A segmented optimal attitude tracking control method for gravity gradient satellite

Abstract

The present application relates to a kind of gravity gradient satellite segmented optimal attitude tracking control method, the present application is aimed at satellite platform, coiled stretch arm and the gravity gradient system of end payload three compositions, adopt dumbbell model to describe its swing motion in coplanar orbit transfer, establish the attitude dynamics model of gravity gradient satellite;Orbit dynamics model is established based on electric propulsion coplanar orbit transfer.Segmented optimal trajectory of gravity gradient satellite under the action of electric propulsion is obtained by designing optimal controller, while realizing the orbit transfer between two coplanar circular orbits, the stability and robustness of system are enhanced.On this basis, based on finite time tracking error function, a kind of segmented adaptive terminal sliding mode control method is designed, the problem of finite time convergence and uncertainty boundary is solved.The present application is specific object in the gravity gradient satellite of coplanar orbit transfer, the control method proposed is conducive to the improvement of control performance, easy to realize.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of space control system, and particularly relates to a segmented optimal attitude tracking control method for a gravity gradient satellite. BACKGROUND

[0002] Various effects in space environment pose a serious threat to the safe operation of on-orbit spacecraft and the physical health of astronauts, so it is necessary to carry out space environment detection and research. Under this background, a gravity gradient satellite composed of a satellite platform, a coiled extension arm and an end payload has broad application prospects. The coiled extension arm, as a typical one-dimensional flexible deployment mechanism, has the advantages of light weight, small power consumption and large deployment and folding ratio, and is very important for microsatellites with limited resources on board. The end payload includes cameras, X-ray spectrometers and microwave radiometers, which can be used for local observation of space physical data. In order to obtain large-scale space data, the payload needs to detect the space environment on different orbits, so there is a problem of orbit transfer. In practical applications, conventional pulse orbit transfer methods such as single-pulse orbit transfer and three-pulse orbit transfer are usually used. However, due to the obvious low-frequency, dense-mode and nonlinear dynamic characteristics of the coiled extension arm system, a small load may also cause a large vibration. Therefore, the sudden impact of pulse thrust is not suitable for gravity gradient microsatellites with coiled extension arms, and continuous thrust is more suitable for orbit transfer of gravity gradient microsatellites with coiled extension arms. With the advancement of electric propulsion technology, using small, continuous and constant thrust has become a practical and effective method to achieve orbit transfer between two orbits. However, most of the current domestic researches are on modeling, dynamic analysis and control of gravity gradient systems on Kepler orbits, and there are few studies on gravity gradient systems in orbit transfer, and no effective control method has been proposed.

[0003] The present application designs a segmented optimal attitude tracking control method for a gravity gradient satellite based on electric propulsion orbit transfer. The method can solve the problems of finite time convergence and uncertainty boundary by designing a segmented optimal trajectory and a segmented adaptive terminal sliding mode control method based on a finite time tracking error function, and can enhance the stability and robustness of the system. SUMMARY

[0004] The present application solves the problem of attitude control of a gravity gradient satellite for space environment detection during coplanar orbit transfer. For a rigid body-flexible appendage-rigid body gravity gradient system in orbit transfer, a segmented optimal attitude tracking control method for a gravity gradient satellite is provided.

[0005] To achieve the above object, the present application provides the following technical solutions:

[0006] A gravity gradient satellite segmented optimal attitude tracking control method, the gravity gradient satellite is composed of a satellite platform, a coiled stretching arm and an end payload, the method comprises the following steps:

[0007] S01, establishing attitude dynamics and orbit dynamics model of the system;

[0008] S02, designing segmented optimal trajectory;

[0009] S03, designing segmented adaptive terminal sliding mode controller.

[0010] As a further technical solution of the application, in step S01, a second-order attitude dynamics model of the gravity gradient satellite is established based on a dumbbell model, and an orbit dynamics model of the gravity gradient satellite is established based on an electric thrust coplanar orbit transfer, the attitude dynamics equation is:

[0011]

[0012] Wherein, x1=θ represents the satellite pitch angle, x2=θ represents the satellite pitch angle velocity, x a =[x1,x2] T ;Δf a (x a ,t) represents the uncertainty of the system, ||Δf a (x a ,t)| x =Δf max (x a ,t), Δd a (x a ,t) is an external disturbance, ||Δd a (x a ,t)| ∞ =Δd max (x a ,t); b=cos(γ-θ)I -1 , the expression of f a (x a ,t) is:

[0013]

[0014] Wherein, γ is defined as the thrust direction angle between the lateral component F α of the electric thrust and the electric thrust F;

[0015] The orbit dynamics equation is:

[0016]

[0017] Wherein, x3=[r,α] T , xb = [x3, x4] T r is the distance from the Earth's center, α is the polar angle, and Δd b (x b ,t) is the disturbance vector, f b (x b The expression for t is:

[0018]

[0019] Among them, F γ =F(M+m) -1 [sinγ,r -1 cosγ] T This represents the horizontal component of the electric thrust.

