Aircraft constraint attitude control method and system based on explicit reference management

Abstract

The application discloses an aircraft constraint attitude control method and system based on explicit reference management, belongs to the field of aerospace, and solves the aircraft attitude maneuver control problem existing multiple constraints (including attitude pointing constraint, angular velocity constraint and control constraint). The application separates constraint processing from control law design, designs a reference manager to generate a reference attitude trajectory, can provide a feasible maneuver trajectory satisfying the constraints and reaching the target attitude from the initial attitude, and designs a feedback control law based on an immersion and invariant disturbance observer to ensure the stability and robustness of the system and realize asymptotic tracking of the reference attitude trajectory. For an aircraft attitude control system with a flywheel as an actuator, the method can realize attitude maneuver control satisfying the pointing constraint, angular velocity constraint and control constraint in the presence of external disturbance. The numerical simulation result of the attitude control method proves the effectiveness and feasibility of the application.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology and relates to a constrained attitude control method and system for aircraft based on explicit reference management. Background Technology

[0002] Attitude control plays a crucial role in aerospace missions. However, actuators, sensors, and onboard equipment are often subject to physical limitations. Therefore, the design of attitude controllers often needs to satisfy various constraints while achieving asymptotic stability. The first type of constraint is the limited output torque of the actuator. When the command torque is too large (exceeding the saturation torque), accurate tracking cannot be achieved, leading to decreased control performance or even system instability. The second type of constraint is attitude pointing constraints, such as the need for the aircraft to maintain communication with the ground or other aircraft to avoid loss of contact, and the need for sensors to avoid direct sunlight from bright celestial bodies. The third type of constraint is angular velocity constraints; to ensure the effectiveness of sensors, the angular velocity of the aircraft is limited by the maximum angular velocity. Furthermore, during flight, the presence of environmental disturbance torques such as aerodynamic torques can affect control performance. Therefore, how to satisfy complex constraints in attitude maneuver control laws under external disturbances is a worthy research problem.

[0003] For constrained problems, existing methods include path planning, artificial potential function methods, and trajectory optimization methods. Path planning algorithms discretize the attitude space and use a search algorithm to generate feasible maneuver trajectories. The control system tracks the maneuver trajectory under unconstrained conditions. Its advantages include the ability to handle complex constraints, but its disadvantages include high computational cost, inability to achieve real-time planning, and inability to guarantee the closed-loop stability of the system. Artificial potential function methods generate feasible control laws by constructing an artificial potential function that is minimal at the target point and maximally large in the constraint region. Its advantages include an explicit structure for the control law, allowing for proof of system stability, and high computational efficiency for implementation. Its disadvantage is that for nonlinear systems, multiple local minima may exist, preventing the system solution from converging to the target point. Trajectory optimization methods include model predictive control (MMCC) and explicit reference management. MMCC obtains control inputs by solving a finite-time optimal control problem at each sampling time. Its results can guarantee optimality or suboptimality and can handle multiple constraints well. However, the computational load increases with the number of constraints, which is not conducive to the onboard computer acquiring control strategies in real time. Explicit reference management is another feasible optimization method. It generates maneuver trajectories that satisfy constraints through a reference manager and tracks the reference trajectory through an inner-loop stable control law. Its advantages are that it has explicit expressions, does not require real-time solving of the optimization problem, has high computational efficiency, and can handle constraints well. The main challenge is that the design of the reference manager needs to construct a safety threshold that satisfies multiple constraints. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of poor robustness of reference managers and design difficulties under multiple constraints in the prior art, and to provide an aircraft constrained attitude control method and system based on explicit reference management.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] The present invention proposes a constraint attitude control method based on explicit reference management, the steps of which are as follows:

[0007] Establish the aircraft attitude motion model and constraint condition model;

[0008] Based on the aircraft attitude motion model, design a feedback control law based on the disturbance observer;

[0009] Design a guidance layer that satisfies the constraint condition model, and implement constrained attitude control based on the feedback control law and the guidance layer.

[0010] Preferably, the steps for establishing the aircraft attitude motion model are as follows:

[0011] The attitude of the aircraft body relative to the inertial frame is represented as follows: ;in, For the corner, For the pivot, Represented as a column vector;

[0012] The kinematic equations of the aircraft attitude are as follows:

[0013] (1)

[0014] in, The attitude of the aircraft body relative to the inertial frame. for The time derivative; for Zhongyu The matrix composed of related terms is defined as follows: ; Represented as transpose; for The corresponding cross product antisymmetric matrix; The absolute angular velocity of the aircraft. ; It is a 3rd order identity matrix;

[0015] The actuator for aircraft attitude control uses a reaction flywheel, and the dynamic equations of the actuator for aircraft attitude control are as follows:

[0016] (2)

[0017] in, The inertia matrix of the aircraft. ; The absolute angular acceleration of the aircraft; This refers to the output torque of the flywheel; External disturbance torque; It is a cross product of an antisymmetric matrix; The angular momentum of the reaction flywheel. It is expressed as follows:

[0018] (3)

[0019] in, For the flywheel mounting matrix, ; The matrix represents the inertia of all flywheels. , Let represent the inertia of the i-th flywheel. The inertia matrix of the flywheel assembly. Represented as the angular velocity matrix of the flywheel assembly. , Let be the angular velocity of the i-th flywheel, and be the total output control torque of the flywheel assembly. as follows:

[0020] (4)

[0021] in, Let ω be the angular acceleration of the flywheel assembly. The expression is as follows:

[0022] (5)

[0023] in, The inertia matrix of the flywheel assembly. The inertia matrix of the flywheel assembly The transpose of .

[0024] Preferably, the constraint model includes attitude pointing constraints, angular velocity constraints, and control constraints;

[0025] Design a guidance layer for the constraint model.

