CN113200154A - Displacement mode drag-free control method for eliminating static error - Google Patents

Displacement mode drag-free control method for eliminating static error Download PDF

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CN113200154A
CN113200154A CN202110350449.0A CN202110350449A CN113200154A CN 113200154 A CN113200154 A CN 113200154A CN 202110350449 A CN202110350449 A CN 202110350449A CN 113200154 A CN113200154 A CN 113200154A
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苟兴宇
邹奎
王丽娇
李明群
蒋庆华
王绍凯
孟超
李鹤
李声涛
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Beijing Institute of Control Engineering
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Abstract

The invention relates to a displacement mode drag-free control method for eliminating static error, which belongs to the technical field of satellite drag-free control and comprises the following steps: establishing a general displacement mode single-degree-of-freedom drag-free control kinetic equation under the condition that a proof mass disturbed force model is not limited; assuming that the test mass disturbance force model is a linear function of displacement and time at the same time, substituting the test mass disturbance force acceleration expression into the kinetic equation to obtain a drag-free control kinetic equation under the condition that the test mass disturbance force is the linear function of the displacement and the time at the same time; obtaining a transfer function of a control object by a drag-free control dynamic equation under the condition that the disturbance force of the inspection mass is a linear function of displacement and time, designing a displacement mode drag-free PID + double-integral controller, and establishing a displacement mode drag-free control system; and injecting the displacement mode drag-free PID + double-integral controller into the spacecraft, and performing series correction unit negative feedback drag-free control on the spacecraft based on the controller.

Description

Displacement mode drag-free control method for eliminating static error
Technical Field
The invention relates to a displacement mode drag-free control method for eliminating steady state static deviation of displacement response of a proof mass under the condition that disturbance force of the proof mass linearly changes along with time, 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 interference force of the proof mass, such as the electrostatic bias, and the like, and the combined action of the atmospheric resistance, the sunlight pressure and the thruster thrust 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 engineering practice, the displacement mode drag-free controller often adopts a PID controller. Conceptually, a unit negative feedback control system using a PID controller for series correction can track a constant signal without a dead-beat. However, in the interpretation of the result of the non-towed PID control test of a certain non-towed test satellite in an orbit displacement mode, the proof mass slowly tends to a state that the mean value is a certain non-zero fixed value for a long time and cannot be converged to a target steady state with the mean value being zero. From a linear system control perspective, this can be understood as a result of the presence of a proof mass disturbance component that increases linearly with time.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, provides a displacement mode drag-free control method for eliminating the static error, and solves the problem that the closed-loop system eliminates the steady-state static error under the condition that a time linear disturbance component exists in a detected mass disturbed force function.
The invention has the technical scheme that the displacement mode drag-free control method for eliminating the static error comprises the following steps of:
(1) establishing a general displacement mode single-degree-of-freedom drag-free control kinetic equation under the condition that the detected mass disturbed force model is not limited;
(2) assuming that the model of the disturbance force of the inspection mass is a linear function of displacement and time at the same time, substituting the expression of the acceleration of the disturbance force of the inspection mass into the kinetic equation in the step (1) to obtain a drag-free control kinetic equation under the condition that the disturbance force of the inspection mass is the linear function of the displacement and the time at the same time;
(3) obtaining a transfer function P(s) of a control object by a drag-free control dynamic equation under the condition that the disturbance force of the inspection mass is a linear function of displacement and time, designing a displacement mode drag-free PID + double-integral controller, and establishing a displacement mode drag-free control system;
(4) and (3) injecting the displacement mode drag-free PID + double-integral controller into the spacecraft, performing series correction unit negative feedback drag-free control on the spacecraft based on the controller, and eliminating the steady static difference of the dynamic response of the dynamic equation obtained in the step (2).
The PID + double integral controller transfer function Gc(s) is:
Figure BDA0003002253090000021
in the formula, kpIs a proportionality coefficient, kdIs a differential coefficient, TdIs a first-order inertia time constant, kiIs a single integral coefficient, kiiIs a double integral coefficient.
The first way to inject the displacement mode drag-free PID + dual-integral controller into the spacecraft is:
(4.1a) PID + double integral controller G for enabling displacement mode to be free of draggingc(s) decomposition into the following form:
Gc(s)＝Gpid(s)Gsf1(s)
wherein G ispid(s) is controlled by a controller Gc(s) PID controller consisting of the first three items, Gsf1(s) is a structured filter:
Figure BDA0003002253090000022
(4.2a) for PID controller Gpid(s) carrying out discretization treatment to obtain a discretization coefficient of the PID controller;
(4.3a) a pair structure filter Gpid(s) carrying out discretization treatment to obtain a discretization coefficient of the structural filter;
and (4.4a) respectively injecting the discretization coefficients of the PID controller and the structure filter into the spacecraft through remote control on-orbit modification binding parameters.
