A full-actuation attitude saturation control method for flexible spacecraft with input constraints

Abstract

The present invention discloses a full - drive attitude saturation control method for a flexible spacecraft with input constraints, which includes the following steps: Step 1, based on the full - drive system theory method, according to the attitude dynamics and kinematics models of the flexible spacecraft, convert the spacecraft attitude model into a full - drive system control model; Step 2, design an attitude controller architecture for the full - drive system control model of the flexible spacecraft in Step 1; Step 3, for the linear feedback part of the control law in Step 2, the parameter matrices A0 and A1 are determined by the "direct parameter method" under the full - drive system theory framework; Step 4, for the non - linear term compensation part of the control law in Step 2, an extended state observer is used for comprehensive observation and estimation; Step 5, for the control law in Step 2, considering the physical limitations of the control actuators, design a saturation function to ensure that the control input torque is within a reasonable range. The present invention can achieve rigid - body attitude and flexible vibration suppression within the capabilities of the actuators.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft attitude control, and in particular to a full-actuator attitude saturation control method for a flexible spacecraft with input constraints. Background Technique

[0002] In recent years, monitoring, countering, etc. of low-earth orbit large-scale constellations typified by "Starlink" and "OneWeb" constellations have become an urgent need for future international competition for space-based information dominance. Considering that countermeasure payloads such as microwaves and lasers have relatively high powers, modern spacecraft usually equip large flexible appendages, and the flexible vibrations caused by the mutual coupling between the large flexible and low-damping appendages and the central rigid body will reduce the satellite attitude pointing accuracy; on the other hand, during the on-orbit operation of the spacecraft, it will inevitably be affected by various complex environmental disturbances, and factors such as payload movement and fuel consumption will cause uncertainties in the spacecraft's moment of inertia. In addition, due to actuator limitations or inherent physical constraints of the system, many actual dynamic systems have input saturation. If saturation is ignored in control design, it often reduces the performance of the control system or leads to instability. Therefore, it is of great significance to design an attitude control method considering saturation to complete the attitude maneuver control and vibration suppression of flexible spacecraft.

[0003] The spacecraft dynamics model is a classical second-order system. The traditional state-space method is to transform the second-order system into a first-order system and then process the system with existing methods, resulting in an increase in the dimension of the transformed system, an increase in computational complexity, and an easy omission of physical characteristics. The fully actuated system theory (FAS) was born under such a background. Different from the state-space method, the FAS theory ensures that, under the condition of unchanged physical environment, regardless of the complexity of the non-linear terms, the fully actuated structure can compensate for the dynamic characteristics of the system. As long as appropriate control parameters are selected theoretically, the controller based on FAS can obtain dynamic performance of any quality, providing a prerequisite for the effective operation of future space-based countermeasure systems. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a full-actuator attitude saturation control method for a flexible spacecraft with input constraints, which can achieve rigid body attitude and flexible vibration suppression within the actuator capacity.

[0005] To solve the above technical problem, the present invention provides a full-actuator attitude saturation control method for a flexible spacecraft with input constraints, including the following steps:

[0006] Step 1: Based on the fully actuated system theory method, according to the attitude dynamics and kinematics models of the flexible spacecraft, convert the spacecraft attitude model into a fully actuated system control model;

[0007] Step 2: Design an attitude controller architecture for the fully actuated system control model of the flexible spacecraft in Step 1;

[0008] Step 3: For the linear feedback part of the control law in Step 2, the parameter matrices A0 and A1 are determined by the "direct parameter method" under the theoretical framework of the fully actuated system;

[0009] Step 4: For the nonlinear term compensation part of the control law in Step 2, an extended state observer is used for comprehensive observation and estimation;

[0010] Step 5: For the control law in Step 2, considering the physical limitations of the control actuator, a saturation function is designed to ensure that the control input torque is within a reasonable range.

