Large loop antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control

Abstract

The invention discloses a large loop antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control, and relates to the technical field of large spacecraft attitude and orbit integrated control. The invention aims to solve the problem that a control method of a large-scale loop antenna satellite model is difficult to give consideration to calculation real-time performance and optimization of large-scale memory occupation in a complex space environment. The method comprises the following steps: parameterizing control input of a large-scale loop antenna satellite by using a Laguerre function, and performing order reduction on the control input to obtain a decision variable; the method comprises the following steps: rewriting a dynamic model of a large-scale loop antenna satellite attitude orbit into a Laguerre model predictive control form with constraints by using decision variables, then converting the Laguerre model predictive control form with constraints into an equivalent multi-parameter quadratic programming form, and carrying out display solution on the multi-parameter quadratic programming form to obtain a segmented affine function; and substituting the observation state of the large-scale loop antenna satellite into the piecewise affine function so as to construct attitude and orbit control input of the large-scale loop antenna satellite.

Description

Technical Field

[0001] The invention belongs to the technical field of attitude and orbit integration control of large spacecraft. Background Art

[0002] Large ring antenna satellites are widely used in the field of communications. They operate in geostationary orbits and require high-precision pointing to ensure stable and high-rate information transmission. Such satellites need to maintain a specified longitude and latitude during the flight cycle and have strict error limits on their attitude to the ground. However, non-spherical perturbations, solar pressure, and three-body perturbations in complex space environments can cause the satellite to gradually deviate from the nominal position. In addition, the vibration of the flexible antenna induces structural deformation, which enhances the coupling effect between orbit and attitude. Therefore, it is particularly important to design an attitude-orbit integrated control system to offset the perturbation force. Full-thrust design has become an important trend in future space exploration because it reduces the internal disturbances caused by reaction flywheels and traditional thrusters. The internal formation gravity field measurement satellite is a typical representative of the full-thrust layout, which is suitable for precise orbit determination and attitude control tasks. By measuring the deviation and compensating it with onboard sensors, attitude-orbit integrated control can effectively deal with non-gravity disturbances and ensure system stability. However, the large ring antenna satellite model has a complex structure, and nonlinear and high-dimensional constraints make the coupled control of orbit and attitude more challenging. Although differential geometry control, artificial potential field method, symplectic algorithm and other methods have been proposed, their practical applications are limited by computational complexity and the particularity of the space environment. Model Predictive Control (MPC) is an effective online optimization method that can compensate for system disturbances through rolling optimization, but in complex space environments, real-time performance is difficult to guarantee. Explicit Model Predictive Control (EMPC) significantly improves computational efficiency by solving control laws offline and calculating optimization problems online through table lookup. However, the high-dimensional optimization control requirements for large systems lead to a significant increase in memory usage, limiting its application in spaceborne computers with limited memory.

[0003] In summary, considering the engineering applicability of the control method, the existing control method is difficult to balance the real-time computing and the optimization of large-scale memory usage in a complex space environment, thus bringing huge challenges to the attitude and orbit integrated control deployed on onboard computers with limited computing resources. Summary of the invention

[0004] The present invention aims to solve the problem that the control method of a large-scale ring antenna satellite model is difficult to balance computational real-time performance and optimization of large-scale memory usage in a complex space environment. A large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control is provided.

[0005] An attitude and orbit integrated control method for large-scale ring antenna satellites based on improved explicit model predictive control is proposed. The control input u(k+j) of the large-scale ring antenna satellite is parameterized using Laguerre function, and the control input u(k+j) is reduced to obtain the decision variable η.

