Active fault-tolerant control method for engineering system under high-order all-drive system framework

Abstract

The invention discloses an engineering system active fault-tolerant control method under a high-order all-drive system framework, and belongs to the field of engineering system advanced control. Comprising the following steps: aiming at an actual controlled engineering system, considering model mismatch and various fault conditions, and establishing a corresponding high-order all-drive model; designing a fault estimator according to the established high-order all-drive model, and estimating the total fault of the system; and designing a fault compensation tracking controller based on the high-order all-drive model, and solving the gain of the controller through a parameterization algorithm. Through the combination of a high-order all-drive model and fault-tolerant control, the robustness of the system to faults is ensured, the calculation amount is remarkably reduced, and the actual meaning of the system state is reserved.

Description

Technical Field

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

[0002] With the development of information technology, engineering systems (such as autonomous vehicles, industrial process control, autonomous underwater robots, etc.) are becoming increasingly complex and prone to failures during operation due to the influence of themselves or the external environment. If the failure is not handled in time, it will cause serious consequences such as property loss, casualties, and environmental pollution. Therefore, engineering systems need to have fault tolerance to ensure safety, reliability, and economic benefits. The research on fault-tolerant control strategies is of great significance. Passive fault-tolerant control designs fixed controllers to deal with all possible faults and has a certain degree of robustness. For example, Zhang Ridong et al. used the minmax theory to design an H infinite linear quadratic controller to handle partial actuator failures, and also extended the theory to batch processes to propose a two-dimensional fault-tolerant control method.

[0003] Active fault-tolerant control uses fault diagnosis information to compensate for fault effects or reconfigure control strategies. It is widely used in different fields, such as wind power and underwater robots. There are relevant research results in the fields of wind power and underwater robots, such as active fault-tolerant control for wind turbine actuator faults and interferences, and various active fault-tolerant control schemes for autonomous underwater robots.

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

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

[0006] 2. Limited fault tolerance range: Passive fault tolerance control is only for preset fault types, and faults beyond the range are difficult to deal with.

[0007] 3. Unable to dynamically adjust the control strategy: The passive fault-tolerant control strategy is fixed and cannot be optimized and adjusted in real time with 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 the definition and physical meaning of the system state to change.

[0009] 5. Time delay leads to an increase in dimensionality: When dealing with discrete models, the typical method is to use a non-minimizing state space model. At this time, as the input time delay increases, the system dimension will continue to increase or even reach infinite dimensions. Summary of the invention

[0010] In view of the above-mentioned technical problems, the present invention provides an active fault-tolerant control method for an engineering system under the framework of a high-order all-wheel drive system, aiming to use the high-order all-wheel drive system to propose a fault-tolerant control strategy based on fault compensation, so that the system can still run smoothly in the event of a fault, specifically including reducing the system dimension, maintaining the actual meaning of the state, effectively estimating the fault and compensating for the impact of the fault to ensure tracking performance, etc.

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

[0012] The present invention provides an active fault-tolerant control method for an engineering system under the framework of a high-order all-wheel drive system, comprising the following steps:

[0013] S1. For the actual controlled engineering system, combined with model mismatch and various fault conditions, establish the corresponding high-order all-wheel drive model;

[0014] S2, design a fault estimator based on the established high-order all-wheel drive model to estimate the total fault of the system;

[0015] S3. Design a fault compensation tracking controller based on a high-order all-wheel drive model, and solve the controller gain through a parameterized algorithm.

[0016] Furthermore, in the actual engineering system, the controlled system is first expressed as follows:

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

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

[0019] Where y(k) and u(k) represent the output and input at time k respectively, H 1 ,…,H n ,L 1 ,…,L m represents the gain of the corresponding historical output input item, Δ 1 ,…,Δ n ,Λ 1 ,…,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 changed into the following form:

[0020]

[0021] in,

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

[0023] Furthermore, the step S2 is specifically as follows:

[0024] S21. Define x 1 (k)=y(k),x 2 (k) = d(k), and the following formula (3) is obtained:

[0025] x 2 (k+1)=d(k+1)=d(k)+Δd(k+1) (3)

[0026] S22. Design state estimator as follows:

[0027]

[0028] Combining equations (2) and (3), we get the following equation (6):

[0029]

[0030] Among them, ω 1 ,ω 2 is the parameter of the estimator, satisfying the matrix The characteristic root of is 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.

