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

Abstract

The invention discloses 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 that the control performance of a satellite is reduced in the attitude maneuver process when external disturbance exists. Firstly, satellite dynamics and kinematics equations are combined, the influence of external disturbance on the rigid satellite maneuvering process is considered, an improved composite nonlinear extended state observer is adopted, and observation error values of two state variables are introduced to correct the output of the observer. Secondly, an improved nonlinear integral sliding mode control method is adopted, a new attenuation function is introduced into a sliding mode area subitem, the situation that the attenuation function attenuates too fast when errors are large is avoided, and then the attitude angle maneuvering speed is improved. The method has better observation performance and shorter attitude angle maneuvering time, and the control precision of the satellite is effectively improved.

Description

Technical Field

[0001] The 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 satellites is affected. Therefore, how to make the satellite have strong anti-interference ability (robustness) during attitude maneuvers has become a problem that needs to be solved urgently.

[0003] In response to the above problems, there are currently two mainstream research solutions: one is to design a corresponding robust control algorithm, and the other is to design an observer to estimate the disturbance and compensate for it to achieve attitude control. Since the second solution can estimate and compensate for the disturbance and improve the system control accuracy, it has gradually become a research hotspot. In terms of observer design, the extended state observer has developed rapidly as an anti-disturbance observer design method that does not rely on disturbance characteristics for estimation and compensation and still has a good estimation effect for more complex nonlinear systems. Summary of the invention

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

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

[0006] Step 1: Based on the satellite attitude dynamics and kinematics 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: According to the rigid 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] The present invention establishes a rigid satellite attitude maneuvering control model by combining satellite dynamics and kinematic equations. Secondly, considering the influence of external disturbances on the rigid satellite maneuvering process, an improved composite nonlinear extended state observer is proposed. The output of the observer is corrected by introducing the observation error values ​​of the two state variables to improve the convergence accuracy and convergence speed of the observer. Then, an improved nonlinear integral sliding mode control method is proposed. A new attenuation function is introduced in the sliding mode area component, which can not only avoid the integral saturation phenomenon when the error is small, but also avoid the attenuation function from decaying too fast 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 proved by the Lyapunov function.

[0011] Compared with the 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 the agile attitude maneuvering mission of remote sensing satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It 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 The comparison of the three-axis disturbance estimation of the front and rear expanded state observer is shown in Figure 2. (a) is the comparison of the yaw axis disturbance estimation before and after the improvement; (b) is the comparison of the pitch axis disturbance estimation before and after the improvement; (c) is the comparison of the roll axis disturbance estimation before and after the improvement;

[0014] Figure 3 The 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 4The three-axis Euler angle comparison diagram of the integral sliding mode algorithm before and after improvement; (a) is the comparison diagram of the yaw axis Euler angle before and after improvement; (b) is the comparison diagram of the pitch axis Euler angle before and after improvement; (c) is the comparison diagram of the roll axis Euler angle before and after improvement;

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

[0017] Figure 6 The three-axis torque comparison diagram of the integral sliding mode algorithm before and after improvement. Among them, (a) is the comparison diagram of the roll axis angular velocity before and after improvement; (b) is the comparison diagram of the pitch axis torque before and after improvement; (c) is the comparison diagram of the roll axis torque before and after improvement. DETAILED DESCRIPTION

[0018] Combination Figures 1 to 6 The present embodiment is described as follows: a remote sensing satellite attitude maneuvering robust control method based on an extended state observer is implemented by the following steps:

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

[0020] In this implementation, a rigid satellite is taken as the research object, and an attitude maneuvering control model for a rigid satellite is established. Due to the advantages of the modified Rodriguez (MRP) parameters, such as no singularity, simple parameters and wide adaptability, the modified Rodriguez parameters are used to describe the satellite attitude model.

[0021] Definition of MRP parameters:

[0022]

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

[0024] Define the attitude error ρ e =ρ-ρ d ,ρ represents the current posture,ρ d Represents the target attitude. 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] In the formula,

[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 the 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 implementation, the dynamics and kinematics equations are further organized into a rigid 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 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 of a rigid satellite with a flywheel as an actuator. d Get the attitude error ρ e , according to the error ρ e The nonlinear integral sliding mode control law is designed to obtain the expected output torque u. Due to the existence of external disturbance d, the accuracy of satellite attitude maneuvers is affected. Therefore, an extended state observer is designed to estimate and compensate for the external disturbance to improve the accuracy of satellite attitude maneuvers.

