CN111258221B - Spacecraft fault-tolerant control method based on self-adaptive sliding mode theory - Google Patents
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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
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;
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 d max Wherein | | · | | is an exponential quantity of 2, d max An 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:
wherein,
is a rotational inertia matrix of the spacecraft; omega-omega ═ omega x ω y ω z ] T Projecting the attitude angular rate of the spacecraft body coordinate system relative to the inertial coordinate system in the spacecraft body system;
an output control torque generated for the actuator;
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:
when the actuator fails partially, adopting a multiplication factor to establish a fault model of the actuator as E (t) u, and rewriting a formula (1) under the condition that the actuator fails partially to obtain an attitude kinetic equation of the spacecraft actuator failure:
wherein e (t) diag (e) 1 (t) e 2 (t) e 3 (t)) is the effective factor of the actuator, t is the spacecraft runtime, e i (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
Wherein Δ E ═ diag (1-E) 1 (t) 1-e 2 (t) 1-e 3 (t)) is a fault factor of the actuator, and | | | Δ E | | | is equal to or less than 1, and γ | | | Δ E | |.
The step 2 is implemented according to the following steps:
according to the sequence of the coordinate system 3-1-2, defining three rotation angles of a spacecraft body coordinate system and an inertial coordinate system as a spacecraft yaw angle psi, a roll angle phi and a pitch angle theta respectively; let alpha be [ psi phi theta] T The attitude angle vector of the spacecraft is defined as the angular velocity relation of the spacecraft and the attitude angle vector of the spacecraft:
wherein,
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,
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:
wherein,
p and D are given positive definite symmetric constant matrices,
is d max The value of the estimated value is,
is composed of
Estimate of (e ∈) 0 、c 0 、c 1 Is 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
Wherein,
in the formula u max To control the saturation value of the output, ∈ 1 And ε 2 Is a normal number.
The invention has the beneficial effects that:
1. the method is oriented to spacecraft attitude fault-tolerant control, and is 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 failure of a spacecraft actuating mechanism, external interference and the like under unknown conditions, and has more engineering significance.
4. The method is not only suitable for the spacecraft attitude fault-tolerant control task, but also suitable for the tasks of fault rescue, quick maneuvering and the like 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 an upper limit estimation curve of external interference in a safety mode of a simulation experiment according to 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;
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 d max Wherein | | · | | is an exponential quantity of 2, d max An 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:
wherein,
is a rotational inertia matrix of the spacecraft; omega ═ omega x ω y ω z ] T Projecting the attitude angular rate of the spacecraft body coordinate system relative to the inertial coordinate system in the spacecraft body system;
an output control torque generated for the actuator;
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:
when the actuator fails partially, a product factor is adopted, a fault model of the actuator is established to be E (t) u, and then the formula (1) is rewritten under the condition that the actuator fails partially, so that an attitude kinetic equation of the spacecraft actuator failure can be obtained:
wherein e (t) diag (e) 1 (t) e 2 (t) e 3 (t)) is the effective factor of the actuator, t is the spacecraft runtime, e i (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
Wherein Δ E ═ diag (1-E) 1 (t) 1-e 2 (t) 1-e 3 (t)) is a fault factor of the actuator, and | | | Δ E | | | is equal to or less than 1, and γ | | | Δ 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 sequence of the coordinate system 3-1-2, defining three rotation angles of a spacecraft body coordinate system and an inertial coordinate system as a spacecraft yaw angle psi, a roll angle phi and a pitch angle theta respectively; let alpha be [ psi phi theta] T The 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:
wherein,
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,
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:
wherein,
p and D are given positive definite symmetric constant arrays,
is d max The value of the estimated value is,
is composed of
Estimate of (e ∈) 0 、c 0 、c 1 Is 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
Wherein,
in the formula u max To control the saturation value of the output, ∈ 1 And ε 2 Is a normal number, epsilon for ensuring approximation effect 1 And ε 2 Generally, the value is small.
The effectiveness of the above scheme is demonstrated by numerical simulation below. The moment of inertia matrix of the spacecraft is
The spacecraft is subjected to external interference torque of
Wherein, A0 for external disturbance torque amplitude, omega 0 Is 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
Under the conditions of 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 conditions of moment deviation, parameter uncertainty and the like of an actuating mechanism to ensure that
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 result, 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 than 1 0X 10-3 degrees, the attitude control system has good robustness, quick response capability and stable precision.
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 (1)
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;
step 4, considering 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 d max Wherein | | · | | is an exponential quantity of 2, d max An upper bound for 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:
wherein,
is a rotational inertia matrix of the spacecraft; omega ═ omega x ω y ω z ] T Projecting the attitude angular rate of the spacecraft body coordinate system relative to the inertial coordinate system in the spacecraft body system;
an output control torque generated for the actuator;
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:
when the actuator fails partially, adopting a multiplication factor to establish a fault model of the actuator as E (t) u, and rewriting a formula (1) under the condition that the actuator fails partially to obtain an attitude kinetic equation of the spacecraft actuator failure:
wherein e (t) diag (e) 1 (t) e 2 (t) e 3 (t)) is the effective factor of the actuator, t is the spacecraft runtime, e i (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
Wherein Δ E ═ diag (1-E) 1 (t) 1-e 2 (t) 1-e 3 (t)) is a fault factor of the actuating mechanism, and | | | Δ E | | ≦ 1, making γ | | | Δ E |;
the step 2 is implemented according to the following steps:
according to the sequence of the coordinate system 3-1-2, defining three rotation angles of a spacecraft body coordinate system and an inertial coordinate system as a spacecraft yaw angle psi, a roll angle phi and a pitch angle theta respectively; let alpha be [ psi phi theta] T The 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:
wherein,
integrating the formula (4) to obtain a yaw angle psi, a roll angle phi and a pitch angle theta of the spacecraft;
in step 3, the selected slip form surface is
s＝ω+kα (5)
In the formula,
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:
wherein,
p and D are given positive definite symmetric constant arrays,
is d max The value of the estimated value is,
is composed of
Estimate of (e ∈) 0 、c 0 、c 1 Is a normal number;
as can be seen from the formula (6), the gamma value of the actuating mechanism is not needed, and the problem of stable control under the conditions of failure of the actuating mechanism of the spacecraft and external interference under the condition of unknown gamma can be effectively solved;
step 4.2, considering the amplitude limiting characteristic of the output control moment 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 dynamic equation (2) of the actuating mechanism of the spacecraft and the output control moment (6) of the actuating mechanism into a dynamic equation (6) of the actuating mechanism of the spacecraft
Wherein,
in the formula u max To control the saturation value of the output,. epsilon 1 And ε 2 Is a normal number.
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| Title |
|---|
| Adaptive Fault-Tolerant Control for Rigid Spacecraft Attitude System Using Fractional Order Sliding Mode;Xiaobo Zhang等;《2019 Chinese Control And Decision Conference(CCDC)》;20190912;第422-427页 * |
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| CN111258221A (en) | 2020-06-09 |
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