An adaptive fixed-time fault estimation method for attitude synchronization control system

Abstract

The present invention discloses an adaptive fixed-time fault estimation method for an attitude synchronization control system, which specifically includes the following steps: Step 1: Performing equivalent transformation on the attitude control system; Step 2: Constructing a fault estimation observer and an adaptive fault estimation algorithm; Step 3: Constructing an angular rate error equation and a fault estimation error equation, and obtaining pending design parameters in the fault estimation observer and the adaptive fault estimation algorithm; Step 4: Obtaining an attitude synchronization control system fault estimation observer according to pending design parameters of the fault estimation observer and the adaptive fault estimation algorithm; Obtaining the actuator fault estimation value of each subsystem, thereby estimating the actuator fault of the attitude control system. The present invention utilizes the relative output of the attitude synchronization control system, designs a distributed fault estimation observer based on fixed-time technology, proposes a fixed-time adaptive fault estimation algorithm, and improves the rapidity of fault estimation.

Description

Technical Field

[0001] The invention belongs to the technical field of fault diagnosis of aircraft attitude synchronization control systems, and specifically relates to an adaptive fixed-time fault estimation method for attitude synchronization control systems. Background Art

[0002] Attitude synchronization control system has important research value in both military and civilian fields. Attitude synchronization is one of the basic operations in the operation of aircraft formation control system. It has been applied to various aircraft formation tasks, such as multi-satellite attitude synchronization control system, quadrotor formation attitude synchronization control system, etc. For aircraft formation control system, in the case of unknown external interference and actuator failure, the attitude synchronization control system is required to have fast fault estimation capability to achieve its high maneuverability to complete the predetermined flight mission. Therefore, it is particularly important to improve the reliability and rapidity of attitude synchronization control system.

[0003] In the past decade, a fixed-time design method aimed at improving the convergence speed of control systems has attracted considerable attention. Compared with finite-time design, the fixed-time method can significantly improve the rapidity of response, estimate the upper bound of the convergence time, and the convergence time is independent of the initial conditions of the system. Fixed-time design methods are mostly used in controller design, while there are relatively few research results on observers based on fixed-time technology. In particular, the adaptive algorithm in the adaptive observer currently still uses the traditional integral design method, and does not consider the introduction of fixed-time design techniques.

[0004] Based on the above research results, the present invention takes the aircraft attitude synchronization control system as the research object, uses the angular rate relative output estimation error, constructs a fixed-time distributed fault estimation observer, and a fixed-time fault estimation algorithm, and improves the convergence speed of fault estimation. At the same time, the proposed fault estimation method can simultaneously estimate all actuator faults of each attitude control system. Summary of the invention

[0005] Purpose of the invention: In view of the above-mentioned prior art, an adaptive fixed-time fault estimation method for an attitude synchronization control system is proposed.

[0006] An adaptive fixed-time fault estimation method for an attitude synchronization control system comprises the following steps:

[0007] 5) Construct an attitude synchronization control system with N subsystems, establish a mathematical model of the i-th subsystem, i = 1, 2, ..., N; obtain the Laplace matrix L and the self-loop matrix G representing the network communication structure;

[0008] 6) Based on the fixed-time method, a fault estimation observer and an adaptive fixed-time fault estimation algorithm are constructed respectively;

[0009] 7) Define the fault estimation error e of the i-th attitude synchronization control system f (t), construct the angular rate error equation and the fault estimation error equation, and obtain the undetermined design constants η, α, β, λ, c1, c2 in the fault estimation observer in step 2) and the undetermined design constant γ in the adaptive fixed-time fault estimation algorithm i , p, q, σ, h1, h2;

[0010] 8) Fault estimation error e f (t) is always bounded and converges to near zero, which means that the fault estimation value converges to the vicinity of the true fault value within a fixed time, thus achieving accurate fault estimation.

[0011] Preferably, in step 1), the mathematical model of the i-th subsystem, i=1, 2, ..., N, is:

[0012]

[0013] Where: J = diag{J1, J2, J3} is the moment of inertia matrix, J1, J2 and J3 are the moments of inertia of the x-axis, y-axis and z-axis respectively; is the attitude angular rate, is the control input torque, is an external disturbance, which means and is bounded to satisfy is a positive scalar, represents an unknown additive actuator fault and is bounded, where 1, 2, and 3 are the x-axis, y-axis, and z-axis respectively.