The second way to inject the displacement mode drag-free PID + dual-integral controller into the spacecraft is:
(4.1b) PID + double integral controller G for enabling displacement mode to be free of draggingc(s) decomposition into the following form:
Gc(s)＝Gc2(s)Gsf2(s)
wherein G isc2(s) a second order controller with two zeros and one pole:
Figure BDA0003002253090000031
Gsf2(s) is a first order structure filter, and a first order structure filter Gsf2(s) is
Figure BDA0003002253090000032
(4.2b) for the second-order controller Gc2(s) carrying out discretization treatment to obtain a discretization coefficient of a second-order controller;
(4.3b) for the first order structure filter Gsf2(s) carrying out discretization treatment to obtain a discretization coefficient of the first-order structure filter;
and (4.4b) respectively injecting the discretization coefficients of the second-order controller and the first-order structure filter into the spacecraft through remote control on-orbit modification binding parameters.
The general displacement mode single-degree-of-freedom drag-free control kinetic equation is as follows:
Figure BDA0003002253090000033
in the formula, x is the component of the displacement vector from the centroid of the satellite inertial sensor electrode chamber to the center of mass of the inspection mass in the direction of single degree of freedom,
Figure BDA0003002253090000034
the component of the acceleration vector corresponding to the x component in the direction of the single degree of freedom, ans(x, t) is a proof mass disturbance force model fns(x, t) an acceleration expression corresponding to the case where the condition is not defined, and u is a generalized acceleration control amount; a isdIs the component of the resultant force of the atmospheric resistance and the sunlight pressure acting on the satellite along the direction of the free-towing control freedom degree.
Said proof mass perturbed force model fns(x, t) acceleration a corresponding to the case where the number of the first and second electrodes is not limitednsThe expression of (x, t) is:
Figure BDA0003002253090000041
in the formula, MTMThe proof mass is a mass in a displacement mode non-towed satellite inertial sensor.
In the step (1), the disturbance force of the proof mass is simultaneously a linear function of displacement and time:
fns(x，t)＝kxx+ktt+b
in the case of the test mass disturbance force being a linear function of displacement and time, the drag-free control kinetic equation is as follows:
Figure BDA0003002253090000042
in the formula (I), the compound is shown in the specification,
Figure BDA0003002253090000043
wherein k isxTo examine the linear coefficient, k, of the disturbance force of a mass linearly varying with displacementtThe linear coefficient of the disturbance force of the proof mass linearly changes along with time, and b is a constant value item in the disturbance force of the proof mass;
Figure BDA0003002253090000044
is a negative stiffness coefficient, aDFor acceleration due to external disturbance in general, xfns0Zero negative stiffness force to check mass, atAnd t is time, and is a linear coefficient for linearly changing the disturbed acceleration of the proof mass along with the time.
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention provides a novel displacement mode drag-free controller which can enable a closed-loop system to respond and eliminate steady-state static error under the condition that a time linear disturbance component exists in a detected mass disturbance force function;
(2) the invention provides two methods for realizing the novel controller by directly utilizing the on-orbit ready-made structure filter, thereby saving the trouble of on-orbit modification and injection of on-board software.
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FIG. 1 is a flow chart of steps of a method according to an embodiment of the present invention.
FIG. 2 is a simulation result of series correction unit negative feedback control based on a PID controller under the condition that the disturbance force of the proof mass is simultaneously a linear function of displacement and time according to the embodiment of the invention.
FIG. 3 is a simulation result of series calibration unit negative feedback control based on the novel controller under the condition that the disturbance force of the proof mass is simultaneously a linear function of displacement and time according to the embodiment of the invention.
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.
