Distributed SAR satellite specified time attitude cooperative anti-saturation control method

Abstract

The invention discloses a distributed satellite predetermined time attitude cooperative anti-saturation control method. The method comprises the following steps: firstly, establishing an SAR satellite formation model considering saturation constraint; then designing a preset performance boundary function which can converge within specified time; solving the problems of external interference, actuator saturation constraint and the like of a satellite formation flight system; and finally, designing an SAR satellite predetermined time attitude cooperative control law based on an anti-saturation compensator, an interference observer and sliding mode control, so that the formation satellites can realize the specified time convergence of the attitude cooperative error under the saturation constraint of the actuator, the attitude cooperative error is within a preset performance boundary, the control precision is high, the control performance is good, and the convergence speed is high.

Description

Technical Field

[0001] The invention belongs to the technical field of spacecraft control, and in particular relates to a distributed SAR satellite designated time attitude coordinated anti-saturation control method. Background Art

[0002] In earth observation, SAR satellite formations are not restricted by lighting and climatic 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, and can even obtain concealed information through shallow surface or sparse vegetation. Therefore, they are irreplaceable and unique in disaster assessment, mineral exploration, military reconnaissance and other fields, and are a hot topic of research in the current aerospace application field.

[0003] With the increase in the number of earth observation missions, SAR satellite formations are often required to observe multiple ground target points within one orbital cycle. For each target point, it can only be observed by the satellite within its visible time window. Therefore, how to choose and arrange the observation tasks within a limited time window is crucial to improving the efficiency of the observation mission. Satellite agility is also a mainstream development direction of current SAR satellite technology. With the help of large torque attitude control mechanisms, remote sensing satellite platforms have the performance of rapid large-range attitude maneuvers and multiple imaging modes. The formation and agility of SAR satellites increase the flexibility of observation missions, but also make the observation mission planning problem more complicated. Research on efficient mission planning technology helps to make full use of the maneuverability of agile satellites and improve the observation benefits of SAR satellite formations.

[0004] When observing ground target points, the satellite formation needs to meet the visible time window constraint of the target point. According to the results of observation mission planning, the attitude transfer time between two adjacent observation targets is limited. How to complete the attitude transfer between targets within a limited time and complete the observation of the target point for a specified time is a key factor in successfully completing the observation mission planning results. Therefore, studying the problem of high-precision designated time SAR satellite formation attitude collaborative control can effectively improve the observation performance of the formation. At the same time, there are various interferences in the space environment, and considering the saturation phenomenon of satellite attitude actuators, it is necessary to study the satellite formation attitude collaborative control under the constraints of external disturbances and actuator saturation. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a distributed SAR (Synthetic Aperture Radar) satellite scheduled time attitude collaborative anti-saturation control method. First, a SAR satellite formation model considering saturation constraints is established; then a preset performance boundary function that can converge within a specified time is designed; next, external interference, actuator saturation constraints and other problems exist in the satellite formation flight system; finally, a SAR satellite scheduled time attitude collaborative control law is designed based on an anti-saturation compensator, an interference observer and a sliding mode control. The method of the present invention can enable the formation satellites to achieve the specified time convergence of the attitude coordination error under the actuator saturation constraint, and be within the preset performance boundary, with high control accuracy, good control performance and fast convergence speed.

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

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

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

[0009] Step 3: Design the SAR satellite scheduled time attitude collaborative control law based on anti-saturation compensator, disturbance observer and sliding mode control.

[0010] Preferably, the step 1 is specifically:

[0011] Step 1-1: The kinematic equation of the formation satellite attitude described by quaternion is:

[0012]

[0013] Among them, q 0,i and q v,i Respectively represent the scalar part and vector part of the attitude quaternion of formation satellite i, ω i represents the attitude angular velocity of the formation satellite i relative to the inertial system;

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

[0015]

[0016] Then the satellite attitude dynamics equation is obtained as:

[0017]

[0018] Among them, J i represents the moment of inertia of formation satellite i, u i ∈R 3represents the control torque, d i ∈R 3 represents the external interference suffered by formation satellite i;

