A design method of adaptive fault-tolerant controller based on global sliding mode

Abstract

The present invention discloses a method for designing an adaptive fault-tolerant controller based on a global sliding mode, belonging to the field of control technology. The present invention takes into account the situations where the generator side is subject to disturbances and the load side controller fails. To reduce the system's maximum deviation and steady-state error under disturbances and compensate for the output amplitude loss caused by controller failures, an adaptive fault-tolerant controller based on a global sliding mode is designed. Simulation results show that the controller of the present invention can eliminate the system's chaotic state. When the system suffers from transmission failures, step disturbances, and controller failures, the system can effectively converge to the target orbit under the action of the adaptive global sliding mode fault-tolerant controller. The system's maximum offset and steady-state error are both small.

Description

Technical Field

[0001] The invention belongs to the field of control technology, and in particular relates to a design method of an adaptive fault-tolerant controller based on a global sliding mode. Background Art

[0002] When a power system experiences external disturbances or its parameters change within a specific range, the system power angle may experience disordered oscillations within a certain range, effectively entering a chaotic state. In recent years, the widespread integration of renewable energy into the power system has alleviated the energy and environmental challenges associated with traditional power generation models. However, the uncertainty of renewable energy power generation can be viewed as a parameter change or external disturbance in the traditional system, potentially causing the system to oscillate. Without timely and effective control, the system may ultimately enter a chaotic state.

[0003] For low-order models, a number of literatures have studied the analysis and control of their chaotic characteristics, and various control strategies have been proposed. For high-order models, the highest-order model currently generally recognized by the academic community is the seventh-order system model, but related research is still relatively limited. For the control of seventh-order systems, domestic and foreign scholars have extended nonlinear theory to seventh-order systems, eliminating the system's chaotic state to varying degrees. Although the controllers designed in the current relevant literature can make the controlled object converge to the target orbit, their controller design is relatively dependent on the precise model of the system, and most of them do not consider the system's situation when it is disturbed or fails, resulting in relatively poor practicality. If the system is subjected to a large disturbance that causes the system model to change, or a controller failure causes the controller output signal amplitude to decrease, the above-mentioned controller may not have sufficient fault tolerance, causing the system state to deviate from the target orbit. Summary of the Invention

[0004] In view of the above technical problems existing in the prior art, the present invention proposes a design method of an adaptive fault-tolerant controller based on a global sliding mode, which has a reasonable design, overcomes the shortcomings of the prior art, and has good effects.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A design method for an adaptive fault-tolerant controller based on a global sliding mode includes the following steps:

[0007] Step 1: To address the generator-side disturbance problem, a combination of fixed gain and adaptive gain is adopted in the controller. The output expression of the generator-side controller based on the adaptive fault-tolerant control of the global sliding mode observer is shown in formula (16):

[0008]

[0009] Where Ka0 With K a1 are fixed gain and adaptive gain respectively, and the adaptive gain expression is designed as shown in formula (17):

[0010]

[0011] Where K a2 With K a3 are all constants and satisfy K a2 >K a3 >0; μ is a constant greater than 0; ε is a positive number;

[0012] Step 2: To avoid controller u f The output is too large, so the adaptive gain K a1 The limiting step is shown in formula (18):

[0013] K min <K a1 <K max (18);

[0014] Step 3: Adaptively estimate the fault degree of the load side controller to compensate for the impact of the controller failure on the system; Let be the estimated value of λ, First, select the following candidate Lyapunov function V2:

[0015]

[0016] Taking the derivative of V2, we get

[0017]

[0018] Among them, when the load side controller fails, the mathematical model of the controller failure is shown as follows:

[0019]

[0020] Where u in is the control signal received by the system, u h is the ideal output signal of the controller, λ is the degree of output amplitude loss caused by controller failure, 1≥λ≥0, the smaller λ is, the higher the degree of controller output amplitude loss is; λ=1 means that the load side controller has no fault, λ=0 means that the load side controller has a complete fault;

[0021] will u in After substitution, we get

[0022]

[0023] To make but Should be

[0024]

[0025] Step 4: To improve the dynamic characteristics of the load-side controller and enhance the controller tracking accuracy, the expression of the adaptive fault estimation is transformed. The transformation result is shown in formula (23):