Example (b):
as shown in fig. 1, a displacement mode drag-free control method for eliminating the static error according to one embodiment of the present invention includes the following steps:
(1) establishing a general displacement mode single-degree-of-freedom drag-free control kinetic equation under the condition that the detected mass disturbed force model is not limited;
taking only x degrees of freedom of a certain satellite as the displacement mode non-towing control degrees of freedom as an example, under the condition that the deviation influence of the satellite attitude angular velocity, the attitude angular acceleration, the orbit angular velocity and the nominal position of the inspection mass relative to the satellite centroid is not considered, the most general displacement mode single-degree-of-freedom non-towing control kinetic equation is established as follows:
Figure BDA0003002253090000051
in the formula, x is the component of the displacement vector from the centroid of the satellite inertial sensor electrode chamber to the center of mass of the inspection mass in the direction of single degree of freedom,
Figure BDA0003002253090000052
the component of the acceleration vector corresponding to the x component in the direction of single degree of freedom, in this embodiment, the direction of single degree of freedom is the satellite body coordinateIs in the x-direction; a isns(x, t) is a proof mass disturbance force model fns(x, t) acceleration expression corresponding to the case where the expression is not limited, ansThe expression of (x, t) is:
Figure BDA0003002253090000053
in the formula, MTMThe proof mass is a mass in a displacement mode non-towed satellite inertial sensor. In the kinetic equation, adIs the component of the resultant force of the atmospheric resistance and the sunlight pressure acting on the satellite along the direction of the free-towing control freedom degree. u is a generalized acceleration control quantity and satisfies the relation:
u＝-au
in the formula, auThe thrust acceleration, i.e., the acceleration control amount, is performed for the drag-free control of the satellite in the direction of the single degree of freedom.
(2) Assuming that the model of the disturbance force of the inspection mass is a linear function of displacement and time at the same time, substituting the expression of the acceleration of the disturbance force of the inspection mass into the kinetic equation in the step (1) to obtain a drag-free control kinetic equation under the condition that the disturbance force of the inspection mass is the linear function of the displacement and the time at the same time;
while proof mass perturbed force is a linear function of both displacement and time:
fns(x，t)＝kxx+ktt+b
in this case, the so-called proof mass perturbed force acceleration in the step (1) kinetic equation is written as:
Figure BDA0003002253090000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003002253090000062
referred to as the negative stiffness coefficient, is generally a known parameter. In the expression of the negative stiffness force acceleration,
Figure BDA0003002253090000063
called the negative stiffness force null, known or unknown.
Figure BDA0003002253090000064
As time-varying linear coefficients. Substituting the expression of the acceleration of the disturbed force of the proof mass into the kinetic equation in the step (1) to obtain the drag-free control kinetic equation under the condition that the disturbed force of the proof mass is a linear function of displacement and time as follows:
Figure BDA0003002253090000065
in the formula (I), the compound is shown in the specification,
Figure BDA0003002253090000066
the linear time-varying acceleration sensor is a generalized disturbance acceleration and has a linear time-varying characteristic.
In the above formulae, wherein kxTo examine the linear coefficient, k, of the disturbance force of a mass linearly varying with displacementtThe linear coefficient of the disturbance force of the proof mass linearly changes along with time, and b is a constant value item in the disturbance force of the proof mass;
Figure BDA0003002253090000067
is a negative stiffness coefficient, aDFor acceleration due to external disturbance in general, xfns0Zero negative stiffness force to check mass, atAnd t is time, and is a linear coefficient for linearly changing the disturbed acceleration of the proof mass along with the time.
(3) Obtaining a transfer function P(s) of a control object by a drag-free control dynamic equation under the condition that the disturbance force of the inspection mass is a linear function of displacement and time, designing a displacement mode drag-free PID + double-integral controller, and establishing a displacement mode drag-free control system;
obtaining a transfer function of a control object by a drag-free control dynamic equation under the condition that the disturbance force of the proof mass is a linear function of displacement and time, namely the transfer function from the generalized acceleration control quantity u to the output displacement x:
Figure BDA0003002253090000071
for a system with time-varying linear disturbance, if a traditional PID controller is used for series correction unit negative feedback control, the steady-state mean value of the dynamic response of the closed-loop system inevitably has static deviation relative to the command displacement. But the following PID + double integral controller is designed to carry out series correction on the control object:
Figure BDA0003002253090000072
the static error can be eliminated. In the formula, kpIs a proportionality coefficient, kdIs a differential coefficient, TdIn order to be a first-order time constant of inertia,iis a single integral coefficient, kiiThe two integral coefficients are all given parameters. The above formula is organized into the following rational fractional format:
Figure BDA0003002253090000073
obviously, the forward channel transfer function of the displacement mode drag-free control system at this time is:
Φ(s)＝Gc(s)Gt(s)P(s)
in the formula, Gt(s) is a transfer function model of the actuator. The forward channel transfer function has the advantage that the transfer function has the tolerance of 2, and a single negative feedback closed-loop system has no static error under the slope disturbance. This conclusion holds whether the ramp disturbance is from proof mass disturbance or other non-conservative external disturbance forces such as atmospheric drag or solar pressure.