[0026] Preferably, the attitude pointing constraint is defined as follows:

[0027] (6)

[0028] in, The set of states that satisfy the orientation constraints; The attitude of the aircraft body relative to the inertial frame; The absolute angular velocity of the aircraft; is the reference unit vector in inertial space; The attitude constraint of the aircraft is defined as a unit vector of the aircraft's own system. Vectors in inertial space The included angle Less than or equal to the field of view ,Right now , It is an inertial vector Representation in a coordinate system This is the attitude matrix of the coordinate system relative to the inertial frame;

[0029] Angular velocity constraints are defined as follows:

[0030] (7)

[0031] in, The set of states that satisfy angular velocity constraints. The attitude of the aircraft body relative to the inertial frame. The absolute angular velocity of the aircraft. The maximum permissible angular velocity;

[0032] For cases where the flywheel is the actuator, control constraints include maximum angular velocity constraints. and maximum angular acceleration constraints The definition is as follows:

[0033] (8)

[0034] in, Indicates the first The maximum angular velocity of each flywheel Indicates the first The maximum angular acceleration of each flywheel;

[0035] Feasible set of aircraft attitude maneuvering processes The representation is as follows:

[0036] (9).

[0037] Preferably, the interference observer is as follows:

[0038] (10)

[0039] in, External disturbance torque Observed values; For dynamic parameters; The observer parameters set by the user satisfy This is used to adjust the upper bound of the estimation error; The absolute angular velocity of the aircraft; estimation error The definition is as follows:

[0040] (11)

[0041] Dynamic part parameters It is expressed as follows:

[0042] (12).

[0043] Preferably, the feedback control law of the interference detector is as follows:

[0044] (13)

[0045] in, To represent the control torque within this system; , The controller parameters selected by the user meet the requirements. ; The Rodriguez parameter represents the deviation between the current attitude and the reference attitude; It is a saturation function. , For standard symbolic functions, External disturbance torque obtained by disturbance observer (1) The estimated value, For the maximum allowable constant, satisfying , The upper bound of the external disturbance torque is... , The upper bound of the derivative of the external disturbance torque with respect to time is... , Observer parameters set by the user; when At that time, the equilibrium point It is asymptotically stable within the allowable set, that is... , The attitude of the reference vector relative to the inertial frame, It is a zero vector; when and When the value is sufficiently large, the state error is sufficiently small.

[0046] Preferably, the guidance layer is designed as follows:

[0047] (14)

[0048] in, For dynamic safety margin, This represents the attitude deviation between the aircraft's current attitude and the reference vector. The absolute angular velocity of the aircraft. The distance between the current state and the safety boundary; For guidance direction, Is it related to the current state? and expected state The relevant guidance direction.

[0049] Preferably, the dynamic safety margin is designed as follows:

[0050] (15)

[0051] in, The dynamic safety margin parameter selected by the user, This represents the threshold corresponding to the constraint. The Lyapunov function representing attitude and angular velocity is... The constraints for the dynamic safety margin are as follows:

[0052] Pointing constraint: The threshold corresponding to the pointing constraint as follows:

[0053] (16)

[0054] in, The positive constants to be selected. Controller parameters set by the user, The pointing angle corresponding to the current attitude. A quantity related to the maximum pointing angle, i.e. , Maximum pointing angle;

[0055] Angular velocity constraint: The threshold corresponding to the angular velocity constraint as follows:

[0056] (17)

[0057] in, Inertia matrix The smallest eigenvalue, It is expressed as the square of the maximum angular velocity;

[0058] Flywheel saturation constraint: The flywheel saturation constraint is described as follows:

[0059] (18)

[0060] in, This represents the absolute value of the angular velocity component of the flywheel assembly. This represents the absolute value of the angular acceleration component of the flywheel assembly. The maximum permissible angular velocity of the flywheel assembly. This is the maximum permissible angular acceleration of the flywheel assembly. This is the transpose of the flywheel inertia matrix;

[0061] The flywheel saturation constraint is transformed into the following two optimization problems:

[0062] Optimization issue 1

[0063]

[0064] Subject to

[0065]

[0066]

[0067]

[0068] Optimization issue 2

[0069]

[0070] Subject to

[0071]

[0072]

[0073]

[0074] Obtain the threshold for optimization problem 1 based on optimization problem 1. Obtain the threshold for optimization problem 2 based on optimization problem 2. The threshold corresponding to the constraint .

[0075] Preferably, the guidance direction is designed as follows:

[0076] Guidance direction The expression is as follows:

[0077] (19)

[0078] in, The deviation between the attitude corresponding to the reference vector and the target attitude. for rate of change and A matrix composed of related terms.

[0079] This invention proposes a constrained attitude control system based on explicit reference management, comprising:

[0080] The model building module is used to build the aircraft attitude motion model and constraint condition model;

[0081] A feedback control law design module is used to design a feedback control law based on an interference observer according to the aircraft attitude motion model.

[0082] The guidance layer design module is used to design a guidance layer that satisfies the constraint condition model, and to achieve constrained attitude control based on the feedback control law and the guidance layer.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] This invention proposes a constrained attitude control method based on explicit reference management for flywheel-driven rigid body aircraft. For attitude control problems of aircraft with flywheels as actuators, this method can achieve attitude maneuver control that satisfies pointing constraints, angular velocity constraints, and control constraints even in the presence of external disturbances. Specifically, by establishing an aircraft attitude motion model, a feedback control law based on immersion and invariant disturbance observers is designed to improve the robustness of the reference manager. By establishing a constraint condition model and designing a guidance layer, the feedback control law and guidance layer are combined to achieve multi-constraint attitude control, thereby satisfying the requirements of multiple constraints. Therefore, this invention can solve the problems of poor robustness of reference managers and the difficulty of designing them under multiple constraints in existing technologies.