[0019] Step 1-3: Set represents the expected attitude quaternion of formation satellite i, ω d,i represents the expected angular velocity of formation satellite i; the attitude error quaternion between the body coordinate system and the expected coordinate system is defined as The attitude angular velocity error is ω e,i , then:

[0020]

[0021] ω e,i =ω i -C i ω d,i (7)

[0022] Among them, C i is the attitude transfer matrix between the formation satellite i's body coordinate system and the desired coordinate system, and satisfies:

[0023]

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

[0025]

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

[0027]

[0028] Step 1-4: Convert the kinematic and dynamic equations of the satellite formation attitude error into the Euler-Lagrangian system form, then the attitude error dynamic equation of formation satellite i is 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] The satellite formation error quaternion and its derivative are defined as:

[0041]

[0042] The external disturbance and control torque of the formation are defined as:

[0043]

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

[0045]

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

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

[0048]

[0049] Combined with the communication topological relationship between the formation members, the attitude coordination error of formation satellite i and its first-order derivative are defined as:

[0050]

[0051] Among them, a ij represents the elements in the graph theory weighted connection matrix A, b i is the element in the degree matrix B;

[0052] Formula (31) and formula (32) are converted into the following description:

[0053]

[0054]

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

[0056] Since the communication topology between the formation satellites is an undirected connected graph, according to graph theory knowledge, H1 is a positive definite matrix and is reversible, so χ1=0, χ2=0 is equivalent to q ev =0, Therefore, the controller is designed to make χ1=0, χ2=0 to satisfy the formation satellite attitude tracking control;

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

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

[0061] According to formula (16), we can get:

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

[0063] Then under the constrained 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, and u sat =u-ψ(u), and substituting it into the model formula (39) yields:

[0071]

[0072] An anti-saturation compensator Xψ(u) is added to the error model (41) for compensation, and the final model of the SAR satellite formation considering the saturation constraint is:

[0073]

[0074] Preferably, the step 2 is specifically:

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

[0076]

[0077] Wherein, ρ(t) is the preset performance boundary function to be designed, δ is the overshoot limit parameter, and when δ = 0, overshoot is not allowed to occur;

[0078] It can be seen from formula (43) that the constraint on the error χ(t) is an inequality constraint. In order 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] Then 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] By taking the derivative of formula (47), we can get:

[0090]

[0091] in

[0092]

[0093] Step 2-3: For the preset performance control with specified time convergence, the boundary function ρ(t) should satisfy:

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

[0095] Among them, ρ0 and ρ ∞ are the initial and final values ​​of the performance boundary function, T f For a user-defined settling time, the boundary function ρ(t) is given by the following first-order derivative form:

[0096]

[0097] in, α is a constant that satisfies

[0098] Preferably, the step 3 is specifically:

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

[0100]

[0101] in, is the auxiliary system state quantity, is the estimated value of the generalized interference upper bound, k, are greater than 0, ε D For a small amount, is the interference estimation error;

[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 is obtained as:

[0106]

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

[0108]

[0109] According to the designed sliding surface, the control law of formation satellite i is designed as:

[0110]

[0111] Among them, k2>0, ε s is a small quantity, and in the error model compensation term:

[0112]

[0113] A computer program enables a computer to execute the anti-saturation control method.

[0114] An electronic device comprises: 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, so that the electronic device executes the above-mentioned anti-saturation control method.

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

[0116] A chip includes: a processor, which is used to call and run a computer program from a memory, so that a device equipped with the chip executes the above anti-saturation control method.

[0117] A computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and the anti-saturation control method is implemented when the instructions are executed by the at least one processor.

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

[0119] The present invention can realize the coordinated control of satellite attitude at designated time under external disturbance and actuator saturation constraints, and can improve the dynamic performance and steady-state performance of the system to meet the working requirements of SAR satellite earth observation, etc. The combination of the predetermined time stability theory makes the dynamic performance of the control law better, which has certain practical significance for the development of distributed SAR satellite attitude coordinated control. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 The figure is a flow chart of the method of the present invention.

[0121] Figure 2 This is a SAR satellite formation parameter diagram used in the present invention.

[0122] Figure 3 This is a communication relationship diagram of the SAR satellite formation adopted in the present invention.

[0123] Figure 4 This is the satellite 1 attitude coordination error curve.

