A pure three-axis magnetic control preset performance attitude control method for on-orbit spacecraft

Abstract

The present invention provides a pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft, comprising the following steps: Step 1: providing a spacecraft control torque calculation formula when a single magnetic torquer is used as an actuator; Step 2: providing a mathematical model of an attitude tracking system; Step 3: designing an attitude controller with preset performance to complete the attitude control with preset performance. The beneficial effects of the present invention are as follows: the pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft of the present invention only uses a magnetic torquer as an actuator, and considering the requirements for static and dynamic performance required by the spacecraft in an actual working environment, a preset performance controller is designed to achieve the control of the dynamic steady-state performance of the attitude response of the spacecraft, thereby improving the safety and performance reliability of the magnetic control spacecraft system, and having broad application prospects in the fields of spacecraft docking and separation, on-orbit assembly, formation flying, rescue of faulty spacecraft, and de-orbiting of abandoned spacecraft.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft attitude control, and in particular to a pure three-axis magnetically controlled preset performance attitude control method for an on-orbit spacecraft. Background Art

[0002] Most of the actuators for spacecraft attitude control currently exist by combining a magnetic torquer with a flywheel. For such spacecraft controlled by inertial thrust, the stored propellant will affect the life and working performance of the spacecraft itself; on the other hand, the inertial thrust will have plume pollution, which will greatly interfere with the optical working measurement device. Therefore, the use of the geomagnetic field alone to control the attitude of the spacecraft has gradually come into people's view due to its simple structure and reliable performance. This method is particularly suitable for designing attitude control systems for spacecraft in low-orbit areas with strong geomagnetic field strength. However, there are few related technologies for using magnetic torquers alone for spacecraft attitude control.

[0003] At the same time, in the working environments of spacecraft docking and separation, on-orbit assembly, formation flying, rescue of faulty spacecraft and deorbiting of abandoned spacecraft, there are certain requirements for the steady-state and transient performance of attitude control systems. Because preset performance control has many advantages such as being able to take into account the steady-state performance and dynamic performance of the system, being able to pre-set the convergence boundary of the tracking error, and being a model-free control, it does not require estimation or identification of the system model, and can improve the dynamic performance and steady-state performance of the system to meet the working requirements of the spacecraft attitude, preset performance controllers are widely used in the aerospace field.

[0004] However, there are very few studies on designing attitude controllers with preset performance using only magnetic torquers as actuators. Summary of the invention

[0005] The present invention provides a pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft, comprising the following steps:

[0006] Step 1: Give the calculation formula of the spacecraft control torque when using only a magnetic torquer as an actuator.

[0007] Step 2: Give the mathematical model of the posture tracking system.

[0008] Step 3: Design a posture controller with preset performance to complete the posture control with preset performance.

[0009] As a further improvement of the present invention, in step 1, the calculation formula of the pure magnetic control torque of the spacecraft is given as follows:

[0010] T=M×B (1)

[0011] Among them, M is the magnetic dipole moment, which is generated by the current in the coil controlled by the magnetic torquer to generate a magnetic dipole moment of a specified direction, which interacts with the earth's magnetic field and then generates a controlled external torque T perpendicular to the earth's magnetic field vector B.

[0012] As a further improvement of the present invention, the output torque of the magnetic torquer is bounded, so the following restrictions are adopted:

[0013] u=[u1,u2,u3] T ,|u i |≤0.005N·m, i=1, 2, 3 (3)

[0014] Among them, u represents the control torque of the spacecraft, and the values ​​of i of 1, 2, and 3 correspond to the components of the output torque of the magnetic torquer in the x-axis, y-axis, and z-axis directions of the body coordinate system, respectively.