[0014] Skew-symmetric matrix It is expressed as:

[0015]

[0016] For the convenience of analysis, since the moment of inertia matrix J is non-singular, the mathematical model of the i-th subsystem is equivalently transformed into:

[0017]

[0018] Laplace matrix L and self-loop matrix G:

[0019]

[0020] Preferably, the implementation process of step 2) is:

[0021] 2.1) For the nonlinear attitude synchronization control system, the following fault estimation observer is constructed based on the fixed time method:

[0022]

[0023] Where: “∧” is the estimated value, η, α, β and λ are the unknown design parameters;

[0024] ξ i (t) is the relative angular rate estimation error defined as:

[0025] ξ i (t) = ∑a ij (ω ei (t)-ω ej (t))+b i ω ei (t)

[0026] Among them, the relative angular rate estimation error is:

[0027] and a ij is the element of the Laplace matrix L, b i are the diagonal elements of the self-loop matrix G;

[0028] Variable -λsign(ξ i (t)) is used to handle external interference d i (t), sign(·) represents the sign function; variable Constants 0<c1<1 and c2>1; |ξ i (t)|denotes ξ i The absolute value of (t);

[0029] Assuming nonlinear terms Satisfy Lipschitz conditions Among them l gi is the Lipschitz constant;

[0030] 2.2) For the nonlinear fault estimation observer, the following adaptive fixed-time fault estimation algorithm is constructed:

[0031]

[0032] Among them, the matrix is the adaptive learning rate, γ i1 ,γ i2 ,γ i3 are the learning rates of the x-axis, y-axis, and z-axis respectively; σ is a design parameter to be determined, scalar p, q>0, constants 01;<h1>

[0033] Preferably, the implementation process of step 3) is:

[0034] Define the fault estimation error of the i-th attitude synchronization control system as The error dynamic equation of the i-th system is as follows:

[0035]

[0036] in, is a nonlinear function in the attitude synchronization control system,

[0037] Define global variables:

[0038] Global angular rate estimation error:

[0039] Estimation of global nonlinear functions:

[0040] Global nonlinear function:

[0041] Global relative output estimation error:

[0042] Global fault estimation error:

[0043] Global interference vector:

[0044] Global adaptive learning rate: Γ = diag{γ1,γ2,…,γ N},

[0045] The angular rate error equation and fault estimation error equation are obtained:

[0046] Angular rate estimation error equation:

[0047]

[0048] Based on the error equation, the unknown design constants η, α, β, λ, c1, c2 in the fault estimation observer are solved;

[0049] Fault estimation equation:

[0050]

[0051] Based on the estimation equation, the undetermined design constant γ of the adaptive fixed-time fault estimation algorithm is solved i ,p,q,σ,h1,h2.

[0052] Preferably, the implementation process of step 4) is:

[0053] For attitude synchronization control systems, if the fault estimation observer and the adaptive fixed-time fault estimation algorithm are established and satisfy:

[0054]

[0055]

[0056] Among them, η, δ, p, ε, q, μ, θ are positive scalars, l g is the Lipschitz constant l of all subsystems gi The maximum value of (i=1,2,...,N), Representation Matrix The minimum eigenvalue of Representation Matrix The maximum eigenvalue of , then the angular rate estimation error ω e (t) and fault estimation error e f (t) is uniformly eventually bounded and practically constant-time stable;

[0057] Finally, the fault estimation error e f (t) is always bounded and converges to the vicinity of zero, and it is concluded that the fault estimation value converges to the vicinity of the true fault value within a fixed time, thus achieving accurate fault estimation.

[0058] Beneficial effects: 1. The present invention utilizes the relative output of the attitude synchronization control system and designs a distributed fault estimation observer based on fixed time technology.

[0059] 2. Based on the fixed-time fault estimation observer, the present invention proposes a fixed-time adaptive fault estimation algorithm, which improves the rapidity of fault estimation. This is a breakthrough technological innovation.

