CN111258221A - Spacecraft fault-tolerant control method based on self-adaptive sliding mode theory - Google Patents

Spacecraft fault-tolerant control method based on self-adaptive sliding mode theory Download PDF

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CN111258221A
CN111258221A CN202010071832.8A CN202010071832A CN111258221A CN 111258221 A CN111258221 A CN 111258221A CN 202010071832 A CN202010071832 A CN 202010071832A CN 111258221 A CN111258221 A CN 111258221A
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sliding mode
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CN111258221B (en
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李安梁
樊恒海
王恒
魏峻
邰能建
王宇红
戴湘军
刘海鹏
王兴
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China Xian Satellite Control Center
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Abstract

The invention discloses a spacecraft fault-tolerant control method based on a self-adaptive sliding mode theory, which is implemented according to the following steps: step 1, defining an inertial coordinate system and a spacecraft body coordinate system, and establishing a spacecraft actuating mechanism fault attitude kinetic equation aiming at a rigid spacecraft; step 2, calculating the attitude of the spacecraft; step 3, selecting a sliding mode surface by using a sliding mode control theory; and 4, considering partial failure faults, uncertain parameters and external interference of the spacecraft, designing a self-adaptive sliding mode fault-tolerant output control torque u, and realizing stable control of the attitude of the spacecraft. The method can solve the problems of long stable convergence time, poor precision and the like of the attitude of the spacecraft under the conditions of failure of an actuating mechanism, input saturation, uncertain model parameters, unknown interference and the like.

Description

Spacecraft fault-tolerant control method based on self-adaptive sliding mode theory
Technical Field
The invention belongs to the field of aerospace measurement and control, and particularly relates to a spacecraft fault-tolerant control method based on a self-adaptive sliding mode theory.
Background
With the blowout type development of the number of spacecrafts in China, civil and civil tasks such as manned spaceflight, space detection, operational support, remote sensing observation, communication, surveying and mapping, weather and the like borne by the spacecrafts are gradually increased, and under the condition that control of faults of actuating mechanisms, sensor failure and the like is limited, higher requirements are provided for the safety, reliability, high precision and the like of autonomous operation of a spacecraft control system, and the high-precision autonomous fault-tolerant control technology is particularly important for the spacecrafts to complete the tasks. However, when the spacecraft runs in severe environments such as weightlessness, high and low temperature, strong radiation and the like for a long time, inherent factors such as aging, abrasion and the like of mechanical or electrical components inevitably cause faults of an actuating mechanism, output control torque is limited, and performance of a control system such as accuracy and stability is reduced, even the spacecraft is broken down and the like.
At present, the conventional method for processing the switching fault of the common mode of the attitude fault-tolerant control of the spacecraft seriously depends on the defects of ground support, weak autonomous operation capability, weak timeliness and the like, and has the defects of long attitude stability convergence time and poor accuracy for the conditions of the spacecraft such as fault of an execution mechanism, input saturation, uncertain model parameters, unknown interference and the like, and the requirement of the spacecraft on the attitude stability accuracy is difficult to meet.
Disclosure of Invention
The invention aims to provide a spacecraft fault-tolerant control method based on a self-adaptive sliding mode theory, which can solve the problems of long spacecraft attitude stability convergence time, poor precision and the like under the conditions of executing mechanism faults, input saturation, uncertain model parameters, unknown interference and the like.
The invention adopts the technical scheme that a spacecraft fault-tolerant control method based on a self-adaptive sliding mode theory is implemented according to the following steps:
step 1, defining an inertial coordinate system and a spacecraft body coordinate system, and establishing a spacecraft actuating mechanism fault attitude kinetic equation aiming at a rigid spacecraft;
step 2, calculating the attitude of the spacecraft;
step 3, selecting a sliding mode surface by using a sliding mode control theory;
and 4, considering partial failure faults, uncertain parameters and external interference of the spacecraft, designing a self-adaptive sliding mode fault-tolerant output control torque u, and realizing stable control of the attitude of the spacecraft.
