CN111338368B - Self-adaptive robust control method for spacecraft rapid maneuver attitude tracking - Google Patents
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Abstract
The invention provides a spacecraft rapid maneuver attitude tracking self-adaptive robust control method, which adopts a tracking differentiator to calculate the transition process of reference input and give the differentiation of the reference input, and solves the contradiction between the overshoot and the rapidity of a system by arranging a proper reference signal transition process. The controller design is based on a cooperative control method, so that the problem of substantial discontinuity of sliding mode variable structure control is solved, the optimization of performance indexes is achieved, the cooperative control method combines the advantages of sliding mode control and optimal control, and meanwhile, the buffeting phenomenon generated by the discontinuity in the sliding mode variable structure control is improved. Based on the self-adaptive control, the problems of uncertainty of rotational inertia and interference suppression of the spacecraft are solved, and the self-adaptive robust high-precision control of the rapid maneuvering attitude tracking of the spacecraft under the interference condition is realized.
Description
Technical Field
The invention relates to a spacecraft rapid maneuver attitude tracking control method, and belongs to the technical field of adaptive robust control of nonlinear control systems.
Background
Currently, complex aerospace tasks require spacecraft to have the capabilities of attitude maneuver and attitude tracking, so that the requirements of attitude pointing and instruction can be met after a series of control. With the development of aerospace tasks, high-resolution remote sensing satellites are paid attention to in various fields of the world because the satellites have extremely high spatial resolution in a full spectrum segment and a multispectral spectrum segment. Along with the continuous improvement of the requirements of high-resolution remote sensing satellite users, the requirements of high space resolution are simultaneously provided for the quick response capability, earth observation efficiency and imaging breadth of the satellite, so that a nonlinear tracking controller is required to be designed after the attitude path planning under multiple constraints is carried out according to the imaging requirements, and the quick maneuvering attitude high-precision tracking task of the spacecraft is realized under the conditions of interference and parameter uncertainty.
The traditional gesture tracking control is mostly PID control or improved PID control, optimal control, variable structure control method, robust control and the like, and the PID controller has simple design and general effect; the optimal control can realize the optimal performance index but the robustness is poor; the variable structure has better control robustness, but can cause jitter of control output; the order of the robust control controller is higher, and the robust control controller is rarely applied to an actual satellite attitude control system.
In recent years, a cooperative control method has been developed rapidly in the nonlinear control field due to better robustness and optimality on interference and parameter uncertainty, and cooperative control, such as Haken description, refers to cooperation of all subsystems, and is collective control of state variables in the control field. Kolesnikov et al developed the idea of cooperative control and applied it to the problem of energy conversion in engineering. Nusawassrdhana et al have studied their superiority more deeply and have application in the control of aeronautical systems.
Aiming at the high-precision tracking task of the spacecraft attitude, the invention designs the nonlinear tracking controller of the spacecraft by applying a cooperative control method, and then identifies the rotational inertia of the spacecraft by adopting a self-adaptive method, and the designed self-adaptive cooperative controller has robustness to interference and parameter uncertainty and is easy for engineering realization.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims at a spacecraft rapid maneuver attitude tracking self-adaptive robust control method, aims at the spacecraft attitude tracking control problem under the condition of given expected attitude, adopts a Tracking Differentiator (TD), calculates the transition process of the reference input and gives the differentiation of the reference input, and designs the spacecraft rapid maneuver attitude tracking self-adaptive robust high-precision control law under the interference condition based on the self-adaptive cooperative control method.
In order to achieve the above object, the technical solution of the present invention is: a spacecraft rapid maneuver attitude tracking self-adaptive robust control method comprises the following steps:
s1, determining satellite attitude tracking attitude errorsAnd angular velocity error omega e ∈R 3 Let ω εR 3 ，/>Respectively representing the rotation angular velocity and attitude quaternion, omega of a satellite body system B relative to an inertial system I d ∈R 3 Representing the desired angular velocity vector in the desired coordinate system, is->A pose quaternion representing the desired coordinate system relative to the inertial coordinate system. q e ，ω e Defined in the spacecraft body coordinate system.
