Fault-tolerant control method based on data driving

Abstract

The invention discloses a fault-tolerant control method based on data driving. According to the method, historical data are analyzed through a machine learning algorithm, a fault feature model is established, early recognition of potential faults of the system is achieved, and control parameters are dynamically adjusted according to real-time data so as to adapt to system change and fault conditions and ensure optimization of system performance. Compared with a traditional control method needing an accurate mathematical model, the control algorithm provided by the invention is more novel and simple in application condition. According to the method, the optimal performance of the system can be kept in various complex and uncertain environments, the control precision is effectively improved, and the method has good engineering application value.

Description

Technical Field

[0001] The invention relates to a data-driven fault-tolerant control method, and in particular to a neural network-based fault-tolerant control method. Background Art

[0002] Development of control theory Traditional control theory relies on accurate mathematical models to design controllers, an approach known as model-based control. However, as the complexity of the system increases, it becomes increasingly difficult to obtain accurate models, which has prompted researchers to explore control methods that do not rely on accurate models, namely data-driven control. The advent of the era of big data With the development of information technology, especially the popularity of the Internet and the Internet of Things, massive amounts of data have been generated. These data provide a new perspective for system analysis and control, making it possible to directly extract system behaviors and laws from data. Advances in artificial intelligence technology Artificial intelligence, especially the development of machine learning and deep learning technologies, provides powerful tools for data-driven control. These technologies can learn the dynamic characteristics of the system from large amounts of data and use them for controller design. Challenges in practical applications In many practical applications, the dynamic characteristics of the system are difficult to describe using traditional physical or mathematical models. For example, in areas such as autonomous driving and intelligent manufacturing, the uncertainty and complexity of the environment require that the control system be able to adapt to rapidly changing conditions, making data-driven control an effective solution. Advantages of data-driven fault-tolerant control Data-driven control does not rely on complex system models, and the input / output data of the system can be directly used to design the controller.

[0003] Fault-tolerant control of the system is one of the core tasks of studying data-driven fault-tolerant control. As modern systems develop towards large-scale and complex directions, the reliability and safety requirements of the system are getting higher and higher. For example, once a failure occurs in critical infrastructure such as aerospace, nuclear power plants, and chemical processes, it may cause huge losses of life and property. Therefore, it is urgent to improve the fault tolerance of these systems. The development of data-driven fault-tolerant control is closely related to the fault diagnosis technology based on neural networks. The development of fault detection and diagnosis technology provides important support for fault-tolerant control, enabling the system to respond in time when a fault occurs. Summary of the invention

[0004] The purpose of the present invention is to propose a data-driven fault-tolerant control method, which can effectively solve the fault problem of complex systems and achieve good control effects.

[0005] The specific technical solution of the present invention is as follows: A data-driven fault-tolerant control method comprises the following steps:

[0006] The system model of data-driven fault-tolerant control is as follows: y(k+1)=f(y(k),y(k-1),...,y(kn y ), u(k)+p(k), u(k-1)+p(k-1),…, u(kn u )+,(kn u ))

[0007] Where y(k)∈R represents the output, u(k)∈R represents the input, p(k)∈R represents the unknown actuator fault, k∈{0, 1,...,} represents the sampling time, f(·) represents the unknown nonlinear function, and n y and n u represents the unknown system order;

[0008] The above nonlinear system is transformed into a linear input-output data model using compact dynamic linearization technology, as shown below: y(k+1)=y(k)+Φ 1 (k)Δu(k)+Φ 2 (k)Δp(k)

[0009] Where, Δu(k)=u(k)-u(k-1), Δp(k)=p(k)-p(k-1), Φ 1 (k)∈R,Φ 2 (k)∈R is called a pseudo partial derivative, which satisfies Φ 1 (k)≤b 1 , Φ 2 (k)≤b 2 , b 1 and b 2 is a positive constant.

