Remote sensing satellite attitude maneuver robust control method based on extended state observer

Abstract

The application relates to a remote sensing satellite attitude maneuver robust control method based on an extended state observer, relates to the technical field of remote sensing satellite attitude control, and solves the problem of control performance decline of a satellite in an attitude maneuver process when external disturbance exists. First, in combination with satellite dynamics and kinematics equations, the influence of external disturbance on the rigid body satellite maneuver process is considered, an improved composite nonlinear extended state observer is adopted, and the output of the observer is corrected by introducing the observation error values of two state variables. Secondly, an improved nonlinear integral sliding mode control method is adopted, a new attenuation function is introduced in the sliding mode area integral term, the attenuation function is prevented from being attenuated too fast when the error is large, and the attitude angle maneuver speed is improved. The application has better observation performance and shorter attitude angle maneuver time, and effectively improves the control precision of the satellite.

Description

Technical Field

[0001] The present invention relates to the technical field of remote sensing satellite attitude control, and in particular to a robust control method for remote sensing satellite attitude maneuvering based on an extended state observer. Background Art

[0002] With the continuous development of remote sensing technology in my country, the use of remote sensing satellites for earth observation and information collection has been widely used in various fields such as national defense, military, resource monitoring and emergency remote sensing. For example: Existing public literature, Zhang Liu, Zhang Xiaohan, Yue Qingxing, Liu Nian, Sun Kaipeng, Sun Jie, Fan Guowei. Optical remote sensing satellite staring imaging attitude planning and rapid simulation method. Journal of Jilin University (Engineering Edition), 2021, 51(1): 340-348. Due to the existence of various external disturbances in space, the attitude maneuvering process of the satellite is affected. Therefore, how to make the satellite have strong anti-interference ability (robustness) during the attitude maneuvering process has become a difficult problem that needs to be solved urgently.

[0003] To address these issues, two mainstream research approaches exist: designing robust control algorithms and designing observers to estimate and compensate for disturbances, thereby achieving attitude control. The latter approach, which can estimate and compensate for disturbances and improve system control accuracy, has become a research hotspot. In observer design, the extended state observer (ESO), a disturbance-tolerant observer design method that does not rely on disturbance signatures for estimation and compensation and exhibits excellent estimation performance for complex nonlinear systems, has seen rapid development. Summary of the Invention

[0004] In order to solve the problem that the control accuracy of a satellite decreases due to the influence of external disturbances during attitude maneuvers, thereby affecting its robustness, the present invention provides a nonlinear integral sliding mode control method based on an extended state observer.

[0005] The nonlinear integral sliding mode control method based on the extended state observer is implemented by the following steps:

[0006] Step 1: Based on the satellite attitude dynamics and kinematic equations, a model for rigid satellite attitude maneuver control is established;

[0007] Step 2: Based on the rigid satellite attitude maneuvering control model described in step 1, combined with the influence of external disturbance on the rigid satellite attitude maneuvering process, an extended state observer is designed to estimate the total disturbance of the system and output an estimated value of the external disturbance.

[0008] Step 3: Based on the rigid body satellite attitude maneuver control model described in step 1, a nonlinear integral sliding mode control method is designed, and the estimated value of the external disturbance output by the extended state observer described in step 2 is used to compensate the nonlinear integral sliding mode control output to realize remote sensing satellite attitude maneuver control.

[0009] Beneficial effects of the present invention:

[0010] This paper establishes a rigid satellite attitude maneuver control model by combining satellite dynamics and kinematic equations. Secondly, considering the impact of external disturbances on the rigid satellite maneuver process, an improved composite nonlinear extended state observer is proposed. By introducing the observation error values ​​of two state variables, the observer output is corrected, thereby improving the observer's convergence accuracy and convergence speed. Then, an improved nonlinear integral sliding mode control method is proposed. A new attenuation function is introduced into the sliding mode area component. This not only prevents integral saturation when the error is small, but also prevents the attenuation function from decaying too quickly when the error is large, thereby improving the maneuvering speed of the attitude angle. Finally, the convergence of the proposed extended state observer and the closed-loop stability of the sliding mode control method are demonstrated using the Lyapunov function.