[0011] Preferably, in Step 1, based on the theoretical method of the fully actuated system, according to the attitude dynamics and kinematics models of the flexible spacecraft, the conversion of the spacecraft attitude model into a fully actuated system control model specifically includes the following steps:

[0012] Step 11: Consider the actual control torque under input saturation;

[0013] Step 12: Consider the classical attitude model, kinematic model and dynamic model of the flexible spacecraft under input saturation;

[0014]

[0015] where J is the spacecraft inertia matrix; δ is the coupling matrix between the central rigid body and the flexible appendage; η is the flexible vibration mode; u is the control torque, and C and K are the damping matrix and stiffness matrix respectively; d = e s (v) + T d is the lumped disturbance; G(σ) = 0.25[(1 - σ T σ)I3 + 2σ × + 2(σ · σ T )] is the coordinate transformation matrix, ω = [ω x ω y ω z T ∈R 3 is the attitude angular velocity of the spacecraft relative to the inertial system in the body frame, I3 is the identity matrix, and the skew-symmetric matrix σ × = [0 -σ z σ y ; σ z 0 -σ x ; -σ y σ x 0];

[0016] Step 13: Convert the classical attitude model of the spacecraft into a second-order fully actuated system. ​

[0017] Preferably, in step 11, considering the saturation of actuators such as flywheels, the actual system control torque u is expressed as u(v)=[sat(v1), sat(v2), sat(v3)] T , where v is the control command torque, and sat(v i ) = sgn(v i )·min{|v i |, u i,max}; u i,max is the maximum allowable output torque of the corresponding actuator. The hyperbolic tangent function g(v) is selected to approximate the saturation nonlinearity. Therefore, the actual control torque u(v)

[0018] u(v) = g(v) + e s (v)

[0019] where g i (v i ) = u i,max ×tanh(v i / u i,max ), i = 1, 2, 3; because |e s (v i )| = |sat(v i ) - g i (v i )| ≤ u i,max (1 - tanh(1)), i = 1, 2, 3, the approximation error vector e s (v) is bounded. In addition, a diagonal matrix H ∈ R 3×3 is defined, and its diagonal element h i = g i (v i ) / v i , h i ∈(0, 1]. Therefore, considering actuator saturation, the actual control torque is converted to

[0020] u(v) = Hv + e s (v)

[0021] where e s (v) For To avoid singularity, when v i = 0, let h i = 1.

[0022] Preferably, in step 13, the classical attitude model of the spacecraft is transformed into a second-order fully actuated system:

[0023]

[0024] In the formula, f1, f2, f3 ∈ R 3respectively characterize the gyroscopic effect, the nonlinear vibration caused by the rigid-flexible coupling, the external disturbance, and the saturation estimation error; in addition, is a continuous vector function. Since the Jacobian matrix G is invertible and the star inertia matrix J is a positive definite matrix, then B≠0, that is, the above system satisfies the full actuation condition.

[0025] Preferably, in step 2, the attitude controller architecture includes a linear state feedback main part u f and a nonlinear term compensation part u d , and gain adjustment is performed on this control input.

[0026] v = N D (χ)τ a

[0027] τ a = u f + u d

[0028] wherein, N D (χ) = diag([N(χ1), N(χ2), N(χ3)]) is a control torque gain adjustment function, and a Nussbaum-type function is selected. Here, u f is the linear state feedback part to obtain the desired linear closed-loop system, and u d is the system lumped nonlinear compensation controller, and τ a is the control law output under the theoretical framework of the full actuation system.

[0029] Preferably, in step 3, the parameter matrices A0 and A1 are determined by the "direct parameter method" under the theoretical framework of the full actuation system:

[0030]

[0031] wherein, is a continuous vector function, R 3×3 is a real matrix of dimension 3×3, serving as the control input matrix of the system, and σ, are respectively the states regarding the attitude of the system, and v ex is the external input.

