CN113200154B - Displacement mode drag-free control method for eliminating static error - Google Patents
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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 a 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
Technical Field
The invention relates to a displacement mode drag-free control method for eliminating steady 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 in the electrode cage by a thruster with continuously adjustable thrust. The acceleration corresponding to the displacement of the proof mass relative to the nominal position is the result of the disturbance of the proof mass, such as electrostatic bias, acting on the satellite by the atmospheric resistance, the sunlight pressure and the thrustor thrust. 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 the result of the proof mass disturbance being present with a 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 detected mass disturbance force model is a linear function of displacement and time at the same time, substituting the detected mass disturbance force acceleration expression into the dynamic equation in the step (1) to obtain a drag-free control dynamic equation under the condition that the detected mass disturbance force is the displacement and time linear function 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 equation dynamic response obtained in the step (2).
The PID + double integral controller transfer function G c (s) is:
in the formula, k p Is a proportionality coefficient, k d Is a differential coefficient, T d Is a first-order inertia time constant, k i Is a single integral coefficient, k ii Is a double integral coefficient.
The first way of injecting the displacement mode drag-free PID + double integral controller into the spacecraft is as follows:
(4.1 a) PID + double integral controller G for enabling displacement mode to be free of dragging c (s) decomposition into the following form:
G c (s)＝G pid (s)G sf1 (s)
wherein, G pid (s) is controlled by a controller G c (s) PID controller consisting of the first three items, G sf1 (s) is a structured filter:
(4.2 a) to PID controller G pid (s) carrying out discretization treatment to obtain a discretization coefficient of the PID controller;
(4.3 a) a pair structure filter G pid (s) carrying out discretization treatment to obtain a discretization coefficient of the structure filter;
and (4.4 a) 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 of injecting the displacement mode drag-free PID + dual integral controller into the spacecraft is:
(4.1 b) non-dragging PID + double integral controller G for displacement mode c (s) decomposition into the following form:
G c (s)＝G c2 (s)G sf2 (s)
wherein G is c2 (s) a second order controller with two zeros and one pole:
G sf2 (s) is a first order structure filter, and a first order structure filter G sf2 (s) is
(4.2 b) for the second-order controller G c2 (s) carrying out discretization treatment to obtain a discretization coefficient of a second-order controller;
(4.3 b) for the first order structure filter G sf2 (s) carrying out discretization treatment to obtain a discretization coefficient of the first-order structure filter;
and (4.4 b) 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:
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,
the component of the acceleration vector corresponding to the x component in the direction of a single degree of freedom, a ns (x, t) is a proof mass disturbance force model f ns (x, t) an acceleration expression corresponding to the case where the condition is not defined, and u is a generalized acceleration control amount; a is d Is 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 f ns (x, t) acceleration a corresponding to the case where the number of the first and second electrodes is not limited ns The expression of (x, t) is:
in the formula, M TM The 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:
f ns (x，t)＝k x x+k t t+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:
in the formula (I), the compound is shown in the specification,
wherein k is x To examine the linear coefficient, k, of the disturbance force of a mass linearly varying with displacement t For testing disturbance of massLinear coefficient of force changing linearly with time, b is constant term in the disturbance force of the proof mass;
is a negative stiffness coefficient, a D For acceleration due to external disturbance in general, x fns0 Zero negative stiffness force to check mass, a t And 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.
Drawings
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 new controller under the condition of inspecting the disturbance force of the mass as 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 drag-free control degree of freedom as an example, under the condition that the deviation influence of the attitude angular velocity, the attitude angular acceleration, the orbit angular velocity and the nominal position of the inspection mass of the satellite relative to the center of mass of the satellite is not considered, the most general form of the displacement mode single degree of freedom drag-free control kinetic equation is established as follows:
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,
the component of the acceleration vector corresponding to the x component in the direction of single degree of freedom is shown, in this embodiment, the direction of single degree of freedom is the x direction of the satellite body coordinate system; a is ns (x, t) is proof mass disturbance model f ns (x, t) acceleration expression corresponding to the case where the expression is not limited, a ns The expression of (x, t) is:
in the formula, M TM The proof mass is a mass in a displacement mode non-towed satellite inertial sensor. In the kinetic equation, a d Is 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＝-a u
in the formula, a u The 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 is perturbed, it is a linear function of both displacement and time:
f ns (x，t)＝k x x+k t t+b
in this case, the so-called proof mass perturbed force acceleration in the step (1) kinetic equation is written as:
in the formula (I), the compound is shown in the specification,
referred to as the negative stiffness coefficient, is generally a known parameter. In the expression of the negative stiffness force acceleration,
called the negative stiffness force null, known or unknown.
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:
in the formula (I), the compound is shown in the specification,
the linear time-varying acceleration sensor is a generalized disturbance acceleration and has a linear time-varying characteristic.
In the above formulae, wherein k x To examine the linear coefficient, k, of the disturbance force of a mass linearly varying with displacement t The 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;
is a negative stiffness coefficient, a D For acceleration due to external disturbance in general, x fns0 Zero negative stiffness force to check mass, a t And 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:
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:
the static error can be eliminated. In the formula, k p Is a proportionality coefficient, k d Is a differential coefficient, T d In order to be a first-order time constant of inertia, i is a single integral coefficient, k ii The two integral coefficients are all given parameters. The above formula is organized into the following rational fractional format:
obviously, the forward channel transfer function of the displacement mode drag-free control system at this time is:
Φ(s)＝G c (s)G t (s)P(s)
in the formula, G t (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 through remote control. 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:
(4.1 a), non-dragging PID + double integral controller G of displacement mode c (s) decomposition into the following form:
G c (s)＝G pid (s)G sf1 (s)
wherein G is pid (s) is controlled by a controller G c (s) PID controller consisting of the first three items, G sf1 (s) is a structured filter;
a PID controller:
this is typically a second order element.
