CN117311377B - Spacecraft fine attitude control method based on composite interference separation estimation - Google Patents
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Abstract
The invention relates to a spacecraft fine attitude control method based on composite interference separation estimation, which belongs to the field of spacecraft control, and comprises the steps of firstly, establishing an attitude dynamics model of a spacecraft under composite interference such as flexible vibration interference, inertia uncertainty, actuator error and the like, and completing mathematical representation of the flexible vibration interference by adopting a recessive interference model; secondly, designing an interference observer to estimate flexible vibration interference, and designing an equivalent input interference estimator to estimate error of an executing mechanism and environmental interference, so as to complete separation estimation of composite interference; finally, based on the interference separation estimation result, designing a fine attitude control method to realize simultaneous suppression and compensation of composite interference, and completing the solution of a gain matrix based on a convex optimization algorithm; the invention has the advantages of strong anti-interference capability, high control precision and the like, and can be used for high-precision attitude control of the spacecraft in a complex interference environment.
Description
Technical Field
The invention belongs to the field of spacecraft control, and particularly relates to a spacecraft fine attitude control method based on composite interference separation estimation, which can realize separation estimation, fine compensation and suppression of composite interference of a spacecraft and can be used for anti-interference attitude control in high-precision aerospace tasks such as inter-satellite laser communication, earth observation and the like.
Background
With the development of the aerospace technology, the spaceflight tasks such as inter-satellite laser chain building, earth observation, scientific experiments and the like are increasingly complicated and precise, and the requirements on the precision and stability of attitude control are increasingly improved. However, interference and uncertainty factors from links such as spacecraft structures and environments are unavoidable. Specifically, multi-source and multi-channel disturbances such as vibration, inertia uncertainty, actuator errors, and spatial environment disturbances (light pressure, geomagnetism, etc.) of flexible components (solar sailboards, antennas, etc.) are widely present in spacecraft attitude control systems, and may cause oscillation or offset of attitude pointing under both floating base and microgravity environments, affecting reliability of tasks. Therefore, anti-interference becomes one of key technologies for improving attitude control performance of the spacecraft. For spacecraft interference, an internal dynamic and static coupling association relationship exists between the interference and an attitude vector, a control input and other interferences, namely the interference presents a composite characteristic. For example, flexural vibration disturbances are dynamically coupled to physical quantities such as spacecraft angular velocity, control inputs, etc. Therefore, accurate estimation, compensation and suppression of the composite interference are key technologies for breakthrough in the anti-interference attitude control of the spacecraft.
The traditional anti-interference attitude control method can be divided into two types of interference suppression and interference compensation according to anti-interference capability. Interference suppression methods (e.gControl) can achieve effective suppression of norm bounded disturbances such as inertia uncertainty. The core of the interference compensation control method (such as the active disturbance rejection control, the control based on an interference observer, the equivalent input interference method and the like) is an interference estimation technology, for example, the active disturbance rejection control method often equates multiple types of interference such as the inertia uncertainty, the flexible vibration interference, the environmental interference and the like of a spacecraft into a single lumped interference, and then estimates by using an extended state observer. However, the above methods are all single type anti-interference control methods, and have certain conservation in dealing with multi-source heterogeneous interference.
For the problem of a multi-source heterogeneous interference control system, the composite layered anti-interference control can realize simultaneous interference suppression and compensation through the control structure of interference estimation, feedforward compensation and feedback suppression, and plays an important role in improving the attitude control performance of a spacecraft. Under the composite layered anti-interference control framework, the Chinese patent application ZL201710904100.0 brings the active disturbance rejection control and the control based on the disturbance observer into a unified framework, and invents a flexible spacecraft strong disturbance rejection attitude control technology. However, the existing composite layered anti-interference control method still has the following problems that breakthrough is needed: the complex characteristics of the spacecraft interference are not fully considered, and the deep excavation of the coupling relation between the interference and other physical quantities is lacking, so that the fine separation of the complex interference is difficult to realize, and the interference estimation and compensation accuracy is restricted. Therefore, how to separate from interference estimation to interference becomes a theoretical bottleneck problem for a composite interference system such as a spacecraft attitude control system.