[0032] Preferably, in step 3, for the linear feedback part of the control law in step 2, the determination of the parameter matrices A0 and A1 by the "direct parameter method" under the theoretical framework of the full actuation system specifically includes the following steps:

[0033] Step 31: Select a Hurwtiz matrix F ∈ R 6×6 , and arbitrarily select Z ∈ R 3×6 satisfying V = (Z, ZF) T , det V(Z, F)≠0, A0～1 = ZF 2 V -1 ; where, R 6×6 , R 3×6 are respectively a real matrix of dimension 6×6 and a real matrix of dimension 3×6;

[0034] Step 32. From the above parameter transformation, the linear feedback controller u f :

[0035]

[0036] where, K p , K d are the proportional and derivative control parameter matrices before parameter transformation, that is, under the action of the parameter matrices F∈R 6×6 , Z∈R 3×6 , the fully actuated system model is converted into a stationary linear system:

[0037]

[0038] where, the augmented variable

[0039] Preferably, in step 4, the non-linear term part is the non-linear term caused by flexible vibration, external disturbance, and input saturation.

[0040] Preferably, in step 4, for the non-linear term compensation part of the control law in step 2, an extended state observer is used to comprehensively observe and estimate it, specifically including the following steps:

[0041] Step 41. Define Let k(t) be unknown and bounded, then the system is converted to;

[0042]

[0043] Step 42. Design a parallel extended non-linear state observer;

[0044]

[0045] where, are the estimated states of z1, z2, and z3 respectively, is the modified error exponential gain function with respect to e1;

[0046] Step 43. The error exponential gain function in step 42

[0047]

[0048] In the formula, δ is a very small positive number, αi ∈(0, 1);

[0049] Step 44, define to obtain the observer observation error dynamics model:

[0050]

[0051] Select appropriate observer parameters β1, β2, β3 such that

[0052] Preferably, in step 5, for the control law in step 2, considering the physical limitations of the control actuator, design a saturation function to ensure that the control input torque is within a reasonable range, including the following steps:

[0053] Step 51, calculate the control law output;

[0054] τ a = u f + u d

[0055] where u f is the linear state feedback part to obtain the desired linear closed-loop system, and u d is the system lumped nonlinear compensation controller, and τ a is the control law output under the theoretical framework of the fully actuated system;

[0056] Step 52, design the variable χ adaptive law of the Nussbaum-type function to associate the system state X with the control law output τ a , and through the adjustment of χ, the system performance and system energy consumption can be effectively coordinated, and it satisfies the update law;

[0057]

[0058] where is the χ update factor; there exists a positive definite matrix P that satisfies the equation , where A c = VFV -1 .

[0059] Step 53, select the Nussbaum-type function N D (χ) = diag([N(χ1), N(χ2), N(χ3)]) as the control torque gain adjustment function, and here take calculate the control command torque v = N D (χ)τ a ;

[0060] Step 54, use the following saturation function sat(v i ) to limit the control command torque;

[0061]

[0062] Among them, sgn(·) is the sign function, and u max is the maximum output capacity of the actuator.

[0063] The beneficial effects of the present invention are as follows: (1) Based on the theoretical framework of the full - drive system, the control algorithm design is simple. The nonlinear attitude dynamics can be designed as a linear time - invariant system with an expected characteristic structure, and it has strong applicability to nonlinearity. (2) An extended nonlinear observer is introduced to estimate and effectively compensate for nonlinear terms such as flexible vibration and external disturbances in the system. Strain sensors, etc. are not required, effectively saving on - satellite resources. (3) The Nussbaum gain technique is used to handle the influence of input saturation, greatly reducing the influence of input saturation on the system, and the control torque is continuous and smooth without sudden changes, which has important practical significance. (4) Fast attitude control and flexible vibration control of flexible spacecraft are achieved, and it has high control steady - state accuracy. The controller considers external disturbances, actuator saturation, etc., and has strong robustness to external disturbances, which has certain reference significance for attitude control engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is the control block diagram of the present invention;

[0065] Figure 2 is the overall work flow chart of the present invention;

[0066] Figure 3 is the schematic diagram of the extended nonlinear observer of the present invention;