[0015] As a further improvement of the present invention, in step 2, it also includes:

[0016] Step 2.1, the spacecraft attitude dynamics model is given as:

[0017]

[0018] in, The unit quaternion representing the attitude direction of the fixed coordinate system relative to the inertial coordinate system and satisfying R 4 represents a four-dimensional vector, q0 is the real part of the attitude quaternion, q is the imaginary part of the quaternion, ω represents the three-axis angular velocity of the spacecraft, ω represents the angular velocity in the fixed coordinate system, J represents the spacecraft moment of inertia matrix, u represents the control torque of the spacecraft, d represents the external interference of the spacecraft, ω x It represents the matrix form of the cross product of coordinate angular velocity, and I3 represents the third-order identity matrix.

[0019] Step 2.2, the spacecraft attitude kinematic model is given as:

[0020]

[0021] in, The unit quaternion representing the error, where R 4 The error quaternion is a four-dimensional number consisting of a real part and three imaginary parts, where q e0 represents the real part of the error quaternion, q e represents the imaginary part of the error quaternion, ω e Represents the angular velocity error, denoted by ω e =ω-Rω d , w d represents the expected value of the angular velocity, represents the derivative of the expected value of the angular velocity, J represents the spacecraft moment of inertia matrix, and R represents the rotation matrix, which is defined as:

[0022]

[0023] Will Denoted as Q, the same below, define the cross product matrix form ×, any three-dimensional variable is denoted as So Step 2.3: The pose tracking model given by equation 6 and equation 7 is:

[0024]

[0025] in,

[0026] P=Q -1 (10)

[0027] M=P T JP (11)

[0028]

[0029] Among them, P is multiplied and recorded as M, which has no specific meaning and is just a code for simplification. D is the thrust distribution matrix, E is the thruster efficiency matrix, C represents the calculation result of formula (12), and H represents the calculation result of formula (13). C and H have no actual meaning.

[0030] As a further improvement of the present invention, in step 2.1, the spacecraft model moment of inertia used is:

[0031] J0=[20,0,0;0,17,0;0.9,0,15];

[0032] J0 represents the moment of inertia of the spacecraft model itself without interference.

[0033] Δ J =0.01×[sin(0.1t),0,0; 0,sin(0.2t),0;0,0,sin(0.3t)];

[0034] Δ J Represents the uncertainty in the spacecraft's moment of inertia.

[0035] The initial six numbers of the orbit are:

[0036] Elements0_up=[7179910,0,0,86,0,0,0]

[0037] The initial angular velocity is:

[0038] W0=[0,0,0]° / s

[0039] The initial Euler angles are:

[0040] Euler0=[0,0,0].

[0041] As a further improvement of the present invention, in step 2.3, the parameter rank(DE)=3 is set to ensure that the spacecraft is not underactuated;

[0042] Property 1: The matrix D is a full row rank matrix and for the designed working scenario, DED T Always be right.

[0043] Property 2: M is a symmetric positive definite matrix, and its bounds are as follows:

[0044]

[0045] where λ min (J) and λ max (J) represents the minimum eigenvalue and maximum eigenvalue of the moment of inertia matrix, P is the inverse matrix of the Q matrix mentioned above, and x is an arbitrary three-dimensional vector;

[0046] Property 3: The matrix M-2C is a skew-symmetric matrix, and for any vector x∈R 3 , x T (M-2C)x=0 always holds true.

[0047] Property 4:

[0048] ||P||=2 / |q e0 | (15)

[0049] Property 5:

[0050]

[0051] As a further improvement of the present invention, in step 3, it also includes:

[0052] Step 3.1, the preset performance function is given as:

[0053] P li (t)<q ei (t)<P ui (t) (17)

[0054] P ui (t) = k si ρ ui (t)+(1-k si ) oi ρ li (t) (18)

[0055] P li (t)=-(k si k oi ρ li (t)+(1-k si )ρ ui (t)) (19)

[0056] where k si and k oi is the design parameter, ρ ji (t) is the performance function, j is the code, and the value of j can only be u or l.

[0057]

[0058] where ρ ji0 , ρ ji∞ and l ji is a positive constant, ρ ji0 =ρ ji (0); P li and P ui are the preset lower and upper bounds of the error quaternion, that is, the error quaternion should be greater than P li , less than P ui .

