Finite time fault-tolerant control method and system for fractional order ship power system

Abstract

The invention relates to a finite-time fault-tolerant control method and system for a fractional-order ship power system, and the method comprises the following steps: building a nonlinear model of the fractional-order ship power system considering the fault of an actuator and multiple disturbances, and carrying out the precise description of the dynamic characteristics of the system through a fractional-order calculus theory; based on the established nonlinear model, constructing a disturbance observer with a finite time convergence characteristic to realize accurate estimation of multiple disturbances; based on a disturbance estimation result, a finite time fault-tolerant control strategy is determined to carry out finite time fault-tolerant control by combining an adaptive method and a terminal sliding mode control method, fault parameters and components are estimated on line in real time based on an adaptive law, and effective compensation for faults and disturbance is realized based on terminal sliding mode control. Compared with the prior art, the method has the advantages that rapid convergence and accurate control of the fractional-order ship power system under multiple disturbance and fault conditions are realized, and an effective solution is provided for safe operation of the ship power system under complex working conditions.

Description

Technical Field

[0001] The present invention relates to the field of fault-tolerant control of control systems, and particularly to a finite-time fault-tolerant control method and system for a fractional-order ship power system. Background Art

[0002] Actuator faults are typical problems in ship power systems, which can significantly reduce the dynamic performance of the system and threaten the operation stability. If not effectively suppressed in time, such faults may trigger a chain reaction and even lead to a ship-wide cascading power outage accident. Therefore, studying a fault-tolerant control method for ship power systems with strong robustness under complex working conditions is of great significance for ensuring the safe operation of ships.

[0003] There are still the following key problems to be solved in the existing research on fault-tolerant control of ship power systems: First, the model adaptability is insufficient: the existing methods are mainly designed for integer-order systems and are difficult to be directly applied to the more general fractional-order ship power system model; Second, the disturbance suppression ability is limited: most methods do not consider the dynamic characteristics of unmatched disturbances, resulting in a decline in the fault-tolerant performance of the system under complex disturbances; Third, the asymptotic convergence speed is slow: traditional asymptotically stable control is difficult to meet the requirements of high-dynamic working conditions, and there is a lack of a fault-tolerant control mechanism with finite-time convergence.

[0004] CN113050427A discloses a new fast terminal sliding mode fault-tolerant control method for a class of nonlinear systems, which is used for the fast terminal sliding mode fault-tolerant control of a class of nonlinear systems with actuator faults. For actuator faults with unknown fault bounds in the system, an extended state observer is designed to estimate the total uncertainty term including the fault term in the system and its derivative, without the need to know the fault bounds in advance, improving the practicability of the fault-tolerant algorithm. For the requirement of the system to be stable in finite time, a new fast terminal sliding mode surface is designed, and the convergence speed is faster than that of the linear sliding mode surface throughout the process, thereby realizing the convergence of the sliding mode surface in finite time. For the chattering problem of the traditional sliding mode control law, the switching term is put into the first derivative of the control law, thus greatly reducing the chattering of the control law. However, this method is based on an integer-order dynamics framework and does not consider the additional dynamic characteristics introduced by fractional-order operators, and is not applicable to fractional-order systems. Moreover, this method is only designed for the case of matched disturbances and does not involve the suppression and compensation of unmatched disturbances, and cannot effectively cope with the fault-tolerant control performance under a wider range of disturbance conditions. Summary of the Invention

[0005] The purpose of the present invention is to provide a finite-time fault-tolerant control method and system for a fractional-order ship power system, to solve the problem of fast and stable control under the coupling of actuator faults and multiple disturbances, and to ensure the reliable operation and dynamic recovery ability of the system under fault conditions.