[0067] Figure 4 is the work flow chart of the input saturation design of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0068] As Figure 1 shown, it is the control block diagram of the present invention. After building a flexible spacecraft attitude model considering input saturation, external disturbances, etc., it is transformed into a full - drive system for control and the corresponding control law is designed; then the direct parameter method is used to determine the feedback parameter matrix of the main part of the linear feedback, and the nonlinearity of the nonlinear compensation part is estimated and compensated based on the extended state observer. Finally, a saturation function and a gain adjustment function of the Nussbaum function are designed to limit the control torque, and an adaptive law is designed for the independent variable of the Nussbaum - type function. This parameter is related to the system state and the output of the control law, so this adaptive law and the Nussbaum - type function together constitute a double constraint on the control torque.

[0069] As Figure 2 shown, a full - drive attitude saturation control method for a flexible spacecraft with input constraints includes the following steps:

[0070] Step 1. Based on the full - drive system theory method, according to the attitude dynamics and kinematics model of a flexible spacecraft, convert the spacecraft attitude model into a full - drive system control model;

[0071] Step 11. Consider the actual control torque under input saturation;

[0072] Considering the saturation of actuators such as flywheels, the actual system control torque \(u\) is generally expressed as \(u(v)=[\text{sat}(v_1),\text{sat}(v_2),\text{sat}(v_3)]\) T , where \(v\) is the control command torque, and \(\text{sat}(v\) i )=\text{sgn}(v\) i )\cdot\min\{|v\) i |,u\) i,max}\), and \(u\) i,max is the maximum allowable output torque of the corresponding actuator. In this paper, the hyperbolic tangent function \(g(v)\) is used to approximate the saturation non - linearity. Therefore, the actual control torque \(u(v)\)

[0073] u(v)=g(v)+e_s(v)\)

[0074] where \(g\) i (v\) i ) = u\) i,max \times\tanh(v\) i / u\) i,max ), \(i = 1,2,3\); because \(|e\) s (v\) i )| = |\text{sat}(v\) i ) - g\) i (v\) i )|\leq u\) i,max (1 - \tanh(1)), \(i = 1,2,3\), the approximation error vector \(e\) s (v)\) is bounded. In addition, define a diagonal matrix \(H\in R\) 3×3 , whose diagonal element \(h\) i = g\) i (v\) i ) / v\) i ), \(h\) i \in(0,1]\). Therefore, considering actuator saturation, the actual control torque can be converted to

[0075] u(v)=Hv + e\) s (v)\)

[0076] where \(e\) s (v)\) is To avoid singularity, when \(v\) i = 0\), let \(h\) i = 1.

[0077] Step 12: Consider the classical attitude model (kinematic model and dynamic model) of a flexible spacecraft with input saturation;

[0078]

[0079] where J is the spacecraft's inertia matrix; δ is the coupling matrix between the central rigid body and the flexible appendages; η is the flexible vibration mode; u is the control torque, and C and K are the damping matrix and stiffness matrix respectively. d = e s (v)+T d is the lumped disturbance; G(σ) = 0.25[(1 - σ T σ)I3 + 2σ × + 2(σ·σ T )] is the coordinate transformation matrix, ω = [ω x ω y ω z T ∈R 3 is the attitude angular velocity of the spacecraft relative to the inertial frame in the body frame, I3 is the identity matrix, and the skew-symmetric matrix σ × = [0 -σ z σ y ; σ z 0 -σ x ; -σ y σ x 0];

[0080] Step 13: Transform the classical attitude model of the spacecraft into a second-order fully actuated system:

[0081]

[0082] where f1, f2, f3 ∈ R 3 represent the gyroscopic effect, the nonlinear vibration caused by the rigid-flexible coupling, the external disturbance, and the saturation estimation error respectively. Additionally, is a continuous vector function. Since the Jacobian matrix G is invertible and the inertia matrix J of the spacecraft is a positive definite matrix, B ≠ 0, that is, the above system satisfies the fully actuated condition.