[0031] Furthermore, the step S3 is specifically as follows:

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

[0033]

[0034] Substituting into the model of formula (2), we get the following formula (8):

[0035]

[0036] in,

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

[0038]

[0039] Among them, K 1 ,K 2 …K e Respectively represent the gain coefficients of the corresponding items

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

[0041]

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

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

[0044]

[0045] in,

[0046]

[0047] Γ=[10…00] T ,

[0048]

[0049] 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;

[0050] S34. Design parameterized algorithm based on the system:

[0051] 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):

[0052] [K 1 K 2 … K e ]=WV -1 (12)

[0053]

[0054] Among them I n+1×n+1 is the unit matrix, Z, F, N are the parameter matrices in the algorithm, and the feedback gain matrix is ​​obtained by the above parameterized algorithm.

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

[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 will be wasted.

[0057] 2. The design of the controller of the present invention does not require the estimated range of the fault. Ideally, all faults that satisfy the bounded Δd(k) can be effectively compensated.

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

[0059] 4. After the high-order all-wheel drive system is introduced into the present invention, the practical significance of the model state does not change, thereby increasing readability.

[0060] 5. In the present invention, since the input time lag term is eliminated, the number of state variables is significantly reduced, thereby reducing the system dimension, avoiding the situation of reaching infinite dimension, and effectively reducing the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0062] Figure 2 are the output and input of Example 1 under normal conditions;

[0063] Figure 3 The outputs of different methods under the fault conditions of Example 1;

[0064] Figure 4 The inputs of different methods under the fault conditions of Example 1;

[0065] Figure 5 Fault estimation for Example 1;

[0066] Figure 6 The output under different fault conditions in Example 2;

[0067] Figure 7 The inputs under different fault conditions in Example 2;

[0068] Figure 8 This is the fault estimation of Example 2. DETAILED DESCRIPTION

[0069] Embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. The following embodiments are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0070] The present invention proposes an active fault-tolerant control method for engineering systems under the framework of a high-order all-wheel drive system to cope with various faults occurring in the control system. This method aims to deal with the mismatch uncertainties and faults existing in the input-output model of a single-input, single-output system, and unify them into a total fault for processing. The present invention designs an estimator that can estimate the fault condition and propose a new equivalent high-order all-wheel drive system model, and on this basis, constructs a fault-tolerant tracking controller. The advantage of this method is that it does not require changing the state structure of the system, thereby maintaining practical significance, and effectively reducing the increase in system dimensionality brought about by the input delay term. In addition, through fault compensation design, the stable operation of the system can be guaranteed during the occurrence of a fault.

[0071] The invention has been verified in the injection molding process and the autonomous underwater robot (AUV) control system, and simulation tests have shown that the system output can be effectively controlled under normal and fault conditions. Through the design of a fault-tolerant tracking controller based on a high-order all-wheel drive system, the system can achieve good tracking control performance even when a fault occurs, ensuring system stability.

[0072] Specifically, an active fault-tolerant control method for an engineering system under a high-order all-wheel drive system framework comprises the following steps:

[0073] S1. For the actual controlled engineering system, combined with model mismatch and various fault conditions, establish the corresponding high-order all-wheel drive model;

[0074] S2, design a fault estimator based on the established high-order all-wheel drive model to estimate the total fault of the system;

[0075] S3. Design a fault compensation tracking controller based on a high-order all-wheel drive model, and solve the controller gain through a parameterized algorithm.

[0076] Wherein, in the step S1, the controlled system is first expressed as follows:

[0077]

[0078] Where y(k) and u(k) represent the output and input at time k respectively, H 1 ,…,H n ,L 1 ,…,L m represents the gain of the corresponding historical output input item, Δ 1 ,…,Δ n ,Λ 1 ,…,Λ mis 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 at this time 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 changed into the following form:

[0079]

[0080] in,

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

[0082] The present invention represents the single-input single-output system model in the actual engineering system as a new type of high-order full-drive system, and unifies the internal faults of the system or the additive and multiplicative faults of the actuator into the total fault of the system. The advantage of this design is that it does not need to destroy the original state structure of the system, thereby retaining the physical characteristics of the original system, so that each state of the model has practical significance.

