CN111562793B - Spacecraft attitude control method considering task time constraint - Google Patents
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Abstract
The invention provides a spacecraft attitude control method considering task time constraint, which comprises the following steps: according to parameter uncertainty, unmodeled dynamics and external disturbance in a spacecraft model, establishing a dynamic model and a kinematic model of a spacecraft attitude error, introducing a preset performance function to constrain the steady-state and transient-state performance of the spacecraft attitude loop tracking error according to the established dynamic model and kinematic model, and designing a controller according to the constraint; designing a linear extended state observer, selecting proper linear extended state observer gain, and acquiring a system state and a total disturbance estimation value; under the condition that the actuator is saturated and partially fails, the tracking error of the system can be converged into a preset area. The method realizes the tracking control of the spacecraft attitude considering the task time constraint, meets the requirements of stability and precision of attitude tracking, and has good robustness.
Description
Technical Field
The invention relates to the technical field of spacecraft attitude control, in particular to a spacecraft attitude control method considering task time constraint.
Background
The spacecraft is various aircrafts which run in the outer space according to the law of celestial mechanics and execute specific tasks such as exploration, development and utilization of the outer space and celestial bodies. Communication spacecrafts, meteorological spacecrafts, scientific exploration spacecrafts, space shuttles, space stations and the like are used as marks for human beings to search the universe, and great changes are brought to human lives. The aerospace technology of China is listed first in the world, and the development of a new aerospace technology puts higher requirements on the platform technology (guidance, navigation and control technology) and the reliability and autonomy of a control system of a spacecraft. Due to the characteristics of diversity of the current spacecraft tasks and high requirement on the attitude control target, the traditional control technology is difficult to meet, so a new spacecraft attitude control method needs to be designed to adapt to the requirement of a novel spacecraft task.
The attitude control of the spacecraft refers to a process that an executing mechanism for controlling the attitude of the spacecraft outputs a control moment according to the requirements of a control law, and the attitude of the spacecraft is adjusted until a desired attitude is realized. According to the requirement of the on-orbit task of the spacecraft, the attitude control of the spacecraft has two types: and (5) posture stabilization and posture tracking control. Attitude stabilization of a spacecraft refers to the superposition of a main system of the spacecraft and an inertial reference system through attitude maneuver of the spacecraft. The attitude tracking of the spacecraft refers to that the main system of the spacecraft is coincided with the main system of another real (virtual) spacecraft through spacecraft attitude maneuver, for example, the final goal of spacecraft formation attitude cooperative control is to make the main system of the slave spacecraft coincide with the main system of the master spacecraft. The stability and the precision of the attitude control of the spacecraft are the key points of the success or failure of the on-orbit task of the spacecraft. In the actual control process, the spacecraft has system uncertainty, external interference and measurement noise, flexible accessories such as a liquid fuel tank, a solar panel and a large antenna are contained, and the stability and the control precision of a spacecraft attitude control system are difficult to guarantee due to the limitation of physical conditions of an actuating mechanism and a measuring element and various constraints caused by task requirements; in addition, modern aerospace industry is developed, and the attitude of the spacecraft can be converged to a balance point as soon as possible while the control performance of the spacecraft is ensured, so that the time constraint of the aerospace mission is met. In response to the above-mentioned problems, researchers have conducted many studies: the method adopts a filtering method to process noise, and realizes attitude control and the like of the flexible spacecraft from multiple aspects such as flexible spacecraft modeling, flexible mode suppression and the like.
Disclosure of Invention
The invention provides a spacecraft attitude control method considering task time constraint, and aims to meet the requirements of stability and precision of attitude tracking.
In order to achieve the above object, an embodiment of the present invention provides a spacecraft attitude control method considering a task time constraint, including:
step 1, establishing a dynamic model and a kinematic model of a spacecraft attitude error according to parameter uncertainty, unmodeled dynamics and external disturbance in a spacecraft model, wherein the parameter uncertainty, the unmodeled dynamics and the external disturbance are collectively called total disturbance;
step 2, according to the established dynamic model and the established kinematic model, introducing a preset performance function to constrain the steady-state and transient performances of the attitude loop tracking error of the spacecraft, and designing a controller according to the constraint;
step 3, designing a linear extended state observer according to the established dynamic model and the established kinematic model, selecting proper linear extended state observer gain, and acquiring a system state and a total disturbance estimation value;
and 4, performing control law design by adopting a backstepping method according to the system state and the total disturbance estimation value, so that the tracking error of the system can be converged into a preset area under the condition of saturation and partial failure of the actuator.