The present invention is also characterized in that,
the step 1 is implemented according to the following steps:
step 1.1, establishing an inertial coordinate system and a spacecraft body coordinate system:
defining the origin of an inertial coordinate system as the geocentric position, pointing the X axis to a J2000 Pingchun point, and enabling the Y axis to be vertical to the X axis in an equatorial platform, wherein the Z axis, the X axis and the Y axis form a right-hand coordinate system; defining the origin of a coordinate system of a spacecraft body as the mass center position of the spacecraft, an X axis as the flight direction of the spacecraft, a Y axis and the X axis vertical to the direction of a solar array, and a Z axis, the X axis and the Y axis forming a right-hand coordinate system pointing to the ground;
step 1.2, in the operation process of the spacecraft, the system is supposed to meet the following conditions:
1, positively determining a rotational inertia matrix I of a spacecraft;
suppose 2, the external disturbance moment d of the spacecraft is bounded, namely, | | d | | | is less than or equal to dmaxWherein | | · | | is an exponential quantity of 2, dmaxAn upper limit of disturbance torque;
aiming at the rigid body spacecraft, when an actuating mechanism has no fault, the attitude kinetic equation of the spacecraft is as follows:
Figure BDA0002377491220000021
wherein,
Figure BDA0002377491220000031
is a rotational inertia matrix of a spacecraft；ω＝[ωxωyωz]TProjecting the attitude angular rate of the spacecraft body coordinate system relative to the inertial coordinate system in the spacecraft body system;
Figure BDA0002377491220000032
an output control torque generated for the actuator;
Figure BDA0002377491220000033
the moment is the external interference moment on the spacecraft; the symbol "x" is the adjoint of the vectors, defining ω×Comprises the following steps:
Figure BDA0002377491220000034
when the executing mechanism fails partially, adopting a multiplication factor to establish a fault model of the executing mechanism as E (t) u, and rewriting a formula (1) under the condition that the executing mechanism fails partially to obtain an attitude kinetic equation of the spacecraft executing mechanism fault:
Figure BDA0002377491220000035
wherein E (t) ═ diag (E)1(t) e2(t) e3(t)) is the effective factor of the actuator, t is the spacecraft runtime, ei(t)∈[0 1]Where i is 1, 2, 3, where the state 0 indicates that the i-th actuator has failed completely, 1 indicates normal operation, and the remaining states indicate that the actuator has failed partially, and the formula (2) is rewritten to
Figure BDA0002377491220000036
wherein △ E ═ diag (1-E)1(t) 1-e2(t) 1-e3(t)) is a fault factor of the actuator, and | | △ E | | | is equal to or less than 1, and γ | | △ E | |.
The step 2 is implemented according to the following steps:
defining the spacecraft body seat according to the 3-1-2 rotation sequence of the coordinate systemthe three rotation angles of the standard system and the inertial coordinate system are respectively a yaw angle psi, a roll angle phi and a pitch angle theta of the spacecraft, and α is made to be [ psi phi theta [ ]]TThe attitude angle vector of the spacecraft is defined as the attitude angle vector of the spacecraft, and the relationship between the attitude angle vector of the spacecraft and the angular rate of the spacecraft is as follows:
Figure BDA0002377491220000037
wherein,
Figure BDA0002377491220000041
and (4) integrating the formula (4) to obtain the yaw angle psi, the roll angle phi and the pitch angle theta of the spacecraft.
In step 3, the selected slip form surface is
s＝ω+kα (5)
In the formula,
Figure BDA0002377491220000042
step 4 is specifically implemented according to the following steps:
step 4.1, for a spacecraft control system (3) with limited control, uncertain parameters and external interference, under the conditions of hypothesis 1 and hypothesis 2, assuming that the fault of a system execution mechanism is unknown, designing the following adaptive sliding mode fault-tolerant control scheme to ensure that an output control torque u generated by the execution mechanism is as follows:
Figure BDA0002377491220000043
wherein,
Figure BDA0002377491220000044
p and D are given positive definite symmetric constant arrays,
Figure BDA0002377491220000045
is dmaxThe value of the estimated value is,
Figure BDA0002377491220000046
is composed of
Figure BDA0002377491220000047
Estimate of (e ∈)0、c0、c1Is a normal number;
as can be seen from the formula (6), the gamma value of the actuator is not needed, and the problem of stable control under the conditions of spacecraft actuator failure, external interference and the like under the condition of unknown gamma can be effectively solved;
step 4.2, considering the limited output control moment amplitude of the actuating mechanism, replacing the output control moment u of the actuating mechanism with a saturation function sat (u), and simultaneously, in order to reduce the buffeting problem of the control system, approximating a nonlinear function x/| x | | by a linear function x/(| x | + epsilon), and rewriting a fault attitude kinetic equation (2) of the actuating mechanism of the spacecraft and the output control moment (6) of the actuating mechanism into
Figure BDA0002377491220000051
Wherein,
Figure BDA0002377491220000052
in the formula umaxTo control the saturation value of the output, ∈1And ε2Is a normal number.