[0124] Figure 5 This is the satellite 2 attitude coordination error curve.

[0125] Figure 6 This is the satellite 3 attitude coordination error curve.

[0126] Figure 7 This is the satellite 1 attitude quaternion tracking error curve.

[0127] Figure 8 This is the satellite 2 attitude quaternion tracking error curve.

[0128] Fig. 9 This is the satellite 3 attitude quaternion tracking error curve.

[0129] Fig.10 This is the satellite 1 attitude angular velocity tracking error curve.

[0130] Fig.11 This is the satellite 2 attitude angular velocity tracking error curve.

[0131] Fig.12 This is the satellite 3 attitude angular velocity tracking error curve.

[0132] Fig.13 It is the control torque curve.

[0133] Fig.14 This is the interference estimation error curve.

[0134] Fig.15 It is the observation error curve of auxiliary system state quantity. DETAILED DESCRIPTION

[0135] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0136] like Figure 1 As shown, in view of the problems of external interference, actuator saturation constraint and the like in the satellite formation flying system, the present invention provides a distributed SAR satellite designated time attitude collaborative anti-saturation control method, comprising the following steps:

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

[0138]

[0139] The kinematic equation of the formation satellite attitude described by quaternion is:

[0140]

[0141] Among them, q 0,i and q v,i Respectively represent the scalar part and vector part of the attitude quaternion of formation satellite i, ω i It represents the attitude angular velocity of the formation satellite i relative to the inertial system.

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

[0143]

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

[0145]

[0146] Among them, J i represents the moment of inertia of formation satellite i, u i ∈R 3 represents the control torque, d i ∈R 3 Indicates the external interference suffered by formation satellite i.

[0147] When analyzing satellite attitude tracking problems, establishing kinematic and dynamic equations described by error quaternions is helpful for problem analysis. represents the expected attitude quaternion of formation satellite i, ω d,i represents the expected angular velocity of formation satellite i. The attitude error quaternion between the body coordinate system and the expected coordinate system is defined as The attitude angular velocity error is ω e,i , then:

[0148]

[0149] ω e,i =ω i -C i ω d,i (73)

[0150] Among them, C i is the attitude transfer matrix between the formation satellite i's body coordinate system and the desired coordinate system, and satisfies:

[0151]

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

[0153]

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

[0155]

[0156] Considering the systematization of controller design and in order to simplify the expression, the kinematic and dynamic equations of the satellite formation attitude error are converted into the Euler-Lagrangian system form. Then the attitude error dynamic equation of formation satellite i 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] The satellite formation error quaternion and its derivative are defined as:

[0169]

[0170] The external disturbance and control torque of the formation are defined as:

[0171]

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

[0173]

[0174] The relative attitude error and the first-order derivative between formation satellite i and formation satellite j are defined as:

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

[0176]

[0177] Combined with the communication topological relationship between the formation members, the attitude coordination error of formation satellite i and its first-order derivative are defined as:

[0178]

[0179] Among them, a ij represents the elements in the graph theory weighted connection matrix A, b i is the element in the degree matrix B;

[0180] Formula (31) and Formula (32) can be converted into the following description:

[0181]

[0182]

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

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

[0185] If the control input of the satellite formation attitude system has saturation constraints, it is necessary to consider the control input representation and the corresponding satellite formation dynamics model, and only on this basis can the next step of controller design be carried out. Assuming that the control input u of the satellite formation attitude system has saturation constraints, the torque range that can be provided is: -u max ≤u≤u max , where u max is the maximum value of the control input, then the constrained control input u satIt can be defined as 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:

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

[0189] According to formula (16), we can get:

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

[0191] Then under the constrained 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, and u sat =u-ψ(u), and substituting it into the model formula, we get:

[0199]

[0200] In order to weaken the impact of saturation constraint 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 the controller so that χ1=0 can satisfy the formation satellite attitude tracking control. For formation satellite i, the error χ 1,i (t) Design the preset performance constraints. To facilitate the following derivation, 1,i (t) is expressed as χ(t), then χ(t) must satisfy:

[0205]

[0206] Wherein, ρ(t) is the preset performance boundary function to be designed, δ is the overshoot limit parameter, and when δ=0, overshoot is not allowed to occur.

