i (16)

[0035] d s,i =-P i T d i (17)

[0036]

[0037]

[0038] definition:

[0039]

[0040] Define the satellite formation error quaternion and its derivative as follows:

[0041]

[0042] Define the external disturbances and control torques experienced by the formation as follows:

[0043]

[0044] The attitude error dynamic equation of the satellite formation is then expressed as:

[0045]

[0046] Steps 1-5: Define the relative attitude error and first derivative between formation satellite i and formation satellite j as follows:

[0047] q ev,ij =q ev,i -q ev,j (29)

[0048]

[0049] Based on the communication topology among the formation members, the attitude coordination error of formation satellite i and its first derivative are defined as follows:

[0050]

[0051] Among them, a ij Let b represent an element in the graph theory weighted connectivity matrix A. i These are elements in the degree matrix B;

[0052] Equations (31) and (32) can be transformed into the following expressions:

[0053]

[0054]

[0055] in, H2 and H1 are inverse matrices.

[0056] Since the communication topology between the satellites in the formation is an undirected connected graph, according to graph theory, H1 is a positive definite matrix and is invertible. Therefore, χ1 = 0 and χ2 = 0 are equivalent to q ev =0, Therefore, designing a controller such that χ1=0 and χ2=0 can satisfy the attitude tracking control of the formation satellites;

[0057] Steps 1-6: Assume that the control input u in the satellite formation attitude system has a saturation constraint, and the range of torque that can be provided is: -u max ≤u≤u max , where u max To control the maximum value of the input, the constrained control input u sat Defined as the following saturation function:

[0058]

[0059] Since the saturation function shown in equation (35) is not differentiable, the hyperbolic tangent function is used to smooth the saturation function, and the control input saturation function is redefined as follows:

[0060] u sat =btanh(au) (36)

[0061] According to equation (16), we can obtain:

[0062] u s,sat =P T u sat (37)

[0063] Then, under the constraint of input u s,sat The satellite error dynamics equation under the action is rewritten as:

[0064]

[0065] Rewrite it as:

[0066]

[0067] in,

[0068] Define the dead-zone nonlinear function:

[0069] ψ(u)=uu sat (40)

[0070] When ψ(u)≠0, the controller enters the saturation region, at which point u sat =u-ψ(u), substituting it into model (39) yields:

[0071]

[0072] By adding an anti-saturation compensator Xψ(u) to the error model (41) for compensation, the final model of the SAR satellite formation considering saturation constraints is as follows:

[0073]

[0074] Preferably, step 2 specifically comprises:

[0075] Step 2-1: When χ1=0, q ev =0; Design a controller such that χ1 = 0, which satisfies the formation satellite attitude tracking control; For formation satellite i, for the error χ 1,i (t) Design preset performance constraints, χ 1,i If χ(t) is denoted as χ(t), then χ(t) must satisfy:

[0076]

[0077] Where ρ(t) is the preset performance boundary function to be designed, and δ is the overshoot limiting parameter. When δ = 0, overshoot is not allowed.

[0078] From equation (43), it can be seen that the constraint on the error χ(t) is an inequality constraint. To simplify the design of the control law, the inequality constraint is converted into an equality constraint, and the normalized error is defined as:

[0079]

[0080] Step 2-2: Construct a smooth and strictly monotonically increasing mapping function S(ε(t)), then the error χ(t) satisfies:

[0081] χ(t)=ρ(t)S(ε(t)) (45)

[0082] Where ε(t) is the conversion error.

[0083] Therefore, we can know that:

[0084]

[0085] The conversion error ε(t) can be obtained by inverse solution:

[0086]

[0087] And the normalized error z(t) satisfies:

[0088]

[0089] Differentiating equation (47) yields:

[0090]

[0091] in

[0092]

[0093] Steps 2-3: For the preset performance control that converges at a specified time, the boundary function ρ(t) should satisfy:

[0094] ρ(0)=ρ0>2ρ(t>T f )=2ρ ∞ >0 (57)

[0095] Where ρ0 and ρ ∞ Let T be the initial and final values ​​of the performance boundary function, respectively. f For a user-defined steady time, the boundary function ρ(t) is given by the following first derivative form:

[0096]

[0097] in, α is a constant and satisfies

[0098] Preferably, step 3 specifically comprises:

[0099] Step 3-1: For the SAR satellite formation model (42) considering saturation constraints, design an interference observer of the following form:

[0100]

[0101] in, To assist the system state variables, Let k be an estimate of the upper bound of the generalized disturbance. All are greater than 0, ε D For a small amount, This is to account for the estimation error due to interference.

