CN111638643A - Displacement mode drag-free control dynamics coordination condition determination method - Google Patents
Displacement mode drag-free control dynamics coordination condition determination method Download PDFInfo
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Abstract
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.
Description
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.
Example (b):
a method for determining a dynamic coordination condition of displacement mode drag-free control, as shown in FIG. 1, includes the following steps:
and (1) establishing a displacement mode single-degree-of-freedom drag-free control kinetic equation under the condition of mass center deviation and posture influence.
Taking only x degrees of freedom of a certain satellite as the displacement mode drag-free control degrees of freedom as an example, under the condition that the drag-free control displacement has deviation relative to the center of mass of the satellite so that the drag-free control displacement is influenced by the attitude, establishing a displacement mode single degree of freedom drag-free control kinetic equation as follows:
wherein x is the component of the centroid of the satellite inertial sensor electrode chamber, namely the displacement vector from the appointed measurement zero position to the mass center of the proof mass in the x direction of the satellite body coordinate system,
is the component of the corresponding acceleration vector in the x-direction of the satellite body coordinate system, auExecuting thrust acceleration, namely an acceleration control quantity, for the non-drag control of the satellite in the x direction; the generalized negative stiffness coefficient is:
the generalized external disturbance acceleration is:
in the formula, ωSCx、ωSCyAnd omegaSCzBeing the component of the inertial angular velocity of the satellite in the satellite body coordinate system,
and
angular acceleration, which is an inertial angular velocity component;
the negative stiffness coefficient of the inertial sensor is obtained, the product of the negative stiffness coefficient of the inertial sensor and the displacement coordinate x is the negative stiffness force, and the negative stiffness force is characterized in that: the method is different from the common situation that the restoring force direction of the spring is opposite to the displacement coordinate, and the negative stiffness force is the same as the positive direction of the displacement coordinate; r isSCIs the length of the sagittal from the geocentric to the satellite centroid; theta, theta,
The attitude angles of the satellite relative to the pitch and roll of the orbit coordinate system of the satellite; x is the number ofH、yHAnd zHThe component of the fixed length vector diameter from the satellite centroid to the electrode chamber centroid in the directions of the three axes of the satellite body coordinate system x, y and z is shown; omega0Is the satellite orbit angular velocity; a isdThe resultant acceleration of the atmospheric resistance and the solar pressure in the x direction is also referred to as resistance acceleration.
The position where the actual negative stiffness force is zero is referred to as the negative stiffness force null position. In a strict sense, the designated measurement zero position is required to coincide with the negative stiffness force zero position, and the error is smaller than the resolution of displacement measurement. At the beginning of this step, the negative stiffness force zero position is assumed to coincide with the measurement zero position, and for the case where the negative stiffness force zero position does not coincide with the measurement zero position, the correction is made in step (7.4).
And (3) simplifying each axis general kinetic equation and characteristics thereof in the step (2).
In engineering practice, the negative stiffness coefficient of the inertial sensor is absolutely dominant in the generalized negative stiffness coefficient, and the atmospheric resistance and the sunlight pressure resultant acceleration are absolutely dominant in the generalized external disturbance acceleration, so that the kinetic equation in the step (1) can be simplified as follows:
for simplicity, the negative stiffness coefficient has been omitted from the above equation
Subscript x of (a). In addition, although the displacement state variable in the above formula is written as x, the above formula is still applicable to the case where the degree of freedom of the drag-free control is y or z, and it is only necessary to use x,
Respectively replaced by y,
Or z,
Then the method is finished; accordingly, ad、auAnd correspondingly represents the resistance acceleration in the y direction or the z direction and the non-dragging control thrust acceleration.
The above formula clearly shows different features from the common kinetic equations. Fig. 2 shows a force diagram of a satellite and its inertial sensor electrode cage with proof masses corresponding to the above formula. The different features are easy to understand in connection with this figure. First, the second term at the left end of the above equation is negative in form, opposite in sign to the conventional positive stiffness term, which is also true
Is known as the root cause of the negative stiffness coefficient. Secondly, since the resistive acceleration is generally opposite to the positive direction of the freedom degree of the drag-free control, i.e. takes a negative value, the resistive acceleration just provides the positive acceleration for the freedom degree of the drag-free control as seen from the above formula. Thirdly, when the thrust acceleration is provided by a thruster with a-x surface outputting the thrust direction pointing to + x, the acceleration is positive, and the acceleration just provides negative acceleration for the control freedom degree without dragging according to the formula; when the thrust acceleration is changed from + xThe acceleration is positive when provided by a thruster with the face output thrust direction pointing at-x, and as can be seen from the above equation, the acceleration provides just a negative acceleration for the no-drag control degree of freedom.