[0207] It can be seen from equation (43) 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] Secondly, 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] Then 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] By taking the derivative of formula (47), we can get:

[0219]

[0220] in,

[0221]

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

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

[0224] Among them, ρ0 and ρ ∞ are the initial and final values ​​of the performance boundary function, T f For a user-defined settling time, the boundary function ρ(t) is given by the following first-order derivative form:

[0225]

[0226] in, α is a constant that satisfies According to the above formula, the first-order derivative of the boundary function ρ(t) is continuous, so it can be seen that ρ(t) is also continuous.

[0227] Step 3: Design the SAR satellite scheduled time attitude coordinated control law based on anti-saturation compensator, disturbance observer and sliding mode control:

[0228]

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

[0230]

[0231] in, is the auxiliary system state quantity, is the estimated value of the generalized interference upper bound, k, are greater than 0, ε D For a small amount. is the interference estimation error.

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

[0233] The designed sliding surface is:

[0234]

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

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

[0237]

[0238] According to the inverse relationship between H1 and H2, we can know that:

[0239]

[0240] According to the designed sliding surface, the control law of formation satellite i is designed as:

[0241]

[0242] Among them, k2>0, ε s For a small amount.

[0243] In the error model compensation term:

[0244]

[0245] Spacecraft parameters used in the present invention:

[0246] In order to verify the effectiveness of the invented satellite formation attitude cooperative anti-saturation controller with preset performance at specified time based on interference observer. Taking the observation target point (108.43°E, 48.6°N, 50.32m) as an example, the camera optical axis needs to point to the target point together within 10.21s, that is, each satellite should track the expected attitude quaternion within 10.21s and keep accurate tracking of the expected attitude within the next 10s. The SAR satellite formation parameters are as follows: Figure 2 shown.

[0247] The parameters in the controller are selected 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 preset performance boundary function is designed as:

[0252] T f =10s, α=0.6

[0253] Considering the uncertainties such as camera startup, the performance function stabilization time is set to 10s. The attitude quaternion of each satellite in the formation at the end of observation of the last target point is used as the initial quaternion for attitude coordinated 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 interference model is:

[0260]

[0261] The SAR satellite formation uses undirected graph communication, and the formation communication relationship can be described as Figure 3 form.

[0262] The simulation step size is set to 0.01s, and the simulation cycle is set to 30s. According to the task background, the simulation starts within 10.21s as the posture transfer stage, and 10.21s-20.21s as the collaborative observation stage. The simulation results are as follows: Figures 4 to 15 shown.

[0263] Figures 4 to 6 They are the coordinated error convergence curves of each satellite in the formation. Figures 4 to 6 It can be seen that each satellite in the formation has a different initial value of the coordination error, but they can all converge to near 0 within 10s and always remain within the preset performance boundary. f =10s before reaching a stable state. In the following 10s, the coordinated errors of each satellite converged within the performance boundary. The convergence of the coordinated errors of the formation sub-satellites is equivalent to the convergence of the attitude quaternion errors, which means that the attitude quaternion of the sub-satellite can track the expected quaternion. Figures 4 to 6 It can be seen from the partial enlarged figure in the figure that the steady-state accuracy of each satellite attitude cooperative control can converge to the boundary of the preset performance, reaching an accuracy within 0.01. According to the above formation satellite cooperative error convergence curve, it can be seen that the satellite formation attitude cooperative anti-saturation controller based on interference observer designed by the present invention has reliable stability and good tracking performance. In addition, due to the influence of saturation constraints, the system convergence speed slows down and the steady-state accuracy decreases, but the controller can still ensure the stability of the formation.