[0060] 3. The present invention analyzes and designs the error dynamic system from the overall perspective, and the method can simultaneously estimate the fault of each subsystem. The present invention has important practical reference value for real-time fault estimation and accurate monitoring of attitude synchronization control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flow chart of the present invention;

[0062] Figure 2 This is the communication topology diagram of the attitude synchronization control system;

[0063] Figure 3 An actuator fault estimation curve of a posture control system 1 designed based on fixed time fault estimation measured in an embodiment of the present invention;

[0064] Figure 4 The actuator fault estimation curve of the attitude control system 2 designed based on fixed time fault estimation measured in the embodiment of the present invention;

[0065] Figure 5 The actuator fault estimation curve of the attitude control system 3 designed based on fixed time fault estimation measured in the embodiment of the present invention;

[0066] Figure 6 The actuator fault estimation curve of the attitude control system 4 designed based on fixed time fault estimation measured in the embodiment of the present invention;

[0067] Figure 7 A comparison curve between an actuator fault estimation curve and an actual actuator fault of a posture control system 1 designed based on fixed time fault estimation measured in an embodiment of the present invention;

[0068] Figure 8 A comparison curve between an actuator fault estimation curve and a real actuator fault of a posture control system 2 designed based on fixed time fault estimation measured in an embodiment of the present invention;

[0069] Fig. 9 A comparison curve between an actuator fault estimation curve and a real actuator fault of a posture control system 3 designed based on fixed time fault estimation measured in an embodiment of the present invention;

[0070] Fig.10 It is a comparison curve between the actuator fault estimation curve and the actual actuator fault of the attitude control system 4 designed based on fixed time fault estimation measured in the embodiment of the present invention. DETAILED DESCRIPTION

[0071] The present invention will be further explained below in conjunction with the accompanying drawings.

[0072] An adaptive fixed-time fault estimation method for an attitude synchronization control system comprises the following steps:

[0073] Step 1: Perform equivalent transformation on the attitude control system;

[0074] Step 2: Based on the fixed time method, construct the fault estimation observer and the adaptive fault estimation algorithm respectively;

[0075] Step 3: Define the global error vector, construct the angular rate error equation and the fault estimation error equation, and obtain the unknown design parameters in the fault estimation observer and the adaptive fault estimation algorithm;

[0076] Step 4: According to the fault estimation observer and adaptive fault estimation algorithm in step 2 and the undetermined design parameters in step 3, the attitude synchronization control system fault estimation observer is obtained; the input data and output data of each attitude control system are input into the distributed fault estimation observer to obtain the actuator fault estimation value of each subsystem, thereby estimating the actuator fault of the attitude control system.

[0077] Lemma 1: For the following continuous-time system:

[0078]

[0079] in, If a Lyapunov function is such that

[0080]

[0081] Among them, 01, α>0, β>0, the origin of the system is the actual fixed time stability, and the residual interval is<h1>

[0082]

[0083] in, is a scalar and satisfies The convergence time T is bounded

[0084]

[0085] Lemma 2: For constants κ1,κ2,...,κ N ≥0, so that the following inequality holds

[0086]

[0087]

[0088] Lemma 3: For any vectors x, y, and constants ε1, ε2, ε3 ≥ 0, the following inequality holds

[0089]

[0090] Furthermore, in the step 1, the attitude synchronization control system has N subsystems, and the mathematical model of the i-th subsystem is:

[0091]

[0092] Among them, J = diag{J1,J2,J3} is the moment of inertia matrix, is the attitude angular rate, is the control input torque, is an external disturbance and is bounded to satisfy is a positive scalar. represents the unknown additive actuator failure and is bounded. The skew-symmetric matrix Expressed as

[0093]

[0094] For the convenience of analysis, since the moment of inertia matrix J is non-singular, the attitude control system is equivalently transformed into:

[0095]

[0096] Furthermore, the step 2 is specifically as follows:

[0097] Step 2.1: For the nonlinear attitude control system, construct the following fixed-time fault estimation observer based on the relative angular rate estimation error:

[0098]

[0099] in, is the angular rate estimate, is the actuator fault estimate, η, α, β and λ are positive scalars to be designed; -λsign(ξ i (t)) is used to deal with external interference d i (t), satisfying sign(·) represents the sign function, 0<c1<1 and c2>1; assume that the nonlinear term satisfies the Lipschitz condition Among them l gi is the Lipschitz constant. At the same time, the relative angular rate estimation error is defined as

[0100] ξ i (t) = ∑a ij (ω ei (t)-ω ej (t))+b i ω ei (t)

[0101] in, and a ij is the element of the Laplace matrix L, b i are the diagonal elements of the self-loop matrix G.

[0102] Step 2.2: For the nonlinear observer, construct the following fixed-time adaptive fault estimation algorithm:

[0103]

[0104] in, is the adaptive learning rate, is the parameter to be designed, scalar p,q>0.