[0006] The decision variable η is used to rewrite the dynamic model of the attitude and orbit of the large ring antenna satellite into a constrained Laguerre model predictive control form:

[0007]

[0008] in, It means that the objective function is minimized by solving the value of η, x(k) is the state of the large ring antenna satellite at time k,

[0009]

[0010] A is the system matrix of the relative orbital dynamics equation, B is the control matrix of the relative orbital dynamics equation, N p and N c are the prediction and control steps of Laguerre model predictive control, L(δ) is the δth Laguerre function set, δ=0,1,...,N p -1, Q and P are positive definite and semi-positive definite performance weight matrices, respectively;

[0011] Defining variables The constrained Laguerre model predictive control form is transformed into an equivalent multi-parameter quadratic programming form:

[0012]

[0013] The multi-parameter quadratic programming form is explicitly solved to obtain the piecewise affine function z * [];

[0014] The observation status of the large ring antenna satellite Substitute the piecewise affine function z * [], and then construct the attitude and orbit control input u(k) of the large ring antenna satellite:

[0015]

[0016] Furthermore, the control input u(k+j) of the large ring antenna satellite is expressed as:

[0017]

[0018] Among them, l i(j) represents the control vector of the i-th row in the j-th Laguerre function set L(j), n represents the dimension of the control vector, i = 1, 2, ..., n.

[0019] Furthermore, the control vector in the Laguerre function set satisfies:

[0020]

[0021] Among them, b i =1-a i 2 , a i is the Laguerre function network scaling factor, N i is the number of expansion terms of the Laguerre function.

[0022] Furthermore, based on the above-mentioned attitude dynamics equations described by the spacecraft kinematic equations and the dual quaternion, a dynamics model of the attitude and orbit of a large ring antenna satellite is established, and its expression is:

[0023]

[0024] Where x is the state vector of the antenna satellite relative to the nominal orbit, Representing quaternions, we have and q and q4 are the vector and scalar parts of the quaternion respectively; ω b is the angular velocity of the antenna satellite relative to the orbit, Y is the thrust of the propeller and the interference force of the space environment acting on the antenna satellite, J is the inertia matrix of the antenna satellite, ω is the absolute angular velocity of the antenna satellite in the inertial system, is the skew matrix of ω, T bo is the rotation matrix of the antenna satellite from the orbital coordinate system to the body coordinate system, T is the composite torque of the control torque generated by the propulsion system and the space environment interference torque, Yes b The skew matrix of ω0 is the steady orbital angular velocity.

[0025] Furthermore, the interference factors of the space environment interference force acting on the antenna satellite include solar pressure, non-spherical perturbation and three-body gravity;

[0026] Solar pressure acceleration a spp :

[0027]

[0028] Among them, C R is the surface reflection coefficient of the satellite, ρ SR is the solar pressure constant, g is the insolation factor, AU is 1 astronomical unit, rSun is the position vector of the sun in the geocentric inertial system, e D represents the unit vector pointing from the satellite to the sun; S Ref It represents the equivalent sun-receiving area of ​​a large ring antenna satellite, and m is the satellite mass;

[0029] The gravity gradient torque under the influence of non-spherical gravitational perturbation is:

[0030]

[0031] Among them, T gx 、T gy 、T gz are the x-, y-, and z-axis components of the gravity gradient torque in the current system, R C is the height of the geostationary orbit, μ is the gravitational constant of the earth, I x ,I y ,I z The x, y, and z axes moments of inertia in the moment of inertia matrix of the large ring antenna satellite are represented by θ and are the pitch angle and the roll angle respectively;

[0032] Three-body perturbation acceleration a TBP :

[0033]

[0034] Among them, μ Sun and μ Moon are the gravitational constants of the sun and the moon, r Sun2Sat is the position of the sun relative to the satellite in the geocentric inertial system, r Moon2Sat is the position of the moon relative to the satellite in the geocentric inertial system; r Moon is the position vector of the moon in the geocentric inertial system.

[0035] Furthermore, the thruster installation matrix acting on the antenna satellite is:

[0036]

[0037] Among them, c = cosα, s = sinα, α is the thruster direction and the inclination angle of the mounting surface, a, b, d are the length, width and height of the satellite body respectively, L1 and L2 are the distances from the satellite body and the feed platform to the center of mass of the antenna satellite respectively.