(4) And (3) injecting the displacement mode drag-free PID + double-integral controller into the spacecraft, performing series correction unit negative feedback drag-free control on the spacecraft based on the controller, and eliminating the steady static difference of the dynamic response of the dynamic equation obtained in the step (2).
The on-orbit implementation of the spacecraft generalized controller generally comprises the links of an anti-aliasing filter, a narrow-sense controller, a standby structure filter and the like. Among them, the narrow-sense controller is often set to a discrete format typified by a PID controller. Therefore, the novel controller can be realized by modifying the discretization coefficient of each link of the generalized controller in a remote control mode. Two transfer function decomposition methods are provided for the novel controller, and the two implementation schemes correspond to two implementation schemes for remotely modifying each link coefficient of the generalized controller.
The first embodiment is:
(4.1a) PID + double integral controller G for enabling displacement mode to be free of draggingc(s) decomposition into the following form:
Gc(s)＝Gpid(s)Gsf1(s)
wherein G ispid(s) is controlled by a controller Gc(s) PID controller consisting of the first three items, Gsf1(s) is a structured filter;
a PID controller:
Figure BDA0003002253090000081
the rational formula format of (1) is:
Figure BDA0003002253090000082
this is typically a second order element.
Structural filter Gsf1(s) is a typical 3-order link, specifically:
Figure BDA0003002253090000083
(4.2a) for PID controller Gpid(s) carrying out discretization treatment to obtain a discretization coefficient of the PID controller;
(4.3a) a pair structure filter Gpid(s) carrying out discretization treatment to obtain a discretization coefficient of the structural filter;
and (4.4a) respectively injecting the discretization coefficients of the PID controller and the structure filter into the spacecraft through remote control on-orbit modification binding parameters.
In other words, the method presented in this step decomposes the new controller into a series result of a PID controller and a 3 rd order structure filter. And then respectively carrying out discretization treatment, giving discretization coefficients corresponding to the PID controller and the 3-order structure filter, and modifying by remote control.
The second embodiment is:
(4.1b) PID + double integral controller G for enabling displacement mode to be free of draggingc(s) decomposition into the following form:
Gc(s)＝Gc2(s)Gsf2(s)
wherein G isc2(s) a second order controller with two zeros and one pole:
Figure BDA0003002253090000091
Gsf2(s) is a first order structure filter, and a first order structure filter Gsf2(s) is
Figure BDA0003002253090000092
(4.2b) for the second-order controller Gc2(s) carrying out discretization treatment to obtain a discretization coefficient of a second-order controller;
(4.3b) for the first order structure filter Gsf2(s) carrying out discretization treatment to obtain a discretization coefficient of the first-order structure filter;
and (4.4b) respectively injecting the discretization coefficients of the second-order controller and the first-order structure filter into the spacecraft through remote control on-orbit modification binding parameters.
In the step, the zpk function of Matlab is adopted to obtain 3 nonzero zero points z of the novel controller1、z2、z31 non-zero pole p3And 1 constant gain coefficient k. The other two zero points of the novel controller are zero. On the basis, the narrow controller is designated as the combination of a certain two zeros and a certain two poles, and the combination of the remaining one zero and the remaining one pole is defined as a structural filter. And then, respectively carrying out discretization processing on the second-order controller and the structural filter, giving discretization coefficients corresponding to the second-order controller and the first-order structural filter, and modifying by remote control.
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 (7)

1. A displacement mode drag-free control method for eliminating static error is characterized in that the following steps are executed for a single degree of freedom:
(1) establishing a general displacement mode single-degree-of-freedom drag-free control kinetic equation under the condition that the detected mass disturbed force model is not limited;
(2) assuming that the model of the disturbance force of the inspection mass is a linear function of displacement and time at the same time, substituting the expression of the acceleration of the disturbance force of the inspection mass into the kinetic equation in the step (1) to obtain a drag-free control kinetic equation under the condition that the disturbance force of the inspection mass is the linear function of the displacement and the time at the same time;
(3) obtaining a transfer function P(s) of a control object by a drag-free control dynamic equation under the condition that the disturbance force of the inspection mass is a linear function of displacement and time, designing a displacement mode drag-free PID + double-integral controller, and establishing a displacement mode drag-free control system;
(4) and (3) injecting the displacement mode drag-free PID + double-integral controller into the spacecraft, performing series correction unit negative feedback drag-free control on the spacecraft based on the controller, and eliminating the steady static difference of the dynamic response of the dynamic equation obtained in the step (2).