[0059] Step 3.2, select the error transformation function as:

[0060]

[0061] The preset performance index is converted to |ε i (t)|<1 always holds true, case q ei (0)=0 requires selection of k oi =1.

[0062] Step 3.3, through error transformation, the attitude error system becomes:

[0063]

[0064] Among them, the comprehensive error State variables Conversion error ε=[ε1,ε2,ε3] T ; D is the thrust distribution matrix, E is the thruster efficiency matrix, and κ is a constant to be designed.

[0065] In step 3.4, the control law is given using the backstepping method.

[0066] As a further improvement of the present invention, in step 3, the Lyapunov function used in designing a posture controller with preset performance is:

[0067]

[0068] Among them, z1, z2, and z3 are three state variables selected in the backstepping design. li , i = 1, 2, 3 are the x, y, z axis components of the state variable z1, and the positive constant σ makes σ ≤ λ min (DED T ) is always established, and are the estimated values ​​of b and λ, respectively, and η i ,i=1,2 are design parameters, and y is the filter error.

[0069] As a further improvement of the present invention, in step 3.4, the control law given by the backstepping method is:

[0070] z1=ε (26)

[0071] z2=x2-x v (27)

[0072]

[0073] x v =-k1q e +0.5(k1P a +diag(P ui -P li )v) (29)

[0074] u v =-D T (k2+k(t))Pz2 (30)

[0075]

[0076] Among them, z1, z2, z3 are three state variables selected in the backstepping design, x v is the virtual control quantity, u v is a smooth virtual control law, a constant k1>0,

[0077] P a =[P u1 +P l1 ,P u2 +P l2 ,P u3 +P l3 ] T , Δu c =g(u c )-u c is the signal u c and g(u c), is a parameter to be designed, and c is the filter constant.

[0078] The beneficial effects of the present invention are as follows: 2. The pure three-axis magnetically controlled preset performance attitude control method for an on-orbit spacecraft of the present invention only uses a magnetic torquer as an actuator, and in view of solving the requirements of the static and dynamic performances required by the spacecraft in the actual working environment, a preset performance controller is designed to realize the control of the dynamic steady-state performance of the attitude response of the spacecraft, thereby improving the safety of the magnetically controlled spacecraft system and the reliability of performance, and has broad application prospects in the fields of spacecraft docking and separation, on-orbit assembly, formation flying, rescue of faulty spacecraft and deorbiting of abandoned spacecraft; 2. The pure three-axis magnetically controlled preset performance attitude control method for an on-orbit spacecraft of the present invention can realize the preset performance attitude control of the on-orbit spacecraft when the actuator only uses a magnetic torquer, with high control accuracy and good control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of the present invention;

[0080] Figure 2 It is a graph of attitude angle changes under the action of the preset performance controller of the present invention;

[0081] Figure 3 It is the attitude angular velocity change diagram under the preset performance controller;

[0082] Figure 4 It is a control torque variation diagram provided by the magnetic torquer of the present invention. DETAILED DESCRIPTION

[0083] The present invention is a pure magnetic control technology with preset three-axis performance for on-orbit spacecraft. It only uses a magnetic torquer as an actuator. In order to solve the limitation of actuator input saturation that the spacecraft is subject to in the actual working environment, a controller is designed to effectively control the attitude of the spacecraft so that it can achieve preset performance indicators.

[0084] like Figure 1 As shown, the present invention discloses a pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft, comprising the following steps:

[0085] Step 1: Give the calculation formula of the spacecraft control torque when using only a magnetic torquer as an actuator.

[0086] The given pure magnetic control torque equation of the spacecraft is:

[0087] T=M×B(1)

[0088] Where M is the magnetic dipole moment in a specified direction generated by the magnetic torquer by controlling the current in the coil. The magnetic dipole moment interacts with the earth's magnetic field to generate a controlled external torque T perpendicular to the earth's magnetic field vector B. Unlike traditional thrust equipment, the control torque provided by using a magnetic torquer alone is small.

