An implementation method of a satellite attitude tracking fault-tolerant controller based on event-triggered learning

Abstract

This invention discloses a method for implementing a fault-tolerant satellite attitude tracking controller based on event-triggered learning, comprising the following steps: S1, establishing a mathematical model of satellite attitude actuator failure; S2, defining a tracking error vector and designing a satellite angular velocity command signal based on the established mathematical model; S3, designing an interference observer based on external interference, and then designing a controller and adaptive law; S4, for cases where the additive failure of the actuator is unknown, introducing a fuzzy logic system to approximate it; and designing event triggering conditions, satisfying the following condition: the weights of the fuzzy logic system are only updated when the additive failure of the actuator triggers the designed event triggering conditions. This invention can save communication resources from ground base stations to satellites and reduce the communication burden.

Description

Technical Field

[0001] This invention relates to a fault-tolerant controller for satellite attitude tracking, and more particularly to an implementation method for a fault-tolerant controller for satellite attitude tracking based on event-triggered learning. Background Technology

[0002] To enable satellites to frequently change attitudes, and given their long-term operation in the complex space environment, satellites are highly susceptible to actuator failures that can prevent them from achieving their intended missions or even lead to loss of control and damage. Therefore, fault-tolerant control for satellite attitude tracking has attracted widespread attention and yielded significant results. However, existing control technologies are time-triggered; that is, whenever an actuator failure occurs, the existing fault-tolerant control technology trains the weights of the fuzzy logic system in real time and then transmits them to the satellite, regardless of whether the actuator failure will degrade the satellite's control performance. Therefore, existing control technologies easily lead to wasted communication resources and increased communication burden. Thus, researching fault-tolerant control methods based on event-triggered learning is of great significance. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method for implementing a fault-tolerant satellite attitude tracking controller based on event-triggered learning, so as to save communication resources and reduce communication burden.

[0004] Technical solution: The implementation method of the satellite attitude tracking fault-tolerant controller based on event-triggered learning of the present invention includes the following steps:

[0005] S1, Establish a mathematical model for satellite attitude actuator failure;

[0006] S2, Define the tracking error vector based on the established mathematical model, and design the satellite angular velocity command signal;

[0007] S3, design an interference observer based on external interference, and then design a controller and adaptive law;

[0008] S4. For cases where the additive fault of the actuator is unknown, a fuzzy logic system is introduced to approximate it; and an event triggering condition is designed to satisfy the following condition: the weights of the fuzzy logic system are only updated when the additive fault of the actuator triggers the designed event triggering condition.

[0009] Furthermore, in step S1, the mathematical model for the satellite attitude actuator failure is expressed as follows:

[0010]

[0011] Where ζ = [ζ1, ζ2, ζ3] T Let ω be a quaternion representation of the satellite's attitude, where ω = [ω1, ω2, ω3]. TLet J be the satellite's angular velocity vector, and let J = diag{J1, J2, J3} be the satellite's damping matrix. Defined as the control torque for satellite attitude. Defined as an additive fault of the satellite actuator, D is defined as the external disturbance vector of the satellite; ζ × Defined as a skew-symmetric matrix of ζ, ω × Defined as an oblique symmetric matrix of ω:

[0012]

[0013] Furthermore, in step S2, the tracking error vector expression is:

[0014]

[0015] Where y d α1 is the given reference signal; α2 is the command signal for the satellite angular velocity, expressed as follows:

[0016]

[0017] Where K1>0 is the control gain matrix to be designed.

[0018] Furthermore, in step S3, the designed interference observer is as follows:

[0019]

[0020]

[0021] Where Γ is the vector of parameters to be designed, W is the ideal weight matrix of the fuzzy logic system, and P is the membership function of the fuzzy logic system. and Estimates of Q and W respectively, with estimation error vectors

[0022] The actual controller is:

[0023]

[0024] in It is the adjustment parameter matrix, where K2 > 0 is the control gain to be designed;

[0025] Let z2 = [z 2,1 ,z 2,2 ,z 2,3 ] T and The constructed adaptive law is as follows:

[0026]

[0027] in With positive adjustment parameters It's about adjusting parameters. It is a weight estimation of the fuzzy logic system after the moment of triggering.

[0028] Furthermore, the event triggering conditions designed in step S4 are as follows:

[0029]

[0030]

[0031] Where z1=[z 1,1 ,z 1,2 ,z 1,3 ] T , δ i ,∈ i and d i For the positive constants to be designed, and 0 < ν i ≤1-δ i These are the adjustment parameters to be designed.