[0026]

[0027] Where K b2 , K b3 , K b4 and η1, η2 are all constants, and satisfy K b2 >K b3 >K b4 ,η1>η2>0;

[0028] Step 5: To avoid controller u n Output is too large, deal with adaptive fault estimation The limiting step is shown in formula (24):

[0029]

[0030] Combining Equation (13) and Equation (23)-(24), the load-side fault-tolerant controller u based on the global sliding mode observer is n The output is shown in formula (25):

[0031]

[0032] Step 6: Reselect the Lyapunov function V3, whose expression is shown in formula (26):

[0033]

[0034] When the system state variables gradually approach the predetermined trajectory, that is, when |s1| < μ, V3 is derived, and the result is shown in formula (27):

[0035]

[0036] After simplifying the above formula, we get

[0037]

[0038] Further simplifying

[0039]

[0040] The above formula is finally transformed into

[0041]

[0042] Step 7: When the system state variable gradually moves away from the predetermined track, that is, when |s1| ≥ μ, the derivative of V3 is calculated, and the derivative result is

[0043]

[0044] From (1)-(31), we know that the expression of the generator side controller for adaptive fault-tolerant control based on the global sliding mode observer is as follows:

[0045]

[0046] The beneficial technical effects brought about by the present invention are:

[0047] The present invention takes into account the situations where the generator side is subjected to disturbances and the load side controller fails. In order to reduce the maximum deviation and steady-state error of the system under disturbances and compensate for the output amplitude loss caused by controller failures, an adaptive fault-tolerant controller based on global sliding mode is designed. Simulation results show that the controller of the present invention can eliminate the chaotic state of the system. When the system suffers from transmission failures, step disturbances and controller failures respectively, the system can effectively converge to the target orbit under the action of the fault-tolerant controller based on adaptive global sliding mode. The maximum offset and steady-state error of the system are both small. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is the block diagram of the adaptive fault-tolerant control system based on the global sliding mode observer;

[0049] Figure 2 It is the time domain diagram of the system state after FTC is put into use; Figure 2 (a) is the time domain diagram of the generator side power angle after FTC is put into operation; Figure 2 (b) is the time domain diagram of the load side power angle after FTC is put into operation; Figure 2 (c) Time domain diagram of each state variable of the system after FTC is put into use; Figure 2 (d) Time domain diagram of observed and observed quantities after FTC input;

[0050] Figure 3 It is the time domain diagram of the system state after each controller is put into operation under transmission failure; Figure 3 (a) is the time domain diagram of the system state variables after DSMC is put into use; Figure 3 (b) is the time domain diagram of each state variable of the system after AFTC is put into use; Figure 3 (c) Time domain diagram of generator side power angle; Figure 3 (d) is the time domain diagram of the load side power angle;

[0051] Figure 4is the time domain diagram of the system state after each controller is put into operation under the action of step disturbance; Figure 4 (a) is the time domain diagram of the generator power angle side; Figure 4 (b) is the time domain diagram of the system state variables after DSMC is put into use; Figure 4 (c) is the time domain diagram of each state variable of the system after AFTC is put into use;

[0052] Figure 5 It is the time domain diagram of the system state after each controller is put into operation under controller failure; Figure 5 (a) is the time domain diagram of the system state variables under the action of DSMC; Figure 5 (b) is the time domain diagram of the system state variables under the action of ATFC; Figure 5 (c) is the time domain diagram of the load side power angle under controller failure; Figure 5 (d) is the time domain diagram of the DSMC controller output; Figure 5 (e) is the time domain diagram of the FTC controller output; Figure 5 (f) in the figure is the time domain diagram of the AFTC controller output. DETAILED DESCRIPTION

[0053] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0054] This application establishes a mathematical model of a seventh-order power system that takes into account external disturbances and controller failures, and designs an adaptive fault-tolerant control strategy (AFTC) based on a global sliding mode for this model. The controller does not require an accurate mathematical model of the system, but only requires information about the system's state variables, which reduces the difficulty of tuning the controller parameters and improves the versatility of the controller. In response to the problems of the seventh-order system's generator side being susceptible to interference and the load-side controller being prone to failure, a control strategy combining fixed gain and adaptive gain is adopted in the generator-side controller, and adaptive fault estimation is used in the load-side controller to compensate for the controller output loss caused by controller failure. Simulation results show that when the system is in the absence of disturbances, external step disturbances, transmission faults, and controller failures, the designed controller can make the system converge to near the predetermined target orbit.

