CN111505941A - Acceleration mode self-adaptive drag-free control method based on first-order feature model - Google Patents

Acceleration mode self-adaptive drag-free control method based on first-order feature model Download PDF

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CN111505941A
CN111505941A CN202010393104.9A CN202010393104A CN111505941A CN 111505941 A CN111505941 A CN 111505941A CN 202010393104 A CN202010393104 A CN 202010393104A CN 111505941 A CN111505941 A CN 111505941A
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drag
acceleration
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王丽娇
苟兴宇
李明群
王绍凯
蒋庆华
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Beijing Institute of Control Engineering
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

The invention relates to an acceleration mode self-adaptive drag-free control method based on a first-order characteristic model, which comprises the following specific steps of: firstly, performing first-order feature modeling on a drag-free loop based on a feature model theory; step two, performing expansion transformation on the state and the parameters of the first-order characteristic model; thirdly, performing online estimation on the characteristic model parameters and the acceleration output through a filtering algorithm based on the expanded state equation; and fourthly, constructing a self-adaptive controller based on the estimated state and the characteristic parameters, and finishing the design of the whole control method. The method can adapt to large uncertainty and measurement noise of parameters of the thruster/sensor, can effectively improve the control performance of an acceleration mode, has the advantages of simple design, small parameter debugging workload and strong engineering practicability, and provides a new idea for the acceleration drag-free control of the spacecraft.

Description

Acceleration mode self-adaptive drag-free control method based on first-order feature model
Technical Field
The invention belongs to the technical field of spacecraft control, and relates to an acceleration mode self-adaptive drag-free control method based on a first-order characteristic model.
Background
The drag-free control is an important way for obtaining the ultra-low microgravity horizontal satellite platform and is also one of the key technologies of experimental researches such as space basic physics, microgravity measurement, earth science, satellite navigation and the like. The general non-towed satellite is divided into a displacement mode and an acceleration mode, the working principle of the former is that a propeller is adopted to counteract non-conservative resultant force applied to a satellite platform, a mass block suspended in the middle of the satellite and the satellite platform move synchronously through relative displacement feedback control, and the latter replaces the mass block with an accelerometer for directly measuring external disturbance and uses an acceleration measured value for feedback control. The accelerometer feedback mode is relatively simple in structure, and a control system of the accelerometer can be designed independently and is commonly used on gravity satellites, such as GOCE and the next generation gravity satellites.
The drag-free satellite controller can not only keep the satellite stable, but also has good control effect which is beneficial to the completion of space missions and the reduction of the requirements on hardware, so the design of the drag-free satellite controller is always the focus of the drag-free satellite research. At present, the mainstream international drag-free control method comprises PID control, EMC and robust control, wherein a considerable part of research does not consider actuator and sensor dynamics, and the practical application value of engineering is lacked. In fact, due to the constraints of ground test conditions, both the drag-free control loop model sensor model and the actuator model contain large uncertainties, which present a significant challenge to the design of the controller.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the acceleration mode of a drag-free satellite, an acceleration mode self-adaptive drag-free control method based on a first-order characteristic model is provided, a complex nonlinear uncertain drag-free loop comprising a satellite model, a sensor model and a propulsion executing mechanism model is equivalent by using the first-order variable coefficient characteristic model, parameter expansion transformation is carried out based on the characteristic model, a self-adaptive control method based on recursive filtering state and parameter joint estimation is designed, the adaptability of a drag-free control system to uncertainty and the suppression capability of measurement noise are improved, and the acceleration output dynamic performance and the frequency domain stability index are effectively improved.
The technical scheme of the invention is as follows: an acceleration mode self-adaptive drag-free control method based on a first-order feature model comprises the following steps:
firstly, performing first-order feature modeling on a drag-free loop based on a feature model theory;
step two, performing expansion transformation on the state and the parameters of the first-order characteristic model;
thirdly, performing online estimation on the characteristic model parameters and the acceleration output through a filtering algorithm based on the expanded state equation;
and fourthly, constructing a self-adaptive controller based on the estimated state and the characteristic parameters, and finishing the design of the whole control method.