[0020] As a further technical solution of the present invention, in step S02, a close-loop optimal control method is designed, and multiple open-loop optimization calculations are performed under the performance constraints of the airborne computer to obtain the segmented optimal trajectory.

[0021] As a further technical solution of the present invention, in step S03, the step of designing a segmented adaptive terminal sliding mode controller includes: designing a finite-time tracking error function; and designing a segmented adaptive terminal sliding mode controller based on the finite-time tracking error function.

[0022] The step of designing the finite-time tracking error function includes: in the period t∈[t i-1 , t i+1 Within [the context], define e(t) = θ(t) - θ c (t) represents the tracking error, where θ c (t) represents the desired pitch angle;

[0023] Define e i (t) represents the desired tracking error. To ensure finite-time convergence, e is... i (t) is defined as a polynomial function:

[0024]

[0025] in, k A =(tt) i-1 )(t i -t i-1 ) -1 ;

[0026] In the definition of the tracking error function, e i (t i-1 )e(t i-1 ), e i (ti ) = 0, It is shown that the system is on the sliding surface at time ti-1, and the reaching phase is eliminated; in addition, ei(t) is convergent to zero in finite time t i -t i-1 approaches 0.

[0027] As a further technical solution of the present application, in step S03, the step of designing the piecewise adaptive terminal sliding mode controller based on the finite time tracking error function comprises:

[0028] The system uncertainty Δf a (x a , t) and external disturbance Δd a (x a , t) satisfy the following inequality in period t ∈ [t i-1 , t i+1 ]:

[0029] ||Δf a (x a , t) + Δd a (x a , t)|| ≤ σ1 + σ2 · ||x a ||;

[0030] wherein, σ1 and σ2 are non-negative constants, θ and are determined by sensors, so and ||x a || are known before the controller is executed;

[0031] Define σ1' and σ2' as the estimated values of adaptive parameters, the expressions of errors e σ1 and e σ2 are as follows:

[0032] e σ1 = σ1' - σ1, e σ2 = σ2' - σ2;

[0033] Based on the attitude dynamics equation, the expected tracking error function and the inequality of uncertainty and system disturbance, the sliding surface is designed as s = c (E - E i ), wherein, c = [c, 1], and t ∈ [t i-1 , t i+1 ], the terminal sliding mode controller is designed as follows:

[0034]

[0035] wherein, η = η0 + σ1' + σ2' · ||x a ||, and η0 > 0;

[0036] In addition, the estimated value of the adaptive parameter satisfies the following equation:

[0037]

[0038] where p and q are positive values, and σ1'(0) and σ2'(0) are initial values of σ1' and σ2'.

[0039] Compared with the prior art, the present application has the following advantages:

[0040] The present application is directed to a gravity gradient satellite in orbit transfer, adopts a dumbbell model to describe the swing motion of the gravity gradient satellite in coplanar orbit transfer, and establishes attitude dynamics; and establishes an orbit dynamics model based on electric propulsion coplanar orbit transfer. The model fully considers the structural characteristics and mechanical properties of each component of the gravity gradient satellite, and simplifies the problem as much as possible under the premise of ensuring the reliability and accuracy of the model. Based on close-loop (CL) optimal control, a piecewise optimal trajectory is designed, which fully considers the influence of calculation delay, eliminates the optimal trajectory deviation caused by the uncertainty of the system and external disturbance, and improves the stability and robustness of the system. On this basis, a finite time tracking error function is designed to soften the chattering of the system and ensure the stability and robustness of the system in each cycle. Based on the finite time tracking error function, an adaptive terminal sliding mode control method is designed to realize the attitude tracking in each cycle, and the problems of finite time convergence and uncertainty boundary are solved.

[0041] The piecewise optimal attitude tracking control method proposed in the present application is beneficial to improve the control performance, has a simple structure, is easy to implement, and has practical engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 FIG. 1 is a schematic diagram of the structure of a gravity gradient satellite.

