System dynamic fault-tolerant control method and system for actuator faults

Abstract

The invention relates to the technical field of communication networks, and discloses a system dynamic fault-tolerant control method and system for an actuator fault, and the method comprises the steps: building a state space model of the actuator fault in a control system; a control law and a 2D dynamic model of the control system are constructed according to the state space model, the control law is based on a dynamic iterative learning updating law, the control law is used for controlling an input vector of an actuator, and the control law is used for ensuring stable operation of the control system when the actuator breaks down; analyzing the stability of the control system according to a stability condition and the 2D dynamic model; based on the stability of the control system, designing controller parameters of the control system; the robustness of the control system is analyzed through the controller parameters, the robustness of the control system is ensured, the robustness and stability of the control system can be improved, and the continuity of the system is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of communication networks, and in particular to a system dynamic fault-tolerant control method and system for actuator failures. Background Art

[0002] In the design of automated robotic arm control systems on current industrial production lines, many use static state feedback and feedforward information to improve the control performance of the system. Static iterative learning control mainly relies on feedforward information to correct the control signal to achieve complete tracking tasks within a limited time. However, this method has some limitations, such as the blindness of learning law parameter selection and the weak anti-interference ability of the algorithm. In the case of actuator failure, the system may not be able to maintain stable control. In contrast, the dynamic iterative learning controller is more flexible and uses more signals inside the system to build and update the controller. By combining the open-closed loop comprehensive iterative learning control structure with feedback and feedforward effects, the application scope of iterative learning control is broadened and its practicality is enhanced. In the face of actuator failure, the output can better track the desired trajectory.

[0003] The prior art discloses a reliable control method for a nonlinear switching system with an actuator failure, comprising: step 1: giving a mathematical description of the nonlinear switching system through a TS fuzzy model, designing a reliable static output feedback controller according to the system switching rules and fuzzy basis functions, and assuming that the parameters of the reliable static output feedback controller are known, to obtain a mathematical expression of the closed-loop system; step 2: constructing a random Lyapunov function and giving a dissipative performance index, establishing sufficient conditions to ensure the random stability and dissipativeness of the closed-loop system; step 3: using an iterative algorithm to linearize the sufficient conditions in step 2 and solve the parameters of the reliable static output feedback controller. The problem that the system performance deteriorates or even becomes unstable due to actuator failure is solved; the nonlinear switching system can still be effectively controlled when the actuator fails, and the static output feedback controller depends on the measured value of the system, and does not require the system state to be measurable, thereby improving practicality. In the prior art, the problem that the system performance deteriorates or even becomes unstable due to actuator failure is solved by designing a static output feedback controller, but the learning law parameters are selected blindly and the system has weak anti-interference ability. Summary of the invention

[0004] The primary purpose of the present invention is to overcome the problems existing in the prior art and provide a system dynamic fault-tolerant control method for actuator failures. The present invention can improve the robustness and stability of the control system and ensure the continuity of the system.

[0005] As another object of the present invention, a system adapted to the method based on the aforementioned object is provided.

[0006] As another object of the present invention, a non-volatile storage medium suitable for storing a computer program implemented according to the method described is provided.

[0007] In order to achieve the above object, the present invention provides a system dynamic fault-tolerant control method for actuator failure, comprising the following steps: Establish state-space models of actuator failures in control systems; Constructing a control law and a 2D dynamic model of the control system according to the state space model, wherein the control law is based on a dynamic iterative learning update law, the control law is used to control an input vector of an actuator, and the control law is used to ensure that the control system operates stably when an actuator fails; Analyzing the stability of the control system based on stability conditions and the 2D dynamic model; Designing controller parameters of the control system based on the stability of the control system; The robustness of the control system is analyzed using the controller parameters to ensure the robustness of the control system.

