Space solar power station attitude compound control method based on incremental PID and MPC

Abstract

The invention belongs to the technical field of space solar power station attitude control, and particularly relates to a space solar power station attitude compound control method based on incremental PID and MPC. In the initial stage of attitude adjustment, the incremental PID controller quickly compensates errors, and the response time of the system is shortened; and when the attitude is close to the target state, the MPC controller takes over the system and carries out accurate adjustment by predicting future attitude change, so that the system is ensured to stably and accurately reach the target attitude. Through a composite control method combining incremental PID and MPC, the defects in the prior art are overcome, the method has the advantages of being high in response speed, high in control precision, high in system robustness and the like, the attitude control capability of the space solar power station can be effectively improved, and the method has wide application prospects in a complex multi-rotary-joint structure and is suitable for popularization and application. And a more efficient solution is provided for solar energy utilization in the future.

Description

Technical Field

[0001] The present invention belongs to the technical field of attitude control of space solar power stations, and in particular relates to an attitude composite control method of a space solar power station based on incremental PID and MPC. Background Art

[0002] As global energy demand grows, solar energy, as a renewable and clean energy source, plays an important role in energy supply. Space Solar Power Station (SSPS) can effectively avoid absorption and scattering by the atmosphere, can receive solar energy all day and convert it into electrical energy, and has broad application prospects. However, the structure of space solar power stations is complex, especially its attitude control is one of the key technologies to achieve efficient energy capture. The China Academy of Space Technology compared typical domestic and international configurations and proposed a multi-rotation joint space solar power station. This type of space solar power station needs to have precise attitude adjustment capabilities to ensure that its battery array is always facing the sun, maximizing the reception of solar radiation, and the antenna is directional tracking the ground receiving station to continuously transmit energy. Due to the complex structure of the space solar power station, especially its multi-rotation joint design, the stability of the power station attitude is the key to ensure high-precision pointing of the antenna and efficient energy transmission. During the on-orbit operation of the power station, the attitude change of the central truss structure will directly affect the pointing accuracy of the antenna. If the attitude is not stable enough, the antenna will not be able to accurately point to the ground receiving station, resulting in a significant reduction in energy transmission efficiency.

[0003] In the field of traditional spacecraft attitude control and antenna pointing control, single control strategies are usually adopted, such as proportional integral derivative (PID) control, optimal control, and sliding mode control. These methods can effectively solve simple control problems to a certain extent. However, when faced with complex dynamic systems with multiple rotating joints, these traditional methods have great limitations in achieving high attitude stability and high antenna pointing accuracy. In particular, when the system is required to perform complex attitude adjustments and high-precision antenna pointing simultaneously, traditional control strategies often fail to meet strict requirements in terms of performance. In addition, the synchronous adjustment of attitude control and antenna pointing tasks will further increase the complexity of system control, resulting in reduced control accuracy and a significant increase in fuel consumption during the control process, thereby affecting the overall performance of the spacecraft. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a composite control method for the attitude of a space solar power station based on incremental PID and MPC. By combining the rapid response capability of incremental PID and the predictive control characteristics of model predictive control MPC, the on-orbit mission of the power station is divided into two stages: attitude stabilization and antenna pointing. A composite controller is designed to ensure the coordinated work of attitude adjustment and antenna pointing, so as to achieve efficient and stable control of complex attitude systems.

[0005] The space solar power station attitude composite control method based on incremental PID and MPC of the present invention comprises the following steps:

[0006] S1. The attitude coupling dynamics model of the multi-rotation joint space solar power station is established based on the Euler method. The multi-rotation joint space solar power station consists of a central truss structure, a microwave transmitting antenna, a solar panel, an attitude sensor, a controller and an actuator. The microwave transmitting antenna is hinged to the central truss and can rotate around its own pitch axis and roll axis to point to the ground receiving station with high precision. The solar panel can rotate around its own pitch axis to ensure that its photovoltaic array always maintains the best angle toward the sun. The attitude dynamics basic equation of the attitude coupling dynamics model is:

[0007]

[0008]

[0009] Among them, I b is the SPS moment of inertia matrix, I s(i) is the moment of inertia matrix of the ith solar panel, I m is the antenna moment of inertia matrix, R s(i) is the coupling matrix of the solar panel rotation to the central truss, R m Antenna rotation to the central truss coupling matrix, ω is the angular velocity of the central truss rotation, is the angular velocity of the solar panel, is the angular velocity of the antenna, T is the external moment on the central truss, T s(i) is the external torque on the solar panel, T m is the external torque acting on the antenna, “~” represents the skew-symmetric matrix of the vector;

[0010] The attitude dynamics equations (1)-(3) are expressed in matrix form:

[0011]

[0012] Where n represents the number of solar cell arrays.