[0043] Figure 2 FIG. 4 is a schematic diagram of a dumbbell model of a gravity gradient satellite.

[0044] Figure 3 FIG. 6 is a flow chart of close-loop optimal control.

[0045] Figure 4 FIG. 8 is a principle block diagram of the piecewise optimal attitude tracking control method.

[0046] Figure 5 FIG. 11 is a time response curve under different cost functions.

[0047] Figure 6 FIG. 13 is a time response curve under different control methods.

[0048] Figure 7Time response curve under the segmented attitude tracking control method. DETAILED DESCRIPTION

[0049] The technical solutions of the patent will be further described in detail in combination with specific embodiments.

[0050] Referring to Figure 1 The gravity gradient satellite comprises a satellite platform, a coiled stretching arm and an end payload. Compared with the satellite platform and the payload, the coiled stretching arm has a small mass and a long length, and its mass can be ignored in the study of the swing motion. In addition, the rotation around the coiled stretching arm has little effect on the swing motion, and the momentum wheel can also damp it. Figure 2 In this paper, a dumbbell model is used to describe the swing motion of the gravity gradient satellite in orbit transfer.

[0051] Referring to Figure 3 and Figure 4 A segmented optimal attitude tracking control method for a gravity gradient satellite, the method comprising the following steps:

[0052] S01, establishing the attitude dynamics and orbit dynamics model of the system;

[0053] In the dumbbell model, because the rotation around the coiled stretching arm has little effect on the swing motion, the yaw angle Ψ is not discussed; and the invention studies coplanar orbit transfer, and the transfer orbit is in a plane, so the attitude motion can be considered as two-dimensional, and the roll angle Φ is always 0; in addition, although there is atmospheric resistance in the orbit transfer process, the atmospheric resistance is less than 10 -5 N, the electric thrust is between 10 -3 -10 -2 N, and the gravity gradient force is greater than 10 -3 N, so the atmospheric resistance can be ignored. Based on the dumbbell model, the attitude dynamics model of the gravity gradient satellite is established, the model is as simple as possible while ensuring its accuracy and reliability, and the attitude dynamics equation is:

[0054]

[0055] Wherein, x1=θ represents the satellite pitch angle, x2=θ represents the satellite pitch angle velocity, x a =[x1, x2] T ; Δf a (x a , t) represents the uncertainty of the system, Δf a (x a , t)| ∞ =Δf max (x a , t), Δd a(x a , t) is the external disturbance,

[0056] ||Δd a (x a , t)| ∞ = Δd max (x a , t); b = cos(γ - θ) -1 , f a (x a , t) is given by:

[0057]

[0058] where γ is defined as the thrust direction angle between the lateral component of the electric thrust F α and the electric thrust F;

[0059] The orbit dynamics equation is:

[0060]

[0061] where x3 = [r, α] T , x b = [x3, x4] T ; r is the geocentric distance, α is the polar angle, Δd b (x b , t) is the disturbance vector, f b (x b , t) is given by:

[0062]

[0063] where F γ = F(M + m) -1 [sin γ, r -1 cos γ] T is the horizontal component of the electric thrust.

[0064] S02, design a piecewise optimal trajectory;

[0065] According to the description of the orbit transfer, let x = [x a , x b ] T , u = γ, M c = 0, and the boundary conditions are as follows:

[0066]

[0067]

[0068] where r0 is the initial geocentric distance, r fis the final geocentric distance, a0 is the initial polar angle, a f is the final polar angle;

[0069] The expression of the cost function is as follows:

[0070]

[0071] The application applies MATLAB software General Pseudospectral Optimization Software (GPOPS) to solve the optimal control problem.

[0072] In engineering, the uncertainty of the system and external disturbance can cause significant deviation of the optimal trajectory. In order to improve the stability and robustness of the system, the application adopts the method of close-loop (CL) optimal control to perform multiple open-loop (OL) optimization calculations under the performance constraint of the onboard computer. The specific steps are as follows:

[0073] 1) At t0, the OL optimal controller generates the optimal trajectory x 0 (t) and the optimal control variable u 0 (t), wherein t is in [t0, t f ], at this time, the gravity gradient satellite is driven by u 0 (t);

[0074] 2) At t1 or t i (i=3, 5,...), the OL optimal controller starts to calculate the new optimal trajectory x 1 (t) or x i (t) and the new optimal control variable u 1 (t) or u i (t), wherein t is in [t1, t f ] or t is in [t i , t f ], due to the time delay, at this time, the gravity gradient satellite is still driven by u 0 (t) or u i-2 (t);

[0075] 3) At t2 or t i+1 (i=3, 5,...), the gravity gradient satellite is driven by u 1 (t) or u i (t) instead of u 0 (t) or u i-2 (t), wherein t is in [t2, t f ] or t is in [t i+1 , t f ];

[0076] 4) At t3 or ti+2 A new cycle starts at time i = 3, 5,... and lasts T c = t i+2 -t i；

[0077] 5) At time t k , the last cycle ends and T c < t f -t k <2T c .