[0008] Furthermore, the establishment of a state space model of actuator failure in the control system specifically includes: (1) Construct an initial state space model of the actuators in the control system that repeatedly execute batch processing over a period of time; (3) Establish a fault model when the actuator fails. The actuator failure includes three types: Conditions: no failure, complete failure and partial failure; (3) Establishing the state space model based on the initial state space model and the fault model.

[0009] Furthermore, the initial state space model is as follows:

[0010] in, , and The control system is The state vector, input vector, and output vector of each run, , , and are the parameter matrices of the corresponding dimensions of the system, is the time period, To run the batch.

[0011] Furthermore, the fault model for establishing a fault in the actuator is as follows:

[0012] in, The first A signal is a variable that fails. is the controlled sequence of the control system, is the failure coefficient when the actuator fails, satisfy:

[0013] If the actuator fails, then ; If the actuator fails completely, then ; If the actuator fails partially, .

[0014] Furthermore, the state space model is as follows: .

[0015] Furthermore, constructing the control law and 2D dynamic model of the control system according to the state space model includes: (1) Establish a dynamic iterative learning update law, which is used to update the correction value of the control system. as follows: ; (2) Based on the dynamic iterative learning update law, the control law of the control system is constructed, and the control law is as follows: ; (3) Discretize the state space model to obtain a 2D dynamic model, which is as follows:

[0016] in, ,

[0017] , .

[0018] Furthermore, the establishment of a dynamic iterative learning update law includes: (1) Establishing an output tracking error based on a control target, wherein the control target is that under the permissible condition of an actuator failure, the trajectory output by the control system is close to the desired trajectory, and the output tracking error The calculation method is as follows:

[0019] in, is the expected trajectory, is the trajectory of the control system output, that is, the output vector; (2) Define an operator, the operator as follows:

[0020] The operator is used to represent along Direction error; (3) Establish the internal state equation of the controller based on the output tracking error and the operator , as follows:

[0021] in, , and They are all gain matrices of the internal state equations of the controller to be designed; (4) Constructing a dynamic iterative learning update law based on the output tracking error, the operator and the internal state equation.

[0022] Furthermore, the stability conditions include: , used to ensure convergence on the output iteration batch; , which is used to ensure the convergence of the repetition cycle time; the transfer function matrix is , , , , which is used to ensure convergence in both time and batch.

[0023] In order to achieve another object of the present invention, the present invention provides a system dynamic fault-tolerant control system for actuator failure, comprising: The first building module is used to build a state space model of actuator failure in the control system; A second building module: used for building a control law and a 2D dynamic model of the control system according to the state space model, wherein the control law is based on a dynamic iterative learning update law, the control law is used to control an input vector of an actuator, and the control law is used to ensure that the control system operates stably when an actuator fails; A first analysis module: used for analyzing the stability of the control system according to the stability condition and the 2D dynamic model; Design module: used for designing controller parameters of the control system based on the stability of the control system; The second analysis module is used to analyze the robustness of the control system using the controller parameters to ensure the robustness of the control system.

[0024] In order to achieve another purpose of the present invention, the present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer-stored program is executed by a processor, the system dynamic fault-tolerant control method for actuator failure is implemented.

[0025] Compared with the prior art, the present invention has the following beneficial effects: The present invention establishes a control system control law based on a dynamic iterative learning update law, optimizes iterative controller parameters, ensures that the actuator can achieve accurate tracking and stable control of the system output in a fault environment, effectively reduces the impact of uncertainty in the control system on the performance, improves the robustness and stability of the control system, and ensures the continuity of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a system dynamic fault-tolerant control method for actuator failure in embodiment 1 of the present invention; Figure 2 This is a block diagram of a system dynamic fault-tolerant control system for actuator failures according to Embodiment 3 of the present invention; Figure 3 A monolithic XY stage for radial and axial motion according to embodiment 2 of the present invention; Figure 4 : are the expected trajectories and output trajectories of different iteration times of embodiment 2 of the present invention; Figure 5 is a spectrum diagram of the desired trajectory after fast Fourier transform according to embodiment 2 of the present invention; Figure 6 is a diagram of expected trajectory and platform output trajectory for robust testing in Example 2 of the present invention; Figure 7 It is a robustness test diagram of four uncertain situations in embodiment 2 of the present invention. DETAILED DESCRIPTION