[0089] According to the above analysis, it can be concluded that due to the limitations of mass, volume, energy consumption, residual magnetism, magnetic materials, coil shape, number of turns, and current, the magnetic dipole moment that can be generated by the magnetic torquer is subject to peak constraints, that is,

[0090] |M|≤M max (2)

[0091] Where M max Represents the maximum magnetic dipole moment.

[0092] Considering that the output torque of the magnetic torquer is bounded, the following restrictions are adopted:

[0093] u=[u1,u2,u3] T ,|u i |≤0.005N·m, i=1, 2, 3 (3)

[0094] Among them, u represents the control torque of the spacecraft, and the values ​​of i of 1, 2, and 3 correspond to the components of the output torque of the magnetic torquer in the x-axis, y-axis, and z-axis directions of the body coordinate system, respectively.

[0095] Step 2: Give the mathematical model of the posture tracking system.

[0096] Step 2.1, the spacecraft attitude dynamics model is given as:

[0097]

[0098] in, in The unit quaternion representing the attitude direction of the fixed coordinate system relative to the inertial coordinate system, R 4 represents a four-dimensional vector, q0 is the real part of the attitude quaternion, q is the imaginary part of the quaternion, and satisfies ω represents the three-axis angular velocity of the spacecraft, ω represents the angular velocity in the fixed coordinate system, J represents the spacecraft moment of inertia matrix, u represents the control torque of the spacecraft, d represents the external disturbance of the spacecraft, q0 2 is the square of the real part of the quaternion, ω x It represents the matrix form of the cross product of coordinate angular velocity, and I3 represents the third-order identity matrix.

[0099] The spacecraft model moment of inertia used in the present invention is:

[0100] J0=[20,0,0;0,17,0;0.9,0,15];

[0101] Δ J =0.01×[sin(0.1t),0,0; 0,sin(0.2t),0;0,0,sin(0.3t)];

[0102] The initial six numbers of the orbit are:

[0103] Elements0_up=[7179910,0,0,86,0,0,0]

[0104] The initial angular velocity is:

[0105] W0=[0,0,0] ° / s

[0106] The initial Euler angles are:

[0107] Euler0=[0,0,0]

[0108] Step 2.2, the spacecraft attitude kinematic model is given as:

[0109]

[0110] in, Represents the error quaternion, including a real part and three imaginary parts, where q e0 represents the real part of the error quaternion, q e represents the imaginary part of the error quaternion, ω e Represents the angular velocity error, denoted by ω e =ω-Rω d , w d represents the expected value of the angular velocity, represents the derivative of the expected value of the angular velocity, J represents the spacecraft moment of inertia matrix, and R represents the rotation matrix, which is defined as:

[0111]

[0112] Will Denoted as Q, the same below, define the cross product matrix form ×, any three-dimensional variable is denoted as So Defining the superscript X is the operation method in the form of a cross product matrix.

[0113] Step 2.3, the posture tracking model given by the combined equation (6) and equation (7) is:

[0114]

[0115] in

[0116] P=Q -1 (10)

[0117] M=P T JP (11)

[0118]

[0119] Among them, P is multiplied and recorded as M, which has no specific meaning and is just a code for simplification. D is the thrust distribution matrix, E is the thruster efficiency matrix, C represents the calculation result of formula (12), and H represents the calculation result of formula (13). C and H have no actual meaning.

[0120] The parameter setting matrix DE of the present invention has a rank of 3, that is, rank(DE)=3, to ensure that the spacecraft is not underactuated.

[0121] Property 1: The matrix D is a full row rank matrix and for the working scenario designed by the present invention, DED T Always be right.

[0122] Property 2: M is a symmetric positive definite matrix, and its bounds are as follows:

[0123]

[0124] where λ min (J) and λ max (J) respectively represent the minimum eigenvalue and maximum eigenvalue of the moment of inertia matrix, P is the inverse matrix of the Q matrix mentioned above, and x is an arbitrary three-dimensional vector. That is to say, for any three-dimensional vector x, for the calculation result matrix M mentioned above, the minimum value is greater than the minimum eigenvalue of the moment of inertia matrix multiplied by the square of the second norm of Px, and the maximum value is less than the maximum eigenvalue of the moment of inertia matrix multiplied by the square of the second norm of Px.

