阅读说明：本技术 一种位移模式无拖曳控制动力学协调条件确定方法 (Displacement mode drag-free control dynamics coordination condition determination method ) 是由 苟兴宇 邹奎 王丽娇 李明群 蒋庆华 王绍凯 李鹤 李声涛 于 2020-05-07 设计创作，主要内容包括：一种位移模式无拖曳控制动力学协调条件确定方法,属于卫星无拖曳控制技术领域,首先假设负刚度力零位与测量零位重合,便于建立位移模式单自由度无拖曳控制动力学方程、简化的各轴通用的动力学方程、退化的切换动力学方程；位移模式无拖曳控制系统最大推力加速度、负刚度系数及机械限位三个参数之间需要满足一个约束关系式,这是这类系统应当满足的基本动力学协调条件；通过求解切换动力学方程在相轨迹图中的四条渐近线形成容许的初始状态棱形区域,形象地给出了无拖曳推力器最大推力不足时的位移模式无拖曳控制让步动力学协调条件。(A method for determining a coordination condition of displacement mode drag-free control dynamics belongs to the technical field of satellite drag-free control, and firstly, a negative stiffness force zero position is assumed to be coincident with a measurement zero position, so that a displacement mode single-degree-of-freedom drag-free control dynamics equation, a simplified dynamics equation common to all axes and a degraded switching dynamics equation are conveniently established; the displacement mode drag-free control system needs to satisfy a constraint relation among three parameters, namely maximum thrust acceleration, negative stiffness coefficient and mechanical limit, which is a basic dynamic coordination condition that the system should satisfy; the allowable initial state prismatic area is formed by solving four asymptotes of a switching kinetic equation in a phase locus diagram, and the coordination condition of the displacement mode drag-free control yielding dynamics when the maximum thrust of the drag-free thruster is insufficient is vividly given.)

1. A method for determining a dynamic coordination condition of displacement mode drag-free control is characterized by comprising the following steps:

s1, assuming that the zero position of the negative stiffness force is coincident with the measurement zero position, and establishing a switching kinetic equation;

s2, solving four asymptotes of a switching kinetic equation in a phase locus diagram under the condition of excitation and no switching; the four asymptotes are crossed to form a prismatic area;

s3, the dynamic coordination condition of the displacement mode drag-free control is at least one of the following two conditions:

basic kinetic coordination conditions: the maximum thrust of the drag-free thruster is larger than the product of the satellite mass, the negative stiffness coefficient and the mechanical limit size;

yielding dynamics coordination conditions: the initial state phase point of the drag-free control degree of freedom must be within the prismatic region.

2. The method for determining the coordination condition of the displacement mode drag-free control dynamics as claimed in claim 1, wherein in S2, the characteristic displacement is defined according to the solution of the switching dynamics equation, the characteristic displacement is corrected according to the sunlight pressure and the atmospheric resistance, the involved acceleration and the thrust noise, and the prism-shaped area in S3 is corrected by using the corrected characteristic displacement.

3. The method for determining the coordination condition of the displacement mode drag-free control dynamics as claimed in claim 1, wherein in S2, the characteristic displacement is defined according to the solution of the switching dynamics equation, the characteristic displacement is corrected according to the propulsion time constant, and the prism-shaped region in S3 is corrected by the corrected characteristic displacement; or; and the moment when the actual output thrust of the drag-free thruster reaches the maximum value for the first time is taken as the corresponding moment of the initial displacement and the initial speed selected by the prismatic area in the S3.

4. The method of claim 1, wherein the prismatic area of S2 is shifted by a negative stiffness force null offset when the negative stiffness force null is not coincident with the measurement null.

5. The method for determining the coordination condition of the displacement mode drag-free control dynamics is characterized in that in S1, a displacement mode single-degree-of-freedom drag-free control dynamics equation is established on the assumption that a negative stiffness force zero position is coincident with a measurement zero position; and obtaining a switching kinetic equation by using a displacement mode single-degree-of-freedom drag-free control kinetic equation.

6. The method for determining the coordination condition of the displacement mode drag-free control dynamics is characterized in that a universal dynamics equation of each axis is obtained after the displacement mode single-degree-of-freedom drag-free control dynamics equation is simplified, and a switching dynamics equation is obtained after the universal dynamics equation of each axis is degenerated.

7. The method for determining the coordination condition of the displacement mode drag-free control dynamics is characterized in that influence factors except the negative stiffness coefficient, the atmospheric resistance and the sunlight pressure resultant acceleration of the inertial sensor are ignored, and a universal dynamic equation of each axis is obtained after the displacement mode single-degree-of-freedom drag-free control dynamics equation is simplified.

8. The method for determining the coordination condition of the displacement mode drag-free control dynamics is characterized in that the maximum thrust configured on the basis of the displacement mode drag-free control actuator is far larger than the resultant force of atmospheric resistance and sunlight pressure, and the switching dynamics equation is obtained after the general dynamics equation of each axis is degraded.