[0102] Step 3-2: Design the sliding surface as follows:

[0103]

[0104] Where k1 is a positive constant that satisfies the Hurwitz condition;

[0105] The derivative of the sliding surface can be obtained as:

[0106]

[0107] Step 3-3: Based on the inverse relationship between H1 and H2, we know that:

[0108]

[0109] Based on the designed sliding surface, the control law for formation satellite i is designed as follows:

[0110]

[0111] Where, k2>0, ε s As a small quantity, in the error model compensation term:

[0112]

[0113] A computer program that causes a computer to perform the above-described anti-saturation control method.

[0114] An electronic device includes: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the above-described anti-saturation control method.

[0115] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described anti-saturation control method.

[0116] A chip includes a processor for retrieving and running a computer program from a memory, causing a device on which the chip is mounted to perform the aforementioned anti-saturation control method.

[0117] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the above-described anti-saturation control method.

[0118] The beneficial effects of this invention are as follows:

[0119] This invention enables coordinated attitude control of satellites at a specified time under external disturbances and actuator saturation constraints, offering numerous advantages such as improved dynamic and steady-state performance to meet the operational requirements of SAR satellite Earth observation. By incorporating predetermined time stability theory, the control law exhibits superior dynamic performance, making it of practical significance for the development of distributed SAR satellite attitude coordinated control. Attached Figure Description

[0120] Figure 1 This is a flowchart of the method of the present invention.

[0121] Figure 2 This is a diagram of SAR satellite formation parameters used in this invention.

[0122] Figure 3 This is a diagram showing the communication relationships of the SAR satellite formation used in this invention.

[0123] Figure 4 This is a graph showing the attitude coordination error of satellite 1.

[0124] Figure 5 This is a graph showing the attitude coordination error of satellite 2.

[0125] Figure 6 This is a graph showing the coordinated attitude error of the three satellites.

[0126] Figure 7 The image shows the attitude quaternion tracking error curve for satellite 1.

[0127] Figure 8 The image shows the tracking error curve of the satellite's attitude quaternion.

[0128] Figure 9 This is a graph showing the tracking error curve of satellite attitude quaternions.

[0129] Figure 10 This is a graph showing the attitude angular velocity tracking error of satellite 1.

[0130] Figure 11 This is a graph showing the tracking error curve of the attitude angular velocity of satellite 2.

[0131] Figure 12 This is a graph showing the tracking error curves of the satellite's attitude angular velocity.

[0132] Figure 13 To control the torque curve.

[0133] Figure 14 This is a graph showing the error curve for interference estimation.

[0134] Figure 15 This is a graph showing the error curves for observing the state variables of the auxiliary system. Detailed Implementation

[0135] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0136] like Figure 1 As shown, to address the problems of external interference and actuator saturation constraints in satellite formation flight systems, this invention provides a distributed SAR satellite time-specified attitude cooperative anti-saturation control method, comprising the following steps:

[0137] Step 1: Establish a SAR satellite formation model considering saturation constraints:

[0138]

[0139] The kinematic equations of the formation satellite attitude described by quaternions are as follows:

[0140]

[0141] Where, q 0,i and q v,i Let ω represent the scalar and vector parts of the attitude quaternion of satellite i in the formation, respectively. i This represents the attitude angular velocity of the formation satellite i relative to the inertial frame.

[0142] For any vector Define the cross product operator ζ × for:

[0143]

[0144] Then the satellite attitude dynamics equations can be obtained as follows:

[0145]

[0146] Among them, J i U represents the moment of inertia of satellite i in the formation. i ∈R 3 d represents the control torque. i ∈R 3 This indicates the external interference experienced by satellite i in the formation.