The invention has the beneficial effects that:
1. the method is oriented to spacecraft attitude fault-tolerant control, easy to realize, high in stability and precision and short in convergence time.
2. The method of the invention integrates the self-adaptive sliding mode control theory into the method, and the established fault-tolerant control method of the spacecraft based on the self-adaptive sliding mode theory is not available in the traditional method.
3. The output control torque (control law) designed by the method can effectively solve the problem of stable control under the conditions of spacecraft actuating mechanism failure, external interference and the like under unknown conditions, and has more engineering significance.
4. The method is not only suitable for spacecraft attitude fault-tolerant control tasks, but also suitable for fault rescue, quick maneuvering and other tasks of the spacecraft.
Drawings
FIG. 1 is a graph showing the response curve of the attitude angle in the safety mode of the simulation experiment of the present invention;
FIG. 2 is a graph of angular rate response in a safety mode of a simulation experiment according to the present invention;
FIG. 3 is a control torque response curve diagram in a safety mode of a simulation experiment according to the present invention;
FIG. 4 is a three-axis attitude motion phase trajectory graph in a safety mode of a simulation experiment according to the present invention;
FIG. 5 is a curve of the estimation of the upper limit of external interference in the safety mode of the simulation experiment of the present invention;
FIG. 6 is a graph showing the response curve of the attitude angle in the failure mode of the simulation experiment of the present invention;
FIG. 7 is a graph of angular rate response in a failure mode of a simulation experiment according to the present invention;
FIG. 8 is a control torque response curve diagram in a fault mode of a simulation experiment according to the present invention;
FIG. 9 is a three-axis attitude motion phase trajectory graph in a fault mode of a simulation experiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a spacecraft fault-tolerant control method based on a self-adaptive sliding mode theory, which is implemented according to the following steps:
step 1, defining an inertial coordinate system and a spacecraft body coordinate system, and establishing a spacecraft actuating mechanism fault attitude kinetic equation aiming at a rigid spacecraft;
step 2, calculating the attitude of the spacecraft;
step 3, selecting a sliding mode surface by using a sliding mode control theory;
and 4, considering partial failure faults, uncertain parameters and external interference of the spacecraft, designing a self-adaptive sliding mode fault-tolerant output control torque u, and realizing stable control of the attitude of the spacecraft.
The step 1 is implemented according to the following steps:
step 1.1, establishing an inertial coordinate system and a spacecraft body coordinate system:
defining the origin of an inertial coordinate system as the geocentric position, pointing the X axis to a J2000 Pingchun point, and enabling the Y axis to be vertical to the X axis in an equatorial platform, wherein the Z axis, the X axis and the Y axis form a right-hand coordinate system; defining the origin of a coordinate system of a spacecraft body as the mass center position of the spacecraft, an X axis as the flight direction of the spacecraft, a Y axis and the X axis vertical to the direction of a solar array, and a Z axis, the X axis and the Y axis forming a right-hand coordinate system pointing to the ground;
step 1.2, in the operation process of the spacecraft, the system is supposed to meet the following conditions:
1, positively determining a rotational inertia matrix I of a spacecraft;
suppose 2, the external disturbance moment d of the spacecraft is bounded, namely, | | d | | | is less than or equal to dmaxWherein | | · | | is an exponential quantity of 2, dmaxAn upper limit of disturbance torque;
aiming at the rigid body spacecraft, when an actuating mechanism has no fault, the attitude kinetic equation of the spacecraft is as follows:
Figure BDA0002377491220000071
wherein,
Figure BDA0002377491220000072
is a rotational inertia matrix of the spacecraft; omega ═ omegaxωyωz]TProjecting the attitude angular rate of the spacecraft body coordinate system relative to the inertial coordinate system in the spacecraft body system;
Figure BDA0002377491220000073
an output control torque generated for the actuator;
Figure BDA0002377491220000074
the moment is the external interference moment on the spacecraft; the symbol "x" is the accompanying moment of the vectorArray, defining ω×Comprises the following steps:
Figure BDA0002377491220000075
when the executing mechanism fails partially, adopting a multiplication factor to establish a fault model of the executing mechanism as E (t) u, and rewriting a formula (1) under the condition that the executing mechanism fails partially to obtain an attitude kinetic equation of the spacecraft executing mechanism fault:
Figure BDA0002377491220000076
wherein E (t) ═ diag (E)1(t) e2(t) e3(t)) is the effective factor of the actuator, t is the spacecraft runtime, ei(t)∈[0 1]Where i is 1, 2, 3, where the state 0 indicates that the i-th actuator has failed completely, 1 indicates normal operation, and the remaining states indicate that the actuator has failed partially, and the formula (2) is rewritten to
Figure BDA0002377491220000077
wherein △ E ═ diag (1-E)1(t) 1-e2(t) 1-e3(t)) is a fault factor of the actuator, and | | △ E | | | is equal to or less than 1, and γ | | △ E | |.