[0125] Property 3: The matrix M-2C is a skew-symmetric matrix, and for any vector x∈R 3 , x T (M-2C)x=0 always holds, where x is an arbitrary vector code with no real meaning, R3 represents a three-dimensional vector, x∈R 3 It is a common mathematical notation that represents any vector in three-dimensional space.

[0126] Property 4:

[0127] ||P||=2 / |q e0 | (15)

[0128] Property 5:

[0129]

[0130] After the posture tracking model is given by equations 6 and 7, there are some matrices in it, such as Q, M, P, D, E, etc. The above five properties are related to the matrices below, which lay the foundation for the design of the preset performance controller below.

[0131] Step 3: Design a posture controller with preset performance to complete the posture control with preset performance.

[0132] P li (t) ei (t)<P ui (t) (17)

[0133] P ui (t) = k si ρ ui (t)+(1-k si ) oi ρ li (t) (18)

[0134] P li (t)=-(k si k oi ρ li (t)+(1-k si )ρ ui (t)) (19)

[0135] where k si and k oi is the design parameter, ρ ji (t) is the performance function, expressed as

[0136]

[0137] where ρ ji0 , ρ ji∞ and l ji is a positive constant. ji0 =ρ ji (0).

[0138] By choosing a suitable performance function ρ ji (t), j∈{l,u} and the design constant k si and k oi , the tracking error q ei The expected transient and steady-state behavior of (t) is preset.

[0139] Step 3.2, the error transformation function is:

[0140]

[0141] The preset performance index is converted to |ε​i (t)|<1 always holds. It is worth noting that in case q ei (o)=0 requires selection of k oi =1.

[0142] Step 3.3 Through error transformation, the attitude error system becomes:

[0143]

[0144] The comprehensive error State variables Conversion error ε=[ε1,ε2,ε3] T ; D is the thrust distribution matrix, E is the thruster efficiency matrix, and κ is a constant to be designed.

[0145] In order to compensate for the adverse effects of input saturation, the following auxiliary systems are introduced:

[0146]

[0147] Among them, Δu c =g(u c )-u c is the signal u c and g(u c ), It is a parameter to be designed.

[0148] Construct the following low-pass filter to avoid the "parameter explosion" caused by multiple derivatives:

[0149]

[0150] Where c is a positive constant representing the filter bandwidth.

[0151] The filter error is defined as:

[0152]

[0153] Since there are often some saturation, nonlinear links and some environmental requirements in engineering practice, the following assumptions are proposed to maximize the simulation of the actual engineering environment.

[0154] Assumption 1: The spacecraft's inertial matrix remains constant (or changes slowly with time) throughout the attitude maneuver, but is unknown due to fuel consumption, solar array rotation, and vehicle load changes.

[0155] Assumption 2: External disturbance d and additional faults is bounded, and there exists a positive constant d m Make ||d1||≤d m .

[0156] Assume that each component of the control input u is subject to a single maximum amplitude u imax The constraints are then given as follows: The dynamic system generates the control input u.

[0157]

[0158] Among them, κ>0, g(u c )=[g(u c1 ),g(u c2 ),…,g(u cn )] T is an auxiliary intermediate signal to be designed, u c =[u c1 ,u c2 ,…,u cn ] T .

[0159]

[0160] in, Represents the function g(u ci ) maximum value allowed.

[0161] Step 3.4, use the backstepping method to give the control law;

[0162] Step 3.4.1, first define:

[0163] z1=ε

[0164] z2=x2-x v

[0165]

[0166] Consider the following Lyapunov function:

[0167]

[0168] Where k0>0 is a constant.