The scheme of the invention has the following beneficial effects:
according to the spacecraft attitude control method considering the task time constraint, the input saturation of the execution mechanism is approximated by adopting the hyperbolic tangent function, and the saturated input is processed; neural networks and fuzzy control techniques have been used in prior studies to achieve approximations to unknown portions of the model. In the invention, model uncertainty and external disturbance of the system are taken together to be regarded as total disturbance, and the estimation of the total disturbance is realized by designing a linear active disturbance rejection controller, so that the defect that a neural network and a fuzzy control technology are only effective on certain tight sets is avoided; the constraint on the steady-state performance and the transient performance of the tracking error of the attitude loop is realized by designing a novel finite time preset performance function, so that the spacecraft can obtain ideal tracking performance within the task set time; the design of the control law is realized by adopting the thought of a backstepping method, and the stability of the whole control system is realized.
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FIG. 1 is a block diagram of the spacecraft attitude control method of the present invention taking into account task time constraints;
FIG. 2 is a flowchart of a spacecraft attitude control method taking into account task time constraints in accordance with the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1 and 2, an embodiment of the present invention provides a spacecraft attitude control method considering a task time constraint, including:
step 1, establishing a dynamic model and a kinematic model of a spacecraft attitude error according to parameter uncertainty, unmodeled dynamics and external disturbance in a spacecraft model, wherein the parameter uncertainty, the unmodeled dynamics and the external disturbance are collectively called total disturbance;
step 2, according to the established dynamic model and the established kinematic model, introducing a preset performance function to constrain the steady-state and transient performances of the attitude loop tracking error of the spacecraft, and designing a controller according to the constraint;
step 3, designing a linear extended state observer according to the established dynamic model and the established kinematic model, selecting proper linear extended state observer gain, and acquiring a system state and a total disturbance estimation value;
and 4, performing control law design by adopting a backstepping method according to the system state and the total disturbance estimation value, so that the tracking error of the system can be converged into a preset area under the condition of saturation and partial failure of the actuator.
Preferably, in step 1, the expression of the mathematical model of dynamics and kinematics of the attitude error of the spacecraft, which is suitable for the design of the controller, is as follows:
wherein x is1＝[x11,x12,x13]T,x2＝[x21,x22,x23]TRespectively, the tracking error of the attitude and angular velocity of the spacecraft, G (x)1) Is and x1The relevant known non-linear function; f represents the unmodeled dynamics of the model, i.e., the unknown part of the model; f is known model information; d is external disturbance; u is the control input and the expression is
Wherein: u. ofcIs the control input to be designed, umiIs the known upper and lower bounds of the ith loop control input.
b＝diag(δ1,δ2,δ3),0＜δi1(i ═ 1,2,3) or less as control input gain, where δi1 represents the normal operation of the ith actuator, and 0 < deltai≦ 1 indicates that the ith actuator partially failed, but is still running. Partial actuator failure has two forms: addition failures and multiplication failures. Delta is more than 0iA1 indicates a multiplication fault, while sensor noise and spacecraft component faults can be considered additive faults and thus can be factored into external disturbances for processing.
Equation (2) indicates that the actuators of the spacecraft have input saturation constraints. In order to better process the saturated input, the hyperbolic tangent function is adopted to realize the satt (u) of the saturation function in the inventionci) Approximation of (d):
let dui＝sat(uci)-h(uci),i＝1,2,3，
According to formula (4), there is a positive integer
So that
The formulae (4) (5) indicate du＝[du1,du2,du3]TIs bounded and can be processed by being subsumed into the unknown information of the model.
In order to simplify the design process of the controller, the mean theorem is adopted to carry out the function h (u)ci) Carrying out linearization:
wherein u isci,λ＝λuci+(1-λ)uci,0I is 1,2, 3; λ is more than 0 and less than 1, order uci,0Equation (6) can be written as 0:
wherein, h (u)ci) Is a strictly monotonically increasing function, equation (7) can be written in the form of a vector as shown in equation (8):
h(uc)＝ζ(uc)uc (8)
wherein, ζ (u)c)＝diag(ζ(uc1),ζ(uc2),ζ(uc3))。
The compound represented by formula (8) may be substituted for formula (1):
wherein: b ζ (u)c)。
In order to avoid singularity in the subsequent controller design process, a reversible matrix B is designed0Instead of B for the controller design, equation (9) can be written as follows:
wherein x is3＝F+bdu+d+(B-B0)ucThe total perturbations, including unmodeled dynamics of the model and external perturbations, are represented.
Preferably, in the step 2, e ═ e is defined1,e2,e3]T＝x1According to the preset performance control method, the following constraint conditions are required to be met for the tracking error e of the system at any time according to the regulation:
wherein: mu.si∈(0,1]For the parameter to be designed, t ∈ [0, ∞), the performance function ρ is preseti(t) is a smooth, bounded, positive and strictly decreasing performance function, the predetermined performance function ρij(t) may be designed in the form of:
wherein: k is a radical ofi＞0，
ρi0Greater than 0, and rho is selectedi0So that-pi0＜ei(0)＜ρi0；ki,ρi0,ρi∞Is a pre-designed positive real number.