[0105] Furthermore, in step 3, the fault estimation error of the i-th attitude synchronization control system is first defined as The error dynamic equation of the i-th system is as follows:

[0106]

[0107] in,

[0108] Define the following global variables

[0109]

[0110]

[0111]

[0112] Γ=diag{γ1,γ2,…,γ N},σ=diag{σ1,σ2,…,σ N},

[0113] The following angular rate error equation and fault estimation error equation can be obtained:

[0114]

[0115]

[0116] Furthermore, the parameters for constructing the fault estimation observer and the adaptive fault estimation algorithm in step 3 are selected as follows:

[0117] Step 4: For the attitude synchronization control system, if the distributed fault estimation observer and the adaptive fault estimation algorithm are established, then the angular rate estimation error ω e (t) and fault estimation error e f (t) is uniformly eventually bounded and is practically constant-time stable.

[0118] Consider a Lyapunov function of the following form:

[0119] V(t)=V1(t)+V2(t)

[0120] in, The matrix L represents the Laplace matrix of the undirected communication link topology of the attitude synchronization control system, and the matrix G is a self-loop matrix. Since the matrix (L+G) and the adaptive learning rate matrix Γ are both symmetric positive definite, V1(t)>0, V2(t)>0.

[0121] Take the time derivative of V1(t) as

[0122]

[0123] According to Young's inequality theorem, we can get

[0124]

[0125] Among them, δ is a positive scalar, l g Yes gi The maximum value of (i=1,2,...,N), Representation Matrix The minimum eigenvalue of Representation Matrix The maximum eigenvalue of .

[0126]

[0127] According to Lemma 2, we can get

[0128]

[0129] in, yes The smallest characteristic root of .

[0130]

[0131] Secondly, based on the adaptive fault estimation algorithm, the time derivative of V2(t) is

[0132]

[0133] Further, the following inequality can be obtained:

[0134]

[0135]

[0136]

[0137]

[0138] in, and is a positive scalar.

[0139] In summary, we can conclude

[0140]

[0141] in,

[0142] If the following three conditions are met

[0143]

[0144]

[0145] At the same time, Further available

[0146]

[0147] According to Lemma 3, and because the following inequality holds:

[0148]

[0149] It can be further concluded that

[0150]

[0151] in,

[0152] Define two new scalars as follows:

[0153]

[0154]

[0155] Finally, we can conclude that:

[0156]

[0157] where υ is the upper bound of υ1(t)+υ2(t).

[0158] Therefore, according to Lemma 1, we can conclude that the angular rate estimation error ω e (t) and fault estimation error e f (t) is the actual fixed time convergence, and the residual interval is

[0159]

[0160] At the same time, the convergence time can be obtained:

[0161]

[0162] Among them, the scalar satisfies

[0163] based on Figure 2 ,This embodiment considers the following four attitude control systems to verify the ,effectiveness of the proposed fixed time fault estimation observer design method.

[0164]

[0165] Among them, the moment of inertia matrix J = diag{20,17,15}kgm 2 , external interference

[0166] d i (t)=0.001[sin(0.8t) cos(0.5t) sin(0.3t)] T Nm.

[0167] from Figure 1 The Laplace matrix L and the self-loop matrix G can be obtained:

[0168]

[0169] It is further concluded that the matrix (L+B) is symmetric and non-singular.

[0170] The parameters in the distributed fixed-time fault estimation observer are selected as η = 6, α = 0.4, β = 1, λ = 0.01, c1 = 0.1, c2 = 1.1. The parameters in the fixed-time adaptive fault estimation algorithm are selected as γ i =diag{500,500,500}, p=0.5, q=1, σ i =0.001.

[0171] In order to verify the effects of the distributed fault estimation observer and the adaptive fault estimation algorithm based on the fixed time technology of the present invention, the following simulation example is used for verification.

[0172] Assume that each attitude control system has an actuator failure f ij (t)(i=1,2,...,N;j=1,2,3)respectively represent the following: Actuator failure of the first attitude control system:

[0173]

[0174] Actuator failure of the second attitude control system:

[0175]

[0176] Actuator failure of the third attitude control system:

[0177]

[0178] Actuator failure of the 4th attitude control system:

[0179]

[0180] The fixed-time distributed fault estimation simulation curves of the four attitude control systems are shown in Figure 2. Figure 3-6From the simulation diagram, it can be seen that the fault estimation technique based on fixed time technology can estimate the fault quickly and accurately. Even if multiple systems fail at the same time, the proposed design method can accurately estimate each fault.