[0169] Design of virtual control law

[0170] x v =-k1q e +0.5(k1P a +diag(P ui -P li )v) (38)

[0171] Where k1>0, P a =[P u1 +P l1 ,Pu2 +P l2 ,P u3 +P l3 ] T

[0172] Taking its derivative, we get

[0173]

[0174] We can get:

[0175]

[0176] in

[0177]

[0178] R can be linearized as R = P T (Y(·)+d1), Y(·) is a known regression matrix. We can get:

[0179]

[0180] in Φ1=[||Y(·)||,1] T .

[0181] According to Property 1, the present invention states that the matrix DED T This means that there exists a positive constant σ such that σ≤λ min (DED T ) always holds true. Define λ=1 / σ, and where b2 is a positive constant which will be defined later.

[0182] Step 3.4.2, consider the following Lyapunov function:

[0183]

[0184] in, and are the estimated values ​​of b and λ, respectively, and η i ,i=1,2 are design parameters.

[0185] Taking the derivative of the above formula, we can get:

[0186]

[0187] therefore, It can be written as:

[0188]

[0189] It can be written as:

[0190]

[0191] according to

[0192]

[0193]

[0194] You can get:

[0195]

[0196] in

[0197]

[0198] because

[0199]

[0200] in, is a constant greater than 0.

[0201] also

[0202]

[0203] Here, α is a positive constant.

[0204] Select the smooth virtual control law and the corresponding adaptive law:

[0205] u v =-D T (k2+k(t))Pz2 (55)

[0206]

[0207] Where k2>0,η i >0,γ i > 0, b0 and λ0 are non-negative parameters, and the initial values ​​of the adaptive variables are chosen to be non-negative, k(t) is defined as

[0208]

[0209] Therefore, we can get:

[0210]

[0211] in,

[0212] Step 3.4.3, consider the following Lyapunov function:

[0213]

[0214] The derivative is:

[0215]

[0216] We can get:

[0217]

[0218] therefore:

[0219]

[0220] design:

[0221]

[0222] We can get:

[0223]

[0224] Among them, α1>0 is a normal number. The above formula can be written as

[0225]

[0226] because is a continuous function, so for any p>0, the compact set Therefore, There exists a maximum value M on the compact set Π, The compact set Π is bounded and satisfies available:

[0227]

[0228] Let α * >0 is a sufficiently small constant. available

[0229]

[0230] in:

[0231] a1=min{2k1,2α * / λ max (J),2α * ,η1γ1,η2γ2} (69)

[0232]

[0233] Step 3.4.4, based on the above, the control law used is given

[0234] z1=ε (26)

[0235] z2=x2-x v (27)

[0236]

[0237] x v =-k1q e +0.5(k1P a +diag(P ui -P li )v) (29)

[0238] u v =-D T (k2+k(t))Pz2 (30)

[0239]

[0240] The κ used in the present invention is 0.1, u imax =0.005, c=0.1, k0=0.1, k1=0.5, k2=5, k3=0.05;

[0241] eta1=eta2=21, γ1=γ2=0.5, b0=[0,0,0] T ,λ0=0,

[0242] D=E=I3,

[0243] Figure 2 This is a graph of attitude angle changes under the parameter conditions selected by the present invention. It can be seen that the roll angle and pitch angle basically converge to around 0°, while the yaw angle fluctuates due to the large number of uncontrollable areas on the Z axis and the small magnetic torque provided. When it runs to the uncontrollable area, the yaw angle diverges slightly, and when it runs to the controllable area, the yaw angle converges again, but the overall yaw angle converges within 1°. The attitude angle changes under the preset performance control converge quickly, the yaw angle overshoot is small, and the control effect is relatively ideal.

[0244] Figure 3 This is a schematic diagram of the attitude angular velocity under the parameter conditions selected by the present invention. It can be seen that the roll angular velocity and the pitch angular velocity basically converge to around 0, while the yaw angular velocity fluctuates due to the uncontrollable area. Under the algorithm proposed in the present invention, the attitude angular velocity converges quickly.

[0245] Figure 4 This is a schematic diagram of the control torque provided by the magnetic torquer under the parameter conditions selected by the present invention, which is within 0.5% and meets the actual situation.