[0055] Power System Controller Design

[0056] 1. Power system model considering faults and external disturbances

[0057] Signal transmission components are crucial in power systems. However, these components are generally highly sensitive and susceptible to interference, which can reduce their accuracy and lead to oscillations in the power system. This application considers the case of a transmission failure between the controlled system and the designed observer. The mathematical model of the controlled object considering the transmission failure is shown below.

[0058]

[0059] Where x is the state variable; f(x) is the nonlinear function containing the state variable; u is the control quantity output by the controller; ξ is the degree of transmission amplitude loss, 1 ≥ ξ ≥ 0, the smaller ξ, the greater the transmission amplitude loss, when ξ = 1, there is no transmission failure; σ(tT) is expressed as

[0060]

[0061] Where T is the time when the fault occurs, and formula (3) indicates that the sensor fails at time T.

[0062] In the model shown in formula (1), the stability of the power supply end is crucial to the stability of the power system. Its primary control goal is to stabilize the generator power angle to prevent the entire system from entering an oscillation state. Secondly, to ensure the stability of the load voltage phase angle, the primary control goal of the load end is to stabilize the load bus voltage phase angle. Therefore, δ m and δ L is the control target. Combining formula (2), the power system model considering transmission failure can be obtained as

[0063]

[0064] The generator is the core equipment in the power system. To ensure the stable operation of the generator, the influence of external disturbance dis should be considered in the generator model. t With n t As shown in formula (5).

[0065]

[0066] In addition to the frequent disturbances experienced by the generator side, the load-side controller's complex operating environment significantly increases its failure rate. Furthermore, its remote location from the operation center hinders timely repairs when a controller failure occurs. This can cause the load voltage and phase angle to deviate from their preset values, resulting in a degradation of the load voltage quality. Therefore, the load-side controller needs to have a certain degree of fault tolerance to cope with potential failures.

[0067] When the load end controller fails, the mathematical model of the controller failure is shown in formula (6):

[0068] u in=λu h (6)

[0069] Where u in is the control signal received by the system, u h is the ideal output signal of the controller, and λ is the degree of output amplitude loss caused by controller failure. 1 ≥ λ ≥ 0. The smaller λ is, the higher the degree of controller output amplitude loss is. λ = 1 indicates that the load-side controller has no faults, and λ = 0 indicates that the load-side controller has completely failed.

[0070] 2. Design of fault-tolerant controller based on global sliding mode

[0071] In the design of traditional nonlinear sliding mode controller, the controller output is required to contain the nonlinear term of the system, so the accurate mathematical expression of the system and the values ​​of each parameter must be known, which brings great limitations to the design of the controller. The nonlinear extended observer has the advantages of requiring less system information, not relying on the system model and having high observation accuracy.

[24] The system model is observed and the observed system items are input into the controller, which solves the problem of not being able to obtain changes in system items in a timely manner due to faults and disturbances.

[0072] First, an observer is designed to observe the operating characteristics of the synchronous generator rotor. Since there is a second-order derivative relationship between the generator side power angle and the system term, a third-order expanded observer is designed as shown in Equation (7).

[0073]

[0074] Where, β f1 , β f2 , β f3 , β f4 , β f5 are all constants greater than 0. The convergence characteristics of the observer are given by β f1 , β f2 and β f3 The value of β is determined by the characteristics of the observed object. f1 >β f2 >β f3 The final steady-state error of the observer is given by β f4 , β f5 The value of is determined, generally β f4 =2β f5 In order to reduce the chattering phenomenon of the control system, the switching function sgn used in the traditional observer is replaced by a relay function θ with smooth characteristics.

[0075] Secondly, an observer is designed for the load-side bus. Since there is a first-order derivative relationship between the load-side power angle and the expression of the load-side system term, a second-order expanded observer is designed as shown in formula (8).