[0038] Furthermore, the above-mentioned decision variable η is used to rewrite the dynamic model of the attitude and orbit of the large ring antenna satellite into a constrained Laguerre model predictive control form, including:

[0039] The dynamic model of the attitude and orbit of the large ring antenna satellite is linearized and discretized and written into a compact form;

[0040] The objective function and constraints of the compact form model are combined into a constrained Laguerre model predictive control form.

[0041] Furthermore, the above dynamic model of the large-scale ring antenna satellite attitude and orbit is linearized and discretized to obtain:

[0042]

[0043] Furthermore, the above compact form model expression is:

[0044] X=Fx(k)+Φη.

[0045] Furthermore, the objective function of the above compact form model is expressed as:

[0046]

[0047] Where ψ represents the objective function;

[0048] The constraints of the objective function are:

[0049]

[0050] Among them, u M To control the maximum value of the input, I is the j-dimensional unit matrix.

[0051] The beneficial effects of the large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control described in the present invention are:

[0052] 1. The present invention combines a high-precision orbit prediction algorithm with a mathematical modeling method for large-scale ring antenna satellites, considers the satellite's special configuration and the complex dynamic changes in its position relative to the sun and the earth, and accurately analyzes the disturbance law of the main space environment on large-scale ring antenna satellites. It provides a dynamic basis for the satellite's full thruster layout design and attitude-orbit integrated control strategy.

[0053] 2. The distributed thruster layout strategy for large ring antenna satellites proposed in this invention can simplify the control system, improve fault tolerance, reduce propellant consumption, and extend the satellite's on-orbit operation life. At the same time, small thrust continuous control is more suitable for complex space missions such as attitude and orbit integrated control.

[0054] 3. The present invention proposes an improved explicit model predictive control algorithm (LEMPC) based on the Laguerre function for the attitude and orbit integrated control task of large ring antenna satellites in geostationary orbit. The LEMPC algorithm solves the problem of poor real-time calculation of online optimized MPC and LMPC algorithms by solving the control law offline and performing online table lookup calculation, which significantly improves the controller calculation efficiency. In addition, the Laguerre function reduces the order of the control sequence by parameterizing it, and optimizes the memory usage of the pre-stored large-scale offline control law, which is about 17.7% of that of the EMPC algorithm.

[0055] 4. The LEMPC algorithm proposed in the present invention retains the dynamic characteristics of LMPC, has a smaller initial oscillation amplitude and stronger ability to resist interference. Its advantages in thrust output optimization distribution enable it to exhibit better control accuracy and stability. Compared with ordinary EMPC, it has obvious improvements in memory optimization, and provides a solution for large ring antenna satellites with limited computing resources to perform full-thrust attitude and orbit integrated control in complex space environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of the attitude and orbit integrated control method of large-scale ring antenna satellite based on improved explicit model predictive control;

[0057] Figure 2 It is a schematic diagram of the distributed thruster layout of a large ring antenna satellite;

[0058] Figure 3 It is a simulation diagram of the perturbations of three space environments when a large ring antenna satellite is in orbit for 24 hours. Sub-figure (a) is the non-spherical perturbation force and gravity gradient moment, sub-figure (b) is the sunlight pressure and moment, and sub-figure (c) is the solar gravity and lunar gravity.

[0059] Figure 4 It is a comparative simulation diagram of LEMPC, MPC and LMPC algorithms under controlled conditions, where sub-figures (a) to (c) are relative position errors, sub-figures (d) to (f) are relative velocity errors, sub-figures (g) to (i) are relative attitude angle errors, and sub-figures (j) to (l) are relative angular velocity errors;

[0060] Figure 5 Output curve diagram of thrusters 1 to 6. DETAILED DESCRIPTION

[0061] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0062] Reference Figures 1 to 3 The present embodiment is specifically described. The attitude and orbit integrated control method of a large-scale ring antenna satellite based on improved explicit model predictive control described in the present embodiment takes into account the disturbance of complex space environment and the special configuration of large-scale ring antenna satellites, and combines the distributed full thrust layout strategy. On the basis of meeting the attitude and orbit integrated control requirements, the control real-time performance of online calculation is significantly improved, and the thrust optimization distribution is more stable. Compared with the ordinary EMPC memory optimization, the improvement is obvious, as follows:

[0063] Step 1: Based on the Clohessy-Wiltshire (CW) kinematic equations of the spacecraft and the attitude dynamics equations described by dual quaternions, an integrated nonlinear attitude-orbit coupling dynamics model of a large ring antenna satellite is established.

