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CN-122009527-A - Spacecraft magnetic moment attitude control method based on non-inverse iterative algorithm

CN122009527ACN 122009527 ACN122009527 ACN 122009527ACN-122009527-A

Abstract

The invention discloses a spacecraft magnetic moment attitude control method based on an inverse iteration algorithm, which aims at a spacecraft attitude control system only relying on magnetic moment to establish a linearization periodic model, converts an optimal controller design problem into a solution problem of a discrete period Riccati equation connected with the optimal controller design problem according to a linear quadratic optimal control theory on the basis, solves the discrete period Riccati equation by constructing an error function on the basis of a gradient descent principle, avoids matrix inversion operation in the traditional solution method, effectively improves calculation efficiency and numerical stability, and obtains an optimal state feedback control law by utilizing the solved Riccati equation, thereby realizing optimal control of spacecraft attitude only using magnetic moment and providing a new solution for the attitude control problem of a limited actuator in a space task.

Inventors

  • ZHANG YING
  • WANG YURUI
  • LI ZHI
  • DONG RUIQI
  • XU YUTIAN

Assignees

  • 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院)

Dates

Publication Date
20260512
Application Date
20260119

Claims (7)

  1. 1. A spacecraft magnetic moment attitude control method based on a non-inverse iterative algorithm is characterized by comprising the following steps: Step 1, establishing a spacecraft attitude control system linearization period model only using a magnetic torquer based on a simplified quaternion and linearization method; step 2, converting the design problem of the optimal controller into a solution problem of a discrete period Riccati equation connected with the design problem according to a linear quadratic optimal control theory; step 3, based on the gradient descent principle, providing a discrete period Riccati equation solving method based on an inverse iteration algorithm of the gradient descent principle by constructing an error function; And step 4, obtaining an optimal state feedback control law by utilizing the Riccati equation solution obtained in the step 3, thereby realizing the optimal control of the spacecraft attitude by using only magnetic moment.
  2. 2. The spacecraft magnetic moment attitude control method based on the non-inverse iterative algorithm according to claim 1, wherein the specific steps of the step 1 are as follows: Step 1-1, setting an inertial matrix of a spacecraft The definition is as follows: Wherein, the Is a constant value, and is used for the treatment of the skin, , ; Step 1-2, the gesture of the spacecraft is expressed as the rotation of the spacecraft body coordinate system relative to the local horizontal LVLH coordinate system of the local vertical line, so that For the angular velocity of the body relative to the LVLH coordinate system expressed in the LVLH coordinate system, Is a constant value, and is used for the treatment of the skin, Representing a quaternion of the rotation of the body coordinate system relative to the LVLH coordinate system, wherein, Is the four components of the unit quaternion, Is a rotation axis per unit length, Is wound around The control moment generated by the interaction of the magnetic coil with the earth's magnetic field is as follows: Wherein, the Is the geomagnetic field in the spacecraft coordinate system, All are time-varying numbers; Is the magnetic moment induced by the spacecraft magnetic coil in the spacecraft coordinate system, All are time-varying numbers; The approximation is expressed as: Wherein, the For the inclination angle of the spacecraft orbit with respect to the magnetic equator, For magnetic field dipole intensity, time Defined as the moment when the spacecraft crosses the magnetic equatorial rise intersection, Is the angular velocity of the track relative to the inertial coordinate system; Step 1-3, the simplified quaternion linear time-varying system is expressed as follows: Wherein the method comprises the steps of And is also provided with Wherein, the Is a unit matrix with proper dimension.
  3. 3. The spacecraft magnetic moment attitude control method based on the non-inverse iterative algorithm according to claim 2, characterized in that the method comprises the following steps of Wherein For the orbital period, the expression is as follows: In the formula, For the radius of the track, 。
  4. 4. The spacecraft magnetic moment attitude control method based on the non-inverse iterative algorithm according to claim 2, wherein the specific steps of the step 2 are as follows: step 2-1, the spacecraft controller adopts the following discrete periodic system: (1) Wherein, the Representing a discrete time sequence number, And Respectively represent the systems in The state of the moment of time and the controller, And Are all system matrixes; Step 2-2, for the discrete periodic system (1), consider the quadratic performance index function as follows: (2) Wherein, the And Is of period of Is a weight matrix of (2); Step 2-3, if the discrete periodic system (1) is tranquilizable, the only optimal control law to minimize the quadratic performance index function (2) is: (3) Wherein, the Representing the maximum period solution of a given discrete period Riccati equation in the infinite time domain, the discrete period Riccati equation is in the form: (4) since equation (4) has periodicity, solving equation (4) is equivalent to solving equation (5): (5) wherein the matrix Is the only positive solution to equation (5); Further, by applying the matrix inversion argument, equation (5) is equivalent to: (6) Wherein the method comprises the steps of 。
  5. 5. The spacecraft magnetic moment attitude control method based on the non-inverse iterative algorithm according to claim 4, wherein in the step 2-1, the following is performed For sampling time, then 。
  6. 6. The spacecraft magnetic moment attitude control method based on the non-inverse iterative algorithm according to claim 4, wherein the specific steps of the step 3 are as follows: step 3-1, for any of And (3) making: (7) wherein the matrix Respectively a nonsingular matrix with proper dimension; Equation (6) is equivalent to: (8) From (7), it can be seen that: based on this, a set of matrix value error functions is established: (9) Further, the following objective function is constructed: (10) Wherein, the , Representative of A norm; step 3-2, calculating an objective function With respect to matrix groups And The results are shown below: on the basis, an improved non-inverse iterative algorithm based on the gradient descent principle is constructed: Wherein, the Is an adjustable parameter.
  7. 7. The spacecraft magnetic moment attitude control method based on the non-inverse iterative algorithm of claim 6, wherein the specific steps of the step 4 are as follows: from the modified non-inverse iterative algorithm based on gradient descent principle proposed in step 3, the solution is found Thereby obtaining a unique positive solution of the discrete period Riccati matrix equation And (3) combining the optimal control law given in the step (2) to obtain a linear quadratic optimal controller, and realizing spacecraft attitude control by using only magnetic moment.