[0147] When analyzing satellite attitude tracking problems, establishing kinematic and dynamic equations described by error quaternions is beneficial for problem analysis. Let ω represent the expected attitude quaternion of satellite i in the formation. d,i Let represent the desired angular velocity of satellite i in the formation. The attitude error quaternion between the body coordinate system and the desired coordinate system is defined as . The attitude angular velocity error is ω e,i Then we have:

[0148]

[0149] ω e,i =ω i -C i ω d,i (73)

[0150] Among them, C i Let be the attitude transfer matrix between the body coordinate system and the desired coordinate system of satellite i in the formation, and satisfy:

[0151]

[0152] The kinematic equation for the attitude error of satellite i in the formation is:

[0153]

[0154] The dynamic equation for the attitude error of satellite i in the formation is:

[0155]

[0156] Considering the systematic nature of the controller design and for the sake of simplicity, the kinematic and dynamic equations of the satellite formation attitude error are transformed into Eulerian-Lagrange system form. Therefore, the dynamic equation of the attitude error of satellite i in the formation can be expressed as:

[0157]

[0158] in,

[0159] M a,i =P i T J i P i (79)

[0160] P i =T i -1 (80)

[0161]

[0162] u s,i =P i T u i (82)

[0163] d s,i =-P i T d i (83)

[0164]

[0165]

[0166] definition:

[0167]

[0168] Define the satellite formation error quaternion and its derivative as follows:

[0169]

[0170] Define the external disturbances and control torques experienced by the formation as follows:

[0171]

[0172] The attitude error dynamic equation of the satellite formation can then be expressed as:

[0173]

[0174] Define the relative attitude error and first derivative between formation satellite i and formation satellite j as follows:

[0175] q ev,ij =q ev,i -q ev,j (95)

[0176]

[0177] Based on the communication topology among the formation members, the attitude coordination error of formation satellite i and its first derivative are defined as follows:

[0178]

[0179] Among them, a ij Let b represent an element in the graph theory weighted connectivity matrix A. i These are elements in the degree matrix B;

[0180] Equations (31) and (32) can be transformed into the following description:

[0181]

[0182]

[0183] in, H2 and H1 are inverse matrices.

[0184] Since the communication topology between the satellite formations considered in this invention is an undirected connected graph, according to graph theory, H1 is a positive definite matrix and is invertible. Therefore, χ1 = 0 and χ2 = 0 are equivalent to q ev =0, Therefore, designing a controller such that χ1=0 and χ2=0 can satisfy the attitude tracking control of the formation satellites.

[0185] If the control input of the satellite formation attitude system has saturation constraints, then the representation of the control input and the corresponding satellite formation dynamics model need to be considered before proceeding to the next step of controller design. Assuming the control input u in the satellite formation attitude system has saturation constraints, the range of torque it can provide is: -u max ≤u≤u max , where u max To control the maximum value of the input, the constrained control input u satIt can be defined in the form of the following saturation function.

[0186]

[0187] Since the saturation function shown in equation (35) is not differentiable, the hyperbolic tangent function is used to smooth the saturation function, and the control input saturation function is redefined as follows:

[0188] u sat =btanh(au) (102)

[0189] According to equation (16), we can obtain:

[0190] u s,sat =P T u sat (103)

[0191] Then, under the constraint of input u s,sat The satellite error dynamics equation under the action can be rewritten as:

[0192]

[0193] Rewrite it as:

[0194]

[0195] in,

[0196] Define the dead-zone nonlinear function:

[0197] ψ(u)=uu sat (106)

[0198] When ψ(u)≠0, the controller enters the saturation region, at which point u sat =u-ψ(u), substituting it into the model formula, we get:

[0199]

[0200] To mitigate the impact of saturation constraints on the system, an anti-saturation compensator Xψ(u) is added to the error model for compensation.

[0201]

[0202] Step 2: Design a preset performance boundary function that converges within a specified time:

[0203]

[0204] When χ1=0, q ev=0. Therefore, designing a controller such that χ1 = 0 is sufficient to satisfy the attitude tracking control of the formation satellites. For formation satellite i, the error χ... 1,i (t) Design preset performance constraints. For ease of derivation later, χ is... 1,i If χ(t) is denoted as χ(t), then χ(t) must satisfy:

[0205]

[0206] Where ρ(t) is the preset performance boundary function to be designed, and δ is the overshoot limiting parameter. When δ = 0, overshoot is not allowed.

[0207] From equation (43), it can be seen that the constraint on the error χ(t) is an inequality constraint. To simplify the design of the control law, the inequality constraint is converted into an equality constraint. The normalized error is defined as:

[0208]

[0209] Next, construct a smooth and strictly monotonically increasing mapping function S(ε(t)), then the error χ(t) satisfies:

[0210] χ(t)=ρ(t)S(ε(t)) (112)

[0211] Where ε(t) is the conversion error.