[0064] The attitude-orbit coupling dynamics model of a large-scale annular truss antenna satellite is established by combining the Lagrange equation and the CW equation using the floating coordinate method. This method can effectively capture the dynamic characteristics of the satellite body, flexible antenna, and flexible solar wing. It decomposes the complex dynamics problem into two parts: rigid body motion and elastic deformation. The former describes the overall large-scale motion of the flexible component, and the latter describes the small-scale elastic deformation relative to the rigid body motion. The rigid body part uses the Newton-Euler equation to describe the center of mass motion and attitude changes of the satellite body. The motion equation of the flexible component is obtained by the Lagrange equation. The CW equation is used to describe the relative motion of the satellite in orbit. The rigid body part, the flexible part, and the attitude and orbit coupling part are combined to obtain a complete dynamic model:

[0065]

[0066] Where x∈R 6×1 is the state vector of the antenna satellite relative to the nominal orbit, including relative position and relative velocity;

[0067] Quaternions are used in this embodiment and are defined as and where q∈R 3×1 is the vector part of the quaternion, q4 is a scalar;

[0068] ω b∈R 3×1 is the angular velocity of the antenna satellite relative to the orbit; Y∈R 3×1 It is composed of the thrust of the propeller acting on the antenna satellite and the interference force of the space environment; J∈R 3×1 is the antenna satellite inertia matrix; ω∈R 3×1 is the absolute angular velocity of the antenna satellite inertial system, and ω=ω b +T bo ω0, is the skew matrix of ω; T bo is the rotation matrix of the antenna satellite from the orbital coordinate system to the body coordinate system; T∈R 3×1 is the resultant torque applied to the antenna satellite, including the control torque generated by the propulsion system and the space environment disturbance torque; A is the system matrix of the relative orbital dynamics equation; Yes b ω0 is the constant orbital angular velocity; B is the control matrix of the relative orbital dynamics equation, Represents the transpose of a matrix.

[0069] Step 2: Combine high-precision orbit prediction algorithms and mathematical modeling methods to analyze the dynamic impact of key space environmental factors such as solar pressure, non-spherical perturbations and three-body gravity on the space operation of large ring antenna satellites.

[0070] The space environment interference force acting on the antenna satellite is composed of key space environment factors such as solar pressure, non-spherical perturbation and three-body gravity. In this embodiment, the UTC (Coordinated Universal Time) time is set to 0:0:00 on March 21, 2030 (the vernal equinox), and the simulation analysis of space perturbation of the large ring antenna satellite is as follows: Figure 3 shown.

[0071] The non-spherical gravitational perturbation caused by the uneven distribution of the Earth's mass has a significant impact on the orbit maintenance of high-orbit satellites. The position deviation can reach 104 meters within 24 hours, which is much higher than other perturbation factors. And because the antenna satellite structure is large, the gravity gradient torque will cause attitude deviation, and it is related to the pitch axis and roll axis angles. The calculation formula is as follows:

[0072]

[0073] Among them, T gx 、T gy 、T gz are the x-, y-, and z-axis components of the gravity gradient torque in the current system; R C is the altitude of the geostationary orbit; μ is the Earth's gravitational constant; I x ,I y ,I zRespectively represent the x-, y-, and z-axis moments of inertia in the moment of inertia matrix of the large ring antenna satellite; θ and They are the pitch angle and roll angle respectively.