[0246] Table 1 is a diagram of parameters related to the preset performance functions used in the present invention.

[0247] Table 1

[0248]

[0249] The pure three-axis magnetically controlled preset performance attitude control method for an on-orbit spacecraft of the present invention proposes a preset performance adaptive attitude controller that only uses a magnetic torquer as an actuator, which can avoid many problems caused by traditional thrust devices and realize preset performance control of the spacecraft attitude, and has great practical value.

[0250] The beneficial effects of the present invention are: 1. The pure three-axis magnetically controlled preset performance attitude control method for an on-orbit spacecraft of the present invention only uses a magnetic torquer as an actuator, and in view of solving the requirements of the static and dynamic performances required by the spacecraft in the actual working environment, a preset performance controller is designed to realize the control of the dynamic steady-state performance of the attitude response of the spacecraft, thereby improving the safety of the magnetically controlled spacecraft system and the reliability of performance, and has broad application prospects in the fields of spacecraft docking and separation, on-orbit assembly, formation flying, rescue of faulty spacecraft and deorbiting of abandoned spacecraft; 2. The pure three-axis magnetically controlled preset performance attitude control method for an on-orbit spacecraft of the present invention can realize the preset performance attitude control of the on-orbit spacecraft when the actuator only uses a magnetic torquer, with high control accuracy and good control performance.

[0251] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft, characterized in that: The following steps are involved: Step 1: Give the calculation formula of the spacecraft control torque when the magnetic torquer is used as the actuator alone; Step 2: Give the mathematical model of the posture tracking system; Step 3: Design a posture controller with preset performance to complete the posture control with preset performance; In step 1, the calculation formula for the pure magnetic control torque of the spacecraft is given as: T=M×B (1) Wherein, M is the magnetic dipole moment, which is generated by the current in the coil controlled by the magnetic torquer to generate a magnetic dipole moment in a specified direction, which interacts with the earth's magnetic field and then generates a controlled external torque T perpendicular to the earth's magnetic field vector B; The output torque of the magnetic torquer is bounded, so the following restrictions are adopted: u=[u1,u2,u3] T ,|u i |≤0.005N·m,i=1,2,3 (3) Among them, u represents the control torque of the spacecraft, and the values ​​of i, 1, 2, and 3, correspond to the components of the output torque of the magnetic torquer in the x-axis, y-axis, and z-axis directions of the body coordinate system respectively; In step 2, it also includes: Step 2.1, the spacecraft attitude dynamics model is given as: in, in The unit quaternion representing the attitude direction of the fixed coordinate system relative to the inertial coordinate system, R 4 represents a four-dimensional vector, q0 is the real part of the attitude quaternion, q is the imaginary part of the quaternion, and satisfies ω represents the three-axis angular velocity of the spacecraft in the fixed coordinate system, J represents the spacecraft moment of inertia matrix, u represents the control torque of the spacecraft, d represents the external disturbance of the spacecraft, q0 2 is the square of the real part of the quaternion, ω x represents the matrix form of the cross product of coordinate angular velocity, I3 represents the third-order identity matrix; Step 2.2, the spacecraft attitude kinematic model is given as: in, The unit quaternion representing the error, where R 4 The error quaternion is a four-dimensional number consisting of a real part and three imaginary parts, where q e0 represents the real part of the error quaternion, q e represents the imaginary part of the error quaternion, ω e Represents the angular velocity error, denoted by ω e =ω-Rω d , w d represents the expected value of the angular velocity, represents the derivative of the expected value of the angular velocity, J represents the spacecraft moment of inertia matrix, and R represents the rotation matrix, which is defined as: Step 2.3: The pose tracking model given by equation 6 and equation 7 is: in, P=Q -1 (10) M=P T JP (11) in, is an additional fault, P is multiplied and recorded as M, which has no specific meaning and is just a code for simplification, D is the thrust distribution matrix, E is the thruster efficiency matrix, C represents the calculation result of formula (12), and H represents the calculation result of formula (13). C and H have no actual meaning; In step 3, it also includes: Step 3.1, the preset performance function is given as: P li (t)<q ei (t)<P ui (t) (17) P ui (t)=k si ρ ui (t)+(1-k si )k oi ρ li (t) (18) P li (t)=-(k si k oi ρ li (t)+(1-k si )ρ ui (t)) (19) where k si and k oi is the design parameter, ρ ji (t) is the performance function, j is the code, and the value of j can only be u or l; where ρ ji0 , ρ ji∞ and l ji is a positive constant, ρ ji0 =ρ ji (0); P li and P ui are the preset lower and upper bounds of the error quaternion, respectively. The error quaternion should be greater than P li , less than P ui ; Step 3.2, select the error transformation function as: The preset performance index is converted to |ε i (t)|<1 always holds true, case q ei (0)=0 requires selection of k oi =1; Step 3.3, through error transformation, the attitude error system becomes: Among them, the comprehensive error State variables Conversion error ε=[ε1,ε2,ε3] T ; D is the thrust distribution matrix, E is the propeller efficiency matrix, κ is a constant to be designed, g(u c ) is an auxiliary intermediate signal to be designed; In step 3.4, the control law is given using the backstepping method.