[0181] To verify the effect of fault estimation, we compared the actual value with the fault estimation value. Figure 7-10 It can be seen that the proposed method can accurately estimate the true value of the fault and is also robust to external interference.

[0182] For simulation, Figure 3 This is an actuator fault estimation curve of the attitude control system 1 designed based on fixed time fault estimation measured in an embodiment of the present invention, wherein: Represents the actuator failure f of attitude control system 1 11 The estimated value of (t), Represents the actuator failure f of attitude control system 1 12 The estimated value of (t), Represents the actuator failure f of attitude control system 1 13 (t) is an estimated value.

[0183] Figure 4 This is an actuator fault estimation curve of the attitude control system 2 designed based on fixed time fault estimation measured in an embodiment of the present invention, where: Represents the actuator failure f of attitude control system 2 21 The estimated value of (t), Represents the actuator failure f of attitude control system 2 22 The estimated value of (t), Represents the actuator failure f of attitude control system 2 23 (t) is an estimated value.

[0184] Figure 5 It is the actuator fault estimation curve of the attitude control system 3 designed based on fixed time fault estimation measured in the embodiment of the present invention, where: Represents the actuator failure f of attitude control system 3 31 The estimated value of (t), Represents the actuator failure f of attitude control system 3 32 The estimated value of (t), Represents the actuator failure f of attitude control system 3 33 (t) is an estimated value.

[0185] Figure 6 This is an actuator fault estimation curve of the attitude control system 4 designed based on fixed time fault estimation measured in an embodiment of the present invention, where: Represents the actuator failure f of attitude control system 441 The estimated value of (t), Represents the actuator failure f of attitude control system 4 42 The estimated value of (t), Represents the actuator failure f of attitude control system 4 43 (t) is an estimated value.

[0186] Figure 7 is a comparison curve between the actuator fault estimation curve and the actual actuator fault of the attitude control system 1 designed based on fixed time fault estimation measured in the embodiment of the present invention, wherein: 11 (t) represents the real failure of the first actuator of attitude control system 1, Represents the actuator failure f of attitude control system 1 11 The estimated value of (t); f 12 (t) represents the real fault of the second actuator of attitude control system 1, Represents the actuator failure f of attitude control system 1 12 (t) is an estimated value.

[0187] Figure 8 is a comparison curve between the actuator fault estimation curve and the actual actuator fault of the attitude control system 2 designed based on fixed time fault estimation measured in the embodiment of the present invention, wherein: 21 (t) represents the real failure of the first actuator of attitude control system 2, Represents the actuator failure f of attitude control system 2 21 The estimated value of (t); f 23 (t) represents the actual fault of the third actuator of attitude control system 2, Represents the actuator failure f of attitude control system 2 23 (t) is an estimated value.

[0188] Fig. 9 is a comparison curve between the actuator fault estimation curve and the actual actuator fault of the attitude control system 3 designed based on fixed time fault estimation measured in the embodiment of the present invention, wherein: 32 (t) represents the real fault of the second actuator of attitude control system 3, Represents the actuator failure f of attitude control system 3 32 The estimated value of (t); f 33 (t) represents the actual fault of the third actuator of attitude control system 3, Represents the actuator failure f of attitude control system 3 33 (t) is an estimated value.

[0189] Fig.10is a comparison curve between the actuator fault estimation curve and the actual actuator fault of the attitude control system 4 designed based on fixed time fault estimation measured in the embodiment of the present invention, wherein: 41 (t) represents the real failure of the first actuator of attitude control system 4, Represents the actuator failure f of attitude control system 4 41 The estimated value of (t); f 43 (t) represents the actual fault of the third actuator of attitude control system 4, Represents the actuator failure f of attitude control system 4 43 (t) is an estimated value.

[0190] The fault estimation curve obtained online and the actual fault curve are placed in the same coordinates for comparison in order to verify the estimation effect of the proposed actuator fault estimation observer. It can be concluded from the simulation results that when one or more systems in the attitude synchronization control system have actuator faults, the fixed-time-based fault estimation designed by the present invention can improve the rapidity of fault estimation, has good robustness to external interference, and accurately detects and estimates the unknown actuator torque faults in the four subsystems.

[0191] The present invention has important practical reference value for fault estimation and accurate monitoring of attitude synchronization control systems. Any description not involved in the specific implementation of the present invention belongs to the known technology in the art and can be implemented with reference to the known technology.