therefore, under the conditions of 1 and 2, the adaptive sliding mode fault-tolerant output control torque u designed by the invention can enable the system (3) to meet the conditions of t → ∞ alpha → 0 and omega → 0, and solves the problem of autonomous fault-tolerant control of the spacecraft under the conditions of actuator failure, uncertain model parameters, external interference and the like.
The step 2 is implemented according to the following steps:
according to the 3-1-2 rotation sequence of coordinate system, defining three rotation angles of spacecraft body coordinate system and inertial coordinate system as spacecraft yaw angle psi, roll angle phi and pitch angle theta, and making α [ psi phi theta ]]TThe attitude angle vector of the spacecraft is defined as the attitude angle vector of the spacecraft, and the relationship between the attitude angle vector of the spacecraft and the angular rate of the spacecraft is as follows:
Figure BDA0002377491220000081
wherein,
Figure BDA0002377491220000082
and (4) integrating the formula (4) to obtain the yaw angle psi, the roll angle phi and the pitch angle theta of the spacecraft.
In step 3, the selected slip form surface is
s＝ω+kα (5)
In the formula,
Figure BDA0002377491220000083
step 4 is specifically implemented according to the following steps:
step 4.1, for a spacecraft control system (3) with limited control, uncertain parameters and external interference, under the conditions of hypothesis 1 and hypothesis 2, assuming that the fault of a system execution mechanism is unknown, designing the following adaptive sliding mode fault-tolerant control scheme to ensure that an output control torque u generated by the execution mechanism is as follows:
Figure BDA0002377491220000084
wherein,
Figure BDA0002377491220000085
p and D are given positive definite symmetric constant arrays,
Figure BDA0002377491220000086
is dmaxThe value of the estimated value is,
Figure BDA0002377491220000087
is composed of
Figure BDA0002377491220000088
Estimate of (e ∈)0、c0、c1Is a normal number;
as can be seen from the formula (6), the gamma value of the actuator is not needed, and the problem of stable control under the conditions of spacecraft actuator failure, external interference and the like under the condition of unknown gamma can be effectively solved;
step 4.2, considering the limited output control moment amplitude of the actuating mechanism, replacing the output control moment u of the actuating mechanism with a saturation function sat (u), and simultaneously, in order to reduce the buffeting problem of the control system, approximating a nonlinear function x/| x | | by a linear function x/(| x | + epsilon), and rewriting a fault attitude kinetic equation (2) of the actuating mechanism of the spacecraft and the output control moment (6) of the actuating mechanism into
Figure BDA0002377491220000091
Wherein,
Figure BDA0002377491220000092
in the formula umaxTo control the saturation value of the output, ∈1And ε2Is a normal number, epsilon for ensuring approximation effect1And ε2Generally, the value is small.
The effectiveness of the above scheme is demonstrated by numerical simulation below. The rotational inertia matrix of the spacecraft is
Figure BDA0002377491220000093
The spacecraft is subjected to external interference torque of
Figure BDA0002377491220000094
Wherein,A0for external disturbance of torque amplitude, omega0Is the spacecraft orbital angular velocity.