[0078] In the process of designing the optimal controller, the influence of time delay is fully considered. Time delay mainly includes calculation delay and driving delay. Calculation delay is variable, related to the control accuracy, calculation efficiency and performance of the computer, and can be measured in hardware testing, generally in the range of 10-60s. Driving time is relatively constant, related to response time, start-up time and acceleration, and can also be measured in hardware testing, in the range of 0.1-10s.

[0079] The proposed method is mainly used to track the optimal attitude trajectory, without considering the orbit motion of the gravity gradient microsatellite. The main reasons include two aspects: (1) The orbit disturbance can be ignored relative to the thrust. Moreover, the main disturbance is the control accuracy Δγ, which is limited and inevitable. (2) For the orbit motion, the influence of system uncertainty and external disturbance is particularly obvious. Moreover, if the expected attitude at time ti cannot be guaranteed, the newly updated trajectory may change greatly, which will reduce the optimal performance to some extent.

[0080] By the proposed optimal controller, the optimal trajectory is divided into several cycles. In each cycle t ∈ [t i-1 , t i+1 ], although the actual trajectory x(t) is close to x i (t), it does not constitute a closed-loop system. In order to further improve the accuracy and robustness of the system, segmented attitude tracking control is also needed in each cycle using momentum wheels.

[0081] S03、designing a segmented adaptive terminal sliding mode controller, proposing segmented attitude tracking control to improve the control accuracy in the cycle t ∈ [t i-1 , t i+1 ].

[0082] In step S03, the step of designing a segmented adaptive terminal sliding mode controller includes: designing a finite-time tracking error function; based on the finite-time tracking error function, designing a segmented adaptive terminal sliding mode controller.

[0083] The step of designing the finite-time tracking error function includes: in the period t∈[t i-1 ,t i+1 Within [the context], define e(t) = θ(t) - θ c (t) represents the tracking error, where θ c (t) represents the desired pitch angle;

[0084] Define e i (t) represents the desired tracking error. To ensure finite-time convergence, e is... i (t) is defined as a polynomial function:

[0085]

[0086] in, k A =(tt) i-1 )(t i -t i-1 ) -1 ;

[0087] In the definition of the tracking error function, e i (t i-1 )=e(t i-1 ), e i (t i ) = 0, This indicates that the system is on the sliding surface at time ti-1, eliminating the arrival segment; furthermore, ei(t) in finite time t i -t i-1 Close to 0.

[0088] In step S03, the step of designing a piecewise adaptive terminal sliding mode controller based on the finite-time tracking error function includes:

[0089] In the dynamic model, the system's uncertainty Δf a (x a The error (t) mainly stems from the measurement error of the moment of inertia, which is typically measured precisely before satellite launch. External disturbance Δd a (x a The torque (t) mainly originates from the space environment, including solar radiation torque, aerodynamic torque, and geomagnetic torque, and its value is typically less than 10. -6 Nm. Therefore, both the uncertainty of the system and external disturbances are bounded. This invention employs an adaptive method to address the uncertainty boundary problem.

[0090] Define the system uncertainty Δf a (x a ,t) and external disturbance Δd a (x a, t) satisfies the following inequality: i-1 , t i+1 ] as follows:

[0091] Δf a (x a , t) + Δd a (x a , t) || ≤ σ1+ σ2·||x a ||;

[0092] where σ1and σ2are non-negative constants, θ and are determined by the sensors, so and ||x a || are known before the proposed controller is executed;

[0093] Let σ1′and σ2′be the estimates of the adaptive parameters, the expressions of the errors e σ1 and e σ2 are as follows:

[0094] e σ1 = σ1- σ1, e σ2 = σ2- σ2;

[0095] Based on the posture dynamics equation, the desired tracking error function and the inequality of uncertainty and system disturbance, the sliding mode surface is designed as s = c (E-E i ), where c = [c, 1], and t ∈ [t i-1 , t i+1 ], the terminal sliding mode controller is designed as follows:

[0096]

[0097] where η = η0+ σ1′+ σ2′·||x a ||, and η0> 0;

[0098] In addition, the estimates of the adaptive parameters satisfy the following equation:

[0099]

[0100] where p and q are positive values, σ1′(0) and σ2′(0) are the initial values of σ1′and σ2′.

