Active Fault Tolerant Control Method for Engineering Systems under the Framework of High-Order All-Drive System

Abstract

An active fault-tolerant control method for an engineering system under a high-order fully actuated system framework, belonging to the field of advanced control of engineering systems. The method includes the following steps: for an actual controlled engineering system, considering model mismatch and various fault situations, a corresponding high-order fully actuated model is established; a fault estimator is designed based on the established high-order fully actuated model to estimate the total fault of the system; a fault compensation tracking controller is designed based on the high-order fully actuated model, and the controller gain is solved through a parameterization algorithm. Through the combination of the high-order fully actuated model and fault-tolerant control, both the robustness of the system to faults is ensured, and the computational amount is significantly reduced while retaining the actual meaning of the system state.

Description

Technical Field

[0001] The present invention belongs to the field of advanced control of engineering systems and relates to an active fault-tolerant control method for engineering systems. Background Art

[0002] With the development of information technology, engineering systems (such as autonomous driving vehicles, industrial process control, autonomous underwater vehicles, etc.) are becoming increasingly complex and are prone to failures during operation due to their own or external environmental influences. If the failures cannot be processed in time, serious consequences such as property losses, casualties, and environmental pollution will occur. Therefore, engineering systems need to have fault-tolerant capabilities to ensure safety, reliability, and economic benefits, and the research on fault-tolerant control strategies is of great significance. Passive fault-tolerant control designs fixed controllers to handle all possible failures and has certain robustness. For example, Zhang Ridong et al. used the minmax theory to design an H-infinity linear quadratic controller to handle actuator part failures and also extended this theory to batch processes to propose a two-dimensional fault-tolerant control method, etc.

[0003] Active fault-tolerant control uses fault diagnosis information to compensate for the impact of faults or reconfigure control strategies. It is widely applied in different fields, and there are relevant research results in fields such as wind power and underwater robots, such as active fault-tolerant control for wind turbine actuators' faults and disturbances, various active fault-tolerant control schemes for autonomous underwater vehicles, etc.

[0004] The technical problems existing in the existing system modeling and control methods are as follows:

[0005] 1. Resource waste: Passive fault-tolerant control reserves redundant resources to handle failures, and these resources are not fully utilized under normal circumstances.

[0006] 2. Limited fault-tolerant range: Passive fault-tolerant control only targets preset fault types and it is difficult to handle faults beyond the range.

[0007] 3. Unable to dynamically adjust control strategies: The passive fault-tolerant control strategy is fixed and cannot be optimized and adjusted in real time according to faults.

[0008] 4. Change in state meaning: When dealing with continuous models, the first-order difference method is often used for discretization, which will cause changes in the definition and physical meaning of the system state.

[0009] 5. Increase in dimension caused by time delay: When dealing with discrete models, the typical method is to use a non-minimal state space model, and at this time, as the input time delay increases, the system dimension will continuously increase and even reach an infinite dimension. Summary of the Invention

[0010] To address the above existing technical problems, the present invention provides an active fault-tolerant control method for an engineering system under a high-order fully actuated system framework, aiming to propose a fault-tolerant control strategy based on fault compensation using the high-order fully actuated system, so as to enable the system to still operate smoothly in case of faults, specifically including reducing the system dimension, maintaining the practical meaning of the state, effectively estimating faults and compensating for the impact of faults to ensure tracking performance, etc.

[0011] To achieve the above object, the present invention adopts the following technical solutions:

[0012] An active fault-tolerant control method for an engineering system under a high-order fully actuated system framework of the present invention includes the following steps:

[0013] S1. For the actual controlled engineering system, in combination with model mismatch and various fault conditions, establish a corresponding high-order fully actuated model;

[0014] S2. Design a fault estimator based on the established high-order fully actuated model to estimate the total fault of the system;

[0015] S3. Design a fault compensation tracking controller based on the high-order fully actuated model and solve the controller gain through a parameterization algorithm.