[0013] Under the assumption of small attitude angle, the attitude angular velocity is linearized, which is specifically expressed as:

[0014]

[0015] in, θ and ψ are the roll angle, pitch angle and yaw angle of the central truss structure respectively, θ s(i) Rotate the pitch angle of the solar panel. θ m They are the roll angle and pitch angle of the antenna respectively;

[0016] The moment of inertia of a space solar power station will change with the rotation of the antenna and panels, expressed as:

[0017]

[0018] Among them, I b0 is the moment of inertia matrix of the central truss structure, are the position vectors of the center of mass of the solar panel and antenna in the main coordinate system, A s(i) , A m They are the coordinate rotation matrices of the solar panel and antenna respectively;

[0019]

[0020]

[0021] Substituting equations (5)-(7) into equation (4), we can obtain α s =[θ s(1) …θ s(i) …θ s(n) ] T , The linearized attitude dynamics equation is obtained:

[0022]

[0023] in,

[0024] S2. Set the initial attitude angle, system parameters and target attitude according to the initial state of the space solar power station, obtain the current attitude using the attitude sensor, and calculate the error between the current attitude and the target attitude;

[0025] S3, performing attitude adjustment according to the attitude error, dividing the attitude adjustment task of the power station into an attitude stabilization stage and an antenna pointing stage;

[0026] S3.1, attitude stabilization stage: First, adjust the overall attitude of the power station to achieve stable control of the central truss and antenna attitudes, and control the solar panel pointing to the sun, to ensure the high stability of the solar power station attitude. In this stage, the PID controller is used to quickly adjust the attitude error to reduce the dynamic deviation of the power station attitude. When the attitude error is reduced to the preset threshold, switch to the antenna pointing stage;

[0027] S3.2, antenna pointing stage: On the basis of attitude stabilization, enter the antenna pointing adjustment stage to achieve the integrated control of the center truss attitude stabilization, solar panel pointing to the sun, and antenna pointing to the ground. MPC is used to accurately point the antenna. By predicting the future state, the optimal control input of the antenna is calculated to ensure the high-precision pointing of the antenna to the ground receiving station. The expected attitude angle of the antenna is described as:

[0028]

[0029] Among them, t switch Switch control time for different stages;

[0030] S4. Construct a PID-MPC incremental composite controller and use incremental constraint control to constrain the increment of the control input to avoid sudden changes when switching between PID and MPC, ensure the control smoothness of the system, and reduce fuel consumption and attitude oscillation; take the state quantity as Transforming equation (11) into a state space equation, we get the discretization

[0031] system:

[0032]

[0033] The controller solves the control increment and adds it to the control amount at the previous moment to get the control amount at the new moment to act on the controlled object. The control amount at the new moment is expressed as:

[0034] u(k)=u(k-1)+Δu(k) (15)

[0035] In the attitude stabilization and antenna pointing stages, the incremental PID and MPC controllers are used respectively, and the control increment can be expressed as:

[0036]

[0037] S4.1, incremental PID controller: When the sampling period is small enough, a discrete PID can be obtained

[0038] Controlling expression:

[0039]

[0040] Incremental PID control is expressed as:

[0041] Δu PID (k) = K p (e(k)-e(k-1))+K i e(k)+K d (e(k)-2e(k-1)+e(k-2)) (18)

[0042] S4.2, Incremental MPC controller: Take the system prediction time domain as N p , the control time domain is N c , and N p =N c , based on the discretized system (13), the state of the subsystem in the prediction domain is predicted under the control action, and the predicted system state can be expressed as:

[0043]

[0044] in,

[0045] In order to enhance the robustness of the control system, the expected reference trajectory adopts a smooth tracking strategy.

[0046] Shown as:

[0047] x ie (k+j)=ρ j x(k+j|k)+(1-ρ j )x i-ref (20)

[0048] Among them, x i-ref is the actual expected reference trajectory, ρ is the softening coefficient, 0<ρ<1;

[0049] In the prediction time domain, a performance indicator function including state quantity and control increment is constructed to show

[0050] Shown as:

[0051]

[0052] Among them, Q i , R i is the subsystem weight matrix, and Q i >0、R i >0;

[0053] For the optimization objective of formula (21), it is transformed into:

[0054]

[0055] in,

[0056] In each control cycle, the optimal solution of equation (22) is obtained under the condition of satisfying (14) to obtain the control quantity sequence:

[0057]

[0058] The first element in the control sequence is used as the actual control variable to act on the system.