[0101] The following specific examples are proposed in combination with the above embodiments, and the following specific examples are only exemplary descriptions of the specific implementation of the above embodiments, and do not limit the technical solutions of the above embodiments.

[0102] Simulation experiments are performed based on the gravity gradient micro-satellite SSS-1, which consists of a satellite platform (35 kg), a coiled boom (0.3 kg, 2.3 m) and a terminal payload (5 kg). According to the dumbbell model, I = Mm(M + m) -1 l 2 = 22.67 kg m 2 ; the electric thrust is 3 mN. In order to obtain a wide range of space data, the orbit height is increased or decreased by at least 1 km in one orbit transfer, and a change of 10-20 km can be achieved by multiple maneuvers.

[0103] Before orbit transfer, the gravity gradient satellite points to the earth, the pitch angle θ0= 0 rad, and is in the equilibrium position. During orbit transfer, the gravity gradient satellite does not need to explore the space environment, so it does not need to limit the pitch angle θ, and the equilibrium position no longer exists. However, in order to avoid strong vibration of the coiled boom, the pitch angle velocity

[0104] The simulation parameters are as follows:

[0105] F = 3 mN

[0106] r0= 7000 km

[0107] r f = 7001 km

[0108]

[0109]

[0110]

[0111]

[0112] θ0= 0 rad

[0113] θ f = 0 rad

[0114]

[0115]

[0116] In GPOPS, the number of nodes n ∈ [6, 12], and the error accuracy is less than 10 -6 . First, the OL optimal control is adopted without considering external disturbances. Let |γ| ≤ 70°, and take the cost functions as 1 and L = 1 means that the orbit transfer time is the shortest, and L = θ 2 means that the change of the pitch angle θ is the smallest, see Figure 5When the cost function L = 1, the thrust direction angle y varies between -30° and 30°, and the orbital transfer time t f =6623s, pitch angle θ varies within the range of -180° to 40°, pitch angular velocity It varies within the range of -0.6° / s to 0.6° / s. Relative to the cost function. When L = i, θ varies over a wider range, but the y-curve is smoother, which is easier to implement in engineering. Conversely, if the cost function... Although θ varies within a smaller range of -160° to 20°, the orbital transfer time t f =9903s, and γ also changes drastically, which violates flight safety.

[0117] In engineering, system uncertainties and external disturbances are not negligible. Generally, let the external disturbance be Δγ = 1°sin(100t), Δd... a =10 -6 The system uncertainty is I = 1.5 kg·m·s, given by cos(100t) N·m·s. 2 The simulation results are as follows Figure 6 As shown. Simulation results show that when OL optimal control is executed and L=1 is taken, the pitch angle θ reaches 163.1° at the final moment, which does not meet the requirements of OL optimal control. This indicates that the influence of system uncertainty and external disturbances on the oscillating motion is not negligible. To enhance robustness to disturbances, CL optimal control is used to obtain the segmented optimal trajectory. Considering the computation time delay, the period is set to 200s. Simulation results show that the pitch angle reaches 28.8° at the final moment, but the orbital transfer time t... f The timeframe was extended to 6837s. Compared with the results of OL optimal control, CL optimal control showed some improvement in control performance, but it still could not meet the control requirements. Therefore, it is necessary to design a piecewise attitude tracking control method.

[0118] The controller parameters are as follows:

[0119] p = 1

[0120] q=1

[0121] c = 1

[0122] η0 = 0.1;

[0123] σ1′(0)=0

[0124] σ2′(0)=0;

[0125] Figure 7The simulation results of the piecewise optimal attitude tracking control method for a gravity gradient satellite using the electric orbit transfer. The simulation results show that the pitch angle θ effectively tracks the piecewise optimal trajectory in the orbit transfer. θ varies in the range of -180° to 40° and reaches 0° at the final time. In addition, t f is 6652 s, which is shorter than that of the CL optimal control. In summary, the results are significantly improved by using the proposed controller.