[0085] Furthermore, the estimated value obtained by the observer is used as a compensation term in the control law, which can improve the robustness to external disturbances; the controller adopts the form of a saturation function, which can avoid excessive control torque when the initial disturbance estimation error is too large.

[0086] Furthermore, for aircraft using flywheels as actuators, the flywheel's rotational speed and output torque are typically limited. This invention analyzes the impact of saturation constraints from the perspective of angular momentum conservation. Flywheel rotational speed saturation is avoided by limiting the maximum angular velocity.

[0087] The present invention proposes a constraint attitude control system based on explicit reference management. By dividing the system into a model building module, a feedback control law design module, and a guidance layer design module, the modular approach makes each module independent of the others, which facilitates unified management of each module. Attached Figure Description

[0088] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0089] Figure 1 This is a flowchart of the attitude control method based on explicit reference management according to the present invention.

[0090] Figure 2 This is the algorithm framework for the attitude control method based on explicit reference management in this invention.

[0091] Figure 3 This is a set representation of the attitude constraint region of the aircraft in this invention.

[0092] Figure 4 The simulation results show the estimation error of the interference observer in this invention.

[0093] Figure 5 The numerical simulation results are for the attitude pointing angle of the aircraft of this invention.

[0094] Figure 6 Numerical simulation of the angular velocity of the aircraft of this invention.

[0095] Figure 7 This is a simulation result diagram of the reference attitude trajectory generated by the guidance layer of this invention.

[0096] Figure 8 This is a three-dimensional schematic diagram of the attitude trajectory changes of the aircraft of the present invention.

[0097] Figure 9 This is a graph showing the angular acceleration curve of the flywheel in the numerical simulation of this invention.

[0098] Figure 10 This is a graph showing the angular velocity curve of the flywheel in the numerical simulation of this invention.

[0099] Figure 11 This is a curve of the control torque in the numerical simulation of this invention.

[0100] Figure 12 This refers to the changes in the Lyapunov function value and the safety threshold in this invention.

[0101] Figure 13 This is a diagram of the attitude control system based on explicit reference management according to the present invention. Detailed Implementation

[0102] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0103] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0104] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0105] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0106] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0107] The present invention will now be described in further detail with reference to the accompanying drawings:

[0108] This invention proposes a constrained attitude control method for aircraft based on explicit reference management, such as... Figure 1 As shown, it includes the following steps:

[0109] S1. Establish the aircraft attitude motion model and constraint condition model;

[0110] The steps to establish an aircraft attitude motion model are as follows:

[0111] The attitude of the aircraft body relative to the inertial frame is represented as follows: ;in, For the corner, For the pivot, Represented as a column vector;

[0112] The kinematic equations of the aircraft attitude are as follows:

[0113] (1)

[0114] in, The attitude of the aircraft body relative to the inertial frame. for The time derivative; for Zhongyu The matrix composed of related terms is defined as follows: ; Represented as transpose; for The corresponding cross product antisymmetric matrix; The absolute angular velocity of the aircraft. ; It is a 3rd order identity matrix;

[0115] The actuator for aircraft attitude control uses a reaction flywheel, and the dynamic equations of the actuator for aircraft attitude control are as follows:

[0116] (2)

[0117] in, The inertia matrix of the aircraft. ; The absolute angular acceleration of the aircraft; This refers to the output torque of the flywheel; External disturbance torque; It is a cross product of an antisymmetric matrix; The angular momentum of the reaction flywheel. It is expressed as follows:

[0118] (3)

[0119] in, For the flywheel mounting matrix, ; The matrix represents the inertia of all flywheels. , Let represent the inertia of the i-th flywheel. The inertia matrix of the flywheel assembly. Represented as the angular velocity matrix of the flywheel assembly. , Let be the angular velocity of the i-th flywheel, and be the total output control torque of the flywheel assembly. as follows:

[0120] (4)

[0121] in, Let ω be the angular acceleration of the flywheel assembly. The expression is as follows:

[0122] (5)

[0123] in, Here is the inertia matrix of the flywheel assembly. The inertia matrix of the flywheel assembly The transpose of .

[0124] The constraint model includes attitude pointing constraints, angular velocity constraints, and control constraints;

[0125] Design a guidance layer for the constraint model.

[0126] The attitude pointing constraint is defined as follows:

[0127] (6)

[0128] in, The set of states that satisfy the orientation constraints; The attitude of the aircraft body relative to the inertial frame; The absolute angular velocity of the aircraft; is the reference unit vector in inertial space; The attitude constraint of the aircraft is defined as a unit vector of the aircraft's own system. Vectors in inertial space The included angle Less than or equal to the field of view ,Right now , It is an inertial vector Representation in a coordinate system This is the attitude matrix of the coordinate system relative to the inertial frame;

[0129] Angular velocity constraints are defined as follows:

[0130] (7)

[0131] in, The set of states that satisfy angular velocity constraints. The attitude of the aircraft body relative to the inertial frame. The absolute angular velocity of the aircraft. The maximum permissible angular velocity;

[0132] For cases where the flywheel is the actuator, control constraints include maximum angular velocity constraints. and maximum angular acceleration constraints The definition is as follows:

[0133] (8)

[0134] in, Indicates the first The maximum angular velocity of each flywheel Indicates the first The maximum angular acceleration of each flywheel;

[0135] Feasible set of aircraft attitude maneuvering processes The representation is as follows:

[0136] (9).

[0137] S2. Based on the aircraft attitude motion model, design a feedback control law based on the disturbance observer;

[0138] The interference observer is as follows:

[0139] (10)

[0140] in, External disturbance torque Observed values; For dynamic parameters; The observer parameters set by the user satisfy This is used to adjust the upper bound of the estimation error; The absolute angular velocity of the aircraft; estimation error The definition is as follows:

[0141] (11)

[0142] Dynamic part parameters It is expressed as follows:

[0143] (12).