[0016] Further, in an actual engineering system, first represent the controlled system in the following form:

[0017] y(k)+(H1±Δ1)y(k - 1)+…+(H n ±Δ n )y(k - n)(1)

[0018] =(L1±Λ1)u(k - 1)+…+(L m ±Λ m )u(k - m)

[0019] where y(k) and u(k) respectively represent the output and input at time k, H1,…,H n ,L1,…,L m represent the gains of the corresponding historical output and input terms, Δ1,…,Δ n ,Λ1,…,Λ m are the fault factors of the system, which vary with the actual fault conditions of the system; meanwhile, define the occurrence time of the partial actuator failure fault as k, and the actual control input is expressed as: u F (k)=βu(k), where u F (k) is the actual output of the actuator, and β is the actuator failure factor and 0<β≤1 or β≥1; change the system into the following form:

[0020]

[0021] where,

[0022] d(k) = L1(β - 1)u(k) ± Δ1y(k) ± … ± Δ n y(k - n + 1) ± Λ1u(k) ± … ± Λ m u(k - m + 1).

[0023] Furthermore, the specific steps of step S2 are as follows:

[0024] S21. Define x1(k) = y(k), x2(k) = d(k), and obtain the following formula (3):

[0025] x2(k + 1) = d(k + 1) = d(k) + Δd(k + 1) (3)

[0026] S22. Design a state estimator as follows:

[0027]

[0028] Combining formula (2) and (3) to obtain the following formula (6):

[0029]

[0030] where ω1, ω2 are the parameters of the estimator, satisfying that the eigenvalues of the matrix are inside the unit circle, that is: Then is convergent, that is, the estimated state is bounded and stable; complete the effective design of the estimator for the output and the fault.

[0031] Furthermore, the specific steps of step S3 are as follows:

[0032] S31. Design the controller u(k) as follows:

[0033]

[0034] Substitute it into the model of formula (2) to obtain the following formula (8):

[0035]

[0036] where

[0037] S32. Design an intermediate variable: v(k), satisfying the following formula:

[0038]

[0039] where K1, K2…K e respectively represent the gain coefficients of the corresponding terms

[0040] Multiply both sides of Equation (8) by the Δ operator and combine with Equation (9) to obtain

[0041]

[0042] where δ i = Δy(k - i + 1), i = {1, 2, …, n}, δ k+1 = Δy(k + 1)

[0043] The following Equation (11) is obtained:

[0044]

[0045] where

[0046]

[0047] Γ = [1 0 … 0 0] T ,

[0048]

[0049] where, if the characteristic roots of are inside the unit circle, when Δe d (k) = 0, k → ∞, when Δe d (k) ≠ 0, k → ∞, at this time y(k) → r(k), k → ∞ still holds, ensuring that the controller realizes system stability;

[0050] S34. According to the system design parameterization algorithm:

[0051] The feedback gain matrix of the active fault-tolerant compensation tracking controller based on the high-order fully actuated system method is obtained from the following Equations (12) and (13):

[0052] [K1 K2 … K e = WV -1 (12)

[0053]

[0054] where I n+1×n+1 is the identity matrix, and Z, F, N are parameter matrices in the algorithm, and the feedback gain matrix obtained through the above parameterization algorithm.

[0055] The beneficial effects of the present invention are as follows:

[0056] 1. The output of the controller of the present invention depends on the estimation of the fault d(k). When the fault does not occur, no redundant resources are wasted.

[0057] 2. The design of the controller of the present invention does not require the estimated range of faults, and can effectively compensate for all faults satisfying that Δd(k) is bounded under ideal conditions.

[0058] 3. The output of the controller of the present invention changes with the change of d(k), where d(k) is the total fault of the system including various faults. At this time, the controller will dynamically adjust the control strategy according to actual needs.

[0059] 4. After introducing the high-order fully actuated system in the present invention, the practical meanings of the model states have not changed, which increases the readability.