[0011] Compared with existing methods, the extended state observer and product sliding mode control method proposed in the present invention have higher observer convergence accuracy and faster convergence speed, and shorter satellite attitude angle maneuvering time, which can provide a design basis for agile attitude maneuvering missions of remote sensing satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a principle block diagram of the nonlinear integral sliding mode control method based on the extended state observer described in the present invention;

[0013] Figure 2 Comparison of the three-axis disturbance estimation results of the expanded state observer before and after improvement; (a) is the comparison of the yaw axis disturbance estimation results before and after improvement; (b) is the comparison of the pitch axis disturbance estimation results before and after improvement; (c) is the comparison of the roll axis disturbance estimation results before and after improvement;

[0014] Figure 3 Comparison of the three-axis disturbance estimation errors of the expanded state observer before and after improvement; (a) is the comparison of the yaw axis disturbance estimation errors before and after improvement; (b) is the comparison of the pitch axis disturbance estimation errors before and after improvement; (c) is the comparison of the roll axis disturbance estimation errors before and after improvement;

[0015] Figure 4Comparison of the three-axis Euler angles of the integral sliding mode algorithm before and after improvement; (a) is the comparison of the yaw axis Euler angle before and after improvement; (b) is the comparison of the pitch axis Euler angle before and after improvement; (c) is the comparison of the roll axis Euler angle before and after improvement;

[0016] Figure 5 Comparison of the three-axis angular velocity of the integral sliding mode algorithm before and after improvement; (a) is the comparison of the yaw axis angular velocity before and after improvement; (b) is the comparison of the pitch axis angular velocity before and after improvement; (c) is the comparison of the roll axis angular velocity before and after improvement;

[0017] Figure 6 Comparison of the three-axis torque effects of the integral sliding mode algorithm before and after improvement. (a) Comparison of the roll axis angular velocity before and after improvement; (b) Comparison of the pitch axis torque before and after improvement; (c) Comparison of the roll axis torque before and after improvement. DETAILED DESCRIPTION

[0018] Combine Figures 1 to 6 This embodiment describes a remote sensing satellite attitude maneuver robust control method based on an extended state observer. The method is implemented by the following steps:

[0019] Step 1: Combine satellite attitude dynamics and kinematic equations to establish a model for rigid satellite attitude maneuver control;

[0020] In this implementation, a rigid satellite is used as the research object and a rigid satellite attitude maneuvering control model is established. Modified Rodrigues parameters (MRP) are used to describe the satellite attitude model due to their advantages of no singularity, simple parameters, and wide adaptability.

[0021] Definition of MRP parameters:

[0022]

[0023] Where ρ represents the modified Rodriguez parameter (current posture), represents the Euler axis direction, θ represents the Euler angle, and q0, q1, q2, and q3 represent the satellite attitude quaternion.

[0024] Define the attitude error ρ e =ρ-ρ d ,ρ represents the current posture,ρ d Indicates the target posture. Angular velocity error ω e =ω-ω d ,ω d =

[000] T ,ω represents the current attitude angular velocity, ω d Indicates the target attitude angular velocity.

[0025] The satellite attitude kinematic equation is established using the MRP parameters. The equation is as follows:

[0026]

[0027] Where,

[0028] The dynamic equation is established with the flywheel as the actuator, and the equation is as follows:

[0029]

[0030] Where J represents the moment of inertia of the satellite and flywheel, h represents the total angular momentum of the flywheel, d represents the external disturbance, and u represents the desired output torque of the flywheel.

[0031] In this embodiment, the dynamics and kinematics equations are further organized into a rigid body satellite attitude maneuver control model as follows:

[0032]

[0033] Where f = -J -1 ω×(Jω),b=J -1 ,δ=J -1 d is the total disturbance of the system.