Disclosure of Invention
Aiming at the problems that the existing spacecraft attitude control method ignores the interference composite characteristic and is difficult to realize the fine interference separation, the invention provides the spacecraft fine attitude control method based on the composite interference separation estimation, and the attitude pointing and alignment control precision of the spacecraft under the composite interference is improved. Specifically, the internal deep coupling association relation of composite interference such as flexible vibration interference, inertia uncertainty, actuator error and the like and the inherent characteristics of interference are fully excavated, the characteristics and coupling relation of spacecraft interference are utilized, the fine separation of interference is realized by means of different methods such as an interference observer, an equivalent input interference estimator and the like, and then the attitude control of the spacecraft with high precision and high stability is realized by means of feedforward compensation, feedback inhibition and the like, so that the precision, stability and reliability of the attitude control system of the spacecraft are improved.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a spacecraft fine attitude control method based on composite interference separation estimation comprises the following steps:
step 1, establishing a gesture dynamics model of a spacecraft under composite interference, and completing mathematical representation of flexible vibration interference by adopting a hidden interference model; the composite interference comprises flexible vibration interference, inertia uncertainty, actuator error and environmental interference;
step 2, designing an interference observer to estimate flexible vibration interference, and designing an equivalent input interference estimator to estimate error of an executing mechanism and environmental interference, so as to complete separation estimation of composite interference;
and 3, designing a fine attitude control method based on the result of the separation estimation of the composite interference to realize simultaneous suppression and compensation of the composite interference, and completing the solution of a gain matrix based on a convex optimization algorithm.
Compared with the prior art, the invention has the beneficial effects that:
aiming at the problem of attitude control of a spacecraft under the complex interference of flexible vibration interference, inertia uncertainty, actuator error, environmental interference and the like, the invention designs an interference separation estimation and fine attitude control method based on fully utilizing the complex interference additivity, multiplicative and recessive coupling incidence relation, fully utilizes the coupling incidence relation and inherent characteristics of different interferences, further reduces the conservation of attitude control, and can obviously improve the accuracy and stability of the attitude control in complex precise space tasks such as inter-satellite laser communication and the like.
Drawings
Fig. 1 is a flow chart of a spacecraft fine attitude control method based on composite interference separation estimation.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in fig. 1, the spacecraft fine attitude control method based on the composite interference separation estimation comprises the following steps:
firstly, establishing a gesture dynamics model of the spacecraft under the complex interference of flexible vibration interference, inertia uncertainty, actuator error, environmental interference and the like, and adopting a hidden interference model to complete mathematical representation of the flexible vibration interference:
spacecraft attitude kinematics equation based on Euler angles is:
，
wherein,、/>and->The rolling angular velocity, the pitch angle velocity and the yaw angle velocity of the spacecraft are respectively;、/>、/>representing roll angle, pitch angle and yaw angle of spacecraft,/->、/>And->Respectively->、/>And->Is a first order time derivative of (a); />Is the track angular velocity;
considering the composite interference including flexible vibration interference, inertia uncertainty, actuator error and environmental interference, the attitude of the spacecraft satisfies the following dynamic equation:
，
wherein,for the nominal inertia matrix of the spacecraft, the sign is thatRepresenting diagonal matrix +.>、/>And->The rotational inertia of a rolling axis, a pitching axis and a yawing axis of the spacecraft are respectively represented; />Representing an inertia uncertainty matrix of the spacecraft, +.>、And->The rotational inertia uncertainty of a rolling axis, a pitching axis and a yawing axis of the spacecraft is respectively represented;is->、/>And->The upper mark "T" of the spacecraft angular velocity vector is expressed as transpose operation, < ->Is->First order time derivative of>Representation about->Is a cross-product of the matrix; />Representing the rigid-flex coupling matrix,representation->Transposed matrix of>Representing control input +.>Is a disturbance moment including an actuator error and environmental disturbance; />Representing the modal displacement of the flexible member->And->Respectively indicate->First and second time derivatives, respectively>And->Respectively representing a damping matrix and a stiffness matrix of the flexible component;
defining attitude vectors consisting of roll, pitch and yaw angles of a spacecraftPosture dynamics model of spacecraft>Expressed as:
，
wherein,and->Respectively representing gesture vector +>First and second time derivatives of (a);representing a flexural vibration disturbance; matrix->And matrix->Is a known coefficient matrix, and the expression is as follows:
，sign->Representing a diagonal matrix;for matrix->The elements of row 1 and column 3 of the formula are；/>For matrix->The elements of row 3 and column 1 of the formula +.>；/>And->The state derivative uncertainty matrix and the state uncertainty matrix are respectively represented, and the expressions are as follows:
，；/>for matrix->The elements of row 1 and column 3 of the formula +.>；/>For matrix->The elements of row 3 and column 1 of the formula +.>；