Therefore, in actual engineering, the non-drag thruster outputs the maximum thrust max (F) in the forward directiont) The following conditions must be satisfied:
where M is the satellite mass (mass not including the proof mass itself). When the above conditions are met, the drag-free control may have the ability to provide negative acceleration in the corresponding control degree of freedom. The satellite is usually equipped with a negative thruster, and the flexible positive acceleration capability is realized without dragging control.
And (4) degenerate switching kinetic equation and meaning thereof in the step (3).
In engineering practice, in order to ensure the rapidity of the control transition process, a thruster with the maximum thrust far greater than the resultant force of atmospheric resistance and sunlight pressure is generally configured as an actuating mechanism for displacement mode drag-free control, namely:
max(Ft)＞＞M·max(|ad|)
the same thrusters are arranged in the positive and negative directions of the satellite non-dragging control freedom degree. On the basis of the general kinetic equation of each axis in the step (2), obtaining a switching kinetic equation through degeneration as follows:
in the formula (I), the compound is shown in the specification,
the implication of this switching kinetics equation is: the inspection mass in the satellite inertial sensor electrode cage only has the motion freedom degree in the +/-x direction and is subjected to negative rigidity force
The non-conservative external disturbance force of the satellite is only the thrust in the +/-x direction. And when the detected mass state displacement x is positive, the non-dragging control propulsion system outputs negative maximum thrust. When proof mass state displacement x is negative, the non-towed control propulsion system outputs a positive maximum thrust.
And (4) carrying out analytic solution, phase locus, asymptote and special state point on the switching kinetic equation when no switching is excited and the switching kinetic equation is designated as-a.
The analytical solution can be obtained by integrating the switching dynamics equation as follows:
in the formula, x0X (0) represents the initial displacement,
represents the initial velocity, thereby
Is the initial state phase point. The time history of the velocity state quantity derived from the above equation is:
synthesizing the two formulas to obtain a phase plane
The phase trajectory equation in (1) is:
this is the phase plane
One quadratic curve of the above. This formula can be further rewritten as:
in the formula (I), the compound is shown in the specification,
as can be seen from the phase trajectory rewrite, there are two asymptotes when the constant excitation term at the right end of the switching kinetics equation is-a:
obviously, this is also exactly the coefficient b1Phase trajectory function at 0. For simplicity of expression, let:
xmreferred to as feature displacement. If the maximum thrusts of the positive and negative direction thrusters without the dragging freedom degrees are not consistent, a smaller alternative formula is conservatively taken to calculate the characteristic displacement. b1Three special phase points are also given when 0:
where the first phase point is exactly the intersection of the two asymptotes. Starting from the second phase point, the phase trajectory approaches the first phase point infinitely along a second asymptote, but never reaches it. Starting from some initial value slightly off the first phase point to the left and at the first asymptote, the third phase point may be reached faster and faster.
And (5) switching an analytic solution, a phase locus, an asymptote and a special state point of the kinetic equation when no switching is excited and the appointed value is + a.
The analytical solution can be obtained by integrating the switching dynamics equation as follows:
the time history of the velocity state quantity is:
the following two equations are synthesized to obtain a phase trajectory equation:
still a quadratic curve. This formula can be further rewritten as:
in the formula (I), the compound is shown in the specification,
it can be seen that this case adds two asymptotes on the basis of the excitation fixation to the-a case:
and a special phase point:
the phase point is just the intersection point of the two newly added asymptotes. From the third phase point, the phase track infinitely approaches the phase point along the newly added second asymptote, but can never reach the phase point. The second phase point may be reached more and more quickly starting from an initial value that is slightly off to the right of the newly added phase point and is at the newly added first asymptote.
And (6) controlling 7 special phase points, global phase tracks and dynamics coordination conditions of the degraded switching dynamics system in the displacement mode without dragging.
In engineering practice, the range of motion of the proof mass centroid is always constrained by mechanical limits, and the mechanical limits are left-right symmetric about the state origin. Let the right mechanical limit be xdThen, generally, there are 7 phase points that determine the proof mass centroid relative to the inertial sensor electrode centroid motion phase trajectory. Wherein the first 4 phase points are shown in the step (4) and the step (5), and in the other 3 phase points,
is a right mechanical limit phase point;
is a left mechanical limit phase point;
is a phase plane
Upper origin.
At a-0.5882 μm/s2、
xdAs an example, 10 μm, the above 4 asymptotes are drawn on the phase plane, the 7 points are marked, and the initial phase point is optionally selected for simulation, so as to obtain the global phase trajectory diagram shown in fig. 3. In the figure, the dotted line is an asymptote line, the star point is a special phase point, the round point is an initial state point arbitrarily selected by simulation, and the solid line is an initial state point arbitrarily selected from the beginningThe phase locus of the phase point moves away from the dots.