9. The method for determining the coordination condition of the displacement mode drag-free control dynamics as claimed in any one of claims 1 to 8, wherein four asymptotes of the switching dynamics equation in the phase trajectory diagram are solved according to the direction of the excitation.

10. The method for determining the coordinated dynamic condition of the displacement mode drag-free control according to any one of claims 1 to 8, wherein the basic dynamic coordination condition is as follows: the maximum thrust of the drag-free thruster is one order of magnitude or more larger than the product of the mass of the satellite, the negative stiffness coefficient and the mechanical limit size.

Technical Field

The invention relates to a method for determining a dynamic coordination condition of displacement mode drag-free control, and belongs to the technical field of satellite drag-free control.

Background

The non-dragging control technology is a key technology in the technical field of gravity field measurement satellites, gravitational wave detection satellites and equivalent principle inspection satellite control. According to different control targets, the drag-free control is divided into two types, namely acceleration mode drag-free control and displacement mode drag-free control.

The displacement mode drag-free control requires that the proof mass in the on-board inertial sensor be controlled within a small variation range near the nominal position within its electrode cage by a thruster whose thrust is continuously adjustable. The acceleration corresponding to the displacement of the proof mass relative to the nominal position is the result of the combined action of the negative stiffness force of the proof mass under the electrostatic bias and the atmospheric resistance, the sunlight pressure and the thrusting force of the thruster on the satellite. The relative displacement of the proof mass is typically limited within the electrode cage by mechanical limiting means between specified maximum positive and negative displacements.

In the research of a certain non-towing test satellite control scheme, the characteristic of the displacement mode non-towing control system requires that the negative stiffness coefficient, the mechanical limit and the maximum thrust value are mutually constrained. For example, if the thrust maximum is too small, it will result in a transient period of relative displacement control response that is too long, or even not at all, capable of controlling the proof mass back to the nominal position from some harsh initial condition. In the latter possible consequence situation, the inertial sensor must establish proper relative displacement and relative velocity initial value conditions by itself, and the displacement mode can be started and acted normally without dragging control.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: firstly, supposing that a negative stiffness force zero position is coincident with a measurement zero position, a displacement mode single-degree-of-freedom drag-free control dynamics equation, a simplified dynamics equation universal to each axis and a degraded switching dynamics equation are conveniently established; the displacement mode drag-free control system needs to satisfy a constraint relation among three parameters, namely maximum thrust acceleration, negative stiffness coefficient and mechanical limit, which is a basic dynamic coordination condition that the system should satisfy; the allowable initial state prismatic area is formed by solving four asymptotes of a switching kinetic equation in a phase locus diagram, and the coordination condition of the displacement mode drag-free control yielding dynamics when the maximum thrust of the drag-free thruster is insufficient is vividly given. In addition, under the complex environment of actual engineering, the method can also correct the prismatic area by using the involved acceleration, the thrust noise, the propulsion time constant and the zero deviation of the negative stiffness force, so that the coordination condition of the drag-free control yielding dynamics in the displacement mode is more applicable.

The purpose of the invention is realized by the following technical scheme:

a method for determining a dynamic coordination condition of displacement mode drag-free control comprises the following steps:

s1, assuming that the zero position of the negative stiffness force is coincident with the measurement zero position, and establishing a switching kinetic equation;

s2, solving four asymptotes of a switching kinetic equation in a phase locus diagram under the condition of excitation and no switching; the four asymptotes are crossed to form a prismatic area;

s3, the dynamic coordination condition of the displacement mode drag-free control is at least one of the following two conditions:

basic kinetic coordination conditions: the maximum thrust of the drag-free thruster is larger than the product of the satellite mass, the negative stiffness coefficient and the mechanical limit size;

yielding dynamics coordination conditions: the initial state phase point of the drag-free control degree of freedom must be within the prismatic region.

Preferably, in step S2, the characteristic displacement is defined according to a solution of a switching dynamics equation, the characteristic displacement is corrected according to the sunlight pressure, the atmospheric resistance, the involved acceleration and the thrust noise, and the prism region in step S3 is corrected by using the corrected characteristic displacement.

Preferably, in step S2, the characteristic displacement is defined according to a solution of a switching dynamics equation, the characteristic displacement is corrected according to a propulsion time constant, and the prism-shaped region in step S3 is corrected by using the corrected characteristic displacement; or; and the moment when the actual output thrust of the drag-free thruster reaches the maximum value for the first time is taken as the corresponding moment of the initial displacement and the initial speed selected by the prismatic area in the S3.

In the method for determining the coordination condition of the displacement mode drag-free control dynamics, preferably, when the zero position of the negative stiffness force is not coincident with the zero position of the measurement, the prismatic area in the S2 is displaced by using the zero position deviation of the negative stiffness force.