[0212] Therefore, we can know that:

[0213]

[0214] The conversion error ε(t) can be obtained by inverse solution:

[0215]

[0216] And the normalized error z(t) satisfies:

[0217]

[0218] Differentiating equation (47) yields:

[0219]

[0220] in,

[0221]

[0222] For the new preset performance control with convergence at a specified time, the boundary function ρ(t) should satisfy:

[0223] ρ(0)=ρ0>2ρ(t>T f )=2ρ ∞ >0 (124)

[0224] Where ρ0 and ρ ∞ Let T be the initial and final values ​​of the performance boundary function, respectively. f For a user-defined steady time, the boundary function ρ(t) is given by the following first derivative form:

[0225]

[0226] in, α is a constant and satisfies According to the above formula, the first derivative of the boundary function ρ(t) is continuous, and therefore ρ(t) is also continuous.

[0227] Step 3: Design a SAR satellite attitude coordination control law for predetermined time based on anti-saturation compensators, interference observers, and sliding mode control:

[0228]

[0229] For the formation satellite error dynamics system considering saturation constraints, equation (42) is used to design an interference observer of the following form:

[0230]

[0231] in, To assist the system state variables, Let k be an estimate of the upper bound of the generalized disturbance. All are greater than 0, ε D It is a small amount. This represents the interference estimation error.

[0232] Auxiliary system estimation error With disturbance estimation error It can converge to a compact set containing the equilibrium point.

[0233] The sliding surface is designed as follows:

[0234]

[0235] Here, k1 is a positive constant that satisfies the Hurwitz condition.

[0236] The derivative of the sliding surface can be obtained as:

[0237]

[0238] Based on the inverse relationship between H1 and H2, we know that:

[0239]

[0240] Based on the designed sliding surface, the control law for formation satellite i is designed as follows:

[0241]

[0242] Where, k2>0, ε s It is a small amount.

[0243] In the error model compensation term:

[0244]

[0245] Spacecraft parameters used in this invention:

[0246] To verify the effectiveness of the invented time-preset performance satellite formation attitude cooperative anti-saturation controller based on an interference observer, the following example was used: Taking the target point (108.43°E, 48.6°N, 50.32m), the camera optical axes needed to point towards the target point within 10.21s. This means each satellite should track the desired attitude quaternion within 10.21s and maintain accurate tracking of the desired attitude for the following 10s. SAR satellite formation parameters are as follows: Figure 2 As shown.

[0247] The parameters selected in the controller are as follows:

[0248] δ = 0.8, T f =10s

[0249] k1 = 1.5, k2 = 2, k = 3, k D =5, ε D =0.001, ε s =0.001,

[0250] a = 1, b = 100

[0251] The default performance boundary function is designed as follows:

[0252] T f =10s, α=0.6

[0253] Considering uncertainties such as camera startup, the performance function stabilization time is set to 10 seconds. The attitude quaternions of each sub-satellite at the end of its observation of the previous target point are used as the initial quaternions for attitude cooperative control.

[0254]

[0255] The initial attitude angular velocity is:

[0256] ω1 = [0.0177 - 0.5705 - 0.1595]T rad / s

[0257] ω2=[0.0153-0.5355-0.1482] T rad / s

[0258] ω3 = [0.02 - 0.599 - 0.1692] T rad / s

[0259] The external disturbance model is:

[0260]

[0261] SAR satellite formations use undirected graph communication, and the communication relationships within the formation can be described as follows: Figure 3 In the form of.

[0262] The simulation step size was set to 0.01s, and the simulation period was set to 30s. Based on the mission context, the first 10.21s of the simulation was the attitude transfer phase, and 10.21s-20.21s was the cooperative observation phase. The simulation results are as follows: Figures 4 to 15 As shown.

[0263] Figures 4 to 6 These are the convergence curves of the cooperative error of each satellite in the formation, from... Figures 4 to 6 It can be seen that each satellite in the formation has a different initial value of cooperative error, but all of them can converge to near 0 within 10s and always remain within the preset performance boundary, at a specified time T. f = Reached a stable state 10 seconds ago. Within the next 10 seconds, the coordination errors of all satellites converged within the performance boundaries. The convergence of the coordination errors of the formation sub-satellites is equivalent to the convergence of the attitude quaternion errors, meaning that the attitude quaternions of the sub-satellites can track the desired quaternion. From Figures 4 to 6 As shown in the magnified view, the steady-state accuracy of the coordinated attitude control of each satellite converges to the preset performance boundary, achieving an accuracy within 0.01. Based on the above convergence curves of the coordinated satellite formation error, the satellite formation attitude coordination anti-saturation controller based on the interference observer designed in this invention exhibits reliable stability and good tracking performance. Furthermore, due to the influence of saturation constraints, the system convergence speed slows down, and the steady-state accuracy decreases somewhat, but the controller still ensures the stability of the formation.