[0060] 5. Since the input time-delay term is eliminated in the present invention, the number of state variables is significantly reduced, thereby reducing the system dimension, avoiding the situation where it reaches an infinite dimension, and effectively reducing the computational amount. Brief Description of the Drawings

[0061] Figure 1 is the overall flow schematic diagram of the present invention;

[0062] Figure 2 is the output and input under normal conditions in Embodiment 1;

[0063] Figure 3 is the output under different methods in the fault situation of Embodiment 1;

[0064] Figure 4 is the input under different methods in the fault situation of Embodiment 1;

[0065] Figure 5 is the fault estimation of Embodiment 1;

[0066] Figure 6 is the output under different fault situations in Embodiment 2;

[0067] Figure 7 is the input under different fault situations in Embodiment 2;

[0068] Figure 8 is the fault estimation of Embodiment 2. Detailed Embodiments

[0069] The embodiments of the present invention will be described in detail below with reference to the drawings. The following embodiments are exemplary and are only used to explain the present invention and should not be construed as a limitation to the present invention.

[0070] The present invention proposes an active fault-tolerant control method for an engineering system under a high-order fully actuated system framework to cope with various faults that occur in the control system. This method aims to handle the mismatched uncertainties and faults existing in the input-output model of a single-input, single-output system and unify them for overall fault handling. The present invention designs an estimator that can estimate the fault situation and proposes a new equivalent high-order fully actuated system model. On this basis, a fault-tolerant tracking controller is constructed. The advantage of this method is that it does not require changing the state structure of the system, thus maintaining practical significance and effectively reducing the increase in system dimension caused by the input delay term. In addition, through fault compensation design, it can ensure the stable operation of the system during the occurrence of faults.

[0071] The present invention has been verified in the injection molding process and the control system of an autonomous underwater vehicle (AUV). Simulation tests show that it can effectively control the system output under normal and fault conditions. Through the design of a fault-tolerant tracking controller based on a high-order fully actuated system, the system can also achieve good tracking control performance when a fault occurs, ensuring system stability.

[0072] Specifically, an active fault-tolerant control method for an engineering system under a high-order fully actuated system framework includes the following steps:

[0073] S1. For the actual controlled engineering system, combine the model mismatch and various fault situations to establish a corresponding high-order fully actuated model;

[0074] S2. Design a fault estimator based on the established high-order fully actuated model to estimate the overall fault of the system;

[0075] S3. Design a fault compensation tracking controller based on the high-order fully actuated model and solve the controller gain through a parameterization algorithm.

[0076] Among them, in step S1, first, the controlled system is expressed in the following form:

[0077]

[0078] where y(k) and u(k) respectively represent the output and input at time k, H1, …, H n , L1, …, L m represent the gains of the corresponding historical output and input terms, Δ1, …, Δ n , Λ1, …, Λ m are the fault factors of the system, which vary with the actual fault situation of the system; meanwhile, define the occurrence time of the partial actuator failure fault as k, and at this time, the actual control input is expressed as: u F (k) = βu(k), where u F(k) is the actual output of the actuator, β is the actuator failure factor and 0 < β ≤ 1 or β ≥ 1; the system is transformed into the following form:

[0079]

[0080] where,

[0081] d(k) = L1(β - 1)u(k) ± Δ1y(k) ± … ± Δ n y(k - n + 1) ± Λ1u(k) ± … ± Λ m u(k - m + 1)

[0082] The present invention represents the single - input single - output system model in an actual engineering system as a novel high - order fully - actuated system, and unifies the internal faults existing in the system or the additive and multiplicative faults existing in the actuator into the total faults of the system. The advantage of this design is that it does not need to destroy the original state structure of the system, thus retaining the physical characteristics of the original system, making each state of the model have practical significance.

[0083] Among them, the specific content of S2 is as follows:

[0084] S21. Define x1(k) = y(k), x2(k) = d(k), and the following formula (3) can be obtained:

[0085] x2(k + 1) = d(k + 1) = d(k)+Δd(k + 1) (3)

[0086] S22. Design the state estimator as follows:

[0087]

[0088] Combining formula (2) and formula (3) to obtain the following formula (6):

[0089]

[0090] Among them, ω1, ω2 are parameters designed according to the actual situation. When designing, the characteristic roots of the matrix need to satisfy being inside the unit circle, that is At this time is convergent. Also, since Δd(k + 1) is bounded, will converge to a certain bounded range, that is, the estimated state is bounded and stable. In summary, the estimator design for the output and faults is completed, and its effectiveness is proved. After obtaining the estimated value of the total fault d(k), an active fault - tolerant controller can be designed to compensate for the faults.