Preferably, in step S1, assuming that the negative stiffness force zero position coincides with the measurement zero position, establishing a displacement mode single degree of freedom drag-free control dynamics equation; and obtaining a switching kinetic equation by using a displacement mode single-degree-of-freedom drag-free control kinetic equation.

Preferably, the method for determining the coordination condition of the displacement mode drag-free control dynamics is used for obtaining a general dynamics equation of each axis after simplifying the displacement mode single-degree-of-freedom drag-free control dynamics equation, and obtaining a switching dynamics equation after degrading the general dynamics equation of each axis.

Preferably, influence factors except for the negative stiffness coefficient, the atmospheric resistance and the sunlight pressure resultant acceleration of the inertial sensor are ignored, and the displacement mode single-degree-of-freedom drag-free control kinetic equation is simplified to obtain the universal kinetic equation of each axis.

Preferably, the maximum thrust configured on the basis of the displacement mode drag-free control actuator is far greater than the resultant force of the atmospheric resistance and the sunlight pressure, and the switching kinetic equation is obtained after the general kinetic equation of each axis is degraded.

Preferably, according to the excitation direction, the method for determining the coordination condition of the displacement mode drag-free control dynamics solves four asymptotes of the switching dynamics equation in the phase trajectory diagram.

The method for determining the dynamic coordination condition of the displacement mode drag-free control comprises the following steps: the maximum thrust of the drag-free thruster is one order of magnitude or more larger than the product of the mass of the satellite, the negative stiffness coefficient and the mechanical limit size.

Compared with the prior art, the invention has the following beneficial effects:

(1) the method provides a displacement mode single-degree-of-freedom drag-free control kinetic equation considering the mass center deviation and the attitude influence;

(2) the method of the invention provides a simplified general kinetic equation of each axis without considering the mass center deviation and the posture influence;

(3) the method gives a switching dynamic equation only considering the degradation of the static negative stiffness force acceleration and the thrust acceleration;

(4) the method provides an analytic solution, a phase locus, an asymptote and a special state point of a switching kinetic equation under the condition of excitation and no switching;

(5) the method provides 7 special phase points, a global phase track and a dynamics coordination condition of a switching dynamics system for controlling degradation in a displacement mode without dragging;

(6) the method of the invention provides a correction strategy when the prismatic area condition is applied in consideration of various complex engineering factor situations.

Drawings

FIG. 1 is a flow chart of the steps of the method of the present invention.

FIG. 2 is a force diagram of a proof mass within an electrode cage of a satellite and its inertial sensors.

FIG. 3 is a schematic diagram of a global phase trajectory of a displacement mode non-drag system degraded switching dynamics system.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

A method for determining a dynamic coordination condition of displacement mode drag-free control comprises the following steps:

s1, assuming that the zero position of the negative stiffness force is coincident with the measurement zero position, and establishing a displacement mode single-degree-of-freedom drag-free control kinetic equation; influence factors except the negative stiffness coefficient, the atmospheric resistance and the sunlight pressure resultant acceleration of the inertial sensor are ignored, the universal kinetic equation of each axis is obtained after the single-degree-of-freedom drag-free control kinetic equation of the displacement mode is simplified, the maximum thrust configured on the basis of the execution mechanism of the displacement mode drag-free control is far larger than the resultant force of the atmospheric resistance and the sunlight pressure, and the switching kinetic equation is obtained after the universal kinetic equation of each axis is degraded;

s2, under the condition of no excitation switching, four asymptotes of a switching kinetic equation in a phase locus diagram are solved according to the direction of excitation; the four asymptotes are crossed to form a prismatic area;

s3, the dynamic coordination condition of the displacement mode drag-free control is at least one of the following two conditions:

basic kinetic coordination conditions: the maximum thrust of the drag-free thruster is larger than the product of the satellite mass, the negative stiffness coefficient and the mechanical limit size;

yielding dynamics coordination conditions: the initial state phase point of the drag-free control degree of freedom must be within the prismatic region.

Further, the basic kinetic coordination conditions are: the maximum thrust of the drag-free thruster is one order of magnitude or more larger than the product of the mass of the satellite, the negative stiffness coefficient and the mechanical limit size.

In S2, characteristic displacement is defined according to the solution of the switching kinetic equation, corrected according to sunlight pressure, atmospheric resistance, involved acceleration and thrust noise, and the corrected characteristic displacement is used for correcting the prismatic area in S3. In addition, in the step S2, the characteristic displacement may be corrected according to the propulsion time constant, and the corrected characteristic displacement is used to correct the prismatic area in the step S3; or; and the moment when the actual output thrust of the drag-free thruster reaches the maximum value for the first time is taken as the corresponding moment of the initial displacement and the initial speed selected by the prismatic area in the S3.

When the negative stiffness force null is not coincident with the measurement null, the prismatic area described in S2 is shifted with a negative stiffness force null bias.