[0059] The beneficial effects of the present invention are:

[0060] (1) Fast response speed: Different from traditional PID control, incremental PID only adjusts the change in error in each control cycle, so it can effectively reduce the overshoot phenomenon of the system and respond quickly in the early stage of attitude adjustment to reduce attitude error.

[0061] (2) High control accuracy: The role of MPC in attitude control is to optimize the control input by predicting the future state of the system. Through the MPC prediction model, the system can achieve high-precision attitude adjustment in the fine control stage.

[0062] (3) Strong applicability: By rationally dividing the system’s mission phases, fuel consumption is reduced. The incremental constraint control method ensures the smoothness of controller switching, avoids sudden changes in attitude adjustment, and achieves a balance between high stability and high-precision control. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0064] Figure 1 It is a spatial configuration diagram of a multi-rotating joint space solar power station.

[0065] Figure 2 It is a schematic diagram of the two-stage attitude control of a space solar power station.

[0066] Figure 3 It is a curve diagram of attitude angle change of space solar power station.

[0067] Figure 4 It is the curve diagram of control torque variation of space solar power station.

[0068] Figure 5 It is a curve diagram of the change of pointing error of the space solar power station antenna.

[0069] Figure 6It is a curve diagram of the change of attitude angle of the antenna of the space solar power station.

[0070] Figure 7 It is a curve diagram of the control torque variation of the antenna of the space solar power station. DETAILED DESCRIPTION

[0071] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0072] like Figure 1 As shown in the figure, the multi-rotation joint space solar power station is a distributed spacecraft composed of multiple module components, which mainly consists of a central truss structure, a microwave transmitting antenna, a solar panel, an attitude sensor, a controller and an actuator. The microwave transmitting antenna is hinged to the central truss and can rotate around its own pitch axis and roll axis to be responsible for high-precision pointing to the ground receiving station; the solar panel can rotate around its own pitch axis to ensure that its photovoltaic array always maintains the best angle facing the sun.

[0073] Example 1

[0074] The space solar power station attitude composite control method based on incremental PID and MPC of this embodiment includes the following steps:

[0075] S1. Considering the coupling effect between the rotating joints and the influence of the vibration of the truss structure on the overall attitude, the attitude coupling dynamic model of the power station is established based on the Euler method, which mainly includes three parts: (1) the rotation equation of the central truss structure; (2) the rotation equation of the solar panel; (3) the rotation equation of the microwave transmitting antenna. This dynamic model is used to describe the attitude changes of the power station during its on-orbit operation, the pointing of the solar panel to the sun and the pointing of the antenna to the ground. The basic equation of attitude dynamics is:

[0076]

[0077] Among them, I b is the SPS moment of inertia matrix, I s(i) is the moment of inertia matrix of the ith solar panel, I m is the antenna moment of inertia matrix, R s(i) is the coupling matrix of the solar panel rotation to the central truss, R m Antenna rotation to the central truss coupling matrix, ω is the angular velocity of the central truss rotation, is the angular velocity of the solar panel, is the angular velocity of the antenna, T is the external moment on the central truss, T s(i) is the external torque on the solar panel, T m is the external torque acting on the antenna, and “~” represents the skew-symmetric matrix of the vector.

[0078] The attitude dynamics equations (1)-(3) can be expressed in matrix form:

[0079]

[0080] Wherein, n represents the number of solar cell arrays.

[0081] Under the assumption of small attitude angle, the attitude angular velocity can be linearized, which can be expressed as:

[0082]

[0083] in, θ and ψ are the roll angle, pitch angle and yaw angle of the central truss structure respectively, θ s(i) Rotate the pitch angle of the solar panel. θ m They are the roll angle and pitch angle of the antenna respectively.

[0084] The moment of inertia of a space solar power station will change with the rotation of the antenna and panels, which can be expressed as:

[0085]

[0086] Among them, I b0 is the moment of inertia matrix of the central truss structure, are the position vectors of the center of mass of the solar panel and antenna in the main coordinate system, A s(i) , A m They are the coordinate rotation matrices of the solar panel and antenna respectively.