[0264] Figures 7 to 12 These are the attitude quaternion tracking error curves and attitude angular velocity tracking curves for each satellite in the formation. Figures 7 to 12 As can be seen from this, under the condition of initial attitude error, the attitude quaternion tracking error curves of each sub-satellite can all be found in T. f=Stable convergence within 10 seconds indicates that in the formation's observation mission of ground target points, before the observation mission begins, the attitude quaternions of each sub-satellite in the formation can track the desired attitude quaternion, that is, to achieve the control target that the optical axes of their respective cameras are all pointing towards the target point to be observed. From Figures 7 to 12 As can be seen from the magnified view in the middle section, before 10 seconds, that is, before the start of the formation observation mission, the attitude quaternions of each satellite in the formation all reached 10. -4 The tracking accuracy and attitude angular velocity tracking accuracy both reached 0.01 rad / s, indicating that under the control of the controller, each satellite in the formation can complete the tracking of the desired attitude in a relatively short time. Moreover, the formation has good tracking accuracy and steady-state accuracy, enabling the SAR satellite formation to point to the target point in a common direction before and after the start of the ground target point observation mission.

[0265] Figure 13 The figure shows the three-axis control torque curves for each satellite in the formation. As can be seen from the figure, in the initial stage, the control torque of each satellite is relatively large. This is because the initial attitude of each satellite deviates significantly from the desired attitude. The components of the control torque in all three directions stabilize within 10 seconds. According to the magnified view, the amplitude of the control torque after stabilization is 0.03 N·m. The control torque always meets the maximum torque that a single axis of the satellite can provide.

[0266] Figure 14 and Figure 15 The figures show the interference estimation error curve and the auxiliary system state quantity observation error curve, where error1 represents the interference estimation error and error2 represents the interference observer state quantity estimation error. The curves show that the components of both the interference estimation error and the state quantity estimation error gradually converge to 0 in all three directions. Furthermore, a magnified view shows that the interference estimation error reaches 10. -4 The convergence accuracy is high, and the state quantity estimation error reaches 10. -3 The high convergence accuracy indicates that the designed disturbance observer can accurately observe the external disturbances to the system while converging rapidly, and ultimately compensate for them in the controller.

[0267] The simulation results and analysis above verify the effectiveness of the satellite formation attitude coordination anti-saturation controller based on an interference observer designed in this invention. Even under saturation constraints, the controller can still ensure that the attitude coordination error of each satellite in the formation converges within a specified time and remains within the preset performance boundary. Furthermore, it can be verified that the attitude quaternions of each satellite can track the desired attitude quaternion within a specified time and have good steady-state accuracy, achieving common pointing towards the target point by each satellite in the formation before and after the start of the formation satellite observation mission.