Wherein the method comprises the steps ofRepresenting quaternion multiplication, ++>Is a rotation matrix represented by an error quaternion.
S2, determining planning information of the expected gesture and a Tracking Differentiator (TD) of approximate differentiation of the planning information, wherein the tracking differentiator is used for solving the contradiction between system overshoot and rapidity and enhancing the robustness of a control system.
S3, determining quaternion to describe a satellite attitude kinematics equation. According to Euler theorem, satellite kinematics and dynamics models based on error quaternion can be obtained respectively as follows
Wherein the method comprises the steps of
u∈R 3 Representing a control moment applied by a satellite triaxial; d E R 3 The method mainly comprises the steps of representing disturbance moment born by satellites, wherein the disturbance moment mainly comprises moment generated by rotation of a movable part of a payload, moment generated by installation error of a flywheel, other friction moment difficult to accurately model, driving moment of a solar cell array, gravity gradient disturbance moment, solar light pressure disturbance moment, disturbance moment generated by aerodynamic force, remanence disturbance moment and the like; j represents a positively symmetric moment of inertia matrix.
S4, determining a spacecraft attitude cooperative optimal tracking controller, wherein the aim is to design the cooperative optimal tracking controller under the condition that the moment of inertia J of the spacecraft is assumed to be precisely known, so that a closed-loop system is asymptotically stable, and the state of the closed-loop system meets lim t→∞ q e (t)＝[1 0 0 0] T ,lim t→∞ ω e (t)＝[0 0 0] T 。
S5, determining a spacecraft attitude self-adaptive collaborative tracking robust controller, and designing the self-adaptive collaborative tracking robust controller under the condition of considering uncertainty of moment of inertia J of the spacecraft and external interference so that a closed-loop system is asymptotically stable and is designedThe state satisfies lim t→∞ q e (t)＝[1 0 0 0] T ,lim t→∞ ω e (t)＝[0 0 0] T The problems of uncertainty of rotational inertia and interference suppression of the spacecraft are solved, and the rapid maneuvering attitude tracking self-adaptive robust high-precision control of the spacecraft under the interference condition is realized.
In the step S2, the tracking differentiator is designed as
Wherein omega di (i=1, 2, 3) represents the desired angular velocity of each axis,representing a smoothed reference angular velocity signal omega td >0 represents the TD bandwidth, which is an adjustable parameter.
In the step S4, according to spacecraft error attitude kinematics and dynamics equation, the method can obtain
The design step of cooperative control is to select the sliding plane meeting the control target and then design the sliding condition meeting the plane. In order to improve the steady-state accuracy of the system in the presence of disturbances, the integral term is added to the design of the controller on the basis of the sliding plane of the usual design.
The method comprises the following specific steps:
first, design sliding plane s= [ s ] 1 s 2 s 3 ] T Is that
Wherein lambda is 1 >0，λ 2 >0 is a design parameter, further design
Wherein Γ=Γ T Is a positive definite matrix. The system will asymptotically converge to a sliding plane s (x) =0. At this time, the liquid crystal display device,
second step, determining spacecraft attitude tracking controller u s
The method is the optimal tracking controller for the coordination of the required spacecraft posture. Meets the performance index
Minimizing. Since the cooperative optimal control is developed from the sliding mode variable structure control, the cooperative optimal control has similarities with the sliding mode variable structure control.
In the step S5, without losing generality, the following assumptions are made:
the moment of inertia matrix J of the spacecraft is an unknown, positively symmetric constant matrix, the disturbance moment vector d is bounded and meets
||d||≤d b
Wherein d b Is an unknown positive constant.