[0087]

[0088] Substituting equations (5)-(7) into equation (4), we can obtain α s =[θ s(1) …θ s(i) …θ s(n) ] T , The linearized attitude dynamics equation is obtained:

[0089]

[0090] in,

[0091] S2. Set the initial attitude angle, system parameters and target attitude according to the initial state of the space solar power station, obtain the current attitude using the attitude sensor, and calculate the error between the current attitude and the target attitude;

[0092] S3. Perform attitude adjustment based on attitude error. The expected attitude angle of the antenna pointing to the ground is closely related to the system state. When the system has not reached a relatively stable state, it is not advisable to adjust the antenna attitude at the same time. Figure 2 As shown, the attitude adjustment task of the power station is divided into the attitude stabilization stage and the antenna pointing stage;

[0093] S3.1, attitude stabilization stage: First, adjust the overall attitude of the power station to achieve stable control of the central truss and antenna attitudes, and control the solar panel pointing to the sun, to ensure the high stability of the solar power station attitude. In this stage, the PID controller is used to quickly adjust the attitude error to reduce the dynamic deviation of the power station attitude. When the attitude error is reduced to the preset threshold, switch to the antenna pointing stage;

[0094] S3.2, antenna pointing stage: On the basis of attitude stabilization, enter the antenna pointing adjustment stage to achieve the integrated control of the center truss attitude stabilization, solar panel pointing to the sun, and antenna pointing to the ground. MPC is used to accurately point the antenna. By predicting the future state, the optimal control input of the antenna is calculated to ensure the high-precision pointing of the antenna to the ground receiving station. The expected attitude angle of the antenna is described as:

[0095]

[0096] Among them, t switch Switch control time for different stages;

[0097] S4, construct a PID-MPC incremental composite controller, taking the state quantity as Transforming equation (11) into a state space equation, we get the discretized system:

[0098]

[0099] In the present invention, a two-stage control scheme is adopted to realize SPS attitude control. However, when different controllers are used to solve, smooth switching between controllers needs to be realized. Saturation function, hyperbolic tangent function, etc. are often used as switching controllers of different controllers. In order to ensure smooth switching of control strategies, an incremental constraint control method is proposed. By constraining the increment of control input, sudden changes are avoided when switching between PID and MPC, the control smoothness of the system is guaranteed, and fuel consumption and attitude oscillation are reduced.

[0100]

[0101] The controller solves the control increment and adds it to the control amount at the previous moment to get the control amount at the new moment to act on the controlled object. The control amount at the new moment is expressed as:

[0102] u(k)=u(k-1)+Δu(k) (15)

[0103] In the attitude stabilization and antenna pointing stages, incremental PID and MPC controllers are used respectively. The control increment can be expressed as:

[0104]

[0105] (1) Incremental PID controller

[0106] When the sampling period is small enough, the discrete PID control expression can be obtained:

[0107]

[0108] It can be seen from equation (17) that the control output is related to the past deviation signal, and the deviation e(i) needs to be accumulated, which will take up a lot of computing performance and storage space. For this reason, we seek incremental PID control with higher computing performance. Incremental PID control can be expressed as:

[0109] Δu PID (k) = K p (e(k)-e(k-1))+K i e(k)+K d (e(k)-2e(k-1)+e(k-2)) (18)

[0110] (2) Incremental MPC controller

[0111] Take the system prediction time domain as N p , the control time domain is N c , and N p =N c , based on the discretized system (13), the state of the subsystem in the prediction domain is predicted under the control action, and the predicted system state can be expressed as:

[0112]

[0113] in,

[0114] In order to enhance the robustness of the control system, the expected reference trajectory adopts a smooth tracking strategy.

[0115] Shown as:

[0116] x ie (k+j)=ρ j x(k+j|k)+(1-ρ j )x i-ref (20)

[0117] Among them, x i-refis the actual expected reference trajectory, ρ is the softening coefficient, 0<ρ<1.

[0118] In the prediction time domain, a performance indicator function including state quantity and control increment is constructed to show

[0119] Shown as:

[0120]

[0121] Among them, Q i , R i is the subsystem weight matrix, and Q i >0、R i >0.

[0122] For the optimization objective of formula (21), it is transformed into:

[0123]

[0124] in,

[0125] In each control cycle, the optimal solution of equation (22) is obtained under the condition of satisfying (14).

[0126] To the control quantity sequence:

[0127]

[0128] The first element in the control sequence is used as the actual control variable to act on the system.

