Integrated permanent magnet direct current motor dynamic event trigger fault estimation and state interval generation method

Abstract

The invention discloses an integrated permanent magnet direct current motor dynamic event trigger fault estimation and state interval generation method. The method comprises the following steps: firstly, designing a dynamic event triggering mechanism based on a system output real-time value and a historical value to balance triggering performance and system performance; then designing an integrated fault estimation method based on a trigger output signal to simultaneously estimate the system state, the system fault and the sensor fault of the permanent magnet direct current motor and generate a state interval; when the method is applied to the permanent magnet direct current motor, the fault estimation effect is good, the state interval generation is tight, and the communication frequency is remarkably reduced.

Description

Technical Field

[0001] The invention relates to an integrated fault estimation and state interval generation method, and in particular to an integrated permanent magnet direct current motor dynamic event triggered fault estimation and state interval generation method. Background Art

[0002] In recent years, governments and enterprises have stepped up efforts to promote the widespread use of renewable energy and actively advocated the use of clean energy for electricity production. Among them, wind energy is widely regarded as a clean and sustainable energy solution due to its higher cost-effectiveness compared to traditional fossil fuels and nuclear energy. This advantage has promoted the academic community to conduct in-depth research on the stability issues of wind turbine systems. In the field of wind power generation, permanent magnet DC generators are widely used, mainly due to their direct drive capability, low speed and low maintenance cost. However, industrial systems are inevitably affected by adverse factors such as external interference, environmental noise and component failures, which may cause abnormal operation or even shutdown of wind turbine systems. To this end, developing efficient fault estimation methods to detect and compensate for the impact of faults in a timely manner has become the focus and challenge of current research.

[0003] In addition, with the rapid development of communication technology and its deep integration with industrial systems, networked control has gradually become an important means to promote the development of industrial systems. In the networked control framework, data exchange is usually carried out through a time-triggered (periodic) network channel. However, with the expansion of the system scale and the frequent transmission of redundant data packets, the problem of network congestion has become increasingly prominent, seriously affecting the performance of the system. Therefore, it is urgent to introduce efficient communication strategies in networked control systems to reduce the frequency of data transmission and save limited network resources. Existing research is mostly integrated with static event triggering strategies, which have limited effects in reducing network load. To this end, improving the existing event triggering strategy to further optimize bandwidth usage has become one of the key directions of current research. Summary of the invention

[0004] The purpose of the present invention is to propose an integrated method for dynamic event-triggered fault estimation and state interval generation of permanent magnet DC motors, which can effectively improve the fault estimation and state interval generation effects of permanent magnet DC motors in an industrial network environment.

[0005] The specific technical solution of the present invention is as follows: An integrated method for estimating faults triggered by dynamic events of permanent magnet DC motors and generating state intervals, comprising the following steps:

[0006] Design a dynamic event trigger mechanism based on the real-time and historical values ​​of the system output to balance the trigger performance and system performance:

[0007] The dynamic model of permanent magnet DC motor is as follows:

[0008]

[0009] Among them, F M represents the friction coefficient, J represents the rotor inertia, C M Represents the motor constant, R M Indicates the armature resistance, L M represents armature inductance, θ represents position, ω represents speed, i represents current, d represents load torque disturbance, and V represents voltage;

[0010] Next, set the sampling interval to T and use the Euler method to transform the above continuous-time permanent magnet DC motor model into the following discrete system model:

[0011]

[0012] where x(k) = [θ ω i] T ,u(k)=V,f a (k) indicates system failure, f s (k) represents sensor failure, v(k) represents sensor noise,

[0013] For the above discrete permanent magnet DC motor model, in order to reduce the network transmission burden, a dynamic event trigger mechanism based on the real-time value and historical value of the system output is designed to balance the trigger performance and system performance; first, the estimated signal is verified by the event criterion, and then it is transmitted to the integrated fault estimator through the ideal network; the dynamic event trigger mechanism is constructed as follows:

[0014] k s+1 =inf{k>k s |||e y (k)|| 2 ≥σ(k)}

[0015] Among them, e y (k) = y(k) - y(k s ) represents the output trigger error, k s Indicates the last triggering time, k s+1 represents the next triggering moment, and the dynamic threshold σ(k) is updated by the following formula:

[0016]

[0017] in, μ is the weight parameter and h is the summation length.

[0018] Furthermore, an integrated fault estimation method based on the trigger output signal is designed to simultaneously estimate the system state, system fault and sensor fault of the permanent magnet DC motor and generate the state interval. The specific steps are as follows:

[0019] First, construct the following augmented system:

[0020]

[0021] in, I represents the identity matrix of appropriate dimension;

[0022] Next, based on and adding H1y(k+1) on both sides of the equation, the above system can be rewritten as:

[0023]

[0024] in, H2 is a diagonal matrix of suitable dimensions,

[0025] By multiplying the inverse matrix of matrix E on both sides, we can get the following integrated system model:

[0026]

[0027] in,

[0028] Based on the above integrated system model, the following integrated auxiliary estimation system is designed:

[0029]

[0030] in, Δf a (k) = f a (k+1)-f a (k) α is a positive constant;