[0034] like Figure 1 As shown in the figure, in this embodiment, the attitude maneuver control of a rigid satellite with a flywheel as an actuator is studied, and the current attitude ρ and the target attitude ρ are used to calculate the attitude maneuver control. d Get the attitude error ρ e , according to the error ρ e A nonlinear integral sliding mode control law is designed to obtain the desired output torque u. Since the external disturbance d affects the accuracy of satellite attitude maneuvers, an extended state observer is designed to estimate and compensate for the external disturbance, thereby improving the accuracy of satellite attitude maneuvers.

[0035] Step 2: Based on the rigid satellite attitude maneuver control model established in Step 1, consider the impact of the external disturbance d on the rigid satellite attitude maneuver process and design an improved composite nonlinear extended state observer to estimate the total system disturbance. The total system disturbance of the original control system is used as the state variable of the new control system. The estimated value of the external disturbance is obtained by observing the state variable. The convergence of the proposed improved composite nonlinear extended state observer is proved using the Lyapunov function.

[0036] In this embodiment, for the second-order system of the rigid body satellite attitude maneuvering control model described in step 1, a new control system is set as:

[0037]

[0038] Where Z1=x2, Z2=δ, and h(t) is the derivative of δ.

[0039] Considering the control system described in equation (6), an improved composite nonlinear extended state observer is designed. The observation error values ​​of two state variables are introduced to correct the output of the extended state observer. The equation is:

[0040]

[0041] Where,

[0042] ρ1(t)=exp(-γ||e1||2),ρ2(t)=exp(-γ||e2||2), e1=Z1-z1, e2=Z2-z2; z1 is the estimated value of the state variable Z1, z2 is the estimated value of the state variable Z2, that is, the estimated value of the total disturbance δ of the system; l1, l2, k1, k2, k3, β1, γ, α1, α2, α3 are the parameters to be designed. sign represents the symbolic operation on the vector elements, and · operation represents the multiplication of the corresponding elements of the vector. It means taking the absolute value of each element of the vector and raising it to a power.

[0043] Finally, the estimated value z of the external interference d is obtained:

[0044] z=Jz2 (8)

[0045] In this embodiment, the Lyapunov function is used to prove the convergence of the extended state observer designed in step 2. The specific process is as follows:

[0046] First, design the estimation error system:

[0047]

[0048] Then the error state space equation is in the form of:

[0049]

[0050] Where:

[0051]

[0052] g2=-ρ1(t)k2g2(e1)-ρ2(t)k3g3(e2),I 3×3 It is a 3×3 unit matrix, 0 3×3 is a 3×3 order zero matrix.

[0053] For equation (9), select appropriate parameters l1, l2, β1 such that the A matrix is a Hurwitz matrix, then there will exist a positive definite matrix Q, satisfying (A T + B) = -Q, λ min (Q) is the minimum eigenvalue of Q. λ min represents the minimum eigenvalue of the matrix.

[0054] According to the error state space equation of equation (9), there will exist c δ > c μ , α i ∈ (1-ε, 1), and such that if the estimation error then it will converge to the set {R 6 \Ω1}∩Ω2. is a constant boundary, here, satisfying

[0055] Let the Lyapunov function be The derivative along the estimation error system is:

[0056]

[0057] where the positive definite symmetric matrix -Q = (A T + B) satisfies the condition:

[0058]

[0059] Since:

[0060] λ min (Q) e T e≤e T Qe (13)

[0061] Therefore:

[0062] -e T Qe≤-2λ min (Q) V(t) (14)

[0063] According to the matrix inequality, we get:

[0064]

[0065] When the estimation error we get:

[0066]

[0067] Define φ(α, e) = e T G(t): R + ×Ω2→R, here α = [α1 α2 α3]T , Where,

[0068] For the above formula, consider the expression Choose appropriate parameters k1, k2, k3 to ensure Satisfying the Hurwitz condition, there exists a negative definite pairing matrix

[0069] Therefore, we get Since the set Ω2 contains all its own boundary points and is also bounded, Ω2 is a compact set, so for all (α, e)∈ξ there exists a tube ξ=(1-μ1,1+μ2)×Ω2 such that φ(α, e)<0. Therefore, for all α∈(1-ε,1), there will be a constant ε>0, satisfying e T G(t)<0.