[0129] The posture control process in this embodiment includes the following steps:

[0130] Step 1: Initialization

[0131] The initial attitude angle, system parameters and target attitude are set according to the initial state of the space solar power station.

[0132] Step 2: Calculate the attitude error

[0133] The current posture is obtained by using the posture sensor, and the error between the current posture and the target posture is calculated.

[0134] Step 3: Incremental PID Control

[0135] According to the attitude error, the incremental PID controller first makes preliminary adjustments, responds quickly to reduce the attitude error, reduces system vibration, and ensures that the system smoothly enters a stable state.

[0136] Step 4: Incremental MPC Control

[0137] After the attitude error is reduced to a certain range, the MPC controller takes over the attitude control task and uses the prediction model to further optimize the control input to achieve high-precision attitude control of the power station.

[0138] Step 5: Posture adjustment completed

[0139] When the system reaches the target posture and the error meets the accuracy requirement, the controller stops adjusting and the system remains in a stable state.

[0140] Simulation Example

[0141] Aiming at the attitude control problem of multi-rotation joint space solar power station, the incremental PID-MPC composite control method of the present invention is used for attitude adjustment. The on-orbit simulation time is 4 hours, and the controller switching time is t switch = 2 hours. Assume that the initial posture angle of the main structure is α = [3°2°-1°] T , the attitude angular velocity is The microwave transmitting antenna is in the same posture as the central truss structure, the solar cell array is in a nominal state, and the attitude angle and angular velocity are both 0.

[0142] In the initial state, the system has a large error. First, the incremental PID controller is used to quickly adjust the attitude, so that the system attitude deviation can be reduced to within 0.1 degrees within 2 hours, which verifies that the strategy has the advantage of fast response speed in the early stage of control. Then it switches to the antenna pointing stage, and the MPC controller takes over the attitude control task, accurately adjusts the attitude to the target position, and controls the antenna pointing error within 0.001 degrees by predicting the future state. The simulation results show that Figure 3 As shown in the figure, there is an attitude error within 3° in the initial state. Through the rapid adjustment of the incremental PID controller, it is quickly reduced to within 0.1 degree within 2 hours, and then further accurately adjusted to the target position by the MPC controller. The rapidly declining part of the curve shows that the incremental PID controller has a fast response speed, while the flat part of the curve shows the precise control capability of the MPC controller. Figure 4 The time-varying curve of the control torque of the space solar power station is shown. The control torque is used to adjust the attitude of the space solar power station. In the initial stage, the control torque is large to quickly adjust the attitude; in the MPC control stage, the control torque becomes more refined to achieve precise attitude adjustment. Since the constraint on the control torque increment reduces the sudden change of the torque, a smooth transition of the control curve is achieved, which helps to protect the equipment. Figure 5 and Figure 6The curves of the pointing error and attitude angle change of the antenna of the space solar power station are shown. In the attitude stabilization stage, the antenna and the central truss structure remain relatively still. Once the system attitude deviation is reduced to within 0.1 degrees, the control strategy switches to the antenna pointing stage. At this time, the incremental MPC controller takes over the attitude control task. Through the precise adjustment of the MPC controller, the error is finally controlled within 0.001 degrees. The rapid decline of the curve and the final low error level show the advantages of the MPC controller in high-precision control. Figure 7 The change of the control torque used to adjust the antenna attitude over time is demonstrated. In the attitude stabilization stage, it is used to ensure the relative stability of the antenna and the central truss structure. When the central truss structure tends to be stable, a larger control torque is used to achieve precise ground pointing.

[0143] The embodiments of the present invention are described in detail above, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions and variations of these embodiments are made without departing from the principles and spirit of the present invention, and still fall within the protection scope of the present invention.