The initial values of main simulation parameters of the self-adaptive sliding mode fault-tolerant control scheme of the spacecraft are shown in table 1.
TABLE 1 initial values of the main simulation parameters
Figure BDA0002377491220000095
Under the initial value, the external interference and the parameter change, the simulation is carried out for the following 2 situations:
case 1 safety mode, i.e. the actuator works well without failure;
case 2 failure mode, the actuator experiences a known failure, partially fails, and produces a constant fault. Considering the moment deviation, the uncertain parameters and the like of the actuating mechanism, order
Figure BDA0002377491220000101
The simulation results are as follows:
(1) in the safe mode, the executing mechanism works normally, under the action of the fault-tolerant control scheme designed by the scheme, the response curves of the attitude angle, the angular rate, the control moment and the phase trajectory movement of the spacecraft are shown in figures 1-4, and the upper-bound estimation value of the external interference is shown in figure 5.
From simulation results, under the action of the fault-tolerant control scheme designed in the method, the spacecraft attitude control system is stable within 60s, and the control accuracy is superior to 1.0 multiplied by 10-4°。
According to the simulation results, in the control process of the spacecraft, the controller effectively inhibits buffeting caused by sliding mode control, the pitching, yawing and rolling channels of the spacecraft move stably, and the self-adaptive rate can effectively estimate the interference upper bound of the system.
(2) The failure mode, under the same initial conditions and controller parameter conditions, the simulation results are shown in fig. 6-9.
As can be seen from FIGS. 6-9, in the failure mode, the control system of the spacecraft can still effectively control the attitude angle to be stable, the control process is kept stable, the stabilization time is less than 70s, and the precision is not lower than10 x 10-3 DEG, the attitude control system has good robustness and quick response capabilityAnd stable accuracy.
Therefore, the self-adaptive sliding mode fault-tolerant control scheme designed by the invention can keep good control performance in a safety mode and a fault mode, can meet the requirements of a spacecraft control system, and particularly has good robust fault-tolerant capability in the fault mode.

Claims (5)

1. A spacecraft fault-tolerant control method based on a self-adaptive sliding mode theory is characterized by comprising the following steps:
step 1, defining an inertial coordinate system and a spacecraft body coordinate system, and establishing a spacecraft actuating mechanism fault attitude kinetic equation aiming at a rigid spacecraft;
step 2, calculating the attitude of the spacecraft;
step 3, selecting a sliding mode surface by using a sliding mode control theory;
and 4, considering partial failure faults, uncertain parameters and external interference of the spacecraft, designing a self-adaptive sliding mode fault-tolerant output control torque u, and realizing stable control of the attitude of the spacecraft.
2. The spacecraft fault-tolerant control method based on the adaptive sliding mode theory according to claim 1, wherein the step 1 is implemented specifically according to the following steps:
step 1.1, establishing an inertial coordinate system and a spacecraft body coordinate system:
defining the origin of an inertial coordinate system as the geocentric position, pointing the X axis to a J2000 Pingchun point, and enabling the Y axis to be vertical to the X axis in an equatorial platform, wherein the Z axis, the X axis and the Y axis form a right-hand coordinate system; defining the origin of a coordinate system of a spacecraft body as the mass center position of the spacecraft, an X axis as the flight direction of the spacecraft, a Y axis and the X axis vertical to the direction of a solar array, and a Z axis, the X axis and the Y axis forming a right-hand coordinate system pointing to the ground;
step 1.2, in the operation process of the spacecraft, the system is supposed to meet the following conditions:
1, positively determining a rotational inertia matrix I of a spacecraft;
suppose 2 that the external disturbance moment d of the spacecraft is bounded, namely, the requirement of meeting||d||≤dmaxWherein | | · | | is an exponential quantity of 2, dmaxAn upper limit of disturbance torque;
aiming at the rigid body spacecraft, when an actuating mechanism has no fault, the attitude kinetic equation of the spacecraft is as follows:
Figure FDA0002377491210000011
wherein,
Figure FDA0002377491210000021
is a rotational inertia matrix of the spacecraft; omega ═ omegaxωyωz]TProjecting the attitude angular rate of the spacecraft body coordinate system relative to the inertial coordinate system in the spacecraft body system;
Figure FDA0002377491210000022
an output control torque generated for the actuator;
Figure FDA0002377491210000023
the moment is the external interference moment on the spacecraft; the symbol "x" is the adjoint of the vectors, defining ω×Comprises the following steps:
Figure FDA0002377491210000024
when the executing mechanism fails partially, adopting a multiplication factor to establish a fault model of the executing mechanism as E (t) u, and rewriting a formula (1) under the condition that the executing mechanism fails partially to obtain an attitude kinetic equation of the spacecraft executing mechanism fault:
Figure FDA0002377491210000025
wherein E (t) ═ diag (E)1(t) e2(t) e3(t)) is the effective factor of the actuator, t is the spacecraft runtime, ei(t)∈[0 1]Where i is 1, 2, 3, where the state 0 indicates that the i-th actuator has failed completely, 1 indicates normal operation, and the remaining states indicate that the actuator has failed partially, and the formula (2) is rewritten to
Figure FDA0002377491210000026
wherein △ E ═ diag (1-E)1(t) 1-e2(t) 1-e3(t)) is a fault factor of the actuator, and | | △ E | | | is equal to or less than 1, and γ | | △ E | |.