[0032] Compared with the prior art, the significant advantages of this invention are as follows:

[0033] This invention applies a fuzzy logic system to approximate the situation where the satellite actuator failure is unknown. Considering that the existing time-triggered technology is prone to wasting communication resources and increasing the communication burden, an event triggering condition is designed so that the weights of the fuzzy logic system will only be updated when the satellite actuator failure triggers the designed event triggering condition, thus saving communication resources from the ground base station to the satellite and reducing the communication burden. Attached Figure Description

[0034] Figure 1 This is a block diagram of the closed-loop system of the present invention. Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0036] This invention proposes a method for implementing a satellite attitude tracking fault-tolerant controller based on event-triggered learning, within the framework of backstepping design technology. For unknown actuator faults, a fuzzy logic system is introduced for approximation. To fully utilize the advantages of highly intelligent components, the fuzzy logic system is trained at a ground base station. Simultaneously, due to the sudden nature of actuator faults, an event-triggered training mechanism is employed. That is, the weights of the fuzzy logic system used to approximate the unknown fault are only updated when the actuator fault triggers the designed triggering condition. Therefore, the designed controller can save communication resources and reduce the burden on satellite communication. The closed-loop system block diagram of this invention is shown below. Figure 1 As shown.

[0037] The implementation method of the satellite attitude tracking fault-tolerant controller of the present invention includes the following steps:

[0038] Step 1: Establish a mathematical model for satellite attitude actuator failure.

[0039] The mathematical model for satellite attitude actuator failure is expressed as follows:

[0040]

[0041] Where ζ = [ζ1, ζ2, ζ3] T Let ω be a quaternion representation of the satellite's attitude, where ω = [ω1, ω2, ω3]. T Let J be the satellite's angular velocity vector, and let J = diag{J1, J2, J3} be the satellite's damping matrix. Defined as the control torque for satellite attitude. Represent real numbers; Defined as an additive fault of the satellite actuator, D is defined as the external disturbance vector of the satellite, and I 3×3 Represents a 3×3 identity matrix; ζ × Defined as a skew-symmetric matrix of ζ, ω × Defined as an oblique symmetric matrix of ω:

[0042]

[0043] The control objective of this invention is to design an adaptive attitude tracking controller for a satellite experiencing actuator failures and external disturbances, satisfying the following conditions:

[0044] (a) Tracking error vector z1=ζ-y d It converges to an arbitrarily small neighborhood of zero. It is a reference signal;

[0045] (b) The signals of all closed-loop systems are bounded;

[0046] (c) Zeno’s behavior will not occur.

[0047] Step 2: Define the tracking error vector and design the satellite angular velocity command signal.

[0048] To design the satellite's attitude tracking controller, the following tracking error vector is defined:

[0049]

[0050] Where z2 is the angular velocity error, This is the command signal for the satellite's angular velocity. Combining equations (1) and (2) and differentiating with respect to z1, we obtain:

[0051]

[0052] Selecting Lyapunov functions Considering equation (3), the derivative with respect to V1 is:

[0053]

[0054] The angular velocity command signal (i.e., the virtual controller) is constructed as follows:

[0055]

[0056] Where K1>0 is the first control gain matrix to be designed. Substituting equation (5) into equation (4) yields:

[0057]

[0058] “T” represents the matrix transpose, and “-1” represents the matrix inverse.

[0059] Step 3: Design the disturbance observer, the real controller, and the adaptive law.

[0060] The derivative of z² calculated from equations (1) and (2) is:

[0061]

[0062] To approximate unknown actuator failures, the following fuzzy logic system is introduced:

[0063] ΓJ -1 Δf=W T (t)P+ε (7)

[0064] Where ε is the approximation error vector and ||ε||≤ξ with a constant ξ, W(t) is the weight matrix of the fuzzy logic system, and P is the membership function. Substituting equation (6) into equation (7) yields:

[0065]

[0066] Where Q = D + Γ -1 ε represents composite interference.

[0067] To handle composite interference Q and improve the satellite's anti-jamming capability, the following interference observer is designed:

[0068]

[0069] Where Γ is the vector of parameters to be designed. and Given estimates of Q and W respectively, we have the estimation error vector.

[0070] Then, the real controller u is designed as follows:

[0071]

[0072] in, K2 is the adjustment parameter matrix, and K2 > 0 is the second control gain matrix to be designed.

[0073] Let z2 = [z 2,1 ,z 2,2 ,z 2,3 ] T and Then, the following adaptive law is constructed:

[0074]

[0075] in, With positive adjustment parameters It's about adjusting parameters. It is the weight estimate of the fuzzy logic system after the trigger moment; i = 1, 2, 3.

[0076] Step 4: Design event triggering conditions

[0077] To address the issue of unknown additive actuator faults, a fuzzy logic system is introduced for approximation. Based on this, event triggering conditions are designed so that the weights of the fuzzy logic system are only updated when an additive actuator fault triggers the designed triggering condition. The expression for this is as follows:

[0078]

[0079]

[0080] Where tanh represents the hyperbolic tangent function, inf represents the lower bound; z1 = [z 1,1 ,z 1,2 ,z 1,3 ]T , δ i ,∈ i and d i For the positive constants to be designed, and 0 < ν i ≤1-δ i These are the adjustment parameters to be designed.