[0083] Step 2: Design the attitude controller architecture for the fully actuated system model of the flexible spacecraft in Step 1. Its structure includes a linear state feedback main part u f and a nonlinear term compensation part u d , and finally, gain adjustment is made to this control input;

[0084] v = N D (χ)τ a

[0085] τ a = u f + u​d

[0086] In the formula, the Nussbaum function N is selected D (χ) = diag([N(χ1), N(χ2), N(χ3)]) is the control moment gain adjustment function, where Calculate the control command moment v = N D (χ)τ a , u f is the linear state feedback part to obtain the desired linear closed-loop system, u d is the system lumped nonlinear compensation controller, τ a is the output of the control law under the theoretical framework of the fully actuated system.

[0087] Step 3: For the linear feedback part of the control law in Step 2, A0 and A1 are the parameter matrices determined by the "direct parameter method" under the theoretical framework of the fully actuated system;

[0088]

[0089] In the formula, is a continuous vector function, R 3×3 is a real matrix of dimension 3×3, serving as the control input matrix of the system, σ, are the states regarding the system attitude respectively, v ex is the external input.

[0090] Step 31: Select the Hurwtiz matrix F ∈ R 6×6 , and arbitrarily select Z ∈ R 3×6 to satisfy V = (Z, ZF) T , det V(Z, F) ≠ 0, A 0～1 = ZF 2 V -1 .

[0091] Step 32: From the above parameter transformation, the linear feedback controller u f :

[0092]

[0093] That is, under the action of the parameter matrices F ∈ R 6×6 , Z ∈ R 3×6 , the fully actuated system model is converted into a constant linear system:

[0094]

[0095] Among them, the augmented variable

[0096] Step 4. For the non - linear term compensation part of the control law in Step 2, for the non - linear terms caused by unknown factors such as flexible vibration, external disturbance, input saturation, etc., as Figure 3 shown, an extended state observer is used for comprehensive observation and estimation;

[0097] Step 41. Define \(z_1=\sigma\), \(z_3 = f\), and let \(k(t)\) be unknown and bounded. Then the system (2) can be transformed into;

[0098]

[0099] Step 42. From Step 41,, design an extended non - linear state observer in parallel with it;

[0100]

[0101] where, are the estimated states of \(z_1\), \(z_2\), and \(z_3\) respectively. is the modified error exponential gain function with respect to \(e_1\).

[0102] Step 43. The error exponential gain function in Step 42

[0103]

[0104] In the formula, \(\delta\) is a very small positive number, and \(\alpha\) i \(\in(0,1)\).

[0105] Step 44. From Step 41 and Step 42, define to obtain the observer observation error dynamics model:

[0106]

[0107] Select appropriate observer parameters \(\beta_1\), \(\beta_2\), \(\beta_3\) such that

[0108] Step 5. For the control law in Step 2, considering the physical limitations of the control actuator, design a saturation function to ensure that the control input torque is within a reasonable range;

[0109] Step 51. Use the following saturation function sat(u i ) to limit the input torque;

[0110]

[0111] Step 52. Design an adaptive variable \(\chi\) of the Nussbaum - type function to associate the system state with the control command. Through the adjustment of \(\chi\), the system performance and system energy consumption can be effectively coordinated, and it satisfies the update law;

[0112]

[0113] In the formula, is the χ update factor, and τ a is the control law output under the theoretical framework of the fully actuated system.

[0114] As Figure 4 shown, a full-actuated attitude saturation control method for a flexible spacecraft with input constraints, in which the working process for input saturation includes the following steps:

[0115] (1) First, calculate the control law output;

[0116] τ a = u f + u d

[0117] In the formula, u f is the linear state feedback part to obtain the desired linear closed-loop system, and u d is the system lumped nonlinear compensation controller.

[0118] (2) Design the variable χ adaptive law of the Nussbaum-type function to associate the system state X with the control law output τ a , and through the adjustment of χ, the system performance and system energy consumption can be effectively coordinated, and it satisfies the update law;

[0119]

[0120] In the formula, is the χ update factor, and τ a is the control law output under the theoretical framework of the fully actuated system.