[0076]

[0077] Where, β n1 , β n2 , β n3 are all constants greater than 0. The convergence characteristics of the observer are determined by the characteristics of the observed object β n1 and β n2 The value of is determined, generally β n1 >β n2 The final steady-state error of the observer is given by β n3 The value of is determined, generally β n3 <1.

[0078] Let e zf =f t -z f3 , e zn =n t -z n2 , under the action of observer (7) and observer (8), z f3 With z n2 will approximate f with a certain accuracy t With n t , whose observation error satisfies e zf ≤d f , e zn ≤d n , d f with d n are two positive constants.

[0079] Generator power angle δ m The control target is r f , load bus phase angle δ L The control target is r n , then the control error e f and e n for

[0080]

[0081] The sliding surface of global sliding mode control is taken as

[0082]

[0083] In the formula, c1, c2, c3>0. As their values ​​increase, the output range of the controller becomes larger. However, too large a value will cause the controller output to fluctuate greatly, leading to greater system chattering. p and q are positive odd numbers. The values ​​of p and q should satisfy q <p<2q。

[0084] To design the required controller, take V1 as

[0085]

[0086] Taking the derivative of V1, we get

[0087]

[0088] According to the above formula, the fault-tolerant control (FTC) expression based on the global sliding mode expansion observer should be as follows

[0089]

[0090] Where K a0 , K b0 , K b1 Both γ and γ are constants greater than 0. Their values ​​primarily affect the system's ability to resist disturbances. Larger values ​​increase the controller's output range, but also increase the system's overshoot during control. To balance the dynamic characteristics of the convergence process and increase steady-state convergence accuracy, the values ​​of these parameters should not be too large.

[0091] Substituting formula (13) into formula (12) yields

[0092]

[0093] Because K b0 >0, γ>0, c3>0, and q+p is an even number, the above formula can be transformed into

[0094]

[0095] If K a0 ≥d f , K b0 ≥d n , according to the Lyapunov stability principle, It holds true, that is, the state variables of the system converge to the predetermined orbit, so that the system finally eliminates chaos and enters an asymptotically stable state.

[0096] 3. Design of adaptive fault-tolerant controller based on global sliding mode

[0097] The probability of the generator end being subjected to various disturbances is high. When the disturbance amplitude and rate of change are high, the impact on the system is particularly severe. At this time, the final observation accuracy of the observer may decrease, causing the controller output to deviate from the ideal value, and the time it takes for the system to converge to a stable track is significantly increased. To address the generator side disturbance problem, a combination of fixed gain and adaptive gain is adopted in the controller. Therefore, the output expression of the generator side controller (AFTC) based on the adaptive fault-tolerant control of the global sliding mode observer is as follows:

[0098]

[0099] Where K a0 With K a1 are fixed gain and adaptive gain respectively, and the adaptive gain expression is designed as

[0100]

[0101] Where K a2 With K a3 are all constants and satisfy K a2 >K a3 >0. In order to make the controlled system have better dynamic characteristics, K a2 With K a3 The value of should not be too large. μ is a constant greater than 0. ε is a sufficiently small positive number. Its value is related to the steady-state convergence accuracy of the system. The smaller its value, the closer the system's stable orbit is to the target orbit. However, the controller output may switch during the convergence process. Excessively small ε and μ will cause the output of the switching function sgn to switch repeatedly, resulting in repeated jumps in the controller output.

[0102] From formula (17), we can see that due to K a2 >K a3 , when the system is far away from the target orbit and satisfies |s1|≥μ, then K a1 Continue to increase at a higher speed; after time t0, when the system state variables are close to the target orbit and satisfy |s1|<μ, K a1 Increase at a smaller speed until |s1| < ε after time t1, when the system state variables approach the target orbit. a1 =K * , then K a1 The adaptive gain sets different growth rates for the controller depending on how far the system is from the target trajectory, thereby improving the dynamic characteristics of the system convergence process.

[0103] To avoid the controller u f The output is too large, so the adaptive gain K a1 To limit the amplitude, the limiting steps are as follows

[0104] K min <K a1 <K max (18)

[0105] In order to cope with possible controller failure, the failure degree of the load side controller should be adaptively estimated to compensate for the impact of the controller failure on the system. Let be the estimated value of λ, First, select the following candidate Lyapunov function V2.