[0006] The object of the present invention can be achieved by the following technical solutions:

[0007] A finite-time fault-tolerant control method for a fractional-order ship power system, comprising the following steps:

[0008] Step 1) Establish a non-linear model of the fractional-order ship power system considering actuator faults and multiple disturbances, and accurately describe the system dynamic characteristics through fractional calculus theory;

[0009] Step 2) Based on the established non-linear model, construct a disturbance observer with finite-time convergence characteristics to achieve accurate estimation of multiple disturbances;

[0010] Step 3) Based on the disturbance estimation results, combine the adaptive method and the terminal sliding mode control method to determine the finite-time fault-tolerant control strategy for finite-time fault-tolerant control, online and real-time estimate the fault parameters and components based on the adaptive law, and effectively compensate for faults and disturbances based on the terminal sliding mode control.

[0011] The non-linear model of the fractional-order ship power system is expressed as:

[0012] D q x = v + w m ,

[0013] D q v = ρu + β + f(x, v) + w d ,

[0014]

[0015] where D q is the system fractional order, 0 < q < 1, x and v are the rotor angle and angular velocity respectively, H is the moment of inertia, D is the damping coefficient, P max sin(x) is the actual power, P m is the equivalent generator mechanical power, P e [[ID=4�]]and are the amplitudes and frequencies of the power disturbances, w m is the non-matching disturbance, w d is the matching disturbance, ρu + β is the actuator fault, 0 < ρ < 1 is the fault gain, and β is the fault component.

[0016] For the rotor angle order system of the fractional-order ship power system, i.e., D q x = v + w m , design the first disturbance observer as:

[0017]

[0018]

[0019] Among them, and are the estimated values of the rotor angle x and the unmatched disturbance w m , g > 0 is the observer gain, and the nonlinear term If If

[0020] Regarding the fractional-order ship power system rotor angular velocity order system, that is, D q v = ρu + β + f(x, v) + w d , design the second disturbance observer as:

[0021]

[0022] Among them, and are the estimated values of the rotor angle v and the matched disturbance w d , is the observer gain, and the nonlinear term If If

[0023] In the said step 2), regarding the fractional-order ship power system rotor angle order system, based on the first disturbance observer, define the estimation error and Based on the fractional-order Lyapunov stability theory, construct the Lyapunov function V related to the estimation errors and , and quantitatively analyze the maximum adjustment time required for the estimation errors and to converge to zero.

[0024] In the said step 2), regarding the fractional-order ship power system rotor angular velocity order system, based on the second disturbance observer, define the estimation error and Based on the fractional-order Lyapunov stability theory, construct the Lyapunov function and related to the estimation errors Quantitatively analyze the maximum adjustment time required for the estimation error to converge to zero.

[0025] The said step 3) includes the following steps:

[0026] Step 3-1) Based on the finite-time disturbance estimation result, define the terminal sliding mode function as:

[0027]

[0028] where \(s\) is the terminal sliding mode function, the parameter \(\alpha>1\), and the non-linear term If If

[0029] Step 3-2) Based on the finite-time disturbance estimation result and the terminal sliding mode function, define the benchmark controller \(\tau\) for the case without actuator faults as:

[0030]

[0031] where the gain \(k > 0\), and the parameter \(0<\eta<1\);

[0032] Step 3-3) Based on the finite-time disturbance estimation result, the benchmark controller, and the terminal sliding mode function, determine the gain adaptation law as:

[0033]

[0034] where is the adaptation parameter, the parameter \(\kappa_1>0\), and the parameter \(\kappa_2>0\);

[0035] Step 3-4) Based on the gain adaptation law, determine the finite-time fault-tolerant control strategy \(u\) as:

[0036]

[0037] where if If \(s = 0\), \(sign(s)=0\);

[0038] Step 3-5) Perform fractional-order ship power system control based on the finite-time fault-tolerant control strategy \(u\).

[0039] The method further includes:

[0040] Step 4) Based on the fractional-order Lyapunov stability theory, conduct a rigorous closed-loop system stability analysis for the fractional-order ship power system.