The method comprises the following specific steps:
in a first step, a linear multiplier L (a) R is defined 3 →R 3×6
The rotational inertia of the spacecraft is
Let alpha= [ J ] 11 J 12 J 13 J 22 J 23 J 33 ] T ∈R 6 Then there is
Ja＝L(a)α
Second, to eliminate the need to rotate the inertia parameters J and α in the controller, respectivelyAnd->Representing the estimated values of J and alpha to obtain
Third, the estimated value is used to design the cooperative controller to obtain
Fourth, the update law for determining the moment of inertia is as follows
Wherein Q is a positive definite matrix.
Fifthly, in order to compensate the uncertainty term d caused by the disturbance moment, the cooperative controller is further improved, and an adaptive algorithm is adopted to add a term into the control law, so that a new control law is obtained
Sixthly, designing an adaptive parameter regulation law
In the method, in the process of the invention,an estimated value representing the upper bound of unknown interference is set +.>x 1 ＝ω e ，x 2 ＝sgn(q e0 )q e13 ，M＝[I 3 λ 1 I 3 λ 2 I 3 ]The closed loop system is globally consistent, bounded and stable, and has
Gamma is the positive constant to be determined, eta 3 And epsilon are both normal numbers. Lambda (lambda) min (. Cndot.) and lambda max (. Cndot.) represents the minimum eigenvalue and the maximum eigenvalue of the matrix, respectively.Is a positive definite symmetric matrix, thus ω e ，q e13 And->The system is consistent and finally bounded, the system state can be ensured to be converged to a smaller critical area of the zero point by adjusting design parameters, the problems of uncertainty of rotational inertia of the spacecraft and interference suppression are solved, and the rapid maneuvering attitude tracking self-adaptive robust high-precision control of the spacecraft under the interference condition is realized.
Compared with the prior art, the invention has the following beneficial effects:
(1) The TD tracking differentiator adopted by the invention is mainly used for giving out the transition process of the reference input and giving out the differentiation of the reference input. Reasonably arranging the reference inputs and their differentiated transition information can bring the following benefits to the control system: the overshoot and rapidity of the system in the conventional control method are a group of contradictions that are difficult to reconcile, but can be resolved by arranging a suitable reference signal transition procedure. The selection range of the feedback gain coefficient of the error and the derivative thereof can be increased, so that parameter setting is easy; meanwhile, aiming at a given feedback coefficient, the range of a control object which can be adapted to the feedback coefficient is enlarged, and the control robustness is enhanced.
(2) According to the self-adaptive cooperative control algorithm provided by the invention, under the condition of considering space environment interference and satellite rotational inertia uncertainty, the system state can be ensured to be converged to a smaller critical area of the zero point by adjusting the design parameters, the problems of uncertainty of the rotational inertia of the spacecraft and interference suppression are solved, the rapid maneuvering attitude tracking self-adaptive robust high-precision control of the spacecraft under the interference condition is realized, the reliability and the adaptability of the system are improved, and the method has potential application prospects.
Drawings
FIG. 1 is a block diagram of a control system according to an embodiment of the present invention.
Fig. 2 is a plot of desired angular velocity for satellite attitude.
Fig. 3 is a graph of actual angular velocity of satellite attitude.
Fig. 4 is a satellite attitude tracking angular velocity error curve.
Fig. 5 is a plot of satellite attitude desired triaxial attitude angles.
Fig. 6 is a plot of the actual triaxial attitude angle of the satellite attitude.
Fig. 7 is a satellite attitude tracking attitude angle error curve.
Fig. 8 is a control torque curve.
Detailed Description
The invention can be used for a spacecraft attitude tracking control system. The invention mainly solves the problem of high-precision robust tracking control under the condition that a given spacecraft is rapidly maneuvered to an expected attitude path.
The present invention will be described in further detail with reference to the accompanying drawings.
(1) Satellite attitude tracking attitude errorAnd angular velocity error omega e ∈R 3
Consider the satellite attitude tracking attitude error calculation shown in FIG. 1, let ω εR 3 ，Respectively representing the rotation angular velocity and attitude quaternion, omega of a satellite body system B relative to an inertial system I d ∈R 3 Representing the desired angular velocity vector in the desired coordinate system, is->A pose quaternion representing the desired coordinate system relative to the inertial coordinate system. q e ，ω e Defined in the spacecraft body coordinate system.