[0106]

[0107] Taking the derivative of V2, we get

[0108]

[0109] will u in After substitution, we get

[0110]

[0111] To make but Should be

[0112]

[0113] In order to improve the dynamic characteristics of the load side controller and enhance the tracking accuracy of the controller, the expression of the adaptive fault estimation is transformed. The transformation results are as follows:

[0114]

[0115] Where K b2 , K b3 , K b4 and η1, η2 are all constants, and satisfy K b2 >K b3 >K b4 , η1>η2>0. To avoid overshoot, different gains are selected for the adaptive rate according to the distance of each variable from the target orbit, avoiding repeated jumps in the controller output and reducing the chattering of the system state variables.

[0116] To avoid the controller u n Output is too large, deal with adaptive fault estimation To limit the amplitude, the limiting steps are as follows

[0117]

[0118] Combining Equation (13) and Equation (23)-(24), the load-side fault-tolerant controller u based on the global sliding mode observer is n The output is as follows

[0119]

[0120] Reselect the Lyapunov function V3, its expression is as follows

[0121]

[0122] When the system state variables gradually approach the predetermined trajectory, that is, when |s1|<μ, the derivative of V3 is obtained, and the result is

[0123]

[0124] After simplifying the above formula, we can get

[0125]

[0126] Further simplification yields

[0127]

[0128] The above formula can finally be transformed into

[0129]

[0130] Because K * It's K a1 The upper bound of K a1 <K * , when |s1|<ε, it may appear In this case, the system may be in an unstable state. At this time, the system power angle δ m When the target orbit is deviated, |s1| increases rapidly. When |s1| increases to more than ε, that is, when |s1|>ε, if the controller control parameter is ρK a3 >1, then It will definitely return to a state less than 0, and the system will eventually stabilize.

[0131] When the system state variables gradually move away from the predetermined track, that is, when |s1|≥μ, the derivative of V3 is obtained.

[0132]

[0133] Combining equations (1)-(31), the AFTC expression is as follows:

[0134]

[0135] In summary, considering external disturbances, transmission failures and controller output failures, the AFTC system structure is as follows: Figure 1 As shown;

[0136] 4. Numerical simulation

[0137] In order to compare the control effects of the designed FTC and AFTC, Matlab / Simulink is used for simulation verification. First, the bifurcation parameters of the system are taken as: P0 = 0.4, Q0 = 0.61, and it can be seen that the system is in a chaotic state at this time. The control parameters of FTC are taken as: β f1 =7,β f2 =10,β f3 =3,β f4=0.5,β f5 =0.25,β n1 =15,β n2 =1,β n3 =0.5, c1=14.4, c2=7.2, q=3, p=5, c3=2, K a0 =1,K b0 =2,K b1 = 2. The initial output value z of the expanded observer f1 , z f2 , z f3 , z n1 , z n2 Both are 0. The initial value u of the controller output on the generator side and the load side f and u n The output of the expanded observer and the observed system items, the system state variables and the time domain of the FTC controller output are as follows: Figure 2 shown.

[0138] Depend on Figure 2 (a)-(b) shows that δ m and δ L There is no large-scale fluctuation in the process of converging to the target orbit, and the convergence process is relatively smooth. Figure 2 (c) It can be seen that under the action of FTC, all state variables of the system converge to a fixed orbit. Figure 2 (d) It can be seen that under the action of FTC, the output z of the expanded observer f3 and z n2 Approximate the system term f in finite time t and n t .

[0139] Convergence characteristics of the system under transmission failure

[0140] Both FTC and AFTC have a certain degree of fault tolerance to deal with system transmission failure. In addition to the same parameters as FTC, the control parameters of AFTC are K a2 =1.5, K a3 =0.1, μ=0.1, ε=0.01, K b2 =1,K b3 =0.1, K b3 =0.001, K min =0,K max =2, eta1=1, eta2=0.05, Adaptive gain K a1 The initial value is 0, the fault estimation The initial value of is 1. The transmission fault model parameters are T1 = 30s, T2 = 40s, ζ f =0.5,ζ n=0.5, that is, the system has a transmission failure at 30s and 40s respectively, and the output signal amplitude loss is 50%.