[0144] The feedback control law of the interference detector is as follows:

[0145] (13)

[0146] in, To represent the control torque within this system; , The controller parameters selected by the user meet the requirements. ; The Rodriguez parameter represents the deviation between the current attitude and the reference attitude; It is a saturation function. , For standard symbolic functions, External disturbance torque obtained by disturbance observer (1) The estimated value, For the maximum allowable constant, satisfying , The upper bound of the external disturbance torque is... , The upper bound of the derivative of the external disturbance torque with respect to time is... , Observer parameters set by the user; when At that time, the equilibrium point It is asymptotically stable within the allowable set, that is... , The attitude of the reference vector relative to the inertial frame, It is a zero vector; when and When the value is sufficiently large, the state error is sufficiently small.

[0147] Preferably, the guidance layer is designed as follows:

[0148] (14)

[0149] in, For dynamic safety margin, This represents the attitude deviation between the aircraft's current attitude and the reference vector. The absolute angular velocity of the aircraft. The distance between the current state and the safety boundary; For guidance direction, Is it related to the current state? and expected state The relevant guidance direction.

[0150] The dynamic safety margin design is as follows:

[0151] (15)

[0152] in, The dynamic safety margin parameter selected by the user, This represents the threshold corresponding to the constraint. The Lyapunov function representing attitude and angular velocity is... The constraints for the dynamic safety margin are as follows:

[0153] Pointing constraint: The threshold corresponding to the pointing constraint as follows:

[0154] (16)

[0155] in, The positive constants to be selected. Controller parameters set by the user, The pointing angle corresponding to the current attitude. The quantity relative to the maximum pointing angle, i.e. , Maximum pointing angle;

[0156] Angular velocity constraint: The threshold corresponding to the angular velocity constraint as follows:

[0157] (17)

[0158] in, Inertia matrix The smallest eigenvalue, It is expressed as the square of the maximum angular velocity;

[0159] Flywheel saturation constraint: The flywheel saturation constraint is described as follows:

[0160] (18)

[0161] in, This represents the absolute value of the angular velocity component of the flywheel assembly. This represents the absolute value of the angular acceleration component of the flywheel assembly. The maximum permissible angular velocity of the flywheel assembly. This is the maximum permissible angular acceleration of the flywheel assembly. This is the transpose of the flywheel inertia matrix;

[0162] The flywheel saturation constraint is transformed into the following two optimization problems:

[0163] Optimization issue 1

[0164]

[0165] Subject to

[0166]

[0167]

[0168]

[0169] Optimization issue 2

[0170]

[0171] Subject to

[0172]

[0173]

[0174]

[0175] Obtain the threshold for optimization problem 1 based on optimization problem 1. Obtain the threshold for optimization problem 2 based on optimization problem 2. The threshold corresponding to the constraint .

[0176] The guidance direction is designed as follows:

[0177] Guidance direction The expression is as follows:

[0178] (19)

[0179] in, The deviation between the attitude corresponding to the reference vector and the target attitude. for rate of change and A matrix composed of related terms.

[0180] A constrained attitude control method for aircraft based on explicit reference management, such as Figure 2 As shown, the specific steps include the following:

[0181] Step 1: Establish the aircraft attitude motion model and constraint model

[0182] Based on MRP, the kinematic and dynamic equations of the rigid body aircraft are established. Various constraints on the aircraft's attitude maneuvering process are analyzed and defined. Under the given assumptions, a mathematical model of the constrained attitude maneuvering control problem is established. The specific steps are as follows:

[0183] Step 1.1 Establish the aircraft attitude motion model

[0184] This invention employs Modified Rodrigues parameter (MRP) to describe the attitude motion of the aircraft. First, a relevant coordinate system is defined, and... This refers to the aircraft's core system. The inertial frame of reference is represented. Next, the Rodrigues parameters of the attitude are defined:

[0185]

[0186] in, Representing coordinate system Compared to MRP of posture, For the corner, The rotation axis is defined based on Euler's rotation theorem, which states that any finite number of rotations can be described by a single rotation about a characteristic axis. First, the coordinate systems involved are defined. The aircraft's own system is defined as follows: origin at the aircraft's center of mass, X-axis along the aircraft's longitudinal axis pointing towards the nose, Y-axis perpendicular to the X-axis within the aircraft's longitudinal plane of symmetry, and Z-axis forming a right-handed rectangular coordinate system with the X and Y axes. The geocentric equatorial inertial system is defined as follows: origin at the Earth's center of mass, X-axis in the equatorial plane pointing towards the vernal equinox, Z-axis along the Earth's rotation axis pointing towards the North Pole, and Y-axis determined by the right-hand rule. The inertial system used in this paper is a coordinate system with its center of mass at the aircraft's center of mass and its direction parallel to the inertial system. Therefore, the attitude of the aircraft body relative to the inertial system is represented as follows:

[0187]

[0188] Without causing ambiguity Abbreviated as Obviously, when When the Rodriguez parameter is corrected, MRP exhibits a singularity, and because... , Correcting the fact that the Rodriguez parameter MRP is not unique, according to As can be seen from the definition, when hour Therefore, it can be done in A switching is performed to globally parameterize the spacecraft using the shortest possible rotation, assuming... To describe the attitude and avoid singularities, the attitude kinematics equations are as follows:

[0189] (1)

[0190] in, , This represents the absolute angular velocity of the aircraft. It has the following properties:

[0191]

[0192]

[0193] in, It is a third-order identity matrix. The actuator for the aircraft's attitude control uses a reaction flywheel, hence the dynamic equations are as follows:

[0194] (2)