[0121] (3) Select the Nussbaum-type function N D (χ) = diag([N(χ1), N(χ2), N(χ3)]) as the control torque gain adjustment function, and here take Calculate the control command torque v = N D (χ)τ a .

[0122] (4) Use the following saturation function sat(v i ) to limit the control command torque;

[0123]

[0124] Among them, sgn(i) is the sign function, and u max is the maximum output capacity of the actuator.

Claims

1. A full - drive attitude saturation control method for flexible spacecraft with input constraints, characterized in that, It includes the following steps: Step 1: Based on the full - drive system theory method, convert the spacecraft attitude model into a full - drive system control model according to the flexible spacecraft attitude dynamics and kinematics models. Specifically, it includes the following steps: Step 11: Consider the actual control torque under input saturation; Step 12: Consider the classical attitude model, kinematics model and dynamics model of the flexible spacecraft under input saturation; In the formula, J is the spacecraft inertia matrix; δ is the coupling matrix between the central rigid body and the flexible appendage; η is the flexible vibration mode; u is the control torque, and C and K are the damping matrix and the stiffness matrix respectively; d = e s (v)+T d is the lumped disturbance; G(σ) = 0.25[(1 - σ T σ)I3 + 2σ × + 2(σ·σ T )] is the coordinate transformation matrix, ω = [ω x ω y ω z T ∈R 3 is the attitude angular velocity of the spacecraft relative to the inertial system in this system, I3 is the identity matrix, and the skew-symmetric matrix σ × = [0 -σ z σ y ; σ z 0 -σ x ; -σ y σ x 0];​ Step 13: Convert the classical attitude model of the spacecraft into a second - order full - drive system; Step 2: Design an attitude controller architecture for the fully actuated flexible spacecraft control model in Step 1; the attitude controller architecture includes a linear state feedback main part \(u\) f and a nonlinear term compensation part \(u\) d , and then perform gain adjustment on this control input; v = N D (χ)τ a τ a = u f + u d where N D (χ) = diag([N(χ1), N(χ2), N(χ3)]) is the control torque gain adjustment function, and a Nussbaum-type function is selected. Here, take u f as the linear state feedback part to obtain the desired linear closed-loop system. u d is the lumped nonlinear compensation controller of the system, and τ a is the output of the control law under the theoretical framework of the fully actuated system; Step 3: For the linear feedback part of the control law in Step 2, the parameter matrices A0 and A1 are determined by the "direct parameter method" under the full - drive system theory framework; Step 4: For the non - linear term compensation part of the control law in Step 2, use an extended state observer to comprehensively observe and estimate it; Step 5: For the control law in Step 2, considering the physical limitations of the control actuator, design a saturation function to ensure that the control input torque is within a reasonable range. It includes the following steps: Step 51: Calculate the output of the control law; τ a = u f + u d where \(u\) f is the linear state feedback part to obtain the desired linear closed-loop system, and \(u\) d is the lumped nonlinear compensation controller of the system, and \(\tau\) a is the output of the control law under the theoretical framework of the fully actuated system; Step 52: Design the variable χ adaptation law of the Nussbaum function so that it correlates the system state X with the control law output τ a , and effectively coordinates the system performance and system energy consumption through the adjustment of χ, which satisfies the update law; wherein, is the χ update factor; There exists a positive definite matrix P that satisfies the equation where A c = VFV -1 ; Step 53: Select the Nussbaum function N D (χ) = diag([N(χ1), N(χ2), N(χ3)]) is the control moment gain adjustment function, where Calculate the control command moment v = N D (χ)τ a ; Step 54. Limit the control command torque using the following saturation function sat(v i ); where sgn(·) is the sign function, and u max is the maximum output capacity of the actuator.