[0041] Step 4) includes the following steps:

[0042] Step 4-1) For the gain adaptation law, define the error related to the adaptation parameter as and where \(\mu>0\) and \(h>0\) are the true values of the adaptation parameters;

[0043] Step 4-2) Considering the case where the terminal sliding mode function \(s\neq0\), based on the fractional-order Lyapunov stability theory, construct the Lyapunov function related to the terminal sliding mode function \(s\) and the adaptation parameter error related Quantitatively analyze the maximum adjustment time required for the terminal sliding mode function s to converge to zero;

[0044] Step 4-3) Consider the case where the terminal sliding mode function s = 0. Based on the fractional-order Lyapunov stability theory, construct a Lyapunov function related to the rotor angle x Quantitatively analyze the maximum adjustment time required for the rotor angle to converge to zero.

[0045] A finite-time fault-tolerant control system for a fractional-order ship power system, including a memory and a processor. A computer program is stored on the memory, and when the processor executes the program, the above method is implemented.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) The present invention breaks through the limitations of traditional integer-order system control methods and extends the research object to a more general fractional-order ship power system. Since the fractional-order model can more accurately describe the dynamic characteristics of the actual system, the theoretical framework of the present invention is not only applicable to fractional-order systems, but also covers integer-order ship power systems as special cases, thus having a wider range of applicability.

[0048] (2) The present invention proposes a finite-time disturbance observer applicable to fractional-order ship power systems, which can accurately estimate multiple disturbances (matched and unmatched disturbances) of fractional-order systems within a finite time and gives an explicit expression of the required disturbance estimation time. Compared with existing linear and nonlinear disturbance observers, the finite-time disturbance observer in the present invention has higher estimation accuracy and faster observation speed.

[0049] (3) The present invention combines terminal sliding mode control and adaptive control methods to propose a finite-time fault-tolerant control strategy, which can effectively cope with multiple disturbances and actuator faults in fractional-order ship power systems, ensure the system state converges quickly within a finite time, and achieve high-precision control performance, providing a practical solution for the safe and stable operation of ship power systems under complex working conditions. Description of the Drawings

[0050] Figure 1 is the flowchart of the method of the present invention;

[0051] Figure 2 is the finite-time disturbance estimation result diagram of a fractional-order ship power system in an embodiment;

[0052] Figure 3 is the finite-time fault-tolerant control result diagram of a fractional-order ship power system in an embodiment. Detailed Embodiments

[0053] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0054] This embodiment provides a finite-time fault-tolerant control method for a fractional-order ship power system, which mainly includes four specific steps: fractional-order system modeling and analysis, finite-time disturbance estimation, adaptive fault-tolerant control design, and closed-loop system stability verification, as Figure 1 shown, including the following steps:

[0055] Step 1) Establish a non-linear model of the fractional-order ship power system considering actuator faults and multiple disturbances, and accurately describe the dynamic characteristics of the system through the theory of fractional calculus.

[0056] Establish the dynamic model of the fractional-order ship power system:

[0057] D q x = v,

[0058]

[0059] where D q is the system fractional order, 0 < q < 1, x and v are the rotor angle and angular velocity respectively, τ is the load input, H is the moment of inertia, D is the damping coefficient, P max sin(x) is the actual power, P m is the equivalent generator mechanical power, P e and are the amplitude and frequency of the power disturbance.

[0060] In this embodiment, the parameters of the fractional-order ship power system are set as and Then the system dynamics are:

[0061] D 0.98 x = v,

[0062]

[0063] Considering the unmatched disturbance and actuator fault, the non-linear model of the fractional-order ship power system is expressed as:

[0064] D q x = v + w m ,

[0065] D q v = ρu + β + f(x, v) + w d ,

[0066] where wm is the non - matching perturbation, w d is the matching perturbation, ρu + β is the actuator fault, 0 < ρ < 1 is the fault gain, and β is the fault component.