[0195] in, Represents the inertia matrix. Indicates the external disturbance torque. It is a cross product antisymmetric matrix. The angular momentum of the reaction flywheel can be expressed as:

[0196] , (3)

[0197] in, For the flywheel mounting matrix, , Let represent the inertia of the i-th flywheel. , Let be the angular velocity of the i-th flywheel. The output torque of the flywheel is as follows:

[0198] (4)

[0199] angular acceleration It can be obtained from the configuration matrix and control torque:

[0200] (5)

[0201] Step 1.2: Define attitude pointing constraints, state constraints, and control constraints:

[0202] The first type is attitude pointing constraint. Taking Earth observation as an example, to ensure that the observed target is always within the field of view of the airborne camera, i.e., a unit vector of the aircraft's own system. (Camera mounting orientation) and vector in inertial space The angle between the (target direction) and the field of view is smaller than the angle of view. This constraint is equivalent to

[0203] (6)

[0204] in, It is an inertial vector Representation within this system.

[0205] The second category is state constraints. To meet the measurement accuracy requirements of sensors such as star sensors and gyroscopes, the angular velocity of the spacecraft should not be too large, which can be described as...

[0206] (7)

[0207] in, This is the maximum permissible angular velocity.

[0208] The third type of constraint is the control constraint. For the case where the flywheel is the actuator, the constraints include two aspects: maximum angular velocity constraint and maximum angular acceleration constraint, which can be defined as follows:

[0209] (8)

[0210] in, and They represent the first The maximum angular velocity and maximum angular acceleration of each flywheel.

[0211] In summary, the feasible set of the aircraft attitude maneuver process is the intersection of the four subsets described by formulas (6) to (8), namely:

[0212] (9)

[0213] Step 1.3 Relevant Assumptions and Problem Description

[0214] The objective of this invention is to design a system capable of controlling the state of the system while satisfying formula (9). Maneuver to target status The control law. The overall concept of the control method based on explicit reference management proposed in this invention is as follows: Figure 2 As shown, its structure consists of two parts: a guidance layer and a control layer. The guidance layer is used to generate the reference vector. To ensure that the attitude maneuver process satisfies the constraints, the reference vector needs to be guaranteed. asymptotic convergence to the target posture The control layer consists of a feedback controller based on a disturbance observer, used to track the generated reference vector. This ensures system stability under unconstrained conditions and minimizes attitude tracking errors. It converges to zero. For ease of design, this invention makes the following assumptions:

[0215] 1) The flywheel is fully driven, that is... Ignore the zero motion of the flywheel steering law;

[0216] 2) External interference and its time derivative The norm is bounded, that is... , , Represents the norm, These represent the external disturbance and the upper bound of its time derivative, respectively. ;

[0217] 3) During attitude maneuvers, neglecting the influence of external disturbances on the system's angular momentum, assume that the total angular momentum of the aircraft and flywheel is conserved and satisfies the following conditions: , It is expressed as the angular acceleration of the flywheel assembly (see formula (5)). Let be the norm of the flywheel angular acceleration. This is the maximum permissible angular acceleration;

[0218] 4) Target attitude It is a constant and within the allowable region, that is... When it satisfies formula (6).

[0219] Step 2: Design a feedback control law based on the disturbance observer

[0220] Ignoring constraints, assume a reference vector Since it is a constant vector, a feedback control law based on a disturbance observer is designed to stabilize the system. The specific steps include:

[0221] Step 2.1: Design a disturbance observer based on immersion and invariance theory

[0222] To estimate the time-varying external disturbance torque An interference observer based on I&I theory was designed. express Given the observed values, design an observer with the following form:

[0223] (10)

[0224] in, For the dynamic parameters that need to be designed later, This is a constant value and can be used to adjust the upper bound of the estimation error. The estimation error is defined as follows:

[0225] (11)

[0226] According to I&I theory, dynamic part parameters It can be designed as:

[0227] (12)

[0228] According to formulas (11) to (12), we can obtain:

[0229] (13)

[0230] For constant disturbances ( ), The exponential convergence reaches 0; To make it a fixed value, we can select a sufficiently large one. To ensure The upper bound is small enough, that is... Usually selected The upper bound for the disturbance estimation is as follows:

[0231] (17)

[0232] The estimates obtained by this observer can be used as compensation terms in the control law to improve the robustness to external disturbances.

[0233] Step 2.2: Design the feedback control law.

[0234] For the aircraft attitude motion model described by formulas (1) and (2), let the reference attitude be... As a constant, using the disturbance observer described in formula (10), the following feedback control law is designed:

[0235] (18)

[0236] in, The controller parameters set by the user meet the requirements. , Represents the saturation function, i.e. ,in For standard symbolic functions, This is the maximum allowable constant. When At that time, the equilibrium point It is asymptotically stable within the allowable set, that is... when and When the value is sufficiently large, the state error can be sufficiently small. Among them, the saturation function introduced in formula (18) can prevent the control torque from being too large when the initial disturbance estimation error is too large.

[0237] Step 3: Design the guidance layer to ensure that pointing constraints, angular velocity constraints, and control constraints are met.

[0238] like Figure 2 As shown, the guidance layer's function is to generate a reference trajectory. To satisfy the constraints described by formulas (6) to (8). Due to the interference estimation error It can be adjusted It is small enough that the design of the guidance layer can be ignored. The guidance layer consists of two parts: dynamic safety margin and guidance direction. It is solved using invariant sets in Lyapunov functions and offline optimization problems. The guidance layer takes the following form:

[0239] (twenty three)

[0240] in, The "dynamic safety margin" represents the distance between the current state and the safety boundary, and can give the maximum value that the reference attitude can change without violating constraints; Is it related to the current state? and expected state The relevant "guidance direction" can define the next step. The direction of change. The specific design steps are as follows.