2. The full-actuation attitude saturation control method for an input-constrained flexible spacecraft according to claim 1, wherein In step 11, considering the saturation of actuators such as flywheels, the actual system control torque u is expressed as u(v) = [sat(v1), sat(v2), sat(v3)] T , where v is the control command torque, and sat(v i ) = sgn(v i )·min{|v i |, u i,max}, and u i,max is the maximum allowable output torque of the corresponding actuator; the hyperbolic tangent function g(v) is selected to approximate the saturation nonlinearity. Therefore, the actual control torque u(v) u(v) = g(v) + e s (v) where, g i (v i ) = u i,max ×tanh(v i / u i,max ), i = 1, 2, 3; because |e s (v i )| = |sat(v i ) - g i (v i )| ≤ u i,max (1 - tanh(1)), i = 1, 2, 3, the approximation error vector e s (v) is bounded; in addition, define a diagonal matrix H ∈ R 3×3 , whose diagonal element h i = g i (v i ) / v i , h i ∈ (0, 1]. Therefore, considering actuator saturation, the actual control torque is converted to u(v) = Hv + e s (v) Among them, to avoid singularity, when v i = 0, let h i = 1.

3. The full - drive attitude saturation control method for an input - constrained flexible spacecraft according to claim 1, characterized in that, In Step 13, convert the classical attitude model of the spacecraft into a second - order full - drive system: where \(f_1, f_2, f_3\in R\) 3 respectively represent the gyroscopic effect, the nonlinear vibration caused by the rigid-flexible coupling, the external disturbance and the saturation estimation error; in addition, is a continuous vector function. Since the Jacobian matrix \(G\) is invertible and the inertia matrix \(J\) of the star body is a positive definite matrix, then \(B\neq0\), that is, the above system satisfies the full actuation condition.

4. The full - drive attitude saturation control method for an input - limited flexible spacecraft according to claim 1, characterized in that, In Step 3, the parameter matrices A0 and A1 are determined by the "direct parameter method" under the full - drive system theory framework: In the formula, is a continuous vector function, and R 3×3 is a real matrix of dimension 3×3 and serves as the control input matrix of the system. σ and are the states regarding the attitude of the system, respectively, and v ex is the external input.

5. The full - drive attitude saturation control method for an input - limited flexible spacecraft according to claim 1, characterized in that, In Step 3, for the linear feedback part of the control law in Step 2, the parameter matrices A0 and A1 are determined by the "direct parameter method" under the full - drive system theory framework. Specifically, it includes the following steps: Step 31: Select a Hurwitz matrix \(F\in\mathbb{R}\) 6×6 , arbitrarily select \(Z\in\mathbb{R}\) 3×6 such that \(V=(Z, ZF)\) T , \(\det V(Z,F)\neq0\), \(A\) 0～1 = ZF 2 V -1 ; where \(\mathbb{R}\) 6×6 , \(\mathbb{R}\) 3×6 are a real matrix of dimension \(6\times6\) and a real matrix of dimension \(3\times6\) respectively; Step 32: From the above parameter transformation, the linear feedback controller u f : Among them, K p , K d is the proportional differential control parameter matrix before parameter conversion, that is, under the action of the parameter matrices F ∈ R 6×6 , Z ∈ R 3×6 , the full-drive system model is converted into a steady-state linear system: Among them, the augmented variable 6. The full - drive attitude saturation control method for an input - limited flexible spacecraft according to claim 1, wherein, In Step 4, the non - linear term part is the non - linear term caused by flexible vibration, external disturbance and input saturation.

7. The full - drive attitude saturation control method for an input - constrained flexible spacecraft according to claim 1, characterized in that, In Step 4, for the non - linear term compensation part of the control law in Step 2, use an extended state observer to comprehensively observe and estimate it. Specifically, it includes the following steps: Step 41. Define \(z1 = \sigma\), \(z3 = f\), and let \(k(t)\) be unknown and bounded, then the system is transformed into; Step 42: Design a parallel extended non - linear state observer; Among them, are the estimated states of z1, z2, and z3 respectively, is the correction error exponential gain function with respect to e1; Error exponential gain function in step 43 and step 42 where δ is a very small positive number, and α i ∈(0, 1); Step 44, define to obtain the observer observation error dynamics model: Select appropriate observer parameters β1, β2, β3 such that

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