The flexural vibration disturbances, inertia uncertainties, actuator errors, and environmental disturbances are not independent. Dynamic coupling association relation exists between flexible vibration interference and attitude vectors, control input, inertia uncertainty and the like, and the dynamic coupling association relation has the characteristic of hidden interference and a hidden interference model thereofThe description is as follows:
，
wherein,for modal displacement->And its first order time derivative +.>The composed vector represents the state vector of the implicit interference model; the superscript "T" denotes a transpose operation, +.>Representation->Is a first order time derivative of (a); coefficient matrix、/>、/>And->The expression of (2) is
，，/>，/>，/>And->Respectively indicate->Go->Zero matrix and identity matrix of columns, +.>Representation->Zero matrix of row 3 column,>for modal displacement->Dimension of->Is->An inverse matrix of (a);
secondly, designing an interference observer to estimate flexible vibration interference, and designing an equivalent input interference estimator to estimate the error of an actuating mechanism and the environmental interference, so as to complete the separation estimation of the composite interference:
for flexible vibration interference in composite interference, a hidden interference model is combinedDesign disturbance observer +.>：
，
Wherein,and->Respectively indicate->And->Estimated value of ∈10->For auxiliary state variables>Representation->First order time derivative of>A gain matrix representing the disturbance observer;
definition of variablesAnd->Spacecraft attitude dynamics model>Interference observer +>The following state space equation->：
，
Wherein,representation->And->The posture state of the composition, superscript "T" indicates transpose operation,/->Representing posture state->Is a first order time derivative of (a); />Representing the measurement output, coefficient matrix->And->The expression of (2) is
，，/>And->A zero matrix and an identity matrix respectively representing 3 rows and 3 columns; />For equivalent input interference, representing vectors that produce equivalent output effects with inertia uncertainty, actuator error, environmental interference, and interference observer error;
for the equation of state spaceDesign of the Dragon's observer +.>The method comprises the following steps:
，
wherein,and->Respectively indicate->And->Estimated value of ∈10->Representation->Is a first order time derivative of (a);nominal control of a representation designSignal (I)>For the feedback gain matrix>A gain matrix that is a leberger observer;
equivalent input interference estimatorThe design is as follows:
，
wherein,for the output of the equivalent input interference estimator, the equivalent input interference is represented + ->Is a function of the estimated value of (2);representation->The superscript "T" indicates the transpose operation, ">Representing inversion operation;
to avoid singularities in the interference estimation, a low pass filter is used in combination with an equivalent input interference estimator; state space expression of low-pass filterThe method comprises the following steps:
，
wherein,representing the low-pass filter state,/->Representation->Is a first order time derivative of (a); />、/>And->Is a matrix of known coefficients of the low-pass filter, < >>Representing the output of the low pass filter;
the interference observer is used for estimating flexible vibration interference, and the equivalent input interference estimator is used for estimating the error of the actuating mechanism and the environmental interference, so that the separation estimation of the interference is realized;
thirdly, based on the result of the separation estimation of the composite interference, designing a fine attitude control method to realize simultaneous suppression and compensation of the composite interference, and completing the solution of a gain matrix based on a convex optimization algorithm:
based on the interference separation estimation result, realizing real-time compensation of flexible vibration interference, mechanism error and environmental interference, and inhibiting the uncertainty of the inertia of the spacecraft by using a feedback controller; the control inputs are then designed as:
，
wherein,is a feedback gain matrix;
design of a Lobert-type view by pole allocation methodGain matrix of testerWherein->For a given positive constant, +.>Representing 6 rows and 6 columns of identity matrices; feedback gain matrix->Gain matrix of interference observer->Solving by the following convex optimization algorithm:
，
wherein,representation matrix->The expression of the elements in the 1 st row and the 1 st column is；/>Representation matrix->The elements of row 1 and column 8 of the formula +.>；/>Representation matrix->The expression of the elements in the 2 nd row and the 2 nd column is；/>Representation matrix->The elements of row 2 and column 5 of the formula +.>；/>Representation matrix->The elements of row 2 and column 6 of the formula；/>Representation matrix->The elements of row 2 and column 7 of the formula；/>Representation matrix->The elements of row 3 and column 3 of the formula are；/>Representation ofMatrix->The elements of row 3 and column 4 of the formula +.>；/>Representation matrix->The elements of row 4 and column 4 of the formula +.>The method comprises the steps of carrying out a first treatment on the surface of the Matrix->、/>、/>And->For the positive definite symmetric matrix variable to be solved, matrix +.>And->The matrix variables to be solved are; symmetric matrix->Sign "< > -in lower left corner>"represents the corresponding element in the symmetric matrix; the superscript "T" denotes a transpose operation; matrix->、/>、/>And->Respectively 6 rows and 6 columns>Row 3 column->Zero matrix of row 6 column and 3 row 6 column->For modal displacement->Dimension of (2); />Representing 6 rows and 6 columns of identity matrices; />、/>And->Is a positive constant; matrix->Is a constant matrix>A zero matrix representing 3 rows and 3 columns; matrix->、/>Andis a known matrix>、/>And->For a given constant and respectively satisfy +.>、And->Sign->Representing the 2 norms of the matrix; solving the matrix inequality by means of convex optimization>Feedback gain matrix->Gain matrix of interference observer->Can pass through->Andcalculated out->And->Respectively represent pair->And->Is calculated by inversion of (2);
what is not described in detail in the present specification belongs to the prior art known to those skilled in the art.