[0091] Among them, the specific content of S3 is as follows:

[0092] S31. Design the controller u(k) as follows:

[0093]

[0094] Substitute into the model of Equation (2) to obtain the following equation

[0095]

[0096] where

[0097] S32. Design the intermediate variable: v(k), which satisfies the following equation:

[0098]

[0099] where, K1, K2…K e respectively represent the gain coefficients of the corresponding terms

[0100] Multiply both sides of Equation (4) by the Δ operator and combine with Equation (8) to obtain

[0101]

[0102] where, δ i =Δy(k - i + 1), i = {1, 2, …, n}, δ k+1 =Δy(k + 1)

[0103] Then, the following equation is obtained:

[0104]

[0105] where

[0106]

[0107] Γ = [1 0…0 0] T ,

[0108]

[0109] If the characteristic roots are inside the unit circle, when Δe d (k) = 0, k → ∞, when Δe d (k) ≠ 0, k → ∞, y(k) → r(k), k → ∞ still holds. Thus, it shows that for bounded Δe d (k), as long as the characteristic roots are inside the unit circle, the controller can achieve the stability of the system.

[0110] S34. Parameterize the algorithm according to the system design:

[0111] The feedback gain matrix of the active fault-tolerant compensation tracking controller based on the high-order full-drive system method is obtained from the following equations (12) and (13):

[0112]

[0113]

[0114] where I n+1×n+1 is the identity matrix. The feedback gain matrix obtained through the above parameterization algorithm is uniquely determined by the matrices Z, F, and N. The matrices Z, F, and N need to match the system dimension, and F is a Schur matrix. N and Z need to satisfy the invertibility of the matrix V. Under the condition of meeting the above conditions, the system meets the performance requirements by selecting appropriate matrices Z, F, and N.

[0115] Under the new model of the high-order full-drive system, the present invention designs an active fault-tolerant tracking compensation controller. First, for the existing faults, an observer is designed to estimate their values. Then, a fault-tolerant tracking controller is designed based on fault compensation to achieve fault compensation and good tracking of the given system output. The design of the controller is completed within the framework of the HOFA system, and its value is obtained through the parameterization method. The advantage of this design is that constructing the HOFA system does not change the actual meaning represented by each variable. For the controller design, using the parameterization method is simple and feasible. At the same time, designing an active fault-tolerant tracking controller can effectively reduce the impact of faults on the system control performance.

[0116] The following further illustrates the present invention with specific examples.

[0117] Example 1: In the injection molding process, the control of the holding pressure stage has a great impact on the product quality. Therefore, it is crucial to design an advanced control strategy for the parameter of pressure. In engineering, the digital modeling method is generally used. Through open-loop tests and data analysis, the holding pressure process is approximately described by the following second-order discrete-time input-output model with parameter uncertainties:

[0118]

[0119] The parameter uncertainties here can be regarded as internal faults in the system or gain faults in the actuator, and at the same time, actuator additive faults are considered.

[0120] According to step S1, the above parameter-uncertain model is established as the following high-order full-drive system model:

[0121] y(k + 1) = 1.607y(k) - 0.6086y(k - 1) + 1.239u(k) - 0.9282u(k - 1) + d(k) (17)

[0122] where

[0123] d(k) = 0.03y(k) - 0.04y(k - 1) + 1.239(β - 1)u(k) + 0.05u(k) - 0.07u(k - 1) + 1.239w(k)

[0124] According to step S2, select ω1 = -1.2910 and ω2 = -1.3220. Design the fault estimator as follows:

[0125]

[0126] where x1(k) = y(k) and x2(k) = d(k)

[0127] According to step S3, select the parameters N = 1 and Z = [1 -1 -1], obtain

[0128] [K1 K2 K e = [-1.3640 0.5816 -0.3430]