[0083] Wherein, the S2 is specifically:

[0084] S21. Define x 1 (k)=y(k),x 2 (k) = d(k), we can get the following formula (3):

[0085] x 2 (k+1)=d(k+1)=d(k)+Δd(k+1) (3)

[0086] S22. Design state estimator as follows:

[0087]

[0088] Combining equation (2) and equation (3) we get the following equation (6):

[0089]

[0090] Among them, ω 1 ,ω 2 The design matrix is ​​designed according to the actual situation. The characteristic root of must be within the unit circle, that is at this time is convergent, and since Δd(k+1) is bounded, It will converge to a bounded range, that is, the estimated state is bounded and stable. In summary, the design of the output and fault estimator 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 fault.

[0091] Wherein, the S3 is specifically:

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

[0093]

[0094] Substituting into the model (2) we get the following formula:

[0095]

[0096] in,

[0097] S32. Design the intermediate variable: v(k), satisfying the following formula:

[0098]

[0099] Among them, K 1 ,K 2 …K e Respectively represent the gain coefficients of the corresponding items

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

[0101]

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

[0103] Then, we get the following formula:

[0104]

[0105] in,

[0106]

[0107] Γ=[10…00] T ,

[0108]

[0109] like The characteristic root of is inside the unit circle, when Δed (k)=0, k→∞, when Δe d (k)≠0,k→∞,y(k)→r(k),k→∞ still holds. This shows that for bounded Δe d (k), as long as If the characteristic root of is within the unit circle, the controller can achieve system stability.

[0110] S34. Design parameterized algorithm based on the system:

[0111] 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):

[0112]

[0113]

[0114] Among them I n+1×n+1 is the unit matrix, and the feedback gain matrix obtained by 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 dimensions, and F is a Shure matrix, and N and Z need to satisfy the reversibility of the matrix V. When the above conditions are met, the system can meet the performance requirements by selecting appropriate matrices Z, F, and N.

[0115] Under the new model of high-order all-wheel 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, based on fault compensation, a fault-tolerant tracking controller is designed 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 by a parameterized method. The advantage of this design is that building the HOFA system does not change the actual meaning represented by each variable. For controller design, the use of a parameterized method is simple and feasible. At the same time, the design of an active fault-tolerant tracking controller can effectively reduce the impact of faults on the system control performance.

[0116] The present invention will be further described below in conjunction with specific examples.

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

[0118]

[0119] The parameter uncertainty here can be regarded as an internal fault in the system or a gain fault in the actuator, while the additive fault of the actuator is also considered.

[0120] According to step S1, the above parameter uncertainty model is established as the following high-order all-wheel 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] in,

[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 ω 1 =-1.2910,ω 2 =-1.3220. Design the fault estimator as follows:

[0125]

[0126] where x 1 (k)=y(k),x 2 (k) = d(k)

[0127] According to step S3, select parameters N=1, Z=[1 -1-1], have to

[0128] [K 1 K 2 K e ]=[-1.36400.5816-0.3430]

[0129] Next, the control effect of the fault-tolerant control law based on fault compensation is discussed. In order to show the superiority of the control strategy proposed in this paper, the existing control algorithm is compared 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 obviously has one less dimension, and there is no need to consider Δu(k-1). When the input time lag terms are more, the system dimension proposed in this application is less and less than the first-order state space dimension. This section will discuss the control effects of the two methods by numerical simulation with and without faults. At the same time, in order to show its tracking performance, the following performance index values ​​are introduced

[0130] Situation 1 Normal situation

[0131] from Figure 2 It can be seen that because the method used in this application uses less input information of the system, under the premise of almost consistent input, even without any influence of factors such as failure, the given value of output tracking takes a longer time to use in the initial operation of the system, but 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 Failure Condition

[0133] From the system modeling, we can know that the system fault d(k) includes internal fault, actuator gain fault and additive fault.