When parameters such as maximum thrust acceleration, negative stiffness coefficient, characteristic displacement and mechanical limit change, the positions of 6 special phase points except the origin in fig. 3 also change, and 4 asymptotes also change, but the characteristics of the whole phase plane divided into 5 areas, namely an upper area, a lower area, a left area, a right area and a middle area, by the 4 asymptotes and the evolution trend of the phase trajectory in the 5 areas are always unchanged.
FIG. 3 shows: 4 asymptotes surround the origin to form a prismatic area, the initial phase point is only positioned in the prismatic area to ensure that the subsequent phase locus is limited in the prismatic area, and the characteristic displacement xmIt is an extreme displacement parameter determined by the maximum acceleration together with the negative stiffness coefficient. It will be appreciated that if the initial phase point falls outside this prismatic region, the phase trajectory cannot return to the commanded state, i.e. near the origin, as a displacement mode drag-free control, whatever the control method employed, and will eventually end up at the left or right mechanical limit point under mechanical limit action. Therefore, in engineering practice, relevant parameters of the non-dragging control system should be reasonably selected, so that the mechanical limit phase point falls within the prismatic area, namely:
xm＞xd
based on the above knowledge, the dynamic coordination conditions of the displacement mode drag-free control are summarized as follows:
the maximum thrust, the negative stiffness coefficient and the mechanical limit of the drag-free thruster in the step (6.1) satisfy the following relations:
this is the basic dynamic coordination condition for building a displacement mode drag-free control system.
In engineering practice, in order to ensure the rapidity of the control transition process, the three key parameters are often required to satisfy the following constraint relation:
i.e. | FtThe ratio of I to M,
xdThe product of (a) is one order and more greater.
And (6.2) if the first formula of the step (6.1) is not satisfied, the initial state phase point of the degree of freedom of the drag-free control must fall in the prismatic area, which is called the prismatic area condition for short.
Before initiating displacement mode drag-free control, the proof mass in the inertial sensor electrode cage is in electrostatic levitation control for all 6 degrees of freedom. The satellite establishes an initial state for drag-free control of one or several degrees of freedom by releasing electrostatic levitation control of those degrees of freedom. During the in-orbit test carried out by the non-towed test satellite or the in-orbit test and adjustment carried out by the non-towed scientific mission satellite, the situation that the first type of the step (6.1) cannot be met possibly occurs due to the reason that the static negative stiffness coefficient is set too large and the like, namely the situation that the in-orbit test of a certain type of satellite mentioned in the last paragraph in the background of the invention occurs. In this case, the initial state phase point of any one of the drag-free control degrees of freedom
The inequality of the prismatic zone condition that should be satisfied is:
the above formula shows that under the premise of negative stiffness coefficient specification, the prismatic region can be expressed by only one parameter of characteristic displacement. Therefore, when conservative correction is carried out on the prismatic area by further considering various factors, the characteristic displacement x is directly correctedmAnd (5) correcting.
And (7) further considering various engineering links to correct the characteristic displacement.
And (7.1) correcting the characteristic displacement under the influence of various generalized non-conservative external disturbance force accelerations and noise.
Let the non-conservative external interference force be FdThe acceleration of the attitude motion induced by the centroid deviation at the nominal position of the proof mass is aerkThe latter includes three components of the bulk acceleration, the relative acceleration and the Coriolis acceleration, which are the synthesis results of the components of the three components in the x direction. The attitude of the drag-free satellite moves slowly, the deviation of the mass center reaches to a meter level at most, and the inspection mass is very little relative to the movement speed of the satellite, so that the attitude of the drag-free satellite moves slowly at aerkNeglecting relative acceleration and Coriolis acceleration, namely:
aerk≈ae＝ed
if the displacement mode non-dragging control is performed in the + -x direction of the satellite fixed coordinate system, the above formulaeD is a component of a yoz plane of a satellite fixed coordinate system, and an estimation upper limit value is generally adopted. The rest two axes refer to the method and are not described in detail.
Aiming at the influence of the generalized non-conservative external disturbance force acceleration, a characteristic displacement expression is modified as follows:
make the power spectral density function of thrust noise as St(f) And making the bandwidth of the displacement mode drag-free closed-loop control system be fNSo that the standard deviation of the thrust noise is:
then, under the influence of thrust noise, the characteristic displacement expression is further modified as follows:
displacement mode drag-free closed loop control systems measure relative displacement. In general, the relative displacement measurement accuracy is high, and the contribution of the measurement noise to the characteristic displacement is small and thus ignored.
Step (7.2) is based on step (7.1), and takes into account other factors such as the propulsion time constant.