[0129] Next, discuss the control effect of the fault - compensation - based fault - tolerant control law. To show the superiority of the control strategy proposed in this paper, compare the existing control algorithm with the algorithm proposed in this application. The existing control algorithm uses a typical first - order state - space model, and the state of its controller is z(k) = [Δy(k) Δy(k - 1) Δu(k - 1) e(k)] T ; This application is significantly one - dimension less and does not need to consider Δu(k - 1). When there are more input delay terms, the system dimension proposed in this application is even less than that of the first - order state - space dimension. This part will numerically simulate the control effects of the two methods in the cases of with and without faults. At the same time, to show its tracking performance, introduce the following performance index values

[0130] Case 1 Normal situation

[0131] From Figure 2 it can be seen that because the method adopted in this application uses less input information of the system, on the premise of almost the same input, even without any fault and other factors affecting, in the initial period of the system operation, it takes a longer time for the output to track the given value. However, as time goes by, the two show the same tracking effect. From the value of D(k), the MPC value is smaller, indicating that the two have the same tracking effect.

[0132] Case 2 Fault situation

[0133] As can be seen from the system modeling, the system fault d(k) includes internal faults, actuator gain faults, and additive faults,

[0134] β = 0.02 * sin(0.1k) + 0.8 (18)

[0135] 1.239w(k) = 0.1 * cos(π * k / 60) (19) The existing MPC method needs a relatively large input to achieve good robust control performance, as shown below, but in actual processes, it is sometimes impossible to achieve. By using the observability of the observer, the fault can be estimated, as shown below Figure 4 and by designing an active fault-tolerant controller based on the estimated fault using the estimated fault, the above situation can be avoided, as shown below Figure 5 Figure 3 Figure 3 It also shows the advantages of this design, that is, the tracking effect after compensation is the best, and even can reach the level of the fault-free situation

[0136] Example 2: Take the depth control of an underwater robot AUV as an example. According to the vertical plane motion equation of the underwater robot in existing literature, the linearized model of depth control is

[0137]

[0138] where x1, x2, x3, and u represent the depth, pitch angle, pitch acceleration, and pitch rudder angle of the AUV respectively. 0 < α < 1 represents the actuator gain fault, s a represents its additive fault, and Δ represents the bounded disturbance of x3, which can also be regarded as an internal fault of the system.

[0139] . According to step S1, take the second derivative of x and combine the following two equations to establish the above parameter-uncertain model as the following equivalent third-order fully actuated system model

[0140]

[0141] Then use the forward difference to discretize the above system, and obtain the following discrete-time third-order fully actuated system model

[0142] .

[0143] where d(k) = -ΔT(x1(k + 2) - 2x1(k + 1) + x1(k)) + 0.9081T 3 (α - 1)u + 0.9081T 3 s a

[0144] According to step S2, select ω1 = -0.3, ω2 = -0.32, ω3 = 0.32, ω4 = -0.2, and design the sampling period as 1 second to establish the following estimator

[0145]

[0146] where \(x1(k)=y(k)\), \(x2(k)=y(k + 1)\), \(x3(k)=y(k + 2)\), \(x4(k)=d(k)\)

[0147] According to step S3, select the parameters \(N = 1\), \(Z=[1 -1 1 -1]\) Then, based on the above parameterization, we obtain:

[0148] [K2 K1 K0 K e = [0.8352 -3.4134 2.0887 -0.0446],

[0149] Case 1: Normal situation

[0150] In Figure 6 and Figure 7 the blue curves shown indicate that, in the absence of faults, the output smoothly and stably tracks the set value, and at the same time, the input also remains relatively smooth.

[0151] Case 2: Fault situation

[0152] Here, \(\alpha = 0.8 + 0.02\sin(0.01*k)\)

[0153] The fault \(d(k)= -0.5108*(1 / 3)*(x1(k + 2)-2x1(k + 1)+x1(k))+0.9081(\alpha - 1)u+0.9081s\) a 665. Figure 8 The fault estimation curve is shown, where the fault estimation is achieved through the fault estimation algorithm proposed in this application. When the design of the input (7) does not consider fault compensation, the output curve will fluctuate within a range under the influence of these faults, as shown by the green curve in Figure 6 Once the compensation control is considered, the fluctuation range of the output curve is significantly reduced, as shown by the red curve in Figure 6 To further demonstrate the advantages of active fault-tolerant control (FTC) based on fault compensation, the performance index values are introduced. The control effect is indeed improved, as shown in Table 1.