[0070] So we get:

[0071]

[0072] In summary, when e∈{R 6 \Ω1}∩Ω2, so that According to Lyapunov's stability theorem, we can know that e starts from the set Ω1 and eventually converges to the set e∈{R 6 \Ω1}∩Ω2.

[0073] Because traditional extended state observers only use the error value of a single state variable to correct the observer output, the error values ​​of other state variables cannot be fully utilized. The improved composite nonlinear extended state observer in this embodiment corrects the observer output by introducing the observation error values ​​e1 and e2 of two state variables Z1 and Z2. The introduction of more observation error values ​​can further improve the convergence speed and accuracy of the observer.

[0074] Step 3: Based on the rigid satellite attitude maneuver control model established in Step 1, an integral sliding mode control method is designed. A new decay function is introduced in the sliding mode area component to improve system accuracy and achieve better transient performance. The closed-loop stability of the proposed nonlinear integral sliding mode control method is demonstrated using the Lyapunov function.

[0075] In this embodiment, a nonlinear integral sliding mode control method (control law) is designed, and a new attenuation function is introduced into the nonlinear integral sliding mode surface; it can not only avoid the integral saturation phenomenon when the error is small, but also avoid the attenuation function from decaying too quickly when the error is large, thereby improving the maneuvering speed of the attitude angle.

[0076] Design a nonlinear integral sliding surface s:

[0077]

[0078] Where:

[0079]

[0080]

[0081] s=(s1s2s3) T a1>a2>0,a3>0.

[0082] ω e represents the angular velocity error, h(ρ e ) represents the new attenuation function introduced by the attitude error, c1, c2, a1, a2, a3 represent the parameters to be designed, and sign represents the sign function.

[0083] Derivative the sliding surface s of formula (18):

[0084]

[0085] According to formulas (5) and (18), the equivalent control term U is obtained eq :

[0086]

[0087] Select the switch control U sw :

[0088]

[0089] In the formula, the · operation represents the multiplication of corresponding elements of the vector, |s α It means taking the absolute value of each element of the vector and performing a power operation. k is the parameter to be designed, and η=[η1 η2 η3] T Represents the bounds of the total disturbance, satisfying |δ1|≤η1,|δ2|≤η2,|δ3|≤η3.

[0090] Therefore, the control output U s Designed to:

[0091]

[0092] In this embodiment, the closed-loop stability of the sliding mode control method is proved by the Lyapunov function; the specific process is:

[0093] Take the Lyapunov function:

[0094]

[0095] Taking the derivative of the Lyapunov function we can get:

[0096]

[0097] Where, k>0,α>0, k and α represent the parameters to be designed.

[0098] According to the Lyapunov function stability theorem, the system has global asymptotic stability, that is, when time t→∞,ρ e →0,ρ→ρ d ,

[0099] In this embodiment, the improved integral sliding mode control method is used to appropriately modify the attenuation function in the sliding mode area component on the original basis, further slowing down the attenuation speed of the attenuation function, and avoiding the function decaying too quickly when the error is large, resulting in a slower maneuvering speed.

[0100] Considering that the extended state observer can observe and compensate for external disturbances, the control output u (desired output torque) can be further designed as:

[0101]

[0102] Specific implementation method 2: Figures 1 to 6 This embodiment is described as an example of the robust control method for remote sensing satellite attitude maneuver based on the extended state observer described in the first embodiment.