[0067] In this embodiment, the fractional - order ship power system parameters are set as q = 0.98, the fault parameters are selected as ρ = 0.5, β = 0.1sin(0.5t), and the non - matching perturbation is selected as w m = 2. Then, the dynamics of the fractional - order ship power system considering non - matching perturbation and actuator fault are:

[0068] D 0.98 x = v + 2,

[0069]

[0070] Step 2) Based on the established non - linear model, construct a disturbance observer with finite - time convergence characteristics to achieve accurate estimation of multiple disturbances.

[0071] Step 2) includes the following steps:

[0072] Step 2 - 1) For the rotor - angle order system of the fractional - order ship power system, that is, D q x = v + w m , design the first disturbance observer as:

[0073]

[0074]

[0075] where, and are the estimated values of the rotor angle x and the non - matching perturbation w m , g > 0 is the observer gain, and the non - linear term If If

[0076] In this embodiment, the observer gain is selected as g = 8, then the first disturbance observer for non - matching perturbation is:

[0077] [[ID=�7]]

[0078]

[0079] Step 2 - 2) For the rotor - angular - velocity order system of the fractional - order ship power system, that is, D q v = ρu + β + f(x, v)+w d , design the second disturbance observer as:

[0080]

[0081] Among them, and are the estimated values of the rotor angle v and the matching disturbance w d , is the observer gain, and the non-linear term If If

[0082] In this embodiment, the observer gain is selected as g = 8, and the second disturbance observer for the unmatched disturbance is:

[0083]

[0084] Step 2-3) For the rotor angle order system of the fractional-order ship power system, based on the first disturbance observer, the estimation errors and are defined. Based on the fractional-order Lyapunov stability theory, a Lyapunov function V related to the estimation errors and is constructed, and the maximum adjustment time required for the estimation errors and to converge to zero is quantitatively analyzed.

[0085] The Lyapunov function V is:

[0086]

[0087] Calculate its q-th derivative, which satisfies the following inequality:

[0088]

[0089] Among them, ρ m is the boundary of the q-th derivative of the unmatched disturbance w m , λ m (Q) is the minimum eigenvalue of the matrix Q, and λ M (P) is the maximum eigenvalue of the matrix P. Substituting the observer gain g = 8, we can get λ M (P) = 10.14, λ m (Q) = 0.13, and the above inequality can be further simplified to

[0090]

[0091] From this inequality, it can be quantitatively analyzed that the adjustment time T1 required for the estimation errors and to converge to zero satisfies:

[0092]

[0093] Where V(0) is the initial condition of V, Γ(1+q), Γ(1 / 2), and Γ(1 / 2+q) are gamma functions (gamma function, second-kind Euler integral).

[0094] In this embodiment, Γ(1.98), Γ(0.5), and Γ(1.48) are gamma functions (gamma function, second-kind Euler integral).

[0095] Select Case 1(w m =2, )、Case 2(w m =2t, )、Case 3(w m =0.001sin(v)+0.5, )、Case 4(w m =cos(0.001v+t), ), in 4 cases, such as Figure 2 As shown in (2a), the estimated error and Converges to zero (considering the calculation deviation, below the threshold of 5×10 -3 The adjustment time required to reach 0) is less than 3.0 seconds.

[0096] Step 2-4) For the fractional-order ship power system rotor angular velocity order system, based on the second disturbance observer, define the estimation error and Based on fractional-order Lyapunov stability theory, construction and estimation error and Related Lyapunov functions Quantitatively analyze the maximum adjustment time required for the estimation error to converge to zero.

[0097] Lyapunov function for:

[0098]

[0099] Similar to steps 2-3), analyze The q-order differential of satisfies the following inequality:

[0100]

[0101] Quantitative analysis of estimation errors and The adjustment time T2 required to converge to zero satisfies:

[0102]

[0103] Among them, is the initial condition, and Γ(1 + q), Γ(1 / 2), and Γ(1 / 2 + q) are gamma functions (Gamma function, the second kind of Euler integral).