[0074] When a large ring antenna satellite is operating in a geostationary orbit, the area of ​​the antenna surface exposed to the solar pressure is much larger than the satellite body, so it is even more important to calculate the force and torque of the solar pressure on the antenna satellite. Therefore, the key to designing an attitude and orbit integrated control system is to accurately calculate the force and torque of the solar pressure on the antenna satellite.

[0075] Solar pressure acceleration a spp The calculation formula is as follows:

[0076]

[0077] Among them, C R is the surface reflection coefficient of the satellite; ρ SR is the solar pressure constant; g is the insolation factor; AU is 1 astronomical unit; e is D represents the unit vector pointing from the satellite to the sun; S Ref It represents the equivalent sun-receiving area of ​​a large ring antenna satellite; m is the satellite mass.

[0078] When a shadow appears on the back of the earth, k=0; when the satellite leaves the shadow of the earth, k=1, and the satellite is under the influence of solar light pressure.

[0079] Although the antenna satellite is mainly affected by the Earth's gravity, the gravitational perturbations of the sun, moon and other celestial bodies in the geostationary orbit cannot be ignored. Their magnitude is comparable to that of non-spherical gravity and higher than the solar light pressure. The position deviation can reach 104 meters in the 24-hour forecast. However, compared with the gravitational perturbations of the sun and moon, the perturbations of other celestial bodies are smaller and are usually not considered as the main factor. Three-body perturbation acceleration a based on DE436 ephemeris modeling TBP The formula is as follows:

[0080]

[0081] Among them, μ Sun and μ Moon are the gravitational constants of the sun and the moon respectively; r Sun2Sat is the position of the sun relative to the satellite in the geocentric inertial system; r Moon2Sat is the position of the moon relative to the satellite in the geocentric inertial system; r Sun and r Moon are the position vectors of the sun and the moon in the geocentric inertial system respectively.

[0082] Step 3: Considering the special configuration of large ring antenna satellites and the effects of complex space environment, establish a fully electric propulsion distributed layout plan suitable for large ring antenna satellites.

[0083] In this embodiment, the thruster group is distributed on the satellite body and the antenna end. The satellite body is composed of a normal north-south position maintaining thruster and two micro thrusters responsible for position maintaining and attitude adjustment. The thruster arrangement direction is as follows: Figure 2 As shown in the figure, the thruster arranged on the antenna satellite for normal position maintenance has a maximum thrust of 0.4N, and the microthruster has a maximum thrust of 0.08N. Since the thrusters are all installed in the forward direction, they only generate forward thrust.

[0084] The corresponding thruster installation matrix is:

[0085]

[0086] Where c represents cosα, s represents sinα, and α represents the thruster direction and the inclination angle of the mounting surface (e.g. Figure 2 As shown in the figure, a, b, and d represent the length, width, and height of the satellite body, respectively. L1 and L2 represent the distances from the satellite body and the feed platform to the center of mass of the antenna satellite, respectively.

[0087] Step 4: Introduce the Laguerre function into the MPC design and use a set of discrete Laguerre polynomials to parameterize the control input u(k+j):

[0088]

[0089] Where: l i (j) is the Laguerre function vector, which together constitute the Laguerre function set L(j), η represents the decision variable, which is the coefficient vector of the Laguerre function to parameterize the control input, k is the time corresponding to the state variable after discretization, j represents the sequence number of the control quantity in the control sequence, n represents the dimension of the control vector, i = 1, 2, ..., n.

[0090] The Laguerre function vector satisfies the following equation:

[0091]

[0092] Where bi = 1-ai 2 , N i is the number of extension items, a i ∈[0,1] is the input u i The Laguerre function network scaling factor for (k+j), a i and N i These are all fixed design parameters. Set a i = 0, it degenerates into standard MPC. Choose a suitable i, a trade-off is made between the control effect and the time scale. By setting the Laguerre function extension term, the dimension of the decision variable η is reduced and the calculation is feasible.