[0141] In order to compare the control effect of the designed controller on the system, the seventh-order power system dynamic sliding mode control (DSMC) is introduced. DSMC, FTC and AFTC are all put into use at t = 15s. The system state time domain is as follows Figure 3 As shown in (a)-3(b), the power angle on the generator side and the power angle on the load side in time domain are as follows Figure 3 (c)-3(d) shown.

[0142] Depend on Figure 3 (a) It can be seen that after the transmission failure occurs on the generator side and the load side at t = 30s and t = 40s respectively, the δ m Immediately deviate from the original target orbit and maintain the deviated orbit. Figure 3 (b) It can be seen that the system state only fluctuates briefly under the action of AFTC. Figure 3 (c) It can be seen that under the action of DSMC, δ m The stable deviation between the current orbit and the target orbit is 0.04. Under the action of FTC and AFTC, δ m After deviating from the original orbit, it quickly converges to the original target orbit, and the maximum deviations of the target orbit are 0.022 and 0.009 respectively. Figure 3 (d) It can be seen that under the action of DSMC, δ L The stable deviation between the current orbit and the target orbit is -0.07. Under the action of FTC and AFTC, δ L After deviating from the original orbit, it quickly converged to the original target orbit, with the maximum deviations from the target orbit being -0.038 and -0.037 respectively.

[0143] Convergence characteristics of the system under step disturbance

[0144] In order to compare the anti-disturbance capability of the system under the action of the designed controller, when t = 30s and t = 40s, two step disturbances of the power angle state quantity with an amplitude of 0.5 are added to the generator side. The power angle time domain of the generator side is as follows: Figure 4 (a) is shown. The time domain of each state variable of the system is as follows Figure 4 (b)-4(c) shown.

[0145] Depend on Figure 4 (a) It can be seen that under the action of DSMC, δ m After two perturbations, it finally failed to converge to the original orbit. After two perturbations, δ mThe stable deviations of the target orbit are 0.06 and 0.35 respectively. Under the action of FTC and AFTC, δ m After deviating from the original orbit, it quickly converged to the original target orbit. During the convergence process, the maximum deviations from the target orbit were 0.22 and 0.05, respectively.

[0146] Depend on Figure 4 (b) It can be seen that when the generator side is subjected to the first step disturbance at t = 30s, the state variables under DSMC control immediately deviate from the original target orbit and eventually remain on the deviated orbit after the disturbance. When the generator side is subjected to the second step disturbance at t = 40s, the state variables deviate again and stabilize on the deviated orbit. Figure 4 (c) It can be seen that when the system suffers a step disturbance at the above two moments, the state variables under AFTC control only fluctuate slightly and quickly converge to the original orbit.

[0147] Convergence characteristics of the system under controller failure

[0148] In order to compare the control effect of the designed controller on the system under the condition of controller failure, the fault time T3 of the controller failure mathematical model is taken as 40s, and the output signal amplitude of the load side controller is reduced in the following exponential form.

[0149]

[0150] From Equation (33), we can see that the load side controller fails at t = 40s, and the output signal decays in the form of an exponential function. When t → ∞, λ finally decays to λ = 0.1. DSMC, FTC, and AFTC are all put into operation at t = 15s. The time domain of each state variable of the system is as follows: Figure 5 As shown in (a)-5(b), the load side power angle time domain is as follows Figure 5 As shown in (c), the output time domain of each controller is as follows Figure 5 (d)-5(f) shown.

[0151] Depend on Figure 5 (a) It can be seen that when the load side controller fails at t = 40s, the state variables under DSMC control immediately deviate from the original target orbit and eventually remain on a fixed orbit. Figure 5 (b) It can be seen that under AFTC control, each state variable has a small offset only at the time of fault occurrence. Figure 5 (c) It can be seen that under the action of DSMC, δ L After the controller fails to converge to the original trajectory, δ L The stable deviation of the target orbit is -0.20. Under the action of FTC, δ L It also fails to converge to the original orbit, δ LThe stable deviation of the target orbit is -0.16. Under the action of AFTC, δ L It deviates from the target orbit briefly and then converges to the target orbit again. During the system convergence process, δ L The maximum deviation from the target orbit is -0.11, and the stable deviation is -0.013.