3. The spacecraft fault-tolerant control method based on the adaptive sliding mode theory according to claim 1, wherein the step 2 is implemented specifically according to the following steps:
according to the 3-1-2 rotation sequence of coordinate system, defining three rotation angles of spacecraft body coordinate system and inertial coordinate system as spacecraft yaw angle psi, roll angle phi and pitch angle theta, and making α [ psi phi theta ]]TThe attitude angle vector of the spacecraft is defined as the attitude angle vector of the spacecraft, and the relationship between the attitude angle vector of the spacecraft and the angular rate of the spacecraft is as follows:
Figure FDA0002377491210000027
wherein,
Figure FDA0002377491210000031
and (4) integrating the formula (4) to obtain the yaw angle psi, the roll angle phi and the pitch angle theta of the spacecraft.
4. The spacecraft fault-tolerant control method based on the adaptive sliding mode theory according to claim 1, wherein in the step 3, the selected sliding mode surface is
s＝ω+kα (5)
In the formula,
Figure FDA0002377491210000032
5. the spacecraft fault-tolerant control method based on the adaptive sliding mode theory according to claim 1, wherein the step 4 is implemented specifically according to the following steps:
step 4.1, for a spacecraft control system (3) with limited control, uncertain parameters and external interference, under the conditions of hypothesis 1 and hypothesis 2, assuming that the fault of a system execution mechanism is unknown, designing the following adaptive sliding mode fault-tolerant control scheme to ensure that an output control torque u generated by the execution mechanism is as follows:
Figure FDA0002377491210000033
wherein,
Figure FDA0002377491210000034
p and D are given positive definite symmetric constant arrays,
Figure FDA0002377491210000035
is dmaxThe value of the estimated value is,
Figure FDA0002377491210000036
is composed of
Figure FDA0002377491210000037
Estimate of (e ∈)0、c0、c1Is a normal number;
as can be seen from the formula (6), the gamma value of the actuator is not needed, and the problem of stable control under the conditions of spacecraft actuator failure, external interference and the like under the condition of unknown gamma can be effectively solved;
step 4.2, considering the limited output control moment amplitude of the actuating mechanism, replacing the output control moment u of the actuating mechanism with a saturation function sat (u), and simultaneously, in order to reduce the buffeting problem of the control system, approximating a nonlinear function x/| x | | by a linear function x/(| x | + epsilon), and rewriting a fault attitude kinetic equation (2) of the actuating mechanism of the spacecraft and the output control moment (6) of the actuating mechanism into
Figure FDA0002377491210000041
Wherein,
Figure FDA0002377491210000042
in the formula umaxTo control the saturation value of the output, ∈1And ε2Is a normal number.
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CN112711190A (en) * 2020-12-25 2021-04-27 四川大学 Self-adaptive fault-tolerant controller, control equipment and control system
CN113220007A (en) * 2021-05-14 2021-08-06 哈尔滨工程大学 Flexible spacecraft finite time attitude cooperative control method for executing mechanism faults
CN113885547A (en) * 2021-10-20 2022-01-04 河北工业大学 Fault-tolerant attitude control strategy for rigid spacecraft in preset time
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