[0241] Step 3.1 Dynamic safety margin design

[0242] Dynamic safety margin can be viewed as the distance between the current guidance state of the closed-loop system and the constraint boundary. Let... For Lyapunov functions ,because semidefinite invariant set It can be used to design safety margins. Its upper boundary The constraint formulas (6) to (8) determine this. Due to the existence of disturbance error, the dynamic safety margin of the following form is selected to ensure its non-negativity:

[0243] (twenty four)

[0244] The following section describes the corresponding expressions for each type of constraint.

[0245] Step 3.1.1 Pointing Constraints

[0246] The geometric relationship of the aircraft's pointing constraints is as follows: Figure 3 As shown, where for posture The corresponding safety margin satisfies .make Represented as a reference frame The virtual constant unit vector below, For this system and The corresponding quantities are the same when the system and the reference frame coincide. When the system and the reference frame coincide... When they coincide, the pointing angle It can be represented as:

[0247] (25)

[0248] In this case, the reference attitude Safety margin meets ,in Furthermore, let's assume and pivot The included angle is It satisfies the following expression:

[0249] (26)

[0250] When this system and the reference system When they do not overlap, let express arrive The included angle satisfies the following relationship:

[0251] (27)

[0252] in for posture The corresponding corner. Obviously. and Positive correlation, and satisfying Let the threshold corresponding to the pointing constraint be... express The upper bound, due to ,like Then it can be guaranteed The threshold for a Lyapunov function that satisfies the pointing constraint can be given through the following derivation:

[0253] Consider formula (27) and It can guarantee

[0254] (28)

[0255] when or When, formula (28) always holds true. When applying the following properties of trigonometric functions: , as well as You can get

[0256] (29)

[0257] in, , , .when When, formula (28) always holds true; when At that time, due to , This is impossible, so formula (29) satisfies:

[0258] (30)

[0259] Set threshold It can be designed as:

[0260] (31)

[0261] in, The positive constants to be selected. For controller parameters, The pointing angle corresponding to the current attitude. The quantity relative to the maximum pointing angle, i.e. , This is the maximum pointing angle.

[0262] Step 3.1.2 Angular velocity constraint

[0263] The angular velocity constraint given by formula (7) is a convex set, and the threshold corresponding to the angular velocity constraint is... Options include:

[0264] (32)

[0265] in, Inertia matrix The smallest eigenvalue, It is expressed as the square of the maximum angular velocity.

[0266] Step 3.1.3 Flywheel saturation constraint

[0267] For spacecraft using flywheels as actuators, the flywheel's rotational speed and output torque are typically limited. The influence of saturation constraints can be analyzed from the perspective of angular momentum conservation. The total angular momentum of the system includes both the spacecraft body and the flywheel. Assume the initial angular momentum of the system is... According to assumption 1, the angular momentum of the flywheel determines the maximum angular velocity of the aircraft, which indicates that flywheel speed saturation can be avoided by limiting the maximum angular velocity. Based on formulas (3) and (4), the flywheel constraint can be expressed as:

[0268] (33)

[0269] in, This represents the absolute value of the angular velocity component of the flywheel assembly. This represents the absolute value of the angular acceleration component of the flywheel assembly. The maximum permissible angular velocity of the flywheel assembly. This is the maximum permissible angular acceleration of the flywheel assembly. This is the transpose of the flywheel inertia matrix.

[0270] The constraints of the flywheel can be transformed into the following two optimization problems:

[0271] Optimization issue 1

[0272]

[0273] Subject to

[0274]

[0275]

[0276]

[0277] Optimization issue 2

[0278]

[0279] Subject to

[0280]

[0281]

[0282]

[0283] Solving the above two problems yields the corresponding thresholds. and This optimization problem does not require online solving, thus incurring no additional computational cost.

[0284] It can be proven that for the aircraft attitude motion model constrained by formulas (6) to (8), using control law formula (18), if , And the initial conditions are met. It will never violate the constraints.

[0285] Step 3.2 Design the guidance direction

[0286] To ensure the reference attitude It converges to the desired pose while satisfying the constraints. It is necessary to design the guidance direction. For attitude pointing constraints Since both the initial attitude and the target attitude satisfy the constraints, while the attitude pointing constraint... As a convex set, the shortest attitude maneuver path can be established. MRP describes attitude using the axis and angle of a single Euler rotation, typically providing the direction of the shortest maneuver path relative to the attitude error. Therefore, guidance directions can be designed based on MRP. The design is as follows:

[0287] (34)

[0288] in, The deviation between the attitude corresponding to the reference vector and the target attitude. for rate of change and A matrix composed of related terms.

[0289] Since the equilibrium point of the system is According to assumptions 1-3, the constraint formulas (7) to (8) are always satisfied in steady state.

[0290] In conclusion, the following conclusions can be drawn:

[0291] For the attitude motion model formulas (1) to (2) constrained by formulas (6) to (8), the feedback control law formula (18) based on the I&I disturbance observer is adopted, and the reference attitude trajectory is set as follows: The guidance layer formula (23) is generated, where formula (23) is determined by the dynamic safety margin formula (24) and the guidance direction formula (34), satisfying assumptions 1~3, and satisfying the pointing constraint and initial conditions in the initial attitude. In the case of any constant target pose that satisfies the constraints, The reference attitude trajectory generated by formula (23) can guarantee that the constraints are met and asymptotically converges to the target attitude.

[0292] Step 4:

[0293] For specific spacecraft parameters and attitude control tasks, the motion model, control law, and reference manager established in steps 1 to 3 are used to select appropriate parameters. The effectiveness and practicality of the designed reference management-based spacecraft attitude control algorithm are verified through simulation.

[0294] To verify the effectiveness of the proposed control method, this invention uses an aircraft attitude maneuver mission as an example for simulation verification. The maneuver process is subject to pointing constraints, angular velocity constraints, and flywheel constraints.