Claims

1. A distributed SAR satellite attitude cooperative anti-saturation control method at a predetermined time, characterized in that, Includes the following steps: Step 1: Establish a SAR satellite formation model that considers saturation constraints; Step 1-1: The kinematic equations of the formation satellite attitude described by quaternions are as follows: (1) (2) in, and These represent the satellites in the formation. The scalar and vector parts of the attitude quaternion. Indicates the formation of satellites The attitude angular velocity of this system relative to the inertial frame; Step 1-2: For any vector Define the cross product operator for: (3) The satellite attitude dynamics equations are then obtained as follows: (4) in, Indicates the formation of satellites Moment of inertia, Indicates control torque. Indicates the formation of satellites External interference received; Steps 1-3: Let Indicates the formation of satellites The expected posture quaternion, Indicates the formation of satellites The desired angular velocity; the attitude error quaternion between the body coordinate system and the desired coordinate system is defined as... The attitude angular velocity error is Then we have: (5) (6) (7) in, For formation satellites The attitude transfer matrix between the body coordinate system and the desired coordinate system, satisfying: (8) (9) Formation satellites The kinematic equation for attitude error is: (10) Formation satellites The attitude error dynamic equation is: (11) Steps 1-4: Convert the kinematic and dynamic equations of the satellite formation attitude error into Eulerian-Lagrange system form, then the formation satellites The attitude error dynamic equation is expressed as: (12) in: (13) (14) (15) (16) (17) (18) (19) definition: (20) (21) (22) Define the satellite formation error quaternion and its derivative as follows: (23) (24) (25) Define the external disturbances and control torques experienced by the formation as follows: (26) (27) The attitude error dynamic equation of the satellite formation is then expressed as: (28) Steps 1-5: Define the formation satellites and formation satellites The relative attitude error and the first derivative between them are: (29) (30) Based on the communication topology among the formation members, define the formation satellites. The attitude coordination error and its first derivative are in the form of: (31) (32) in, Represents the weighted connectivity matrix in graph theory The elements in Degree matrix Elements in; Equations (31) and (32) can be transformed into the following expressions: (33) (34) in, , and They are inverse matrices; Since the communication topology between satellites in a formation is an undirected connected graph, according to graph theory... It is a positive definite matrix and is invertible, therefore , Equivalent to , Therefore, the design of the controller makes , This means it can meet the attitude tracking and control requirements of the formation satellites; Steps 1-6: Assume the control input of the satellite formation attitude system With saturation constraints, the range of torque that can be provided is: ,in To control the maximum value of the input, the constrained control input is... Defined as the following saturation function: (35) Since the saturation function shown in equation (35) is not differentiable, the hyperbolic tangent function is used to smooth the saturation function, and the control input saturation function is redefined as follows: (36) According to equation (16), we can obtain: (37) Then in the constrained input The satellite error dynamics equation under the action is rewritten as: (38) Rewrite it as: (39) in, ; Define the dead-zone nonlinear function: (40) when When the controller enters the saturation region, there is... Substituting this into model (39) yields: (41) Add an anti-saturation compensator to the error model (41). After compensation, the final model of the SAR satellite formation considering saturation constraints is as follows: (42)； Step 2: Design a preset performance boundary function that can converge within a specified time; For preset performance control that converges within a specified time, the boundary function It should meet the following requirements: (57) in, and These are the initial and final values ​​of the performance boundary function, respectively. User-defined steady-state time, boundary function It is given by the following first derivative form: (58) in, , It is a constant and satisfies ; Step 3: Design a coordinated control law for the attitude of the SAR satellite at a predetermined time based on the anti-saturation compensator, interference observer, and sliding mode control.

2. The distributed SAR satellite attitude cooperative anti-saturation control method according to claim 1, characterized in that, Step 2 specifically involves: Step 2-1: When hour, The design of the controller enables This means satisfying the attitude tracking and control of the formation satellites; for formation satellites For error Design preset performance constraints, Represented as ,but Must meet: (43) in, The preset performance boundary function to be designed, This is the overshoot limiting parameter, when Overshoot is not allowed. From equation (43), it can be seen that for the error The constraints are inequality constraints. To simplify the design of the control law, the inequality constraints are converted into equality constraints, and the normalized error is defined as: (44) Step 2-2: Construct a smooth and strictly monotonically increasing mapping function Then the error satisfy: (45) in, This is the conversion error; Therefore, we can know that: (46) Conversion error It can be obtained by inverse solution: (47) And normalization error satisfy: (48) Differentiating equation (47) yields: (49) (50) in (51) (52) (53) (54) (55) (56) Steps 2-3: For preset performance control with convergence at a specified time, the boundary function It should meet the following requirements: (57) in, and These are the initial and final values ​​of the performance boundary function, respectively. User-defined steady-state time, boundary function It is given by the following first derivative form: (58) in, , It is a constant and satisfies .

3. The distributed SAR satellite attitude cooperative anti-saturation control method according to claim 2, characterized in that, Step 3 specifically involves: Step 3-1: For the SAR satellite formation model (42) considering saturation constraints, design an interference observer of the following form: (59) (60) in, , To assist the system state variables, This is an estimate of the upper bound of the generalized disturbance. , All are greater than 0. For a small amount, This is to account for the estimation error due to interference. Step 3-2: Design the sliding surface as follows: (61) in, It is a positive constant that satisfies the Hurwitz condition. The derivative of the sliding surface can be obtained as: (62) Step 3-3: According to and From the inverse relationship, we can know that: (63) Based on the designed sliding surface, design the formation satellites. The control law is: (64) in, , As a small quantity, in the error model compensation term: (65)。 4. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 3.

6. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in any one of claims 1 to 3.

7. A computer program product, characterized in that, The computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the method as described in any one of claims 1 to 3.

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