[0104] In this embodiment, Γ(1.98), Γ(0.5), and Γ(1.48) are gamma functions (Gamma function, the second kind of Euler integral).

[0105] As Figure 2 shown in (2b) of and converge to zero (considering the calculation deviation, lower than the threshold of 5×10 -3 is regarded as reaching 0), and the required adjustment time is less than 3.0 seconds for both.

[0106] Based on steps 2-1) to 2-4), the accurate estimation and verification of multiple disturbances in finite time are realized, and combined with Figure 2 as shown in the observation results, in this embodiment, the estimation error can converge to zero within the finite time of 3.00 seconds, verifying the effectiveness of the finite-time disturbance observer.

[0107] Step 3) Based on the disturbance estimation results, combining the adaptive method and the terminal sliding mode control method, determine the finite-time fault-tolerant control strategy for finite-time fault-tolerant control, estimate the fault parameters and components online in real time based on the adaptive law, and realize the effective compensation for faults and disturbances based on the terminal sliding mode control.

[0108] Step 3) includes the following steps:

[0109] Step 3-1) Based on the finite-time disturbance estimation results, define the terminal sliding mode function as:

[0110]

[0111] where s is the terminal sliding mode function, the parameter α > 1, and the non-linear term If If

[0112] In this embodiment, α = 1.4 is selected, then the terminal sliding mode function is:

[0113]

[0114] Step 3-2) Based on the finite-time disturbance estimation results and the terminal sliding mode function, define the reference controller τ for the case without actuator faults as:

[0115]

[0116] Among them, the gain \(k>0\), and the parameter \(0 < \eta < 1\).

[0117] In this embodiment, \(f(x, v)=-[0.02v + \sin(x)]\), \(\alpha = 1.4\), \(k = 0.25\), \(\eta = 0.6\) are selected, then the reference controller \(\tau\) is:

[0118]

[0119] Step 3-3): Based on the finite-time disturbance estimation result, the reference controller, and the terminal sliding mode function, determine the gain adaptation law as:

[0120]

[0121] Among them, is the adaptive parameter, the parameter \(\kappa_1>0\), the parameter \(\kappa_2>0\).

[0122] In this embodiment, select the parameters in the adaptation law as Then the adaptation law is:

[0123]

[0124] Step 3-4): Based on the gain adaptation law, determine the finite-time fault-tolerant control strategy \(u\) as:

[0125]

[0126] Among them, if \(s\neq0\), if \(s = 0\), \(\text{sign}(s)=0\).

[0127] Step 3-5): Based on the finite-time fault-tolerant control strategy \(u\), perform fractional-order ship power system control.

[0128] Based on steps 3-1) to 3-5), the design of the finite-time fault-tolerant control strategy is realized, so as to perform ship power system control.

[0129] Step 4): Based on the fractional-order Lyapunov stability theory, conduct a strict closed-loop system stability analysis on the fractional-order ship power system.

[0130] Step 4) includes the following steps:

[0131] Step 4-1): For the gain adaptation law, define the error related to the adaptive parameter as and Among them, \(\mu>0\) and \(h>0\) are the true values of the adaptive parameters.

[0132] Step 4-2) Considering the case where the terminal sliding mode function \(s\neq0\), based on the fractional-order Lyapunov stability theory, construct a Lyapunov function related to the terminal sliding mode function \(s\) and the adaptive parameter error Quantitatively analyze the maximum adjustment time required for the terminal sliding mode function \(s\) to converge to zero. The Lyapunov function

[0133] is:<0> For:

[0134]

[0135] By solving the \(q\)-order differential of, the following inequality is satisfied:

[0136]

[0137] where \(\kappa\) s \(>0\) is the gain. Solving the above inequality, the adjustment time \(T_3\) required for the terminal sliding mode function \(s\) to converge to zero satisfies:

[0138]

[0139] where and are the initial conditions of, \(\Gamma(1 + q)\), \(\Gamma(1 - c_2)\), and \(\Gamma(1 + q - c_2)\) are gamma functions (Gamma function, the second kind of Euler integral).