In the first step, the whole controlled object of the drag-free loop is a complex nonlinear system, and the object is written into the following first-order characteristic model form by a discretization method:
Figure BDA0002486632490000021
wherein, ykSampling the measured output for the acceleration of the system at the kth beat time, xkAs true value of acceleration, ukTo control the input, vkTo measure noise, here equivalently white noise, αkAnd βkThe two characteristic parameters of the first-order characteristic model satisfy the following conditions:
αk＝1+ηk,|ηk|≤f1(Ts)
β1(Ts)≤βk≤β2(Ts),
Figure BDA0002486632490000022
in the formula, TsIs a sampling period, f1(Ts)、β2(Ts) And β2(Ts) Respectively represent and TsAssociated bounded function, ηkIs a bounded constant.
In the second step, in order to extract the characteristic model parameters and the acceleration output from the noise signals, the formula (1) is further expanded and transformed to obtain
Figure BDA0002486632490000031
Wherein x is1,k＝xk，x2,k＝αk，x3,k＝βk。
In the third step, an extension variable X is definedk＝[xk,αk,βk]Further obtain
Xk+1＝f(Xk,uk)；
Wherein, f (X)k,uk) Is a non-linear function determined by equation (2); designing the following state and parameter joint estimation method based on the extended state equation:
Figure BDA0002486632490000032
Figure BDA0002486632490000033
Figure BDA0002486632490000034
Figure BDA0002486632490000035
Figure BDA0002486632490000036
Figure BDA0002486632490000037
wherein the content of the first and second substances,
Figure BDA0002486632490000038
representing the estimated value of x, r (k +1) representing the output observation error at the moment of r (k +1), and R (k) and Q (k) being a state noise covariance matrix and an output noise covariance matrix, respectively;
Figure BDA0002486632490000039
Figure BDA00024866324900000310
。
in the fourth step, the design of the self-adaptive control law is carried out based on the integrated first-order characteristic model, the controller consists of a self-adaptive part and a logic integral part, and the specific design method is that
Figure BDA00024866324900000311
Wherein the content of the first and second substances,
Figure BDA00024866324900000312
Figure BDA0002486632490000041
Figure BDA0002486632490000042
Figure BDA0002486632490000043
lambda and l1Is an adjustable normal number, ki>0 is the adjustable integral gain, uikAnd uik-1Respectively represent the k-th
The logical integral control quantity of beat and beat k-1,
Figure BDA0002486632490000044
is ykAn estimate of (d).
Compared with the prior art, the invention has the beneficial effects that:
(1) the controller and the filter estimation are integrally designed based on the first-order characteristic model theory, the algorithm is simple, and the control performance is effectively improved;
(2) according to the method, a complex nonlinear uncertain non-towed loop comprising a satellite model, a sensor model and a propulsion actuating mechanism model is subjected to equivalence by using a first-order variable coefficient characteristic model, parameter expansion transformation is carried out based on the characteristic model, and a self-adaptive control method based on recursive filtering state and parameter joint integrated estimation is designed, so that the whole modeling process is greatly simplified, and the stability of parameter identification is effectively improved;
(3) the method is used for designing a first-order adaptive prediction control law based on the estimated state and parameters, and is combined with a logic integral control law to realize high-precision control of a drag-free acceleration mode. The whole algorithm is simple in design, the workload of parameter debugging is small, and the dynamic performance of acceleration output and the frequency domain PSD index can be effectively improved.
Drawings
FIG. 1 is a control flow chart of the present invention.
FIG. 2 is a block diagram of a drag-free control loop.
FIG. 3 is a schematic diagram of accelerometer measurement output.
FIG. 4 is a graph of x-axis non-conservative net forces.
Detailed Description
The invention is further illustrated by the following examples.