Structural filter G sf1 (s) is a typical 3-order link, specifically:
(4.2 a) for PID controller G pid (s) carrying out discretization treatment to obtain a discretization coefficient of the PID controller;
(4.3 a) to the structural filter G pid (s) carrying out discretization treatment to obtain a discretization coefficient of the structural filter;
and (4.4 a) 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 discretizing respectively, giving discretization coefficients corresponding to the PID controller and the 3-order structure filter, and modifying by remote control.
The second embodiment is:
(4.1 b) non-dragging PID + double integral controller G for displacement mode c (s) decomposition into the following form:
G c (s)＝G c2 (s)G sf2 (s)
wherein G is c2 (s) two zeros and one poleSecond order control of points:
G sf2 (s) is a first order structure filter, and a first order structure filter G sf2 (s) is
(4.2 b) for the second-order controller G c2 (s) carrying out discretization treatment to obtain a discretization coefficient of a second-order controller;
(4.3 b) for the first order structure filter G sf2 (s) carrying out discretization treatment to obtain a discretization coefficient of the first-order structure filter;
and (4.4 b) respectively injecting 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, 3 nonzero zero points z of the novel controller are obtained by adopting the zpk function of Matlab 1 、z 2 、z 3 1 non-zero pole p 3 And 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 possible variations and modifications of the present invention using the method and the technical contents disclosed above without departing from the spirit and scope of the present invention, and therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention are all within the scope of the present invention.
Claims (3)
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 disturbance force model is not limited;
the general displacement mode single-degree-of-freedom drag-free control kinetic equation is as follows:
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,
the component of the acceleration vector corresponding to the x component in the direction of the single degree of freedom, a ns (x, t) is proof mass disturbance model f ns (x, t) an acceleration expression corresponding to the situation is not limited, and u is a generalized acceleration control quantity; a is a d The component of the resultant force of the atmospheric resistance and the sunlight pressure acting on the satellite along the direction of the free-dragging control freedom degree;
while proof mass perturbed force is a linear function of both displacement and time:
f ns (x,t)＝k x x+k t t+b
in this case, the proof mass perturbed force acceleration in the kinetic equation is written as:
in the formula (I), the compound is shown in the specification,
called negative stiffness coefficient, in the expression of negative stiffness force acceleration,
referred to as the negative stiffness force null;
is a time-varying linear coefficient;
the drag-free control dynamic equation under the condition that the disturbance force of the proof mass is a linear function of displacement and time is as follows:
in the formula (I), the compound is shown in the specification,
wherein k is x To examine the linear coefficient, k, of the disturbance force of a mass linearly varying with displacement t The 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;
is a negative stiffness coefficient, a D For acceleration due to external disturbance in general, x fns0 Zero negative stiffness force to check mass, a t The linear coefficient of the acceleration of the disturbed force of the proof mass linearly changes along with the time, and t is the time;
said proof mass perturbed force model f ns (x, t) acceleration a corresponding to the case where the number of the first and second electrodes is not limited ns The expression of (x, t) is:
in the formula, M TM Mass of proof mass in a displacement mode drag-free satellite inertial sensor;
(2) Assuming that the detected mass disturbance force model is a linear function of displacement and time at the same time, substituting the detected mass disturbance force acceleration expression into the dynamic equation in the step (1) to obtain a drag-free control dynamic equation under the condition that the detected mass disturbance force is the displacement and time linear function 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 displacement and time linear function, designing a displacement mode drag-free PID + double integral controller, and establishing a displacement mode drag-free control system;
transfer function from the generalized acceleration control amount u to the output displacement x:
the PID + double integral controller transfer function G c (s) is:
in the formula, k p Is a proportionality coefficient, k d Is a differential coefficient, T d Is a first-order inertia time constant, k i Is a single integral coefficient, k ii Is a double integral coefficient;
(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 method for controlling the displacement mode without dragging to eliminate the static error according to claim 1, wherein the following method is adopted to inject the displacement mode without dragging PID + double integral controller into the spacecraft:
(4.1 a), non-dragging PID + double integral controller G of displacement mode c (s) decomposition into the following form:
G c (s)＝G pid (s)G sf1 (s)
wherein G is pid (s) is controlled by a controller G c (s) PID controller consisting of the first three items, G sf1 (s) is a structured filter:
(4.2 a) for PID controller G pid (s) carrying out discretization processing to obtain a discretization coefficient of the PID controller;
(4.3 a) a pair structure filter G pid (s) carrying out discretization treatment to obtain a discretization coefficient of the structural filter;
and (4.4 a) respectively injecting the discretization coefficients of the PID controller and the structure filter into the spacecraft through remote control on-orbit modification binding parameters.
3. The method for controlling the displacement mode without dragging to eliminate the static error according to claim 1, wherein the following method is adopted to inject the displacement mode without dragging PID + double integral controller into the spacecraft:
(4.1 b) PID + double integral controller G for enabling displacement mode to be free of dragging c (s) decomposition into the following form:
G c (s)＝G c2 (s)G sf2 (s)
wherein G is c2 (s) a second order controller with two zeros and one pole:
G sf2 (s) is a first order structure filter, and a first order structure filter G sf2 (s) is
(4.2 b) for the second-order controller G c2 (s) carrying out discretization treatment to obtain a discretization coefficient of a second-order controller;
(4.3 b) for the first order structure filter G sf2 (s) carrying out discretization treatment to obtain a discretization coefficient of the first-order structure filter;
and (4.4 b) respectively injecting discretization coefficients of the second-order controller and the first-order structure filter into the spacecraft through remote control on-orbit modification binding parameters.
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