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Control-limited minisatellite three-axis magnetic moment attitude control method based on algebraic Lyapunov equation

An attitude control, three-axis magnetic technology, applied in attitude control and other directions, can solve problems such as not getting due attention, and achieve the effect of ensuring stability

Active Publication Date: 2015-09-02
哈尔滨工业大学人工智能研究院有限公司
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

However, unlike the control problem of linear time-invariant systems in the case of limited control, the control problem of periodic systems in the case of limited control, especially the problem of global stabilization, has not received due attention. report on the conclusion of the sedation problem

Method used

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  • Control-limited minisatellite three-axis magnetic moment attitude control method based on algebraic Lyapunov equation
  • Control-limited minisatellite three-axis magnetic moment attitude control method based on algebraic Lyapunov equation
  • Control-limited minisatellite three-axis magnetic moment attitude control method based on algebraic Lyapunov equation

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specific Embodiment approach 1

[0019] Specific embodiment one: the three-axis magnetic moment attitude control method of the limited small satellite based on the algebraic Lyapunov equation of the present embodiment, it is realized according to the following steps:

[0020] Step 1: Establish the attitude kinematics and attitude dynamics models for the three-axis magnetic moment attitude control of the control-constrained small satellite, and obtain the state space equation;

[0021] Step 2: Solve the explicit solution P of the algebraic Lyapunov equation 0 :

[0022] A T P 0 +P 0 A=-D T D.

[0023] where A is the system matrix, D is a matrix of any dimension, since the system matrix A is critically stable or Lyapunov stable, it is guaranteed that the above algebraic Lyapunov equation has a positive definite solution P 0 ;

[0024] Step 3: Through the positive definite solution P of the algebraic Lyapunov equation 0 , to design an explicit linear feedback control law in the control-constrained situat...

specific Embodiment approach 2

[0025] Specific implementation mode two: the difference between this implementation mode and specific implementation mode one is that step one is specifically:

[0026] (1) Coordinate system definition

[0027] Introduce the geocentric equatorial inertial coordinate system X-Y-Z denoted as F i , where the X-axis points to the vernal equinox, the X-Y plane is the equatorial plane of the earth, and the Z-axis points to the North Pole along the earth's axis;

[0028] f b Denoted as the satellite body coordinate system, F o is the orbital coordinate system, its coordinate origin is located at the center of mass of the satellite, x o Along the track direction, y o perpendicular to the orbital plane, z o is the direction of the lowest point;

[0029] In the orbital coordinate system F o The attitude of the satellite is described below. If the attitude of the satellite reaches the desired position, the coordinates of the satellite body x b -y b -z b and the orbital coordina...

specific Embodiment approach 3

[0067] Specific embodiment three: what this embodiment is different from specific embodiment one or two is: in the step 2, solve algebraic Lyapunov equation positive definite solution P 0 The specific process:

[0068] Algebraic Lyapunov Equation

[0069] A T P 0 +P 0 A=-D T D (14)

[0070] make where e j Represents the 6th-order identity matrix I 6 The jth column of , then calculate

[0071] HAH - 1 = ω 0 A 2 0 0 0 0 A 1 0 A 3 ...

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Abstract

Provided is a control-limited minisatellite three-axis magnetic moment attitude control method based on an algebraic Lyapunov equation. The invention relates to a control-limited minisatellite three-axis magnetic moment attitude control method based on an algebraic Lyapunov equation. The method is used to realize global stability of a minisatellite three-axis magnetic moment attitude control under control-limited conditions. The method comprises: step 1, establishing attitude kinematics and attitude kinetic models of control-limited minisatellite three-axis magnetic moment attitude control, to obtain a state-space equation; step 2, solving explicit solution P0 of the algebraic Lyapunov equation A<T>P0+P0A=-D<T>D, wherein A is a system matrix, D is a matrix in arbitrary dimensions, the system matrix A being critical stable or Lyapunov stable, ensuring the algebraic Lyapunov equation have a positive definite solution P0; step 3, and through the positive definite solution P0 of the algebraic Lyapunov equation, designing linear feedback control law under explicit control-limited conditions. The method is applied in the field of satellite control.

Description

technical field [0001] The invention relates to a three-axis magnetic moment attitude control method for a control-limited small satellite based on an algebraic Lyapunov equation. Background technique [0002] For the magnetic torque attitude stabilization control system, the only actuator is the magnetic torquer, its weight is lower than that of the gravity gradient control system and the flywheel control system, and the power consumption is lower than that of the flywheel control system, while the weight and power of the small satellite are lower than those of the flywheel control system. The budget is very limited. Based on these advantages, the magnetic torque attitude control system is the first choice for the small satellite attitude control system. [0003] The constraints on the control system play an important role in the design of the magnetic torque attitude control system. Since the magnetic coil can only be driven by a limited current, especially when there are...

Claims

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Application Information

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IPC IPC(8): G05D1/08
Inventor 周彬罗威威
Owner 哈尔滨工业大学人工智能研究院有限公司
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