[0010] According to the data-driven fault-tolerant control method of claim 1, it is characterized in that the actuator fault is estimated by using a neural network and a data-driven fault-tolerant controller is provided, and the specific steps are as follows:

[0011] In the neural network structure, the network input vector is: X=[Δy(k), Δy(k-1), Δu(k-1), Δu(k-2)] T

[0012] The radial basis vector of the neural network L = [l 1 , l 2 ,…l m ] T , where l i is the Gaussian basis function, as shown below:

[0013] The center vector of the jth node in the network is: cj =[c j1 , c j2 , …c jm ]

[0014] The basis width vector of the network is: Q=[q 1 ,q 2 , ...q m ] T , Among them, q j is the base width parameter of node j

[0016] The weight vector of the network is: W=[w 1 , w 2 ,…w m ] T ,

[0017] The output of the neural network looks like this:

[0019] According to the gradient descent method, the iterative algorithm for output weight, node center and node base width parameters is as follows: q j (k) = q j (k-1)+η 1 Δq j +α 1 [q j (k-1)-q j (k-2)] c ji (k) = c ji (k-1)+η 1 Δc ji +α 1 [c ji (k-1)-c ji (k-2)] Among them, η 1 is the learning rate, α 1 is the momentum factor;

[0020] Design of compact dynamic linearization model Φ 1 (k), Φ 2 (k) Corresponding estimated value The update algorithm is as follows: In the formula, μ>0, γ>0, ɑ+β=1, the algorithm can ensure The estimation error is bounded;

[0021] According to the existing control input u(k) update algorithm, the control input update algorithm containing estimated fault information is obtained as follows: In the formula, is Φ 1 (k), Φ 2 (k), the estimated value of Δp(k), where ρ is the step sequence and λ is the weight factor.

[0022] According to claim 1, a data-driven fault-tolerant control method is characterized in that a proof of convergence of the data-driven fault-tolerant control method to ensure that the closed-loop system is consistently and ultimately bounded is provided, and the specific steps are as follows:

[0022] When * (k+1)=y * =const, the system is convergent.

[0023] The systematic error is defined as follows: e(k)=y * (k)-y(k)

[0024] Bringing the control algorithm into the dynamic linearization equation of the system, we can obtain:

[0025] Define the following function:

[0026] Simplify to get the following formula:

[0027] Subtract y from both ends of the above equation * We can get:

[0028] Due to Φ 1 (k), Φ 2 (k), Δp(k), are all bounded, so they satisfy: Where ξ 1 is a small positive number.

[0029] Substituting the above formula into the equation, we get the following formula: |e(k+1)|≤(1-d 1 )|e(k)|+ξ 1 |e(k+1)|≤(1-d 1) 2 |e(k-1)|+(1-d 1 )ξ 1 +ξ 1 |e(k+1)|≤(1-d 1 ) k |e(1)|+(1-d 1 ) k-1 ξ 1 +...(1+d 1 )ξ 1 +ξ 1

[0030] From B007, we can get the following formula: That is, the output error of the system is convergent. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0032] Figure 2 It is a tracking diagram of the system when there is no fault in the present invention;

[0033] Figure 3 The output tracking diagram when a fault is added to the embodiment using the method proposed by the present invention;

[0034] Figure 4 The output tracking diagram after the corresponding fault is processed by the method proposed by the present invention for the embodiment; DETAILED DESCRIPTION

[0036] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0037] like Figure 1 As shown, a data-driven fault-tolerant control method comprises the following steps:

[0038] Step 1: Set the initial value of the parameter;

[0039] Step 2: Update algorithm parameters;

[0040] Step 3: Generate control input u(k) in real time according to the updated algorithm parameters;

[0041] Step 4: Synchronously update the algorithm parameters according to the tracking error and compensation error generated by the control input u(k);

[0042] References

[0043] Z.Hou,R.Chi,and H.Gao,″An Overview of Dynamic-Linearization-BasedData-Driven Control and Applications,″IEEE Transactions on IndustrialElectronics,vol.64,no.5,pp.4076-4090,2017,doi:10.1109 / tie.2016.2636126.

[0046] J.Li,Z.Wang,T. and Y.Shen,“Unknown input observer design forlinear parameter-varying systems in a bounded error context,”IEEETrans.Autom.Control,vol.66,no.9,pp.4246-4251,Sep.2020.doi:10.1109 / TAC.2020.3027646.