As shown in fig. 1, the acceleration mode adaptive drag-free control method based on the first-order feature model of the present invention includes the following steps:
firstly, performing first-order feature modeling on a drag-free loop based on a feature model theory;
step two, performing expansion transformation on the state and the parameters of the first-order characteristic model;
thirdly, performing online estimation on the characteristic model parameters and the acceleration output through a filtering algorithm based on the expanded state equation;
and step four, designing a self-adaptive controller based on the estimated state and the characteristic parameters, and realizing the closed loop of the whole drag-free control method.
In the first step, the whole controlled object of the drag-free loop is a complex nonlinear system, and the object is written into the following first-order characteristic model form by a discretization method:
Figure BDA0002486632490000051
wherein, ykSampling the measured output for the acceleration of the system at the kth beat time, xkAs true value of acceleration, ukTo control the input, vkTo measure noise, here equivalently white noise, αkAnd βkThe two characteristic parameters of the first-order characteristic model satisfy the following conditions:
αk＝1+ηk,|ηk|≤f1(Ts)
β1(Ts)≤βk≤β2(Ts),
Figure BDA0002486632490000052
in the formula, TsIs a sampling period, f1(Ts)、β2(Ts) And β2(Ts) Respectively represent and TsAssociated bounded function, ηkIs a bounded constant.
In the second step, in order to extract the characteristic model parameters and the acceleration output from the noise signals, the formula (1) is further expanded and transformed to obtain
Figure BDA0002486632490000053
Wherein x is1,k＝xk，x2,k＝αk，x3,k＝βkHere, the slowly time-varying characteristic of the characteristic parameter is used. In the absence ofUnder the condition of knowing the parameter change rule, the approximate model is used as a filtering model, and the expected control performance can be realized by combining with self-adaptive control. In the third step, an extension variable X is definedk＝[xk,αk,βk]Further obtain
Xk+1＝f(Xk,uk)；
Wherein, f (X)k,uk) Is a non-linear function determined by (2). Designing the following state and parameter joint estimation method based on the extended state equation:
Figure BDA0002486632490000061
Figure BDA0002486632490000062
Figure BDA0002486632490000063
Figure BDA0002486632490000064
Figure BDA0002486632490000065
Figure BDA0002486632490000066
wherein the content of the first and second substances,
Figure BDA0002486632490000067
denotes the estimated value of x, r (k +1) denotes the output observation error at the time of r (k +1), and r (k) and q (k) are the state noise covariance matrix and the output noise covariance matrix, respectively.
Figure BDA0002486632490000068
Figure BDA0002486632490000069
In the fourth step, the design of the adaptive control law is performed based on the integrated first-order feature model, as follows:
Figure BDA00024866324900000610
wherein the content of the first and second substances,
Figure BDA00024866324900000611
Figure BDA00024866324900000612
Figure BDA00024866324900000613
Figure BDA00024866324900000614
lambda and l1Is an adjustable normal number, ki>0 is the adjustable integral gain, uikAnd uik-1Respectively represent the k-th
The logical integral control quantity of beat and beat k-1,
Figure BDA00024866324900000615
is ykAn estimate of (d).
Example 1
Taking an XX-1 satellite as an example, mathematical simulation is carried out on the self-adaptive control method provided by the patent application, the satellite runs on a 628km sun synchronous circular orbit, and an attitude control loop can ensure zero attitude in a drag-free mode. In order to simplify the simulation, only the drag-free control in the x-axis direction is considered, the whole loop block diagram is shown in fig. 2, the measurement output of the on-orbit accelerometer and the x-axis non-conservative resultant force are respectively shown in fig. 3 and fig. 4, the noise of the acceleration is mainly determined by the measurement noise of the accelerometer and the noise of the thruster, and the self-adaptive control force provided by the invention can well compensate the on-orbit non-conservative interference force, so that the acceleration obtains good control performance.