[0093] Step 5: Determine the appropriate Laguerre function expansion term N i , determine the prediction and control steps Np and Nc of Laguerre model predictive control, and determine the input u i The Laguerre function network scaling factor a of (k+j) i and bi.

[0094] In this embodiment, considering the space environment interference described in step 2, assuming that the state error obtained by the spacecraft sensor is within the allowable range, the prediction and control step number N is set p =N c =10, Laguerre function expansion term N i =2, proportional factor a i =0.67.

[0095] In steps 4 and 5, the Laguerre function is introduced to parameterize the control input u(k+j), and the new decision variable η representing the control quantity is obtained after order reduction. Then, in step 6, the decision variable η obtained by this method is applied to establish the constrained Laguerre model predictive control problem.

[0096] Step 6: Convert the propulsion system equipment capacity limitations and performance requirements into input-output constraints, introduce the Laguerre function into the constraint inequality, and establish the constrained Laguerre model predictive control problem (Laguerre-based Model Predictive Control, LMPC).

[0097] The kinetic model described in step 1 is linearized and discretized to obtain the prediction model:

[0098]

[0099] Prediction sequence N p The size of the decision variable η is independent and the prediction model can be written in a compact form:

[0100] X=Fx(k)+Φη (11),

[0101] in,

[0102]

[0103] Taking into account the output tracking effect and input power consumption, the objective function ψ is taken as the integral of the weighted tracking error and the model correction in the prediction time domain. The discretized objective function ψ is expressed as follows:

[0104]

[0105] and are the positive definite and semi-positive definite performance weight matrices, respectively.

[0106] Considering the input limitation of the thruster and the control accuracy requirement, the Laguerre function is introduced into the constraint inequality:

[0107]

[0108] Among them, u M It refers to the maximum value of the control input. The first inequality constrains the control input. I is the unit matrix, and its dimension is related to j.

[0109] The above constrained Laguerre model predictive control problem (12-13) is replaced by simplified symbols:

[0110]

[0111] Among them, m η in means to minimize the objective function ψ by solving the value of η. G=ΦQF, M, D and E can be obtained by constraining inequalities.

[0112] Step 7: Redefine variables Then, the LMPC in step 6 above is transformed into an equivalent multi-parameter planning problem, and the constraint inequality about the variable z is established.

[0113] The above problem (14) is transformed into an equivalent multi-parameter quadratic programming:

[0114]

[0115] Step 8: For a given state x(k) in a polyhedron set, the equivalent multi-parameter programming problem of step 7 can be solved explicitly, storing the piecewise affine function z on the polyhedron partitions in the form of a lookup table * [x(k)].

[0116] Step 9: Assuming that the system state is observable through the observation of data by onboard optical sensors and other components, obtain the observed state at each sampling time Get the control input command:

[0117]

[0118] Step 10: The online calculation load is converted into the solution of the piecewise affine function, the state space partition is located, and the proposed improved Laguerre function-based explicit model predictive control algorithm (Laguerre-based Explicit Model Predictive Control, LEMPC) is used to obtain the real-time updated control law:

[0119]

[0120] k u and k c are linear feedback coefficients.

[0121] Step 11. Prove the stability of the designed controller according to Lyapunov's second method.

[0122] The Lyapunov function of the system is defined as:

[0123]

[0124] Among them, p m is a positive definite matrix, e(k)=|x(k)-x0|.

[0125] For the sake of proof, let p m =diag(c1,c2,...,c m ). The Lyapunov function is positive definite for the system.

[0126] The difference between Lyapunov functions within one time step is:

[0127] ΔV m (k) = V m (e(k+1))-V m (e(k)) (18),

[0128] Substituting into the Lyapunov function, we can get:

[0129]

[0130] Among them, e(k+1)+e(k)≥0(20).