[0264] Figures 7 to 12 They are the attitude quaternion tracking error curve and attitude angular velocity tracking curve of each satellite in the formation. Figures 7 to 12 It can be seen from the figure that under the condition of the initial attitude error, the tracking error curve of the attitude quaternion of each sub-satellite can be obtained at T f=10s, which means that in the formation's observation mission of ground target points, before the observation mission begins, the attitude quaternion of each satellite in the formation can track the expected attitude quaternion, that is, to achieve the control goal of pointing the optical axis of each camera to the target point to be observed. Figures 7 to 12 The enlarged partial image shows that 10 seconds ago, that is, before the formation observation mission began, the attitude quaternions of all satellites in the formation reached 10 -4 The tracking accuracy and attitude angular velocity tracking accuracy both reached 0.01rad / s, which shows that under the action of the controller, each satellite in the formation can complete the tracking of the desired attitude in a relatively short time, and the formation has good tracking accuracy and steady-state accuracy, realizing the common pointing of each satellite in the SAR satellite formation to the target point before and after the observation mission of the ground target point begins.

[0265] Fig.13 It is the three-axis control torque curve of each satellite in the formation. It can be seen from the figure that in the initial stage, the control torque of each satellite is large. This is because the initial attitude of each satellite has a large deviation from the expected attitude. The components of the control torque of each satellite in the three directions are stable within 10s. According to the local enlarged diagram, the amplitude of the control torque is 0.03N·m after stabilization. The control torque always meets the maximum torque that can be provided by the satellite single axis.

[0266] Fig.14 and Fig.15 is the disturbance estimation error curve and the auxiliary system state quantity observation error curve, where error1 represents the disturbance estimation error and error2 represents the disturbance observer state quantity estimation error. From the curve, we can see that the components of the disturbance estimation error and the state quantity estimation error in the three directions gradually converge to 0. At the same time, from the local enlarged diagram, we can see that the disturbance estimation error reaches 10 -4 The convergence accuracy of the state estimation error is 10 -3 This shows that the designed disturbance observer can not only converge quickly but also accurately observe the external disturbances to the system and finally compensate them in the controller.

[0267] The above simulation results and analysis verify the effectiveness of the satellite formation attitude coordination anti-saturation controller with preset performance at a specified time based on the interference observer designed by the present invention. Under the saturation constraint, the controller can still make the coordination error of the attitudes of each satellite in the formation converge within the specified time and be within the preset performance boundary. It can be further verified that the attitude quaternion of each satellite can track the expected attitude quaternion within the specified time and has good steady-state accuracy, so that the common pointing of each satellite in the formation to the target point can be achieved before and after the formation satellite starts the observation mission of the ground target point.

Claims

1. A distributed SAR satellite predetermined time attitude coordinated anti-saturation control method, characterized in that: The steps include: Step 1: Establish a SAR satellite formation model considering saturation constraints; Step 2: Design a preset performance boundary function that can converge within a specified time; Step 3: Design the SAR satellite scheduled time attitude collaborative control law based on anti-saturation compensator, disturbance observer and sliding mode control.