[0140] In this embodiment, \(q = 0.98\), \(\alpha = 1.4\), \(k = 0.25\), \(\kappa\) s \(>0\) is the gain. Then \(T_3\) satisfies:

[0141]

[0142] Step 4-3) Considering the case where the terminal sliding mode function \(s = 0\), based on the fractional-order Lyapunov stability theory, construct a Lyapunov function related to the rotor angle \(x\) Quantitatively analyze the maximum adjustment time required for the rotor angle to converge to zero.

[0143] The Lyapunov function is:

[0144]

[0145] By solving the \(q\)-order differential of, the following equation is satisfied:

[0146]

[0147] In this embodiment, q = 0.98 and α = 1.4 are selected, and the above equation is:

[0148]

[0149] Solving the above equation, the adjustment time T4 required for the rotor angle x of the fractional-order ship power system to converge to zero satisfies:

[0150]

[0151] where is the initial condition of, Γ(1 + q), and are gamma functions (Gamma function, the second kind of Euler integral).

[0152] In this embodiment, Γ(1.98), Γ(0.1429), and Γ(0.9857) are gamma functions (Gamma function, the second kind of Euler integral).

[0153] Based on steps 4-1) to 4-3), the finite-time stability analysis of the relevant closed-loop system of the fractional-order ship power system is realized. The fault-tolerant control strategy under finite time is tested. As [[ID=?]] Figure 3 shown, SMC represents the sliding mode control method, BC represents the benchmark controller, and FC represents the finite-time fault-tolerant control method proposed in the present invention. It can be found that the rotor angle x of the method adopted in the present invention will converge to zero within a finite time of 4.8 seconds, overcoming the influence of actuator faults and multiple disturbances.

[0154] This embodiment proposes a finite-time fault-tolerant control method for a fractional-order ship power system, establishes a nonlinear model of the fractional-order ship power system considering actuator faults and multiple disturbances, constructs a disturbance observer with finite-time convergence characteristics to achieve accurate estimation of the system composite disturbance, combines the adaptive method with the terminal sliding mode control method to propose an adaptive fault-tolerant control strategy, and conducts a strict stability analysis of the designed fault-tolerant control system based on the fractional-order Lyapunov stability theory to prove that the system state can converge to the desired trajectory within a finite time.

[0155] This embodiment also provides a finite-time fault-tolerant control system for a fractional-order ship power system, including a memory and a processor. A computer program is stored on the memory, and when the processor executes the program, the above method is implemented.

[0156] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A finite-time fault-tolerant control method for a fractional-order ship power system, characterized in that, It includes the following steps: Step 1) Establish a fractional-order nonlinear model of the ship power system considering actuator faults and multiple disturbances, and accurately describe the system dynamic characteristics through fractional calculus theory; Step 2) Based on the established nonlinear model, construct a disturbance observer with finite-time convergence characteristics to achieve accurate estimation of multiple disturbances; Step 3) Based on the disturbance estimation results, combine the adaptive method and the terminal sliding mode control method to determine a finite-time fault-tolerant control strategy for finite-time fault-tolerant control. Online real-time estimate the fault parameters and components based on the adaptive law, and achieve effective compensation for faults and disturbances based on terminal sliding mode control.

2. The finite-time fault-tolerant control method for a fractional-order ship power system according to claim 1, wherein The fractional-order nonlinear model of the ship power system is expressed as: D q x = v + w m , D q v = ρu + β + f(x, v) + w d , where D q is the system fractional order, 0 < q < 1, x and v are the rotor angle and angular velocity respectively, H is the moment of inertia, D is the damping coefficient, P max sin(x) is the actual power, P m is the equivalent generator mechanical power, P e and are the amplitude and frequency of the power perturbation, w m is the non-matching perturbation, w d is the matching perturbation, ρu + β is the actuator fault, 0 < ρ < 1 is the fault gain, and β is the fault component.