Claims

1. A composite control method for attitude of a space solar power station based on incremental PID and MPC, characterized in that: The following steps are involved: S1. The attitude coupling dynamics model of the multi-rotation joint space solar power station is established based on the Euler method. The multi-rotation joint space solar power station consists of a central truss structure, a microwave transmitting antenna, a solar panel, an attitude sensor, a controller and an actuator. The microwave transmitting antenna is hinged to the central truss and can rotate around its own pitch axis and roll axis to point to the ground receiving station with high precision. The solar panel can rotate around its own pitch axis to ensure that its photovoltaic array always maintains the best angle toward the sun. The attitude dynamics basic equation of the attitude coupling dynamics model is: Among them, I b is the SPS moment of inertia matrix, I s(i) is the moment of inertia matrix of the ith solar panel, I m is the antenna moment of inertia matrix, R s(i) is the coupling matrix of the solar panel rotation to the central truss, R m Antenna rotation to the central truss coupling matrix, ω is the angular velocity of the central truss rotation, is the angular velocity of the solar panel, is the angular velocity of the antenna, T is the external moment on the central truss, T s(i) is the external torque on the solar panel, T m is the external torque acting on the antenna, "~" represents the skew-symmetric matrix of the vector; The attitude dynamics equations (1)-(3) are expressed in matrix form: Where n represents the number of solar cell arrays. Under the assumption of small attitude angle, the attitude angular velocity is linearized, which is specifically expressed as: in, θ, ψ are the roll angle, pitch angle, and yaw angle of the central truss structure, θ s(i) Rotate the pitch angle of the solar panel. θ m They are the roll angle and pitch angle of the antenna respectively; The moment of inertia of a space solar power station will change with the rotation of the antenna and panels, expressed as: Among them, I b0 is the moment of inertia matrix of the central truss structure, are the position vectors of the center of mass of the solar panel and antenna in the main coordinate system, A s(i) , A m They are the coordinate rotation matrices of the solar panel and antenna respectively; Substituting equations (5)-(7) into equation (4), we can obtain α s =[θ s(1) … θ s(i) … θ s(n) ] T , The linearized attitude dynamics equation is obtained: in, S2. Set the initial attitude angle, system parameters and target attitude according to the initial state of the space solar power station, obtain the current attitude using the attitude sensor, and calculate the error between the current attitude and the target attitude; S3, performing attitude adjustment according to the attitude error, dividing the attitude adjustment task of the power station into an attitude stabilization stage and an antenna pointing stage; S3.1, attitude stabilization stage: First, adjust the overall attitude of the power station to achieve stable control of the central truss and antenna attitudes, and control the solar panel pointing to the sun, to ensure the high stability of the solar power station attitude. In this stage, the PID controller is used to quickly adjust the attitude error to reduce the dynamic deviation of the power station attitude. When the attitude error is reduced to the preset threshold, switch to the antenna pointing stage; S3.2, antenna pointing stage: On the basis of attitude stabilization, enter the antenna pointing adjustment stage to achieve the integrated control of the center truss attitude stabilization, solar panel pointing to the sun, and antenna pointing to the ground. MPC is used to accurately point the antenna. By predicting the future state, the optimal control input of the antenna is calculated to ensure the high-precision pointing of the antenna to the ground receiving station. The expected attitude angle of the antenna is described as: Among them, t switch Switch control time for different stages; S4. Construct a PID-MPC incremental composite controller and use incremental constraint control to constrain the increment of the control input to avoid sudden changes when switching between PID and MPC, ensure the control smoothness of the system, and reduce fuel consumption and attitude oscillation; take the state quantity as Transforming equation (11) into a state space equation, we get the discretized system: The controller solves the control increment and adds it to the control amount at the previous moment to get the control amount at the new moment to act on the controlled object. The control amount at the new moment is expressed as: u(k)=u(k-1)+Δu(k) (15) In the attitude stabilization and antenna pointing stages, the incremental PID and MPC controllers are used respectively, and the control increment can be expressed as: S4.1, Incremental PID controller: When the sampling period is small enough, the discrete PID control expression can be obtained: Incremental PID control is expressed as: Δu PID (k)=K p (e(k)-e(k-1))+K i e(k)+K d (e(k)-2e(k-1)+e(k-2)) (18) S4.2, Incremental MPC controller: Take the system prediction time domain as N p , the control time domain is N c , and N p =N c , based on the discretized system (13), the state of the subsystem in the prediction domain is predicted under the control action, and the predicted system state can be expressed as: in, In order to enhance the robustness of the control system, the expected reference trajectory adopts a smooth tracking strategy, which can be expressed as: x ie (k+j)=ρ j x(k+j|k)+(1-ρ j )x i-ref (20) Among them, x i-ref is the actual expected reference trajectory, ρ is the softening coefficient, 0<ρ<1; In the prediction time domain, a performance indicator function including state quantity and control increment is constructed, which is expressed as: Among them, Q i , R i is the subsystem weight matrix, and Q i >0、R i >0; For the optimization objective of formula (21), it is transformed into: in, In each control cycle, the optimal solution of equation (22) is obtained under the condition of satisfying (14) to obtain the control quantity sequence: The first element in the control sequence is used as the actual control variable to act on the system.

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