[0031] Next, the integrated fault estimator is designed as follows;

[0032]

[0033] in, represents the estimated value of ξ(k), represents f a The estimated value of (k), represents the estimated value of ψ(k), express The estimated value of and is the observer gain to be designed;

[0034] Select The following error system can be obtained:

[0035] e(k+1)=A a e(k)+E a1 e y (k)+E a2 e y (k+1)+D a ω(k)+N a1 v(k)+N a2 v(k+1)+F a Δf a (k)

[0036] in,

[0037] The integrated fault estimator can simultaneously estimate the system state, system fault and sensor fault of the permanent magnet DC motor. The proof process is as follows:

[0038] D001: Select e(k-1)=E k-1 z(k-1) and let z(k-1) satisfy z T (k-1)z(k-1)≤1, then e(k) can be expressed as:

[0039] e(k)=A a E k-1 z(k-1)+E a1 e y (k-1)+E a2 e y (k)+D a ω(k-1)+N a1 v(k-1)+N a2 v(k)+F a Δf a (k-1)

[0040] Among them, E k-1 From the equation Get, P k-1 Generate a matrix for the interval shape at time k-1;

[0041] D002: Next, select η(k)=[1 z(k-1) e y (k-1) e y (k) ω(k-1) v(k-1) v(k) Δf a (k-1)] T , e(k) can be rewritten as:

[0042] e(k)=∏ k η(k)

[0043] In the formula, ∏ k =[0 A a E k-1 E a1 E a2 D a N a1 N a2 F a ];

[0044] D003: Based on target T (k)P k e(k)≤ 1 and D002, we can get

[0045]

[0046] Where P k Generate a matrix for the interval shape at time k, Φ0 = diag{-1; 0; 0; 0; 0; 0; 0}, diag{.} represents a diagonal matrix;

[0047] D004: Next, suppose d T (k)R -1 d(k)≤1,v T (k)Q -1 v(k)≤1,Δf a T (k)O -1 Δf a (k)≤1 and combined with the event triggering condition, we can get:

[0048]

[0049] D005: Then, using the S process technology, D003 can be scaled to:

[0050]

[0051] Among them, τ i is a positive constant;

[0052] D006: Then, using Schur's complement lemma for D005, we can obtain the following stability condition:

[0053] BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a system structure diagram of an embodiment;

[0055] Figure 2The estimated graph and interval of the motor position θ using the method proposed by the present invention are shown in the embodiment;

[0056] Figure 3 The estimated graph and interval of the motor speed ω using the method proposed by the present invention are shown in the embodiment;

[0057] Figure 4 The estimated graph and interval of the motor current i using the method proposed by the present invention are shown in the embodiment;

[0058] Figure 5 The motor system fault f under the method proposed by the embodiment of the present invention is a Estimation graph of ;

[0059] Figure 6 The motor sensor fault f under the method proposed by the present invention is used in the embodiment s Estimation graph of ;

[0060] Figure 7 The trigger diagram of the event triggering of the embodiment using the method proposed by the present invention; DETAILED DESCRIPTION

[0061] 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.

[0062] like Figure 1 As shown, an integrated method for estimating faults triggered by dynamic events in a permanent magnet DC motor and generating state intervals comprises the following steps:

[0063] Step 1: Set the initial values ​​of various parameters;

[0064] Step 2: sampling sensor output y(k);

[0065] Step 3: Update the threshold parameter σ(k);

[0066] Step 4: Use the threshold parameter σ(k) and the output y(k) to verify the event trigger condition and update the trigger output y(k s );

[0067] Step 5: Use trigger output y(k s ) updating the integrated fault estimator, outputting the estimated values ​​of the system state, system fault and actuator fault of the permanent magnet DC motor and saving them in the register;

[0068] Step 6: Solve the stability condition and obtain the shape matrix P k and observer gain and Using the shape matrix P k Generate state intervals;

[0069] Step 7. Repeat steps 2, 3, 4, 5, and 6 until the simulation time ends.

[0070] An embodiment of the present invention is described below:

[0071] Consider the system parameters shown in the following table: symbol value symbol value symbol value symbol value <![CDATA[F M ]]> 0.001 J 0.0008 <![CDATA[C M ]]> 1.4 <![CDATA[R M ]]> 4.575 <![CDATA[L M ]]> 0.017 T 0.001

[0072] Figure 1 is a system structure diagram of an embodiment of the present invention; Figure 2-Figure 4 It is an estimation diagram and interval of the state of the permanent magnet DC motor using the method proposed by the present invention; Figure 5 and Figure 6 The fault estimation effect of the method proposed in the present invention is demonstrated; Figure 7 The trigger effect diagram of the dynamic event trigger mechanism designed by the present invention is shown; Figure 2-Figure 6 It can be seen from the figure that the proposed method successfully estimates the system state, system fault and actuator fault at the same time, and successfully generates a credible interval of the permanent magnet DC motor state. Figure 7 It can be seen that the proposed event trigger mechanism further reduces the number of signal transmissions and reduces the network bandwidth usage while ensuring the same system performance.