The result of comparing the self-adaptive control method provided by the invention with the residual acceleration output of the corrected PID control shows that the self-adaptive control has a better frequency domain PSD index within a frequency band of 0.001-0.1 Hz.
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 (6)

1. An acceleration mode self-adaptive drag-free control method based on a first-order feature model is characterized by comprising the following steps: the method comprises the following steps:
firstly, performing first-order feature modeling on a drag-free loop based on a feature model theory;
step two, performing expansion transformation on the state and the parameters of the first-order characteristic model;
thirdly, performing online estimation on the characteristic model parameters and the acceleration output through a filtering algorithm based on the expanded state equation;
and fourthly, constructing a self-adaptive controller based on the estimated state and the characteristic parameters, and finishing the design of the whole control method.
2. The acceleration mode adaptive drag-free control method based on the first-order feature model as claimed in claim 1, wherein: in the first step, the whole controlled object of the drag-free loop is a complex nonlinear system, and the object is written into the following first-order characteristic model form by a discretization method:
Figure FDA0002486632480000011
wherein, ykSampling the measured output for the acceleration of the system at the kth beat time, xkAs true value of acceleration, ukTo control the input, vkTo measure noise, here equivalently white noise, αkAnd βkTwo characteristic parameters of the first-order characteristic model.
3. The method of claim 2, wherein α is a method for acceleration mode adaptive drag-free control based on the first-order feature modelkAnd βkThe following conditions are satisfied:
αk＝1+ηk,|ηk|≤f1(Ts)
β1(Ts)≤βk≤β2(Ts),
Figure FDA0002486632480000012
in the formula, TsIs a sampling period, f1(Ts)、β2(Ts) And β2(Ts) Respectively represent and TsAssociated bounded function, ηkIs a bounded constant.
4. The acceleration mode adaptive drag-free control method based on the first-order feature model as claimed in claim 2, wherein: in the second step, in order to extract the characteristic model parameters and the acceleration output from the noise signals, the formula (1) is further expanded and transformed to obtain
Figure FDA0002486632480000021
Wherein x is1,k＝xk，x2,k＝αk，x3,k＝βk。
5. The acceleration mode adaptive drag-free control method based on the first-order feature model as claimed in claim 4, wherein: in the third step, an extension variable X is definedk＝[xk,αk,βk]Further obtain
Xk+1＝f(Xk,uk)；
Wherein, f (X)k,uk) Is a non-linear function determined by equation (2); designing the following state and parameter joint estimation method based on the extended state equation:
Figure FDA0002486632480000022
Figure FDA0002486632480000023
Figure FDA0002486632480000024
Figure FDA0002486632480000025
Figure FDA0002486632480000026
Figure FDA0002486632480000027
wherein the content of the first and second substances,
Figure FDA0002486632480000028
represents the estimated value of x, r (k +1) represents the output observation error at the time of r (k +1), and R (k) and Q (k) are state noise covariance matrixesAnd outputting a noise covariance matrix;
Figure FDA0002486632480000029
Figure FDA00024866324800000210
。
6. the acceleration mode adaptive drag-free control method based on the first-order feature model of claim 5, wherein: in the fourth step, the design of the self-adaptive control law is carried out based on the integrated first-order characteristic model, the controller consists of a self-adaptive part and a logic integral part, and the specific design method is that
Figure FDA0002486632480000031
Wherein the content of the first and second substances,
Figure FDA0002486632480000032
Figure FDA0002486632480000033
Figure FDA0002486632480000036
Figure FDA0002486632480000034
lambda and l1Is an adjustable normal number, ki>0 is the adjustable integral gain, uikAnd uik-1Respectively representing the logic integral control quantity in the k th beat and the k-1 th beat,
Figure FDA0002486632480000035
is ykAn estimate of (d).
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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
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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
CN104090493A (en) * 2014-05-27 2014-10-08 北京航空航天大学 Interference compensation control method of partial drag-free satellite on basis of accelerometers
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
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