[0126] It is apparent for those skilled in the art that the present application is not limited to the details of the foregoing exemplary embodiments, and the present application can be carried out in other concrete forms without departing from the spirit or basic characteristics of the present application. Accordingly, the embodiments are to be considered in all respects as illustrative and not restrictive, the scope of the present application being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

[0127] Furthermore, it should be understood that although the description is made according to the embodiments, not every embodiment contains only one independent technical solution, and the description is made in this way only for the sake of clarity, and those skilled in the art should consider the description as a whole, and the technical solutions in each embodiment can also be combined appropriately to form other embodiments which can be understood by those skilled in the art.

Claims

1. A segmented optimal attitude tracking control method for a gravity gradient satellite, wherein the gravity gradient satellite comprises a satellite platform, a coiled extendable arm, and an end-effector payload, characterized in that, The method includes the following steps: S01. Establish the system's attitude dynamics and orbital dynamics models; S02. Design the optimal segmented trajectory; S03. Design a segmented adaptive terminal sliding mode controller; In step S01, a second-order attitude dynamics model of the gravity gradient satellite is established based on the dumbbell model, and an orbital dynamics model of the gravity gradient satellite is established based on the electric propulsion coplanar orbit transfer. The attitude dynamics equations are: ； Where x1=θ represents the satellite pitch angle, and x2 represents the satellite pitch angular velocity. ; This indicates the uncertainty of the system. , It is an external disturbance. ; , The expression is: ； Wherein, γ is defined as the transverse component of electric thrust F α The thrust direction angle between the electric thrust F and the thrust direction angle; The orbital dynamics equations are: ； in, , , r is the distance from the Earth's center, and α is the polar angle. It is a disturbance vector. The expression is: ； in, This refers to the horizontal component of the electric thrust. In step S02, a close-loop optimal control method is designed, and multiple open-loop optimization calculations are performed under the performance constraints of the onboard computer to obtain the segmented optimal trajectory. The steps are as follows: 1) At time t0, the OL optimal controller pre-generates the optimal trajectory x. 0 (t) and optimal control variable u 0 (t), where t∈[t0,t] f At this time, the gravity gradient satellite is caused by u 0 (t) drive; 2) At time t1, the OL optimal controller begins to calculate the new optimal trajectory x. 1 (t) and the new optimal control variable u 1 (t), where t∈[t1,t2] f Due to the time delay, the gravity gradient satellite is still controlled by u. 0 (t) drive; 3) At time t2, by u 1 (t) replaces u 0 (t) drives the gravity gradient satellite, where t∈[t2,t3] f ]; 4) At time t3, a new period begins, and the duration of the period is T. c =t i+2 -t i； 5) At t k At time T, the last cycle begins, and T c <t f -t k <2T c ; In step S03, the step of designing a piecewise adaptive terminal sliding mode controller includes: designing a finite-time tracking error function; and designing a piecewise adaptive terminal sliding mode controller based on the finite-time tracking error function. The step of designing the finite-time tracking error function includes: in the period t∈[t i-1 ,t i+1 Within [the context], define e(t) = θ(t) - θ c (t) represents the tracking error, where θ c (t) represents the desired pitch angle; Define e i (t) represents the desired tracking error. To ensure finite-time convergence, e is... i (t) is defined as a polynomial function: ； in, , ; In the definition of the tracking error function , , , , , This indicates that the system is on the sliding surface at time ti-1, eliminating the arrival segment; furthermore, ei(t) in finite time t i -t i-1 Close to 0.

2. The gravity gradient satellite segmented optimal attitude tracking control method according to claim 1, characterized in that, In step S03, the step of designing a piecewise adaptive terminal sliding mode controller based on the finite-time tracking error function includes: Setting system uncertainty ∆f a (x a ,t) and external disturbance ∆d a (x a ,t) in period t∈[t i-1 ,t i+1 The following inequalities are satisfied in [the following context:] ； Where σ1 and σ2 are nonnegative constants, θ and Determined by the sensor, therefore and ||x a ||It is known before the proposed controller is executed; definition and The error e is the estimated value of the adaptive parameter. σ1 and e σ2 The expression is as follows: ； Based on the attitude dynamics equations, the desired tracking error function, and the uncertainties and system disturbance inequalities, the sliding surface is designed as... ,in, , , ,and The terminal sliding mode controller is designed as follows: ； in, ,and ; Furthermore, the estimated values ​​of the adaptive parameters satisfy the following equation: ； Where p and q are positive values, and yes and The initial value.

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