[0152] Depend on Figure 5 (d) It can be seen that when the load side controller fails, the amplitude of the DSMC controller output signal drops rapidly and eventually stabilizes at about 0.1 times the ideal controller output. Figure 5 (e) It can be seen that the FTC controller output also eventually stabilizes at about 0.1 times the ideal controller output. Figure 5 (f) It can be seen that due to the compensation effect of the adaptive fault estimation on the controller, the output signal amplitude of the AFTC controller first drops briefly, then increases as the adaptive term decreases, and finally gradually approaches the output signal amplitude before the fault.

[0153] Conclusion and Outlook

[0154] (1) According to the characteristics of the seventh-order system, the chaotic characteristics of the seventh-order system are analyzed using bifurcation diagrams and phase diagrams. The changes in the system state under the changes in the key parameters of the system are characterized, and the system is obtained under the key parameter P. m , P0 and Q0, after analysis, it can be seen that when the above parameters change, the system shows the phenomenon of switching between periodic and chaotic states.

[0155] (2) For the control problem of the seventh-order system, an FTC strategy is proposed to reduce the controller's dependence on the system model. Considering that the generator is susceptible to external disturbances and the load-side controller is susceptible to failures, an AFTC strategy is proposed to improve the system's fault tolerance. Simulation results show that the designed controllers can eliminate the system's chaotic state. When the system is subjected to step disturbances, transmission faults, and controller failures, the maximum offset and steady-state error of the system are both small under the control of AFTC.

[0156] (3) For seventh-order systems, the traditional Wolf method cannot be used to obtain the Lyapunov exponent. Therefore, the chaotic characteristics of seventh-order systems can only be analyzed by combining bifurcation diagrams with phase diagrams.

[0157] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A design method for an adaptive fault-tolerant controller based on a global sliding mode, characterized by: The steps include: Step 1: To address the generator-side disturbance problem, a combination of fixed gain and adaptive gain is adopted in the controller. The output expression of the generator-side controller based on the adaptive fault-tolerant control of the global sliding mode observer is shown in formula (16): Where K a0 With K a1 are fixed gain and adaptive gain respectively, and the adaptive gain expression is designed as shown in formula (17): Where K a2 With K a3 are all constants and satisfy K a2 >K a3 >0; μ is a constant greater than 0; ε is a positive number; Step 2: To avoid controller u f The output is too large, so the adaptive gain K a1 The limiting step is shown in formula (18): K min <K a1 <K max (18); Step 3: Adaptively estimate the fault degree of the load side controller to compensate for the impact of the controller failure on the system; Let be the estimated value of λ, First, select the following candidate Lyapunov function V2: Taking the derivative of V2, we get Among them, when the load side controller fails, the mathematical model of the controller failure is shown as follows: Where u in is the control signal received by the system, u h is the ideal output signal of the controller, λ is the degree of output amplitude loss caused by controller failure, 1≥λ≥0, the smaller λ is, the higher the degree of controller output amplitude loss is; λ=1 means that the load side controller has no fault, λ=0 means that the load side controller has a complete fault; will u in After substitution, we get To make but Should be Step 4: To improve the dynamic characteristics of the load-side controller and enhance the controller tracking accuracy, the expression of the adaptive fault estimation is transformed. The transformation result is shown in formula (23): Where K b2 , K b3 , K b4 and η1, η2 are all constants, and satisfy K b2 >K b3 >K b4 ,η1>η2>0; Step 5: To avoid controller u n Output is too large, deal with adaptive fault estimation The limiting step is shown in formula (24): Combining Equation (13) and Equation (23)-(24), the load-side fault-tolerant controller u based on the global sliding mode observer is n The output is shown in formula (25): Step 6: Reselect the Lyapunov function V3, whose expression is shown in formula (26): When the system state variables gradually approach the predetermined trajectory, that is, when |s1| < μ, V3 is derived, and the result is shown in formula (27): After simplifying the above formula, we get Further simplifying The above formula is finally transformed into Step 7: When the system state variable gradually moves away from the predetermined track, that is, when |s1| ≥ μ, the derivative of V3 is calculated, and the derivative result is From the above formula, the expression of the generator side controller of the adaptive fault-tolerant control based on the global sliding mode observer is as follows:

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