Description

Spacecraft magnetic moment attitude control method based on non-inverse iterative algorithm Technical Field The invention relates to a spacecraft attitude control method, in particular to a spacecraft attitude optimal controller design method only depending on magnetic moment. Background Spacecraft attitude control is a key technology for guaranteeing successful space missions such as earth observation, deep space exploration, satellite communication and the like. The basic aim is to ensure that the spacecraft is kept or adjusted to a specific posture and orientation in a complex space environment so as to meet the task demands of load work, energy acquisition, orbit maintenance and the like. Conventional attitude control relies primarily on propellant injection or momentum exchange devices such as reaction wheels, control moment gyroscopes. These methods are technically mature but face limitations of propellant exhaustion, wear or failure of moving parts in long-term on-orbit tasks. In contrast, the method for generating the control moment by only utilizing the interaction of the satellite-borne magnetic torquer and the geomagnetic field has the remarkable advantages of no working medium consumption, no moving parts, high reliability and long service life, and is widely valued in the attitude control of various long-life spacecrafts, especially microsatellites, so that the method becomes a research hot spot. Because the geomagnetic field changes periodically along with the orbital motion in the spacecraft body coordinate system, the magnetic moment attitude control system is essentially a linear periodic time-varying system. For such periodic time-varying systems, linear quadratic optimal control is a classical theoretical framework for designing high performance controllers. The framework can systematically balance control precision and energy consumption by defining state errors and quadratic performance indexes for controlling the energy consumption, thereby obtaining a periodic optimal state feedback control law. The solution of this control law, in turn, proved to be mathematically equivalent to solving the discrete period Riccati equation accompanying it. Therefore, how to efficiently and stably solve the discrete period Riccati equation is a major concern for designing a magnetic moment optimal controller. At present, matrix inversion operation inevitably occurs in a large number of iterative algorithms in the solving process, so that the matrix inversion operation is high in computational complexity, more importantly, the problem of unstable numerical values can be introduced, and the reliability and the accuracy of the controller are affected particularly under the condition that the number of matrix conditions is large or the computational resources of an embedded system are limited. To overcome the limitations of conventional iterative algorithms, many researchers have sought innovative iterative algorithms to avoid matrix inversion operations. In this context, a spacecraft magnetic moment attitude control method based on a non-inverse iterative algorithm is of great interest. Disclosure of Invention In order to overcome the limitations of the traditional method and provide reliable support for successful execution of aerospace tasks and promotion of scientific research, the invention provides a brand-new spacecraft magnetic moment attitude control method based on a non-inverse iterative algorithm. According to the method, the optimal control problem of the periodic system is combined with a gradient iterative algorithm without inverse demand, and stable and efficient solution of a discrete period Riccati equation is realized by constructing an error function and a gradient descent principle, so that a periodic optimal controller with higher numerical robustness and higher control precision is designed, and a solid technical foundation is provided for stable pointing and long-term reliable operation of a spacecraft which only depends on magnetic moment in a complex space environment. The invention aims at realizing the following technical scheme: a spacecraft magnetic moment attitude control method based on a non-inverse iterative algorithm comprises the following steps: step 1, based on a simplified quaternion and linearization method, establishing a linearization period model of a spacecraft attitude control system only using a magnetic torquer, wherein the method comprises the following specific steps: Step 1-1, setting an inertial matrix of a spacecraft The definition is as follows: Wherein, the Is a constant value, and is used for the treatment of the skin,,; Step 1-2, the gesture of the spacecraft is expressed as the rotation of the spacecraft body coordinate system relative to the local horizontal LVLH coordinate system of the local vertical line, so thatFor the angular velocity of the body relative to the LVLH coordinate system expressed in the LVLH coordinate system,Is a constant value