[0073] References

[0074] [1] Yan, S., Gu, Z., Park, JH, & Xie, X. (2021). Adaptive memory-event-triggered static output control of TS fuzzy wind turbine systems. IEEE Transactions on Fuzzy Systems, 30(9), 3894-3904.

[0075] [2]Peng, C., & Yang, TC (2013). Event-triggered communication and H∞control co-design for networked control systems. Automatica, 49(5), 1326-1332.

Claims

1. An integrated method for estimating faults triggered by dynamic events in permanent magnet DC motors and generating state intervals, characterized in that: The following steps are involved: Design a dynamic event trigger mechanism based on the real-time and historical values ​​of the system output to balance the trigger performance and system performance; An integrated fault estimation method based on trigger output signals is designed to simultaneously estimate the system state, system faults and sensor faults of permanent magnet DC motors and generate state intervals.

2. According to the integrated method for dynamic event-triggered fault estimation and state interval generation of permanent magnet DC motors described in claim 1, a dynamic event trigger mechanism based on real-time value and historical value of system output is designed to balance trigger performance and system performance, and the specific steps are as follows: The dynamic model of permanent magnet DC motor is as follows: in, F M represents the friction coefficient, J represents the rotor inertia, C M Represents the motor constant, R M Indicates the armature resistance, L M represents armature inductance, θ represents position, ω represents speed, i represents current, d represents load torque disturbance, and V represents voltage; Next, set the sampling interval to T and use the Euler method to transform the above continuous-time permanent magnet DC motor model into the following discrete system model: where x(k) = [θ ω i] T ,u(k)=V,f a (k) indicates system failure, f s (k) represents sensor failure, v(k) represents sensor noise, For the above discrete permanent magnet DC motor model, in order to reduce the network transmission burden, a dynamic event trigger mechanism based on the real-time value and historical value of the system output is designed to balance the trigger performance and system performance; first, the estimated signal is verified by the event criterion, and then it is transmitted to the integrated fault estimator through the ideal network; the dynamic event trigger mechanism is constructed as follows: k s+1 =inf{k>k s |||e y (k)|| 2 ≥σ(k)} Among them, e y (k) = y(k) - y(k s ) represents the output trigger error, k s Indicates the last triggering time, k s+1 represents the next triggering moment, and the dynamic threshold σ(k) is updated by the following formula: in, μ is the weight parameter and h is the summation length.

3. According to the integrated method for dynamic event-triggered fault estimation and state interval generation of permanent magnet DC motor in claim 1, an integrated fault estimation method based on trigger output signal is designed to simultaneously estimate the system state, system fault and sensor fault of the permanent magnet DC motor and generate the state interval, and the specific steps are as follows: First, construct the following augmented system: in, I represents the identity matrix of appropriate dimension; Next, based on The fact that H is added to both sides of the equation 1y (k+1), the above system can be rewritten as: in, H2 is a diagonal matrix of suitable dimensions, By multiplying the inverse matrix of matrix E on both sides, we can get the following integrated system model: in, Based on the above integrated system model, the following integrated auxiliary estimation system is designed: in, Δf a (k) = f a (k+1)-f a (k) α is a positive constant; Next, the integrated fault estimator is designed as follows: in, represents the estimated value of ζ(k), represents f a The estimated value of (k), represents the estimated value of ψ(k), express The estimated value of and is the observer gain to be designed; Select The following error system can be obtained: e(k+1)=A a e(k)+E a1 e y (k)+E a2 e y (k+1)+D a ω(k)+N a1 v(k)+N a2 v(k+1)+F a Δf a (k) in, The integrated fault estimator can simultaneously estimate the system state, system faults and sensor faults of the permanent magnet DC motor. The proof process is as follows: B001: Select e(k-1)=E k-1 z(k-1) and let z(k-1) satisfy z T (k-1)z(k-1)≤1, then e(k) can be expressed as: e(k)=A a E k-1 z(k-1)+E a1 e y (k-1)+E a2 e y (k)+D a ω(k-1)+N a1 v(k-1)+N a2 v(k)+F a Δf a (k-1) Among them, E k-1 From the equation Get, P k-1 Generate a matrix for the interval shape at time k-1; B002: Next, select η(k)=[1 z(k-1) e y (k-1) e y (k) ω(k-1) v(k-1) v(k)Δf a (k-1)] T , e(k) can be rewritten as: e(k)=∏ k the(k) In the formula, ∏ k =[0 A a E k-1 E a1 E a2 D a N a1 N a2 F a ]; B003: Based on target T (k)P k e(k)≤1 and B002, we can get Where P k Generate a matrix for the interval shape at time k, Φ0 = diag{-1; 0; 0; 0; 0; 0; 0}, diag{.} represents a diagonal matrix; B004: Next, suppose d T (k)R -1 d(k)≤1,v T (k)Q -1 v(k)≤1,Δf a T (k)O -1 Δf a (k)≤1 and combined with the event triggering condition, we can get: B005: Then, using the S-process technique, B003 can be scaled to: Among them, τ i is a positive constant; B006: Then, using Schur's complement lemma for B005, we can obtain the following stability condition:

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