In the displacement mode drag-free control system, the model parameters, the control period, the controller parameters and the like of the control part all affect the allowable value of the initial phase point. The actual displacement of the proof mass is picked up by a sensor, filtered and output, so that delay is inevitable; the controller takes a certain time for taking the sensor data and outputting the instruction thrust through the operation of a control algorithm; due to its time constant, the non-towed propulsion subsystem often has a longer lag from its receipt of the commanded thrust output by the controller to its output of the actual thrust. The influence of the propulsion time constant dominates among these factors.
The effect of these factors on the conditions of the prismatic zone can be considered in the following two ways.
Firstly, a correction factor is introduced into the expression of the characteristic displacement, namely, the correction is carried out on the basis of (7.1) as follows:
wherein the correction coefficient c is less than 1.
And secondly, judging whether the prismatic area condition in the step (6.2) is met or not based on the characteristic displacement expression in the step (7.1), wherein the selected initial displacement and initial speed are based on the corresponding value of the inspection mass when the actual output thrust reaches the maximum value.
And (7.3) influence of zero offset of negative stiffness force.
In step (1) it has been pointed out that, in a strict sense, the zero negative stiffness force should coincide with the designated zero measurement position. However, it is not easy to do this in the engineering practice, and the actual negative stiffness force zero position xfns0And may even deviate significantly from the measurement null.
In this case, the kinetic equations in steps (1), (2) and (3) need to be modified. The specific method is to replace x in the second term at the left end of the equation by x-xfns0。
In this case, when determining whether the initial phase point satisfies the condition of the prismatic area, the characteristic displacement needs to be further corrected to obtain the condition of the prismatic area shifted in the phase plane. The specific method is that x in the conditional inequality of the prismatic region is dividedmIs replaced by xm-xfns0。
At xmIs replaced by xm-xfns0Before, when xfns0＞xmNo matter where the initial phase point is, no-drag control using the measurement zero as the command position is completely impossible.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.
Claims (10)
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.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113200154A (en) * | 2021-03-31 | 2021-08-03 | 北京控制工程研究所 | Displacement mode drag-free control method for eliminating static error |
| CN113219820A (en) * | 2021-03-31 | 2021-08-06 | 北京控制工程研究所 | Method for extracting zero position of negative stiffness force of inertial sensor by using drag-free control |
| CN114326656A (en) * | 2021-12-06 | 2022-04-12 | 兰州空间技术物理研究所 | Satellite non-dragging technology on-orbit verification method |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106507770B (en) * | 2012-04-05 | 2014-09-10 | 上海新跃仪表厂 | A kind of method with gravity gradient satellite rail control is realized without towing technology |
| CN105629739A (en) * | 2016-03-31 | 2016-06-01 | 北京航空航天大学 | Output feedback anti-interference control method of drag-free satellite relative displacement channel |
| US20170081022A1 (en) * | 2015-09-17 | 2017-03-23 | Airbus Defence and Space GmbH | Cooperative actuator system for active flow control |
| CN107390526A (en) * | 2017-07-31 | 2017-11-24 | 北京控制工程研究所 | A kind of spacecraft of feature based model is without towing control method |
-
2020
- 2020-05-07 CN CN202010377593.9A patent/CN111638643B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106507770B (en) * | 2012-04-05 | 2014-09-10 | 上海新跃仪表厂 | A kind of method with gravity gradient satellite rail control is realized without towing technology |
| US20170081022A1 (en) * | 2015-09-17 | 2017-03-23 | Airbus Defence and Space GmbH | Cooperative actuator system for active flow control |
| CN105629739A (en) * | 2016-03-31 | 2016-06-01 | 北京航空航天大学 | Output feedback anti-interference control method of drag-free satellite relative displacement channel |
| CN107390526A (en) * | 2017-07-31 | 2017-11-24 | 北京控制工程研究所 | A kind of spacecraft of feature based model is without towing control method |
Non-Patent Citations (1)
| Title |
|---|
| 张锦绣 等: ""基于无速度测量的无拖曳卫星自适应控制方法"", 《宇航学报》, vol. 35, no. 4, 30 April 2014 (2014-04-30), pages 447 - 453 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113200154A (en) * | 2021-03-31 | 2021-08-03 | 北京控制工程研究所 | Displacement mode drag-free control method for eliminating static error |
| CN113219820A (en) * | 2021-03-31 | 2021-08-06 | 北京控制工程研究所 | Method for extracting zero position of negative stiffness force of inertial sensor by using drag-free control |
| CN113219820B (en) * | 2021-03-31 | 2023-02-24 | 北京控制工程研究所 | Method for extracting zero position of negative stiffness force of inertial sensor by using drag-free control |
| CN114326656A (en) * | 2021-12-06 | 2022-04-12 | 兰州空间技术物理研究所 | Satellite non-dragging technology on-orbit verification method |
| CN114326656B (en) * | 2021-12-06 | 2024-04-12 | 兰州空间技术物理研究所 | Satellite non-dragging technology on-orbit verification method |
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