[0295] The parameter settings for the numerical simulation are as follows:

[0296] The inertia of the aircraft body is The moment of inertia of a single flywheel is The initial attitude of the simulation is The initial angular velocity is The target attitude is The target angular velocity is The relevant parameters for the attitude pointing constraints imposed on the aircraft are: , , The relevant parameters for angular velocity constraints are: The relevant parameters for flywheel constraints are: , The flywheel mounting matrix is ​​as follows:

[0297]

[0298] The disturbance torque is expressed in an inertial frame as follows:

[0299]

[0300] Assume the upper bound of the interference is and The upper bound value is unknown during controller design. The parameter settings for the safety margins of the observer, controller, and guidance layer are shown in Table 1.

[0301] Table 1

[0302]

[0303] Simulation results are as follows Figures 4 to 12 As shown. Figure 4 The estimation error curve of the disturbance observer shows that the observer can accurately estimate the disturbance, with an estimation error less than [missing value]. The designed controller can effectively compensate for the effects of interference; Figure 4 It also shows different parameters The impact on the observer estimation error can be seen as... Increasing the size of the observer improves both the convergence speed and steady-state accuracy to some extent. It does not affect the controller design, therefore Choose the largest possible value.

[0304] like Figure 5 , Figure 6 and Figure 7 This demonstrates the changes in the aircraft's attitude angles, angular velocities, and reference attitude trajectory during attitude maneuvers. Figure 8 The changes in attitude pointing in three-dimensional space are shown. (a) shows the result obtained without considering constraints, and (b) shows the result of the proposed method. It can be seen that without a guidance layer, the system is stable but does not satisfy the constraints. Figure 4 This indicates that the attitude does not meet the pointing constraint requirements between 23 and 33 seconds. Figure 5 The displayed angular velocity exceeds the maximum permissible angular velocity in the range of 23~33s. Figures 9 to 11 The changes in the flywheel's angular acceleration, angular velocity, and control torque are shown. Figure 9 of (a) Figure 10 (a) and Figure 11 (a) indicates that without a guidance layer, the first and third flywheels saturate at 11~12s and 11~15s respectively. Angular momentum saturation leads to zero angular acceleration, which further reduces the torque output capability, increases the deviation between the command torque and the output torque, and affects the control performance. At the same time, the flywheel saturates the angular acceleration at the initial moment, resulting in excessive control torque. Figure 9 (b) Figure 10 (b) and Figure 11 (b) shows the result of the present invention. There is no saturation of flywheel angular velocity, angular acceleration and angular momentum in the figure. It can be seen that the introduction of the guidance layer can effectively avoid saturation of angular momentum and meet the constraint requirements.

[0305] Figure 7 The variation of the reference trajectory generated by the guidance layer over time is described, showing that its error with the target attitude converges to zero within 60 seconds. The convergence rate is theoretically analyzed in relation to the Lyapunov function. and safety threshold related, Figure 12 show Always below the safety threshold, in summary Figure 7 and Figure 12 It can be seen that in the initial stage, and The value determines The trajectory, but in the final stage, due to the error between the reference attitude and the target attitude... It's already close to zero, therefore and It will no longer have any impact on the system.

[0306] A constrained attitude control system based on explicit reference management, such as Figure 13 As shown, it includes:

[0307] The model building module is used to build the aircraft attitude motion model and constraint condition model;

[0308] A feedback control law design module is used to design a feedback control law based on an interference observer according to the aircraft attitude motion model.

[0309] The guidance layer design module is used to design a guidance layer that satisfies the constraint condition model, and to achieve constrained attitude control based on the feedback control law and the guidance layer.

[0310] In summary, the proposed aircraft constrained attitude control method based on explicit reference management can perform attitude maneuvers while satisfying constraint requirements and exhibiting robustness against disturbances, even under the presence of external disturbances and state / control constraints. This invention addresses the attitude maneuver control problem of an aircraft with a flywheel as the actuator, which faces multiple constraints (including attitude pointing constraints, angular velocity constraints, and control constraints). This invention separates constraint processing from control law design, designing a reference manager to generate a reference attitude trajectory that provides feasible maneuver trajectories from the initial attitude to the target attitude, satisfying the constraints. A feedback control law based on an immersion and invariant disturbance observer is designed to ensure system stability and robustness, achieving asymptotic tracking of the reference attitude trajectory. For aircraft attitude control systems with a flywheel as the actuator, this algorithm can achieve attitude maneuver control satisfying pointing, angular velocity, and control constraints under external disturbances. Specifically, the feasible state set is described as the intersection of all constraints; the safety margin thresholds under different constraints are solved separately; and the minimum value is used as the final threshold to design the reference manager, thus satisfying the requirements of multiple constraints. Numerical simulation results effectively verify the effectiveness and feasibility of this invention.