2. The static-error-eliminating displacement-mode drag-free control method as claimed in claim 1, wherein the PID + double-integral controller transfer function Gc(s) is:
Figure FDA0003002253080000011
in the formula, kpIs a proportionality coefficient, kdIs a differential coefficient, TdIs a first-order inertia time constant, kiIs a single integral coefficient, kiiIs a double integral coefficient.
3. The method for controlling the displacement mode without dragging to eliminate the static error according to claim 2, wherein the following method is adopted to inject the displacement mode without dragging PID + double integral controller into the spacecraft:
(4.1a) PID + double integral controller G for enabling displacement mode to be free of draggingc(s) decomposition into the following form:
Gc(s)＝Gpid(s)Gsf1(s)
wherein G ispia(s) is controlled by a controller Gc(s) PID controller consisting of the first three items, Gsf1(s) is a structured filter:
Figure FDA0003002253080000021
(4.2a) for PID controller Gpia(s) carrying out discretization treatment to obtain a discretization coefficient of the PID controller;
(4.3a) a pair structure filter Gpid(s) performing a discretization process,obtaining a discretization coefficient of the structural filter;
and (4.4a) respectively injecting the discretization coefficients of the PID controller and the structure filter into the spacecraft through remote control on-orbit modification binding parameters.
4. The method for controlling the displacement mode without dragging to eliminate the static error according to claim 2, wherein the following method is adopted to inject the displacement mode without dragging PID + double integral controller into the spacecraft:
(4.1b) PID + double integral controller G for enabling displacement mode to be free of draggingc(s) decomposition into the following form:
Gc(s)＝Gc2(s)Gsf2(s)
wherein G isc2(s) a second order controller with two zeros and one pole:
Figure FDA0003002253080000022
Gsf2(s) is a first order structure filter, and a first order structure filter Gsf2(s) is
Figure FDA0003002253080000023
(4.2b) for the second-order controller Gc2(s) carrying out discretization treatment to obtain a discretization coefficient of a second-order controller;
(4.3b) for the first order structure filter Gsf2(s) carrying out discretization treatment to obtain a discretization coefficient of the first-order structure filter;
and (4.4b) respectively injecting the discretization coefficients of the second-order controller and the first-order structure filter into the spacecraft through remote control on-orbit modification binding parameters.
5. The method according to claim 1, wherein the general form of the single-degree-of-freedom drag-free control dynamics equation of the displacement mode is as follows:
Figure FDA0003002253080000031
in the formula, x is the component of the displacement vector from the centroid of the satellite inertial sensor electrode chamber to the center of mass of the inspection mass in the direction of single degree of freedom,
Figure FDA0003002253080000035
the component of the acceleration vector corresponding to the x component in the direction of the single degree of freedom, ans(x, t) is a proof mass disturbance force model fns(x, t) an acceleration expression corresponding to the case where the condition is not defined, and u is a generalized acceleration control amount; a isdIs the component of the resultant force of the atmospheric resistance and the sunlight pressure acting on the satellite along the direction of the free-towing control freedom degree.
6. The method of claim 5, wherein the proof mass disturbance model f is a model of the proof mass disturbancens(x, t) acceleration a corresponding to the case where the number of the first and second electrodes is not limitednsThe expression of (x, t) is:
Figure FDA0003002253080000032
in the formula, MTMThe proof mass is a mass in a displacement mode non-towed satellite inertial sensor.
7. The method for drag-free control of displacement mode with elimination of static error as claimed in claim 1, wherein in step (1), the proof mass disturbance force is a linear function of both displacement and time:
fns(x，t)＝kxx+ktt+b
in the case of the test mass disturbance force being a linear function of displacement and time, the drag-free control kinetic equation is as follows:
Figure FDA0003002253080000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003002253080000034
wherein k isxTo examine the linear coefficient, k, of the disturbance force of a mass linearly varying with displacementtThe linear coefficient of the disturbance force of the proof mass linearly changes along with time, and b is a constant value item in the disturbance force of the proof mass;
Figure FDA0003002253080000036
is a negative stiffness coefficient, aDFor acceleration due to external disturbance in general, xfns0Zero negative stiffness force to check mass, atAnd t is time, and is a linear coefficient for linearly changing the disturbed acceleration of the proof mass along with the time.
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