Wherein the method comprises the steps ofRepresenting quaternion multiplication, ++>Is a rotation matrix represented by an error quaternion.
(2) Tracking Differentiator (TD)
A Tracking Differentiator (TD) taking into account the planning information of the desired pose and its approximate differentiation shown in fig. 1 is used to solve the contradiction between the system overshoot and the rapidity, while being able to enhance the robustness of the control system.
Designing a tracking differentiator as
Wherein omega di (i=x, y, z) represents the desired angular velocity of each axis,representing a smoothed reference angular velocity signal omega td >0 represents the TD bandwidth, which is an adjustable parameter.
(3) Self-adaptive cooperative control law
Considering the adaptive cooperative control algorithm shown in fig. 1, a quaternion is first determined to describe the satellite attitude kinematics equation. According to Euler theorem, satellite kinematics and dynamics models based on error quaternion can be obtained respectively as follows
Wherein the method comprises the steps of
u∈R 3 Representing a control moment applied by a satellite triaxial; d E R 3 The method mainly comprises the steps of representing disturbance moment born by satellites, wherein the disturbance moment mainly comprises moment generated by rotation of a movable part of a payload, moment generated by installation error of a flywheel, other friction moment difficult to accurately model, driving moment of a solar cell array, gravity gradient disturbance moment, solar light pressure disturbance moment, disturbance moment generated by aerodynamic force, remanence disturbance moment and the like; j represents a positively symmetric moment of inertia matrix.
(4) Determining a spacecraft attitude cooperative optimal tracking controller, wherein the aim is to design the cooperative optimal controller under the condition that the moment of inertia J of the spacecraft is assumed to be precisely known, so that a closed-loop system is asymptotically stable, and the state of the closed-loop system meets lim t→∞ q e (t)＝[1 0 0 0] T ,lim t→∞ ω e (t)＝[0 0 0] T 。
According to spacecraft error attitude kinematics and dynamics equation, can be obtained
The design step of cooperative control is to select the sliding plane meeting the control target and then design the sliding condition meeting the plane. In order to improve the steady-state accuracy of the system in the presence of disturbances, in the design of the controller, the integral term is added to the sliding plane of the usual design,
the specific design process is as follows:
design sliding plane s= [ s ] 1 s 2 s 3 ] T Is that
Wherein lambda is 1 >0，λ 2 >0 is a design parameter, further design
Wherein Γ=Γ T Is a positive definite matrix. The system will asymptotically converge to a sliding plane s (x) =0. At this time, the liquid crystal display device,
determining spacecraft attitude tracking controller u s
The method is the optimal tracking controller for the coordination of the required spacecraft posture. Meets the performance index
Minimizing. Since the cooperative optimal control is developed from the sliding mode variable structure control, the cooperative optimal control has similarities with the sliding mode variable structure control.
(5) Determining a spacecraft attitude self-adaptive collaborative tracking robust controller, aiming at designing the self-adaptive collaborative robust controller under the condition of considering uncertainty of rotational inertia J of the spacecraft and external interference so that a closed-loop system is asymptotically stable,
and the closed loop system state satisfies lim t→∞ q e (t)＝[1 0 0 0] T ,lim t→∞ ω e (t)＝[0 0 0] T The problems of uncertainty of rotational inertia and interference suppression of the spacecraft are solved, and the rapid maneuvering attitude tracking self-adaptive robust high-precision control of the spacecraft under the interference condition is realized.
Without loss of generality, the following assumptions are made:
the moment of inertia matrix J of the spacecraft is an unknown, positively symmetric constant matrix, the disturbance moment vector d is bounded and meets
||d||≤d b
Wherein d b Is an unknown positive constant.