The index form of the preset performance function formula shown in the formula (12) can enable the tracking error of the spacecraft to obtain index stability, however, the spacecraft has time limitation when executing tasks, the index form of the preset performance function can guarantee that the attitude control of the spacecraft has better stability and precision, but the time constraint condition when the spacecraft executes the tasks cannot be met, a novel limited time preset performance function is adopted, so that the control performance of the attitude control of the spacecraft is guaranteed, the time constraint of task execution is met, and the expression of the preset performance function is as follows:
wherein:
the pre-designed performance function is a pre-designed positive real number and the pre-designed performance function designed by equation (13) has the following properties:
ρi(0)＝ρi0＞2ρi(t≥Ti)＝2ρi∞＞0
the preset performance function (13) can ensure that the attitude tracking error of the spacecraft is in the specified time TiConvergence to a desired tracking accuracy ρi∞。
Preferably, in step 3, the following error conversion function epsilon is definedij(t)：
εi(t)＝Φ(zi(t)) (14)
Wherein: phi (-) is a smooth function that strictly monotonically increases,
the form of the transfer function is designed as:
according to the formulas (14) and (15):
let ε (t) equal [ ε ]1(t),ε2(t),ε3(t)]T,γ(t)＝diag(γ1(t),γ2(t),γ3(t)),η(t)＝diag(η1(t),η2(t),η3(t)), then
Preferably, in the step 4, a linear extended state observer is designed to obtain an output estimation value and a total disturbance estimation value of each loop; first, assume that the total disturbance x is unknown3Is bounded and differentiable, and its derivative is also bounded, equation (10) can be written as follows:
for the system shown in the formula (20), a linear extended state observer of the following form can be designed to complete the total disturbance x3Estimation of (2):
wherein, beta1＞0、β20 for a linear extended state observer to be designedGain, z1＝[z11,z12,z13]T、z2＝[z21,z22,z23]TAre respectively a state x2、x3An estimate of (d).
Preferably, in the step 5, the control law design is performed by adopting a counter-step method, and the process is as follows:
from the equation (19), a virtual control law α of the following form can be designed1：
α1＝G-1(-γe-c1ηε) (22)
Wherein, c1> 0 is the virtual control law α to be designed1The gain of (c).
Virtual control law alpha based on dynamic surface control method1Can be obtained by a first order filter of the form
Where κ > 0 is the constant to be designed, v1Is set to v1(0)＝α1(0)。
Let e2＝z1-v1According to the formula (21), the compound can be obtained
Then the law of virtual control alpha is according to equation (24)2The following can be designed:
wherein: c. C2> 0 is the virtual control law α to be designed2The gain of (c).
To achieve compensation for the total disturbance, the control input u to be designedcThe following can be written:
the formula (26) is substituted for the formula (2), so that the actual control input u of the spacecraft attitude tracking control system can be obtained.
The method of the embodiment of the invention adopts the hyperbolic tangent function to approximate the input saturation of the execution mechanism, thereby realizing the processing of the saturated input; neural networks and fuzzy control techniques have been used in prior studies to achieve approximations to unknown portions of the model. In the invention, model uncertainty and external disturbance of the system are taken together to be regarded as total disturbance, and the estimation of the total disturbance is realized by designing a linear active disturbance rejection controller, so that the defect that a neural network and a fuzzy control technology are only effective on certain tight sets is avoided; the constraint on the steady-state performance and the transient performance of the tracking error of the attitude loop is realized by designing a novel finite time preset performance function, so that the spacecraft can obtain ideal tracking performance within the task set time; the design of the control law is realized by adopting the thought of a backstepping method, so that the stability of the whole control system is realized; and in which control method B is used independently of the control input gain B0B is used instead for the design process of the controller, and therefore, the controller can realize excellent attitude tracking control even if the actuator portion fails, i.e., addition failure and multiplication failure occur. This is because the change of B in the multiplication fault does not affect the design process of the controller, and B due to the multiplication fault0The difference between the two signals is already included in the total disturbance for estimation and compensation, so is the addition fault, and the addition fault of the spacecraft actuating mechanism is included in the external disturbance of the system and is also included in the total disturbance for processing, so the spacecraft attitude tracking control method designed by the invention has good robustness.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A spacecraft attitude control method considering task time constraints is characterized by comprising the following steps:
step 1, establishing a dynamic model and a kinematic model of a spacecraft attitude error according to parameter uncertainty, unmodeled dynamics and external disturbance in a spacecraft model, wherein the parameter uncertainty, the unmodeled dynamics and the external disturbance are collectively called total disturbance;
step 2, according to the established dynamic model and the established kinematic model, introducing a preset performance function to constrain the steady-state and transient performances of the attitude loop tracking error of the spacecraft, and designing a controller according to the constraint;
step 3, designing a linear extended state observer according to the established dynamic model and the established kinematic model, selecting proper linear extended state observer gain, and acquiring a system state and a total disturbance estimation value;
step 4, according to the system state and the total disturbance estimation value, a backstepping method is adopted for control law design, so that the tracking error of the system can be converged into a preset area under the condition that the actuator is saturated and partially fails;
according to the preset performance control method, the tracking error of the system in any time is specified to meet the following constraint conditions:
wherein: mu.si∈(0,1]For the parameter to be designed, t ∈ [0, ∞), the performance function ρ is preseti(t) is a smooth, bounded, positive and strictly decreasing performance function;
the expression of the preset performance function is as follows:
wherein:
is a pre-designed positive real number, and the preset performance function has the following properties:
ρi(0)＝ρi0＞2ρi(t≥Ti)＝2ρi∞＞0
the preset performance function ensures that the attitude tracking error of the spacecraft is in the specified time TiConvergence to a desired tracking accuracy ρi∞。
2. A spacecraft attitude control method taking into account mission time constraints according to claim 1, characterized in that the expressions of the dynamical and kinematic models of spacecraft attitude errors are as follows:
wherein x is1＝[x11,x12,x13]T,x2＝[x21,x22,x23]TRespectively, the tracking error of the attitude and angular velocity of the spacecraft, G (x)1) Is and x1The relevant known non-linear function; f represents the unmodeled dynamics of the model, i.e., the unknown part of the model; f is known model information; d is external disturbance, b is diag (delta)1,δ2,δ3),0＜δi1 (i-1, 2,3) represents the control input gain, when deltai1 represents the normal operation of the ith actuator, and 0 < deltai≦ 1 indicates that the ith actuator partial failure, which has two forms: addition fault and multiplication fault, 0 < deltaiMultiplication faults are represented by less than or equal to 1, addition faults are represented by sensor noise and spacecraft part faults, and the sensor noise and the spacecraft part faults can be included in external disturbance for processing;
u is the control input and the expression is
u＝sat(uc)＝[sat(uc1),sat(uc2),sat(uc3)]T
Wherein u iscIs the control input to be designed, umiIs the known upper and lower bounds of the ith loop control input.
3. Method for spacecraft attitude control taking into account mission time constraints according to claim 1, characterized in that the error transfer function εi(t)：
εi(t)＝Φ(zi(t))
Where Φ (·) is a smooth function that strictly monotonically increases,
4. a spacecraft attitude control method taking into account task time constraints according to claim 1, characterized in that said step 3 specifically comprises:
assuming unknown total disturbance x3Is bounded and differentiable, and its derivative is bounded, then
Wherein, B0Is a reversible matrix, G (x)1) Is and x1Related known nonlinear function, f is known model information, x1＝[x11,x12,x13]T,x2＝[x21,x22,x23]TRespectively the tracking error of the attitude and angular velocity of the spacecraft, ucIs a control input to be designed;
the following form of linear extended state observer is designed to complete the estimation of the total disturbance:
wherein: beta is a1＞0、β2> 0 gain of the linear extended state observer to be designed, z1＝[z11,z12,z13]T、z2＝[z21,z22,z23]TAre respectively a state x2、x3An estimate of (d).
5. The spacecraft attitude control method taking into account the task time constraints according to claim 1, wherein the control law design by the back-stepping method specifically comprises:
the virtual control law α is designed in the form1：
α1＝G-1(-γe-c1ηε)
Wherein: c. C1> 0 is the virtual control law α to be designed1E is the tracking error of the system, e ═ e1,e2,e3]T＝x1；
Virtual control law alpha based on dynamic surface control method1Can be obtained by a first order filter of the form
Where κ > 0 is the constant to be designed, v1Is set to v1(0)＝α1(0)；
Let e2＝z1-v1Can obtain
Wherein z is1＝[z11,z12,z13]T、z2＝[z21,z22,z23]TAre respectively a state x2、x3Estimate of beta1> 0 is the gain of the linear extended state observer to be designed, B0Is a reversible matrix, f is known model information;
virtual control law alpha2The following can be designed:
wherein, c2> 0 is the virtual control law α to be designed2A gain of (d);
control input u to be designedcThe following can be written:
and obtaining the actual control input u of the spacecraft attitude tracking control system.
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