2. A distributed SAR satellite predetermined time attitude coordinated anti-saturation control method according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: The kinematic equation of the formation satellite attitude described by quaternion is: Among them, q 0,i and q v,i Respectively represent the scalar part and vector part of the attitude quaternion of formation satellite i, ω i represents the attitude angular velocity of the formation satellite i relative to the inertial system; Step 1-2: For any vector Define the cross product operator ζ × for: Then the satellite attitude dynamics equation is obtained as: Among them, J i represents the moment of inertia of formation satellite i, u i ∈R 3 represents the control torque, d i ∈R 3 represents the external interference suffered by formation satellite i; Step 1-3: Set represents the expected attitude quaternion of formation satellite i, ω d,i represents the expected angular velocity of formation satellite i; the attitude error quaternion between the body coordinate system and the expected coordinate system is defined as The attitude angular velocity error is ω e,i , then: oh e,i =ω i -C i oh d,i (7) Among them, C i is the attitude transfer matrix between the formation satellite i's body coordinate system and the desired coordinate system, and satisfies: The kinematic equation of attitude error of formation satellite i is: The attitude error dynamic equation of formation satellite i is: Step 1-4: Convert the kinematic and dynamic equations of the satellite formation attitude error into the Euler-Lagrangian system form, then the attitude error dynamic equation of formation satellite i is expressed as: in: M a,i =P i T J i P i (13) P i =T i -1 (14) in s,i =P i T in i (16) d s,i =-P i T d i (17) definition: The satellite formation error quaternion and its derivative are defined as: The external disturbance and control torque of the formation are defined as: Then the attitude error dynamic equation of the satellite formation is expressed as: Step 1-5: Define the relative attitude error and first-order derivative between formation satellite i and formation satellite j as: q ev,ij =q ev,i -q ev,j (29) Combined with the communication topological relationship between the formation members, the attitude coordination error of formation satellite i and its first-order derivative are defined as: Among them, a ij represents the elements in the graph theory weighted connection matrix A, b i is the element in the degree matrix B; Formula (31) and formula (32) are converted into the following description: in, H2 and H1 are mutually inverse matrices; Since the communication topology between the formation satellites is an undirected connected graph, according to graph theory knowledge, H1 is a positive definite matrix and is reversible, so χ1=0, χ2=0 is equivalent to q ev =0, Therefore, the controller is designed to make χ1=0, χ2=0 to satisfy the formation satellite attitude tracking control; Step 1-6: Assume that the control input u in the satellite formation attitude system has a saturation constraint, and the torque range that can be provided is: -u max ≤u≤u max , where u max is the maximum value of the control input, then the constrained control input u sat It is defined as a saturation function: 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: in sat =btanh(au) (36) According to formula (16), we can get: in s,sat =P T in sat (37) Then under the constrained input u s,sat The satellite error dynamics equation under the action is rewritten as: Rewrite it as: in, Define the dead zone nonlinear function: ψ(u)=uu sat (40) When ψ(u)≠0, the controller enters the saturation region, and u sat =u-ψ(u), and substituting it into the model formula (39) yields: An anti-saturation compensator Xψ(u) is added to the error model (41) for compensation, and the final model of the SAR satellite formation considering the saturation constraint is:

3. A distributed SAR satellite predetermined time attitude coordinated anti-saturation control method according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: When χ1=0, q ev =0; design the controller so that χ1=0, which satisfies the formation satellite attitude tracking control; for formation satellite i, the error χ 1,i (t) Design the preset performance constraints, and set χ 1,i (t) is expressed as χ(t), then χ(t) must satisfy: Wherein, ρ(t) is the preset performance boundary function to be designed, δ is the overshoot limit parameter, and when δ = 0, overshoot is not allowed to occur; It can be seen from formula (43) that the constraint on the error χ(t) is an inequality constraint. In order to simplify the design of the control law, the inequality constraint is converted into an equality constraint, and the normalized error is defined as: Step 2-2: Construct a smooth and strictly monotonically increasing mapping function S(ε(t)), then the error χ(t) satisfies: χ(t)=ρ(t)S(ε(t)) (45) Where, ε(t) is the conversion error; Then we can know that: The conversion error ε(t) can be obtained by inverse solution: And the normalized error z(t) satisfies: By taking the derivative of formula (47), we can get: in Step 2-3: For the preset performance control with specified time convergence, the boundary function ρ(t) should satisfy: ρ(0)=ρ0>2ρ(t>T f )=2ρ ∞ >0 (57) Among them, ρ0 and ρ ∞ are the initial and final values ​​of the performance boundary function, T f For a user-defined settling time, the boundary function ρ(t) is given by the following first-order derivative form: in, α is a constant that satisfies 4. A distributed SAR satellite predetermined time attitude coordinated anti-saturation control method according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3-1: For the SAR satellite formation model (42) with saturation constraints, design an interference observer of the following form: in, is the auxiliary system state quantity, is the estimated value of the generalized interference upper bound, k, are greater than 0, ε D For a small amount, is the interference estimation error; Step 3-2: Design the sliding surface as follows: Where k1 is a positive constant that satisfies the Hurwitz condition: The derivative of the sliding surface is obtained as: Step 3-3: According to the inverse relationship between H1 and H2, we know that: According to the designed sliding surface, the control law of formation satellite i is designed as: Among them, k2>0, ε s is a small quantity, and in the error model compensation term:

5. A computer program, characterized in that The computer program enables a computer to execute the method according to any one of claims 1 to 4.

6. 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, so that the electronic device executes the method as claimed in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

8. A chip, characterized in that: include: A processor, configured to call and run a computer program from a memory, so that a device equipped with the chip executes a method as claimed in any one of claims 1 to 4.

9. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to any one of claims 1 to 4 is implemented.

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