The specific design process is as follows:
definition of the linear multiplier L (a): R 3 →R 3×6
The rotational inertia of the spacecraft is
Let alpha= [ J ] 11 J 12 J 13 J 22 J 23 J 33 ] T ∈R 6 Then there is
Ja＝L(a)α
To eliminate the need to rotate inertia parameters J and alpha in the controller, respectivelyAnd->Representing the estimated values of J and alpha to obtain
The estimated value is used to design the cooperative controller to obtain
The update law for determining moment of inertia is as follows
Wherein Q is a positive definite matrix.
In order to compensate the uncertainty d caused by the disturbance moment, the cooperative controller is further improved, and an adaptive algorithm is adopted to add one term into the control law, so that a new control law is obtained
Design adaptive parameter adjustment law
In the method, in the process of the invention,an estimated value representing the upper bound of unknown interference is set +.>x 1 ＝ω e ，x 2 ＝sgn(q e0 )q e13 ，M＝[I 3 λ 1 I 3 λ 2 I 3 ]It can be obtained that the closed-loop system is globally consistent and bounded stable, andhas the following components
Gamma is the positive constant to be determined, eta 3 And epsilon are both normal numbers. Lambda (lambda) min (. Cndot.) and lambda max (. Cndot.) represents the minimum eigenvalue and the maximum eigenvalue of the matrix, respectively.Is a positive definite symmetric matrix, thus ω e ，q e13 And->The system is consistent and finally bounded, the system state can be ensured to be converged to a smaller critical area of the zero point by adjusting design parameters, the problems of uncertainty of rotational inertia of the spacecraft and interference suppression are solved, and the rapid maneuvering attitude tracking self-adaptive robust high-precision control of the spacecraft under the interference condition is realized.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
The effectiveness of the embodiments is described below in a practical case simulation. And taking a certain observation satellite as a controlled object, and adopting the control algorithm to verify the validity of the self-adaptive cooperative control algorithm.
The spacecraft inertia matrix is
Taking solar light pressure, air power, residual magnetism interference moment, gyro, star sensor noise and flywheel executing mechanism link into consideration, assuming that the initial angular velocity error is zero and the initial attitude Euler angle error is sigma e (0)＝[0.2 1.1 -0.46] T Degree, desired angular velocity curveThe lines are shown in fig. 2.
The following parameter settings were used:
Γ＝2I 3 ,λ 1 ＝1,λ 2 ＝0.05，Q＝diag[0.005,0.02,0.02,0.006,0.02,0.006]，
m＝0.04，γ＝1，d b (0)＝0.008，ρ＝0.2
the simulation results are shown in fig. 3 to 8: fig. 3 to 8 show time response curves of the spacecraft attitude angular velocity, attitude angular velocity tracking error, desired attitude angle, actual attitude angle, attitude angle error, and control moment based on the co-optimal controller. From the figure, the controller can achieve a high-precision gesture tracking target, and the proposed robust self-adaptive controller has self-adaptability to inertia parameters and robustness to generalized interference.
While the present invention has been described in detail through the foregoing description of the preferred embodiment, it should be understood that the foregoing description is not to be considered as limiting the invention. Many modifications and substitutions of the present invention will become apparent to those of ordinary skill in the art upon reading the foregoing. Accordingly, the scope of the invention should be limited only by the attached claims.