[0035] Step 2: Combined with the rigid satellite attitude maneuvering control model established in step 1, considering the influence of external disturbance d on the rigid satellite attitude maneuvering process, an improved composite nonlinear extended state observer is designed to estimate the total disturbance of the system, and the total 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 by using Lyapunov function;

[0036] In this implementation, for the second-order system of the rigid 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, and the observation error values ​​of two state variables are introduced to correct the output of the extended state observer. The equation is:

[0040]

[0041] In the formula,

[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 means to perform symbolic operation on the vector elements, · operation means to multiply 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 disturbance d is obtained:

[0044] z=Jz2 (8)

[0045] In this implementation, the Lyapunov function is used to prove the convergence of the extended state observer designed in step 2; the specific process is:

[0046] First, design the estimation error system:

[0047]

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

[0049]

[0050] Where:

[0051]

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

[0053] For equation (9), if we choose appropriate parameters l1, l2, β1 so that the matrix A is a Hurwitz matrix, then there will be a positive definite matrix Q that satisfies (A T +A)=-Q,λ min (Q) is the smallest eigenvalue of Q. min Represents the smallest eigenvalue of a matrix.

[0054] According to the error state space equation of formula (9), there exists c δ >c μ ,α i ∈(1-ε,1), and If the estimated error Then it converges to the set {R 6 \Ω1}∩Ω2. is a constant boundary, where it satisfies

[0055] Let the Lyapunov function be The derivative of the estimated error system is:

[0056]

[0057] The positive symmetric matrix -Q = (A T +A), meet the following conditions:

[0058]

[0059] because:

[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 get:

[0066]

[0067] Define φ(α,e)=e T G(t):R + ×Ω2→R, where α=[α1 α2 α3]T , In the formula,

[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 matrix

[0069] So we get Since the set Ω2 contains all of its own boundary points and is 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 will eventually converge to the set e∈{R 6 \Ω1}∩Ω2.

[0073] Since the traditional extended state observer only corrects the output of the observer through the error value of a single state variable, 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, and a new attenuation function is introduced in the sliding mode area component to improve the accuracy of the system and obtain better transient performance. The closed-loop stability of the proposed nonlinear integral sliding mode control method is proved by the Lyapunov function.

[0075] In this embodiment, a nonlinear integral sliding mode control method (control law) is designed to introduce a new attenuation function into the nonlinear integral sliding mode surface. This can not only avoid integral saturation when the error is small, but also prevent 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 item 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 implementation, 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 get:

[0096]

[0097] Wherein, k>0,α>0, k,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 from 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: Combination Figures 1 to 6 This embodiment is described as an example of the remote sensing satellite attitude maneuver robust control method based on the extended state observer described in the specific embodiment 1:

[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, and the parameters of the satellite are as follows:

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

[0105]

[0106] The spatial interference expression 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 estimated value of the external disturbance by the extended state observer and the external disturbance, T = [T x Ty T z ] T Represents the three-axis torque.

[0109] The control system block diagram is as follows Figure 1 As shown. According to the above steps, the extended state observer and integral sliding mode control algorithm are designed. According to step 2, simulation is performed to obtain the following Figure 2-3 The comparison diagram of the extended state observer for three-axis disturbance estimation and the comparison diagram of the extended state observer for three-axis disturbance estimation errors are shown in FIG. According to step three, simulation is performed to obtain the following Figure 4-5 The comparison effect diagram of attitude Euler angle, attitude angular velocity and torque is shown.

[0110] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0111] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A remote sensing satellite attitude maneuvering robust control method based on an extended state observer is characterized by: The method is implemented by the following steps: Step 1: Based on the satellite attitude dynamics and kinematics 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; Step 3: According to the rigid 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.

2. The remote sensing satellite attitude maneuver robust control method based on extended state observer according to claim 1 is characterized by: In step 1, the establishment of a rigid body satellite attitude maneuver control model is as follows: Where ρ is the current posture, ω is the current posture angular velocity, and u is the expected 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; They are the derivatives of x1, ρ, x2, and ω respectively; in, In the formula, I 3×3 It is a 3×3 unit matrix.

3. The remote sensing satellite attitude maneuver robust control method based on extended state observer according to claim 2 is characterized by: In step 2, a new control system is set for the second-order system of the rigid satellite attitude maneuver control model; it is 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: In the formula, 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 amount d: z=Jz2.

4. The remote sensing satellite attitude maneuver robust control method based on extended state observer according to claim 3 is characterized by: In step 3, the nonlinear integral sliding surface s is designed, 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.

5. The remote sensing satellite attitude maneuver robust control method based on extended state observer according to claim 4 is characterized in that: The desired output torque u is expressed as follows: In the formula, k is the parameter to be designed.

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