[0134] β=0.02*sin(0.1k)+0.8 (18)

[0135] 1.239w(k)=0.1*cos(π*k / 60) (19) In order to achieve good robust control performance, the existing MPC method obviously requires a larger input, such as Figure 4 As shown, in actual process, it is sometimes impossible to achieve. Using the observability of the observer, the fault can be estimated, such as Figure 5 , the above situation can be avoided by designing an active fault tolerance device based on fault compensation using the estimated faults, such as Figure 3 shown. Figure 3 The advantage of this design is also shown, that is, the tracking effect is the best after compensation, and can even reach the level of the situation without fault.

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

[0137]

[0138] Among them, x 1 ,x 2 ,x 3 ,u respectively represent the depth, pitch angle, pitch acceleration, and pitch rudder angle of the AUV, 0<α<1 represents the actuator gain failure, s a represents its additive fault, Δ represents x 3 The bounded interference can also be regarded as an internal fault of the system.

[0139] According to step S1, 1 By taking derivatives twice and combining the following two equations, the above parameter uncertainty model is established as the following equivalent third-order all-wheel drive system model:

[0140]

[0141] Reusing forward difference Discretizing the above system, we get the following discrete-time three-order all-wheel drive system model:

[0142]

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

[0144] According to step S2, select ω 1 =-0.3,ω 2 =-0.32,ω 3 =0.32,ω 4 =-0.2, the sampling period is designed to be 1 second, and the following estimator is established:

[0145]

[0146] Among them, x 1 (k)=y(k),x 2 (k) = y(k+1), x 3 (k) = y(k+2), x 4 (k) = d(k)

[0147] According to step S3, select parameters N=1, Z=[1 -1 1 -1], Then according to the above mentioned parameterization we can get:

[0148] [K 2 K 1 K 0 K e ]=[0.8352 -3.4134 2.0887 -0.0446],

[0149] Situation 1 Normal situation

[0150] exist Figure 6 and Figure 7 The blue curve shown in shows that, in the absence of a fault, the output tracks the setpoint smoothly and stably, while the input also remains relatively smooth.

[0151] Case 2 Failure Condition

[0152] Here, α=0.8+0.02sin(0.01*k),

[0153] Fault d(k) = -0.5108*(1 / 3)*(x 1 (k+2)-2x 1 (k+1)+x 1 (k))+0.9081(α-1)u+0.9081s a 665. Figure 8 The fault estimation curve is shown, where the fault estimation is implemented by the fault estimation algorithm proposed in this application. When the design of input (7) does not consider fault compensation, the output curve will fluctuate within a range under the influence of these faults, such as Figure 6 Once the compensation control is considered, the fluctuation range of the output curve is significantly reduced, as shown in Figure 6 As shown in the red curve in . In order to further demonstrate the advantages of active fault-tolerant control (FTC) based on fault compensation, the performance index value is 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 There is interference, no compensation 1.72 There is interference, there is compensation 1.5991

[0156] The technical principle of the present invention is described above in conjunction with specific embodiments. These descriptions are only for explaining the principle of the present invention and cannot be interpreted as limiting the scope of protection of the present invention in any way. Based on the explanations herein, those skilled in the art can associate other specific implementations of the present invention without paying creative labor, and these methods 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, establish the corresponding high-order all-wheel drive model; 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 through a parameterized algorithm.

2. The active fault-tolerant control method for an engineering system under the framework of a high-order all-wheel drive system according to claim 1, characterized in that: In the actual engineering system, the controlled system is first expressed as follows: y(k)+(H1±Δ1)y(k-1)+…+(H n ±Δ n )y(k-n)(1)=(L1±Λ1)u(k-1)+…+(L m ±Λ m )u(k-m) 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 changed 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).

3. The active fault-tolerant control method for an engineering system under the framework of a high-order 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), we get the following equation (6): Among them, ω1, ω2 are the parameters of the estimator, satisfying the matrix The characteristic root of is 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.

4. The active fault-tolerant control method for an engineering system under the framework of a high-order all-wheel drive system according to claim 1, 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 Respectively represent the gain coefficients of the corresponding items 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=[10…00] 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 algorithm 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, N are the parameter matrices in the algorithm, and the feedback gain matrix is ​​obtained by the above parameterized algorithm.

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