[0081] Conclusion: For a satellite attitude control system with external disturbances and actuator failures, we designed an adaptive law for parameter updates (Equation (11), an event-triggered control mechanism (Equations (12) and (13), a virtual controller (Equation (5),) and a real controller (Equation (10), and then obtained the following results:

[0082] (a) The tracking error vector z1 converges to an arbitrarily small neighborhood of zero;

[0083] (b) The signals of all closed-loop systems are bounded;

[0084] (c) Zeno’s behavior will not occur.

[0085] The proof is as follows: We choose the Lyapunov function as...

[0086]

[0087] in W respectively i Approximation errors of (t) and Q.

[0088] Condition 1: When t∈[t k t k+1 ), calculate the time derivative of V2 as

[0089]

[0090] Substituting equation (10) into equation (15) yields

[0091]

[0092] Based on the event triggering mechanism (Equations (12) and (13)), we get:

[0093]

[0094] Where λ i,1 (t)∈[-1,1],λ i,2 ∈[-1,1] is a time-varying parameter.

[0095] Based on λ i,1 (t)∈[-1,1],λ i,2∈[-1,1], Yang's inequality and equation (16)-(17) yield:

[0096]

[0097] From the properties of the hyperbolic tangent function tanh, we can obtain:

[0098]

[0099] Where, ∈>0,

[0100] Considering equations (12) and (19), equation (18) can be rewritten as follows:

[0101]

[0102] make ||P|| 2 ≤P max The constants β and P to be designed max Then, by Young's inequality, we can obtain:

[0103]

[0104]

[0105]

[0106]

[0107] Where υ>0 is the adjustment parameter to be designed.

[0108] Substituting equations (21)-(24) into equation (20), we get:

[0109]

[0110] in,

[0111] Condition 2: When t = t k Calculate the difference between V2 and V2:

[0112]

[0113] Substituting equation (11) into equation (26), we get:

[0114]

[0115] Through application Rewriting equation (27) yields:

[0116]

[0117] Then, we can obtain:

[0118]

[0119] Applying equations (21)-(22), we can obtain:

[0120]

[0121] Where, c1 = 2Λ i P max (1+σ i ), Therefore, the signals of all closed-loop systems are bounded.

[0122] Finally, it was proven that the Zeno phenomenon does not occur.

[0123] Depend on get:

[0124]

[0125] Among them, κ ζ >0 is a constant.

[0126] Due to η(t) k ) = 0 and therefore,

[0127] That is, Zeno's phenomenon will not occur.

Claims

1. A method for implementing a fault-tolerant satellite attitude tracking controller based on event-triggered learning, characterized in that, The steps include the following: S1, Establish a mathematical model for satellite attitude actuator failure; S2, Define the tracking error vector based on the established mathematical model, and design the satellite angular velocity command signal; S3, design an interference observer based on external interference, and then design a controller and adaptive law; S4. For cases where the additive fault of the actuator is unknown, a fuzzy logic system is introduced for approximation; and an event triggering condition is designed, satisfying the following condition: the weights of the fuzzy logic system are only updated when the additive fault of the actuator triggers the designed event triggering condition; the event triggering condition is: ， ， in, Represents the hyperbolic tangent function. Indicates the lower bound; tracking error vector , ; and For the positive constants to be designed, and These are the adjustment parameters to be designed; ; It is the membership function of the fuzzy logic system.

2. The implementation method of the satellite attitude tracking fault-tolerant controller based on event-triggered learning according to claim 1, characterized in that, In step S1, the mathematical model for the satellite attitude actuator failure is expressed as follows: ， Defined as A skew-symmetric matrix, Defined as Oblique symmetric matrix: ， in, The quaternion representation of the satellite attitude. Let be the satellite's angular velocity vector. Defined as the damping matrix of the satellite, Defined as the control torque for satellite attitude. Defined as an additive fault in the satellite actuator. Represent real numbers; Defined as the satellite's external disturbance vector; This represents a 3×3 identity matrix.

3. The implementation method of the satellite attitude tracking fault-tolerant controller based on event-triggered learning according to claim 2, characterized in that: In step S2, the tracking error vector expression is: ， in, For the given reference signal; The command signal for the satellite's angular velocity is expressed as follows: ， in Let be the first control gain matrix to be designed.

4. The implementation method of the satellite attitude tracking fault-tolerant controller based on event-triggered learning according to claim 3, characterized in that, In step S3, the designed interference observer is as follows: ， in It is the vector of parameters to be designed. It is the ideal weight matrix for a fuzzy logic system. It is a membership function of a fuzzy logic system. and They are respectively and The estimate has an estimation error vector. , ; The actual controller is: ， in It is an adjustment parameter matrix. It is the second control gain to be designed; make and The constructed adaptive law is as follows: ， in With positive adjustment parameters , It's about adjusting parameters. It is a weight estimation of the fuzzy logic system after the moment of triggering.

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