[0103] The remote sensing satellite attitude maneuver robust control method based on the extended state observer designed in this embodiment is applied to a certain type of rigid satellite. The satellite parameters are as follows:

[0104] Consider the satellite's moment of inertia:

[0105]

[0106] The expression of space interference at 500km orbit altitude is:

[0107]

[0108] During the satellite attitude maneuver control process, the initial Euler angle is

[000] °, the target Euler angle is [35 20 5]°, and the initial angular velocity and target angular velocity are both [0 0 0](°) / s. The simulation time is 150s. e =[M e1 M e2 M e3 ] T It represents the difference between the external disturbance estimated by the extended state observer and the external disturbance, T = [T x Ty T z ] T represents three-axis moment.

[0109] The control system block diagram is shown in FIG. 3. The extended state observer and integral sliding mode control algorithm are designed according to the above steps. The extended state observer estimation of three-axis disturbance comparison effect diagram and the extended state observer estimation error of three-axis disturbance comparison effect diagram are obtained by simulation according to step two. The attitude Euler angle, attitude angular velocity and moment comparison effect diagram are obtained by simulation according to step three. Figure 1 Figure 2-3 Figure 4-5

[0110] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, but as long as the combinations of the technical features do not contradict, they should be considered within the scope of the present disclosure.

[0111] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.​​​

Claims

1. A robust control method for remote sensing satellite attitude maneuvers based on an extended state observer, characterized by: The method is implemented by the following steps: Step 1: Based on the satellite attitude dynamics and kinematic equations, a model for rigid satellite attitude maneuver control is established; Step 2: Based on the rigid satellite attitude maneuvering control model described in step 1, combined with the influence of external disturbance on the rigid satellite attitude maneuvering process, an extended state observer is designed to estimate the total disturbance of the system and output an estimated value of the external disturbance. For the second-order system of the rigid body satellite attitude maneuver control model, a new control system is set; it can be expressed as follows: Where Z1 = x2, Z2 = δ, h(t) is the derivative of the total disturbance δ of the system; Design an improved composite nonlinear extended state observer, which can be expressed as follows: Where, ρ1(t)=exp(-γ||e1||2), ρ2(t)=exp(-γ||e2||2), e1=Z1-z1, e2=Z2-z2; z1 is the estimated value of the state variable Z1, z2 is the estimated value of the state variable Z2, that is, the estimated value of the total disturbance δ of the system; l1, l2, k1, k2, k3, β1, γ, α1, α2, α3 are the parameters to be designed; sign is the symbolic operation on the vector elements, and the · operation means the multiplication of the corresponding elements of the vector. To take the absolute value of each element of the vector and perform a power operation; Output the estimated value z of the external disturbance d: z = Jz2; Step 3: Design a nonlinear integral sliding mode control method based on the rigid body satellite attitude maneuver control model described in step 1, and use the estimated value of the external disturbance output by the extended state observer described in step 2 to compensate the nonlinear integral sliding mode control output to achieve remote sensing satellite attitude maneuver control; Design the nonlinear integral sliding surface s, which is expressed as follows: Where: C1=c1I 3×3 ,C2=c2I 3×3 ; ω e is the angular velocity error, ρ e is the attitude error, h(ρ e ) is the new attenuation function introduced by the attitude error, c1, c2, a1, a2, a3 are the parameters to be designed, and sign is the sign function.

2. The method for robust control of remote sensing satellite attitude maneuvers based on an extended state observer according to claim 1, characterized in that: In step 1, the rigid body satellite attitude maneuver control model is established as follows: Where ρ is the current posture, ω is the current posture angular velocity, and u is the desired output torque of the flywheel; f=-J -1 ω×(Jω),b=J -1 ,δ=J -1 d is the total disturbance of the system; J is the moment of inertia of the satellite and flywheel; are the derivatives of x1, ρ, x2, and ω respectively; in, Where, I 3×3 It is a 3×3 unit matrix.

3. The method for robust control of remote sensing satellite attitude maneuvers based on an extended state observer according to claim 1, characterized in that: The desired output torque u is expressed as follows: Where k is the parameter to be designed.

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