2. The pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft according to claim 1, characterized in that: In step 2.1, the spacecraft model moment of inertia used is: J0＝[20,0,0；0,17,0；0.9,0,15]； J0 represents the moment of inertia of the spacecraft model itself without interference; Δ J =0.01×[sin(0.1t),0,0;0,sin(0.2t),0;0,0,sin(0.3t)]; Δ J represents the uncertainty in the spacecraft's moment of inertia; The initial six numbers of the orbit are: Elements0_up=[7179910,0,0,86,0,0,0] The initial angular velocity is: W0=[0,0,0]° / s The initial Euler angles are: Euler0=[0,0,0].

3. The pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft according to claim 1, characterized in that: In step 2.3, the rank of the parameter setting matrix DE is set to 3 to ensure that the spacecraft is not underactuated; Property 1: The matrix D is a full row rank matrix and for the designed working scenario, the matrix DED T Always righteous; Property 2: M is a symmetric positive definite matrix, and its bounds are as follows: where λ min (J) and λ max (J) represents the minimum eigenvalue and maximum eigenvalue of the moment of inertia matrix, P is the inverse matrix of the Q matrix mentioned above, and x is an arbitrary three-dimensional vector; Property 3: The matrix M-2C is a skew-symmetric matrix, and for any vector x∈R 3 , x T (M-2C)x=0 always holds; Property 4: ||P||=2 / |q e0 | (15) Property 5:

4. The pure three-axis magnetic control preset performance attitude control method for an on-orbit spacecraft according to claim 1, characterized in that: In step 3, the Lyapunov function used in designing a posture controller with preset performance is: Among them, z1, z2, and z3 are three state variables selected in the backstepping design. 1i , i = 1, 2, 3 are the x, y, z axis components of the state variable z1, and the positive constant σ makes σ ≤ λ min (DED T ) is always established, and are the estimated values ​​of b and λ, respectively, and η i , i=1,2 are design parameters, y is the filter error, k0 is a constant k0>0, and λ=1 / σ.

5. The method for controlling the preset performance attitude of a pure three-axis magnetically controlled on-orbit spacecraft according to claim 4, characterized in that: In step 3.4, the control law given by the backstepping method is: z1=ε (26) z2=x2-x v (27) x v J-k1q e +0.5(k1P). a +diag(P ui -P li )v) (29) u v =-D T (k2+k(t))Pz2 (30) Among them, z1, z2, z3 are three state variables selected in the backstepping design, x v is the virtual control quantity, u v is a smooth virtual control law, k1>0 is a constant, k2>0 is a non-negative parameter, P a =[P u1 +P l1 ,P u2 +P l2 ,P u3 +P l3 ] T , Δu c =g(u c )-u c is the signal u c and g(u c ), is a parameter to be designed, and c is the filter constant.

Images