Claims (2)
1. The self-adaptive robust control method for the rapid maneuvering attitude tracking of the spacecraft is characterized by comprising the following steps of:
step S1, determining satellite attitude tracking attitude errorsAnd angular velocity error omega e ∈R 3 ；
Let ω εR 3 ，Respectively representing the rotation angular velocity and attitude quaternion, omega of a satellite body system B relative to an inertial system I d ∈R 3 Representing the desired angular velocity vector in the desired coordinate system, is->A gesture quaternion representing a desired coordinate system relative to an inertial coordinate system; q e ，ω e Defined in the space vehicle body coordinate system,
wherein the method comprises the steps ofRepresenting quaternion multiplication, ++>Is a rotation matrix represented by an error quaternion;
step S2, determining planning information of the expected gesture and a tracking differentiator for approximate differentiation of the planning information;
the tracking differentiator is
Wherein omega di (i=1, 2, 3) represents the desired angular velocity of each axis,representing a smoothed reference angular velocity signal omega td > 0 represents TD bandwidth, which is an adjustable parameter;
s3, determining quaternion to describe a satellite attitude kinematic equation;
the satellite kinematics and dynamics model based on the error quaternion are obtained according to the Euler theorem
Wherein the method comprises the steps of
u∈R 3 Representing a control moment applied by a satellite triaxial; d E R 3 Representing the disturbance moment to which the satellite is subjected; j represents a positively symmetric moment of inertia matrix;
s4, determining a spacecraft attitude cooperative optimal tracking controller;
the goal is to design a co-optimal controller under the assumption that the spacecraft moment of inertia matrix J is known so that the closed-loop system is asymptotically stable and the closed-loop system state satisfies
lim t→∞ q e (t)＝[1 0 0 0] T ,lim t→∞ ω e (t)＝[0 0 0] T ；
S5, determining a spacecraft attitude self-adaptive collaborative tracking robust controller;
the method aims at designing the self-adaptive collaborative robust controller under the condition of considering uncertainty of the moment of inertia matrix J of the spacecraft and external interference, so that the closed-loop system is asymptotically stable, and the state of the closed-loop system meets the requirement
lim t→∞ q e (t)＝[1 0 0 0] T ,lim t→∞ ω e (t)＝[0 0 0] T
In the step S5, it is assumed that the moment of inertia matrix J of the spacecraft is an unknown, positively symmetric constant matrix, the disturbance moment vector d is bounded, and satisfies
||d||≤d b
Wherein d b Is an unknown positive constant;
the step S5 further comprises:
s5.1 definition of the linear multiplier L (a): R 3 →R 3×6
The rotational inertia of the spacecraft is
Let alpha= [ J ] 11 J 12 J 13 J 22 J 23 J 33 ] T ∈R 6 Then there is
Ja＝L(a)α
S5.2, in order to eliminate the need for rotating inertia parameters J and alpha in the controller, respectivelyAnd->Representing the estimated values of J and alpha to obtain
S5.3, designing a cooperative controller by using the estimated value to obtain
S5.4, determining the update law of moment of inertia as follows
Wherein Q is a positive definite matrix;
s5.5, further improving the cooperative controller to compensate the uncertainty term d caused by the disturbance moment, and obtaining a new control law by adopting an adaptive algorithm
S5.6, designing an adaptive parameter adjustment law
In the method, in the process of the invention,an estimated value representing the upper bound of unknown interference is set +.>x 1 ＝ω e ，x 2 ＝sgn(q e0 )q e13 ，M＝[I 3 λ 1 I 3 λ 2 I 3 ]ObtainingTo a closed loop system is globally consistent, bounded and stable, and has
Gamma is the positive constant to be determined, eta 3 Both epsilon and epsilon are normal numbers; lambda (lambda) min (. Cndot.) and lambda max (. Cndot.) represents the minimum eigenvalue and the maximum eigenvalue of the matrix respectively;is a positive definite symmetric matrix, thus ω e ，q e13 And->Is consistent and eventually bounded, and the system state is guaranteed to converge to a smaller critical domain of zero by adjusting design parameters.
2. The spacecraft fast maneuver attitude tracking adaptive robust control method of claim 1, wherein: in the step S4, according to spacecraft error attitude kinematics and dynamics equation, obtaining
The design step of the cooperative control further comprises the following steps:
s4.1, design sliding plane s= [ S ] 1 s 2 s 3 ] T Is that
Wherein lambda is 1 >0，λ 2 >0 is a design parameter, further design
Wherein Γ=Γ T Is a positive definite matrix; the system converges asymptotically to a sliding plane s (x) =0; at this time, the liquid crystal display device,
s4.2, determining a spacecraft attitude tracking controller u s
The method is the optimal tracking controller for the coordination of the required spacecraft posture; meets the performance index
Minimizing.
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