Claims

1. A data-driven fault-tolerant control method, characterized in that: The following steps are involved: Establish input and output data model containing fault signals; Design a neural network-based fault observer and construct a fault-tolerant controller; A convergence proof of a data-driven fault-tolerant control method is given to ensure that the closed-loop system is consistently and eventually bounded.

2. The data-driven fault-tolerant control method according to claim 1, characterized in that: An input-output data model containing a fault signal is established, and the discrete mathematical expression of the data-driven system containing the fault signal is as follows: y(k+1)=f(y(k),y(k-1),...,y(kn y ), u(k)+p(k), u(k-1)+p(k-1),..., u(kn u )+p(kn u )) where y(k)∈R represents the output, u(k)∈R represents the input, p(k)∈R represents the unknown actuator fault, k∈{0, 1, ...,} represents the sampling time, f(·) represents the unknown nonlinear function, n y and n u represents the unknown system order; The above nonlinear system is transformed into a linear input-output data model using compact dynamic linearization technology, as shown below: y(k+1)=y(k)+Φ1(k)Δu(k)+Φ2(k)Δp(k) In the formula, Δu(k)=u(k)-u(k-1), Δp(k)=p(k)-p(k-1), Φ1(k)∈R, Φ2(k)∈R are called pseudo partial derivatives, which satisfy Φ1(k)≤b1, Φ2(k)≤b2, and b1 and b2 are positive constants.

3. The data-driven fault-tolerant control method according to claim 1, characterized in that: The neural network is used to estimate the actuator fault and a data-driven fault-tolerant controller is given. The specific steps are as follows: In the neural network structure, the network input vector is: X=[Δy(k),Δy(k-1),Δu(k-1),Δu(k-2)] T The radial basis vector of the neural network L = [l1, l2, ...l m ] T , where l i is the Gaussian basis function, as shown below: The center vector of the jth node in the network is: c j =[c j1 ,c j2 ,…c jm 】 The basis width vector of the network is: Q=[q1,q2,…q m ] T , Among them, q j is the base width parameter of node j The weight vector of the network is: W=[w1,w2,…w m ] T , The output of the neural network looks like this: According to the gradient descent method, the iterative algorithm for output weight, node center and node base width parameters is as follows: q j (k)=q j (k-1)+η1Δq j +α1[q j (k-1)-q j (k-2)] c ji (k)=c ji (k-1)+η1Δc ji +α1[c ji (k-1)-c ji (k-2)] Among them, η1 is the learning rate and α1 is the momentum factor; Design the corresponding estimated values ​​of Φ1(k) and Φ2(k) in the compact dynamic linearization model The update algorithm is as follows: In the formula, μ>0, γ>0, α+β=1, the algorithm can ensure The estimation error is bounded; According to the existing control input u(k) update algorithm, the control input update algorithm containing estimated fault information is obtained as follows: In the formula, are the estimated values ​​of Φ1(k), Φ2(k), Δp(k), where ρ is the step sequence and λ is the weight factor.

4. The data-driven fault-tolerant control method according to claim 1, characterized in that: A data-driven fault-tolerant control method is given to ensure that the closed-loop system is uniformly and eventually bounded. The specific steps are as follows: B001: When y * (k+1)=y * =const, the system is convergent. B002: System error is defined as follows: e(k)=y * (k)-y(k) B002: Bringing the control algorithm into the dynamic linearization equation of the system yields: B003: Define the following function: B004: Simplify B002 to obtain the following formula: B005: Subtract y from both ends of the above equation * We can get: B006: Due to Φ1(k), Φ2(k), Δp(k), are all bounded, so they satisfy: Where ξ1 is a small positive number. B007: Substitute B005 into B006 to obtain the following formula: |e(k+1)|≤(1-d1)|e(k)|+ξ1 |e(k+1)|≤(1-d1) 2 |e(k-1)|+(1-d1)ξ1+ξ1 |e(k+1)|≤(1-d1) k |e(1)|+(1-d1) k-1 ξ1+…(1+d1)ξ1+ξ1 B008: From B007, we can get the following formula: That is, the output error of the system is convergent.

Images