[0154] Table 1: D(k)

[0155] Method D(k) No interference, no compensation 1.5737 With interference, no compensation 1.72 With interference, with compensation 1.5991

[0156] The technical principles of the present invention have been described in connection with specific embodiments. These descriptions are only for explaining the principles of the present invention and cannot be construed in any way as limiting the scope of protection of the present invention. Based on the explanations herein, those skilled in the art can readily conceive of other specific embodiments of the present invention without creative efforts, and these embodiments will fall within the scope of protection of the present invention.

Claims

1. An active fault-tolerant control method for an engineering system under the framework of a high-order all-wheel drive system, characterized in that: The steps include: S1. For the actual controlled engineering system, combined with model mismatch and various fault conditions, a corresponding high-order all-wheel drive model is established; S2. Design a fault estimator based on the established high-order all-wheel drive model to estimate the total fault of the system; S3. Design a fault compensation tracking controller based on a high-order all-wheel drive model and solve the controller gain using a parameterized algorithm; In actual engineering systems, the controlled system is first expressed as follows: Where y(k) and u(k) represent the output and input at time k respectively, H1,…,H n ,L1,…,L m represents the gain of the corresponding historical output input item, Δ1,…,Δ n ,Λ1,…,Λ m is the fault factor of the system, which changes with the actual fault situation of the system; at the same time, the moment when the actuator partial failure occurs is defined as k, and the actual control input is expressed as: u F (k) = βu(k), where u F (k) is the actual output of the actuator, β is the actuator failure factor and is 0<β≤1 or β≥1; the system is transformed into the following form: in, d(k)=L1(β-1)u(k)±Δ1y(k)±…±Δ n y(k-n+1)±Λ1u(k)±…±Λ m u(k-m+1)。 2. The active fault-tolerant control method for engineering systems in the framework of a high-level all-wheel drive system according to claim 1, characterized in that: The step S2 is specifically as follows: S21. Define x1(k)=y(k), x2(k)=d(k), and obtain the following formula (3): x2(k+1)=d(k+1)=d(k)+Δd(k+1) (3) S22. Design state estimator as follows: Combining equations (2) and (3) yields the following equation (6): Among them, ω1, ω2 are the parameters of the estimator, satisfying the matrix The characteristic roots of are inside the unit circle, that is: but It is convergent, that is, the estimated state is bounded and stable; it completes the effective design of estimators for output and faults.

3. The active fault-tolerant control method for engineering systems in the framework of a high-level all-wheel drive system according to claim 2, characterized in that: The step S3 is specifically as follows: S31. Design the controller u(k) as follows: Substituting into the model of formula (2) we get the following formula (8): in, S32. Design the intermediate variable: v(k), satisfying the following formula: Among them, K1, K2…K e Represents the gain coefficients of the corresponding items respectively Multiply both sides of formula (8) by the Δ operator and combine with formula (9) to get among them,d i =Δy(k-i+1),i={1,2,…,n},d k+1 =Δy(k+1) The following formula (11) is obtained: in, C=[1 0 … 0 0] T , Among them, if The characteristic root of is inside the unit circle, when Δe d (k)=0, k→∞, when Δe d (k)≠0,k→∞, at this time y(k)→r(k),k→∞ still holds, ensuring that the controller achieves system stability; S34. Design parameterized algorithms based on the system: The feedback gain matrix of the active fault-tolerant compensation tracking controller based on the high-order all-wheel drive system method is obtained by the following equations (12) and (13): [K1 K2 …K e ]=WV -1 (12) Among them I n+1×n+1 is the unit matrix, Z, F, and N are the parameter matrices in the algorithm, and the feedback gain matrix is obtained through the above parameterization algorithm.

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