3. A finite-time fault-tolerant control method for a fractional-order ship power system according to claim 2, characterized in that, For the rotor angle order system of the fractional-order ship power system, that is, D q x = v + w m , design the first disturbance observer as: Among them, and are the estimated values of the rotor angle x and the unmatched disturbance w m , g > 0 is the observer gain, and the non-linear term If If 4. A finite-time fault-tolerant control method for a fractional-order ship power system according to claim 3, characterized in that, The rotor angular velocity order system for the fractional-order ship power system, i.e., D q v = ρu + β + f(x, v) + w d , design the second disturbance observer as: wherein, and are the estimated values of the rotor angle v and the matching disturbance w d , is the observer gain, and the non-linear term if if 5. The finite-time fault-tolerant control method for a fractional-order ship power system according to claim 3, characterized in that, In step 2), for the rotor angle order system of the fractional-order ship power system, based on the first disturbance observer, the estimation errors are defined and Based on the fractional-order Lyapunov stability theory, a Lyapunov function V related to the estimation errors and is constructed, and the maximum adjustment time required for the estimation errors and to converge to zero is quantitatively analyzed.

6. The finite-time fault-tolerant control method for a fractional-order ship power system according to claim 4, characterized in that In the step 2), for the fractional-order ship power system rotor angular velocity order system, based on the second disturbance observer, the estimation errors are defined and Based on the fractional-order Lyapunov stability theory, a Lyapunov function related to the estimation errors and is constructed The maximum adjustment time required for the estimation error to converge to zero is quantitatively analyzed.

7. A finite-time fault-tolerant control method for a fractional-order ship power system according to claim 4, characterized in that Step 3) includes the following steps: Step 3-1) Based on the finite-time disturbance estimation results, define the terminal sliding mode function as: where s is the terminal sliding mode function, the parameter α > 1, and the non-linear term If If Step 3-2) Based on the finite-time disturbance estimation results and the terminal sliding mode function, define the reference controller τ for the case without actuator faults as: where the gain k > 0 and the parameter 0 < η < 1; Step 3-3) Based on the finite-time disturbance estimation results, the reference controller, and the terminal sliding mode function, determine the gain adaptive law as: Among them, is an adaptive parameter, where parameter κ1 > 0 and parameter κ2 > 0; Step 3-4) Based on the gain adaptive law, determine the finite-time fault-tolerant control strategy u as: Wherein, if s≠0, if s = 0, sign(s) = 0; Step 3-5) Perform control of the fractional-order ship power system based on the finite-time fault-tolerant control strategy u.

8. A finite-time fault-tolerant control method for a fractional-order ship power system according to claim 7, characterized in that The method further includes: Step 4) Based on the fractional-order Lyapunov stability theory, conduct a rigorous closed-loop system stability analysis of the fractional-order ship power system.

9. The finite-time fault-tolerant control method for a fractional-order ship power system according to claim 8, characterized in that, Step 4) includes the following steps: Step 4-1): For the gain adaptation law, define the error related to the adaptation parameter as and where μ > 0 and h > 0 are the true values of the adaptation parameters; Step 4-2) Considering the case where the terminal sliding mode function \(s\neq0\), based on the fractional-order Lyapunov stability theory, construct a Lyapunov function related to the terminal sliding mode function \(s\) and the adaptive parameter error associated with Quantitatively analyze the maximum adjustment time required for the terminal sliding mode function \(s\) to converge to zero; Step 4-3) Consider the case where the terminal sliding mode function s = 0. Based on the fractional-order Lyapunov stability theory, construct a Lyapunov function related to the rotor angle x Quantitatively analyze the maximum adjustment time required for the rotor angle to converge to zero.

10. A finite-time fault-tolerant control system for a fractional-order ship power system, comprising a memory and a processor, wherein a computer program is stored on the memory, and is characterized in that, When the processor executes the program, it implements the method described in any one of claims 1 to 9.

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