[0131] Since the objective function is required to be minimized at each controller sampling moment, according to the definition of the objective function, the error variable is gradually reduced in the control algorithm, assuming that the system is observable, thus obtaining Δe(k)≤0;

[0132] At this time, the Lyapunov function satisfies the following conditions:

[0133] (1)Vm [e(k)]≥0;

[0134] (2)ΔV m [e(k)]≤0.

[0135] According to Lyapunov's second method, the system under the LEMPC controller has asymptotic stability.

[0136] Step 12: Add the complex space environment disturbance in step 2 to the control model, and conduct comparative simulation analysis on the proposed LEMPC algorithm and MPC and LMPC algorithms.

[0137] Experimental Section

[0138] According to the first embodiment, the algorithm of the present invention is trained and tested in a simulation environment. For the on-orbit simulation of a large ring antenna satellite, MPC, LMPC and LEMPC control methods are used, such as Figure 4 It shows that the three methods have large oscillations in the initial stage due to the influence of the complex space environment. As the control process progresses, the model predictive controller gradually reduces the oscillation amplitude and finally completes the convergence of attitude and orbit control within 300 seconds. Compared with MPC, LMPC maintains similar dynamic characteristics while reducing the optimization order, and LEMPC further optimizes the control effect by solving the control law offline. It can be stable within 80 seconds, with smaller errors and stronger anti-interference ability, especially in the Y and Z axis angular velocity control.

[0139] Figure 5 It shows that the output of each thruster is within the constraint range, and the dual-platform configuration strategy meets the propulsion needs of the satellite. Orbital thrusters 3 and 6 are mainly responsible for north-south position maintenance, and the thrust amplitude varies due to the difference in center of mass distance. Microthrusters 1 and 5, 2 and 4 work in pairs to generate attitude control torque and are used for east-west position maintenance in the XZ plane.

[0140] Overall, the thrust fluctuations of MPC and LMPC are large, and the steady-state time is about 100 seconds. Shortening the prediction time can increase the calculation speed, but it will affect the attitude control. The initial thrust distribution of LEMPC is more aggressive, and then the oscillation decreases rapidly, showing the advantages of thrust optimization and rapid stabilization.

[0141] In terms of computational efficiency, Table 2 shows the average solution time of the three methods, and the total simulation time is 1500 seconds. LMPC reduces the 60-dimensional control sequence in MPC to 12 dimensions through the Laguerre function, and the average solution time is improved by about 82.2%. As the prediction sequence increases, the efficiency is further improved, but the control accuracy is reduced. EMPC and LEMPC use offline solution of control law and online table optimization, and the calculation speed is significantly better than MPC and LMPC.

[0142] Table 2 Average solution time and memory usage

[0143]

[0144] As online control algorithms, MPC and LMPC do not need to consider memory usage. LEMPC improves EMPC through Laguerre function, and the memory usage of the offline control law is optimized to 17.7% of the original, making it possible to deploy explicit model predictive control algorithms on simple hardware.

[0145] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control, characterized in that: The control input u(k+j) of the large ring antenna satellite is parameterized by Laguerre function, and the control input u(k+j) is reduced to obtain the decision variable η; The decision variable η is used to rewrite the dynamic model of the attitude and orbit of the large ring antenna satellite into a constrained Laguerre model predictive control form: in, It means that the objective function is minimized by solving the value of η, x(k) is the state of the large ring antenna satellite at time k, G=ΦQF, A is the system matrix of the relative orbital dynamics equation, B is the control matrix of the relative orbital dynamics equation, N p and N c are the prediction and control steps of Laguerre model predictive control, L(δ) is the δth Laguerre function set, δ=0,1,...,N p -1, Q and P are positive definite and semi-positive definite performance weight matrices, respectively; Defining variables The constrained Laguerre model predictive control form is transformed into an equivalent multi-parameter quadratic programming form: The multi-parameter quadratic programming form is explicitly solved to obtain the piecewise affine function z * []; The observation status of the large ring antenna satellite Substitute the piecewise affine function z * [], and then construct the attitude and orbit control input u(k) of the large ring antenna satellite:

2. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 1 is characterized in that: The control input u(k+j) of the large ring antenna satellite is expressed as: Among them, l i (j) represents the control vector of the i-th row in the j-th Laguerre function set L(j), n represents the dimension of the control vector, i = 1, 2, ..., n.

3. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 2 is characterized in that: The control vector in the Laguerre function set satisfies: in, a i is the Laguerre function network scaling factor, N i is the number of expansion items of the Laguerre function.

4. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 1 is characterized in that: Based on the spacecraft kinematic equations and the attitude dynamics equations described by dual quaternions, the dynamic model of the attitude and orbit of a large ring antenna satellite is established, and its expression is: Where x is the state vector of the antenna satellite relative to the nominal orbit, Representing quaternions, we have and q and q4 are the vector and scalar parts of the quaternion respectively; ω b is the angular velocity of the antenna satellite relative to the orbit, Y is the thrust of the propeller and the interference force of the space environment acting on the antenna satellite, J is the inertia matrix of the antenna satellite, ω is the absolute angular velocity of the antenna satellite in the inertial system, is the skew matrix of ω, T bo is the rotation matrix of the antenna satellite from the orbital coordinate system to the body coordinate system, T is the composite torque of the control torque generated by the propulsion system and the space environment interference torque, Yes b The skew matrix of ω0 is the steady orbital angular velocity.

5. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 4 is characterized in that: The interference factors of the space environment interference force acting on the antenna satellite include solar pressure, non-spherical perturbation and three-body gravity; Solar pressure acceleration a spp : Among them, C R is the surface reflection coefficient of the satellite, ρ SR is the solar pressure constant, g is the insolation factor, AU is 1 astronomical unit, r Sun is the position vector of the sun in the geocentric inertial system, e D represents the unit vector pointing from the satellite to the sun; S Ref It represents the equivalent sun-receiving area of ​​a large ring antenna satellite, and m is the satellite mass; The gravity gradient moment under the influence of non-spherical gravitational perturbation is: Among them, T gx 、T gy 、T gz are the x-, y-, and z-axis components of the gravity gradient torque in the current system, R C is the height of the geostationary orbit, μ is the gravitational constant of the earth, I x ,I y ,I z The x, y, and z axes moments of inertia in the moment of inertia matrix of the large ring antenna satellite are represented by θ and are the pitch angle and the roll angle respectively; Three-body perturbation acceleration a TBP : Among them, μ Sun and μ Moon are the gravitational constants of the sun and the moon, r Sun2Sat is the position of the sun relative to the satellite in the geocentric inertial system, r Moon2Sat is the position of the moon relative to the satellite in the geocentric inertial system; r Moon is the position vector of the moon in the geocentric inertial system.

6. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 5 is characterized in that: The thruster installation matrix acting on the antenna satellite is: Among them, c = cosα, s = sinα, α is the thruster direction and the inclination angle of the mounting surface, a, b, d are the length, width and height of the satellite body respectively, L1 and L2 are the distances from the satellite body and the feed platform to the center of mass of the antenna satellite respectively.

7. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 1 is characterized in that: The method of rewriting the dynamic model of the attitude and orbit of the large-scale ring antenna satellite into a constrained Laguerre model predictive control form by using the decision variable η includes: The dynamic model of the attitude and orbit of the large ring antenna satellite is linearized and discretized and written into a compact form; The objective function and constraints of the compact form model are combined into a constrained Laguerre model predictive control form.

8. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 7 is characterized in that: The dynamic model of the large-scale ring antenna satellite attitude and orbit is linearized and discretized to obtain:

9. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 8 is characterized in that: The compact form model expression is: X=Fx(k)+Φη.

10. The large-scale ring antenna satellite attitude and orbit integrated control method based on improved explicit model predictive control according to claim 9, characterized in that: The objective function of the compact form model is expressed as: Where ψ represents the objective function; The constraints of the objective function are: Among them, u M To control the maximum value of the input, I is the j-dimensional unit matrix.

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