[0192] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An adaptive fixed-time fault estimation method for an attitude synchronization control system, characterized in that: The following steps are involved: 1) Construct an attitude synchronization control system with N subsystems, establish a mathematical model of the i-th subsystem, i = 1, 2, ..., N; obtain the Laplace matrix L and the self-loop matrix G representing the network communication structure; 2) Based on the fixed-time method, a fault estimation observer and an adaptive fixed-time fault estimation algorithm are constructed respectively; 3) Define the fault estimation error e of the i-th attitude synchronization control system f (t), construct the angular rate error equation and the fault estimation error equation, and obtain the undetermined design constants η, α, β, λ, c1, c2 in the fault estimation observer in step 2) and the undetermined design constant γ in the adaptive fixed-time fault estimation algorithm i , p, q, σ, h1, h2; 4) Fault estimation error e f (t) is always bounded and converges to the vicinity of zero, and the fault estimation value converges to the vicinity of the true fault value within a fixed time, achieving accurate fault estimation; The mathematical model of the i-th subsystem in step 1), i=1,2,...,N is: Where: J = diag{J1, J2, J3} is the moment of inertia matrix, J1, J2 and J3 are the moments of inertia of the x-axis, y-axis and z-axis respectively; is the attitude angular rate, is the control input torque, is an external disturbance, which means and is bounded to satisfy is a positive scalar, represents an unknown additive actuator fault and is bounded, where 1, 2, and 3 are the x-axis, y-axis, and z-axis respectively. Skew-symmetric matrix It is expressed as: For the convenience of analysis, since the moment of inertia matrix J is non-singular, the mathematical model of the i-th subsystem is equivalently transformed into: Laplace matrix L and self-loop matrix G: The implementation process of step 2) is: 2.1) For the nonlinear attitude synchronization control system, the following fault estimation observer is constructed based on the fixed time method: Among them: "∧" is the estimated value, η, α, β and λ are the unknown design parameters; ξ i (t) is the relative angular rate estimation error defined as: Among them, the relative angular rate estimation error is: and a ij is the element of the Laplace matrix L, b i are the diagonal elements of the self-loop matrix G; Variable -λsign(ξ i (t)) is used to handle external interference d i (t), sign(·) represents the sign function; variable The constants 0<c1<1 and c2>1; |ξi(t)| represents ξ i The absolute value of (t); Assuming nonlinear terms Satisfy Lipschitz conditions Among them l gi is the Lipschitz constant; 2.2) For the nonlinear fault estimation observer, the following adaptive fixed-time fault estimation algorithm is constructed: Among them, the matrix is the adaptive learning rate, γ i1 ,γ i2 ,γ i3 are the learning rates of the x-axis, y-axis, and z-axis respectively; σ is a design parameter to be determined, scalar p, q>0, constants 0<h1<1 and h2>1; The implementation process of step 3) is: Define the fault estimation error of the i-th attitude synchronization control system as The error dynamic equation of the i-th system is as follows: in, It is a nonlinear function in the attitude synchronization control system, and defines global variables: Global angular rate estimation error: Estimation of global nonlinear functions: Global nonlinear function: Global relative output estimation error: Global fault estimation error: Global interference vector: Global adaptive learning rate: Γ = diag{γ1,γ2,…,γ N }, The angular rate error equation and fault estimation error equation are obtained: Angular rate estimation error equation: Based on the error equation, the unknown design constants η, α, β, λ, c1, c2 in the fault estimation observer are solved; Fault estimation equation: Based on the estimation equation, the undetermined design constant γ of the adaptive fixed-time fault estimation algorithm is solved i , p, q, σ, h1, h2; The implementation process of step 4) is: For attitude synchronization control systems, if the fault estimation observer and the adaptive fixed-time fault estimation algorithm are established and satisfy: Among them, η, δ, p, ε, q, μ, θ are positive scalars, l g is the Lipschitz constant l of all subsystems gi The maximum value of (i=1,2,...,N), Representation Matrix The minimum eigenvalue of Representation Matrix The maximum eigenvalue of , then the angular rate estimation error ω e (t) and fault estimation error e f (t) is uniformly eventually bounded and practically constant-time stable; Finally, the fault estimation error e f (t) is always bounded and converges to the vicinity of zero, and it is concluded that the fault estimation value converges to the vicinity of the true fault value within a fixed time, thus achieving accurate fault estimation.

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