Claims (2)
1. The spacecraft fine attitude control method based on the composite interference separation estimation is characterized by comprising the following steps of:
step 1, establishing a gesture dynamics model of a spacecraft under composite interference, and completing mathematical representation of flexible vibration interference by adopting a hidden interference model; the composite interference comprises flexible vibration interference, inertia uncertainty, actuator error and environmental interference;
describing attitude kinematics of the spacecraft by adopting Euler angles, and establishing an attitude dynamics model of the spacecraft under the composite interference by taking the composite interference including flexible vibration interference, inertia uncertainty, actuator error and environmental interference into consideration, wherein the attitude dynamics model comprises the following steps:
，
wherein,representing spacecraft attitude vector,/->And->Respectively indicate->First and second time derivatives of (a);/>representing control input +.>Indicating flexible vibration disturbance->Is a disturbance moment including an actuator error and environmental disturbance; />Representing a nominal inertia matrix of the spacecraft, +.>Representing an inertia uncertainty matrix of the spacecraft; />And->Representing a known coefficient matrix,/>And->Representing a state derivative uncertainty matrix and a state uncertainty matrix, respectively;
flexible vibration disturbance and spacecraft attitude vectorControl input->And an inertia uncertainty matrix of the spacecraft +.>The dynamic coupling association relation exists, the characteristic of hidden interference exists, and a hidden interference model of flexible vibration interference is described as follows:
，
wherein,state vector representing implicit interference model, +.>Representation->Is a first order time derivative of (a); />、/>、And->Are known coefficient matrices;
step 2, designing an interference observer to estimate flexible vibration interference, and designing an equivalent input interference estimator to estimate error of an executing mechanism and environmental interference, so as to complete separation estimation of composite interference;
for flexible vibration interference in composite interference, combining with a recessive interference model thereof, designing an interference observer as follows:
，
wherein,and->Respectively represent the state vector in the implicit interference model>Interfering with flexible vibration>Is used for the estimation of the (c),for auxiliary state variables>Representation->First order time derivative of>A gain matrix representing the disturbance observer;
will beAnd->Constitutive column vector as posture state->Define the measurement output as +.>And make it and posture state->Equal, i.e.)>At the moment, converting the spacecraft attitude dynamics model into a state space expression, and designing a Robert observer aiming at the state space expression of the spacecraft attitude dynamics model; defining equivalent input disturbance as +.>Representing vectors that produce equivalent output effects with inertia uncertainty, actuator error and environmental disturbance, and disturbance observer error; the equivalent input interference estimator is designed to:
，
wherein,for the output of the equivalent input interference estimator, the equivalent input interference is represented + ->Is a function of the estimated value of (2);representation->Pseudo-inverse of>Is a known coefficient matrix->Zero matrix representing 3 rows and 3 columns, +.>Representing inversion operations, ++>For the nominal inertia matrix of the spacecraft>Is used for the inverse matrix of (a),representation->Is a transposed matrix of (a); />Gain matrix representing a leberger observer, < >>Indicate the measurement output->Is a function of the estimated value of (2); />Nominal control signal representing design,/->Is a feedback gain matrix;
to avoid the singular problem of interference estimation, a low pass filter is used in combination with an equivalent input interference estimator; will beAs an input value of the low-pass filter, and the output of the low-pass filter is defined as +.>The method comprises the steps of carrying out a first treatment on the surface of the At the moment, the interference observer is used for estimating flexible vibration interference, the equivalent input interference estimator is used for estimating error of the executing mechanism and environmental interference, and therefore separation estimation of interference is achieved;
and 3, designing a fine attitude control method based on the result of the separation estimation of the composite interference to realize simultaneous suppression and compensation of the composite interference, and completing the solution of a gain matrix based on a convex optimization algorithm.
2. The spacecraft fine attitude control method based on composite interference separation estimation according to claim 1, wherein the step 3 comprises: the feedback controller is utilized to restrain the uncertainty of the inertia of the spacecraft, and a fine gesture controller is designed to realize a fine gesture control method; wherein the control input is designed asThe method comprises the steps of carrying out a first treatment on the surface of the Gain matrix of the Lobert observer is completed by pole allocation method>Is solved; feedback gain matrix->Gain matrix with interference observer>And solving by a convex optimization algorithm.
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