[0311] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A constrained attitude control method based on explicit reference management, characterized in that, The steps are as follows: Establish the aircraft attitude motion model and constraint condition model; Based on the aircraft attitude motion model, design a feedback control law based on the disturbance observer; Design a guidance layer that satisfies the constraint condition model, and implement constrained attitude control based on the feedback control law and the guidance layer; The attitude pointing constraint is defined as follows: (6) Angular velocity constraints are defined as follows: (7) For cases where the flywheel is the actuator, control constraints include maximum angular velocity constraints. and maximum angular acceleration constraints The definition is as follows: (8) Feasible set of aircraft attitude maneuvering processes The representation is as follows: (9) The interference observer is as follows: (10) estimation error The definition is as follows: (11) Dynamic part parameters It is expressed as follows: (12) in, The set of states that satisfy the orientation constraints; The attitude of the aircraft body relative to the inertial frame; The absolute angular velocity of the aircraft; is the reference unit vector in inertial space; The attitude constraint of the aircraft is defined as a unit vector of the aircraft's own system. Vectors in inertial space The included angle Less than or equal to the field of view ,Right now , It is an inertial vector Representation in a coordinate system This is the attitude matrix of the coordinate system relative to the inertial frame; The set of states that satisfy angular velocity constraints. The attitude of the aircraft body relative to the inertial frame. The absolute angular velocity of the aircraft. The maximum permissible angular velocity; Indicates the first The maximum angular velocity of each flywheel Indicates the first The maximum angular acceleration of each flywheel; External disturbance torque Observed values; For dynamic parameters; The observer parameters set by the user satisfy This is used to adjust the upper bound of the estimation error; The absolute angular velocity of the aircraft. The inertia matrix of the aircraft. The output torque of the flywheel, The angular momentum of the reaction flywheel; The guidance layer is designed as follows: (14) Guidance direction The expression is as follows: (19) in, For dynamic safety margin, This represents the attitude deviation between the aircraft's current attitude and the reference vector. The absolute angular velocity of the aircraft. The distance between the current state and the safety boundary; For guidance direction, Is it related to the current state? and expected state The relevant guidance direction; The deviation between the attitude corresponding to the reference vector and the target attitude. for rate of change and A matrix composed of related terms.

2. The constraint attitude control method based on explicit reference management according to claim 1, characterized in that, The steps to establish an aircraft attitude motion model are as follows: The attitude of the aircraft body relative to the inertial frame is represented as follows: ;in, For the corner, For the pivot, Represented as a column vector; The kinematic equations of the aircraft attitude are as follows: （1） in, The attitude of the aircraft body relative to the inertial frame. for The time derivative; for Zhongyu The matrix composed of related terms is defined as follows: ; Represented as transpose; for The corresponding cross product antisymmetric matrix; The absolute angular velocity of the aircraft. ; It is a 3rd order identity matrix; The actuator for aircraft attitude control uses a reaction flywheel, and the dynamic equations of the actuator for aircraft attitude control are as follows: （2） in, The inertia matrix of the aircraft. ; The absolute angular acceleration of the aircraft; This refers to the output torque of the flywheel; External disturbance torque; It is a cross product antisymmetric matrix; The angular momentum of the reaction flywheel. It is expressed as follows: （3） in, For the flywheel mounting matrix, ; The matrix represents the inertia of all flywheels. , Let represent the inertia of the i-th flywheel. The inertia matrix of the flywheel assembly. Represented as the angular velocity matrix of the flywheel assembly. , Let be the angular velocity of the i-th flywheel, and be the total output control torque of the flywheel assembly. as follows: （4） in, Let ω be the angular acceleration of the flywheel assembly. The expression is as follows: （5） in, The inertia matrix of the flywheel assembly. The inertia matrix of the flywheel assembly The transpose of .

3. The constraint attitude control method based on explicit reference management according to claim 2, characterized in that, The constraint model includes attitude pointing constraints, angular velocity constraints, and control constraints; Design a guidance layer for the constraint model.

4. The constraint attitude control method based on explicit reference management according to claim 1, characterized in that, The feedback control law of the interference detector is as follows: （13） in, To represent the control torque within this system; , The controller parameters selected by the user meet the requirements. ; The Rodriguez parameter represents the deviation between the current attitude and the reference attitude; It is a saturation function. , For standard symbolic functions, External disturbance torque obtained by disturbance observer (1) The estimated value, For the maximum allowable constant, satisfying , The upper bound of the external disturbance torque is... , The upper bound of the derivative of the external disturbance torque with respect to time is... , Observer parameters set by the user; when At that time, the equilibrium point It is asymptotically stable within the allowable set, that is... , The attitude of the reference vector relative to the inertial frame, It is the absolute angular velocity. It is a zero vector; when and When the value is sufficiently large, the state error is sufficiently small.

5. The constraint attitude control method based on explicit reference management according to claim 1, characterized in that, The dynamic safety margin design is as follows: （15） in, The dynamic safety margin parameter selected by the user, This represents the threshold corresponding to the constraint. The Lyapunov function representing attitude and angular velocity is... The constraints for the dynamic safety margin are as follows: Pointing constraint: The threshold corresponding to the pointing constraint as follows: （16） in, The positive constants to be selected. Controller parameters set by the user, The pointing angle corresponding to the current attitude. A quantity related to the maximum pointing angle, i.e. , Maximum pointing angle; Angular velocity constraint: The threshold corresponding to the angular velocity constraint as follows: （17） in, Inertia matrix The smallest eigenvalue, It is expressed as the square of the maximum angular velocity; Flywheel saturation constraint: The flywheel saturation constraint is described as follows: （18） in, This represents the absolute value of the angular velocity component of the flywheel assembly. This represents the absolute value of the angular acceleration component of the flywheel assembly. The maximum permissible angular velocity of the flywheel assembly. This is the maximum permissible angular acceleration of the flywheel assembly. This is the transpose of the flywheel inertia matrix; The flywheel saturation constraint is transformed into the following two optimization problems: Optimization issue 1 Subject to Optimization issue 2 Subject to Obtain the threshold for optimization problem 1 based on optimization problem 1. Obtain the threshold for optimization problem 2 based on optimization problem 2. The threshold corresponding to the constraint .

6. A constrained attitude control system based on explicit reference management, characterized in that, The constraint attitude control method based on explicit reference management as described in any one of claims 1 to 5 includes: The model building module is used to build the aircraft attitude motion model and constraint condition model; A feedback control law design module is used to design a feedback control law based on an interference observer according to the aircraft attitude motion model. The guidance layer design module is used to design a guidance layer that satisfies the constraint condition model, and to achieve constrained attitude control based on the feedback control law and the guidance layer.

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