[0027] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0028] Example 1 like Figure 1 As shown, a system dynamic fault-tolerant control method for actuator failure according to a preferred embodiment of the present invention includes: Step S1: Establish a state space model of actuator failure in the control system; In an optional embodiment, step S1 specifically includes: (1) Construct an initial state space model of the actuators in the control system that repeatedly execute batch processing over a period of time; Specifically, in the industrial manufacturing process, this embodiment considers a control system that repeatedly performs a given task in a batch process (called a batch process / cycle) over a period of time, and its dynamic characteristics can be described by a state space model: (1) in, , and The control system is The state vector, input vector, and output vector of each run, , , and are the parameter matrices of the corresponding dimensions of the system, is the time period, To run the batch.

[0029] (2) Establish a fault model when the actuator fails. The actuator failures include three types: Conditions: no failure, complete failure and partial failure; Specifically, for the controlled sequence of the operating system , Indicates the first A signal is a variable that causes a fault. The fault model is expressed in the following form: (2) The actuator failure coefficient The following conditions are met: (3) parameter and is a known scalar. The coefficient is unknown, but is assumed to vary within a known range. The actuator fault model considered in this embodiment corresponds to three situations: (I) the industrial control system actuator has no faults, ,(II) Complete failure of industrial control system actuator, ,(III) Operation of the actuator part of the industrial control system, .

[0030] In order to design a reliable control law, the goal is to make the system output as close to the predetermined trajectory as possible. , even in the event of an actuator failure, it can maintain good performance. First, the relevant symbols and parameters need to be defined:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Then, there must be an unknown matrix Enables:

[0038] and The following relations are satisfied:

[0039] in

[0040]

[0041] (3) Establishing a state space model based on the initial state space model and the fault model: Understandably, this means that in an industrial manufacturing process, if an actuator fails, the failure will The entire process is affected in a linear and repetitive manner. The state space model is as follows: (4) Step S2: constructing a control law and a 2D dynamic model of the control system according to the state space model, wherein the control law is based on a dynamic iterative learning update law, the control law is used to control the input vector of the actuator, and the control law is used to ensure that the control system operates stably when an actuator fails; In S1, by modeling the faults of the system actuators in detail, we can understand the impact of different fault states on the dynamic performance of the system. These fault states will be explicitly represented in the state space model. Subsequently, in this step, based on the known fault model, control strategies will be designed to ensure that the system can remain stable or achieve the expected performance when a fault occurs.

[0042] In an optional embodiment, the control law and the 2D dynamic model of the control system are constructed according to the state space model, including: (1) Establish a dynamic iterative learning update law. The dynamic iterative learning fault-tolerant update law is used to update the correction value of the control system. Specifically, a dynamic iterative learning update law is established, including: (a) Establishing an output tracking error based on a control target, wherein the control target is that the trajectory of the control system output is close to the desired trajectory under permissible conditions when the actuator fails, and the output tracking error The calculation method is as follows: (5) in, is the expected trajectory, is the trajectory of the control system output, that is, the output vector; for system (4), the following control law is adopted: (6) In formula (6) Indicates the current control input, is the control input of the previous batch, is the correction amount that the control system updates; (b) Define an operator, the operator as follows: (7) The operator is used to represent along Direction error; (c) Establish the internal state equation of the controller based on the output tracking error and operator , as follows: (8) in, , and They are all gain matrices of the internal state equations of the controller to be designed; (d) Construct dynamic iterative learning update law based on output tracking error, operator and internal state equation, dynamic iterative learning fault-tolerant update law as follows: (9) in , and is the parameter matrix to be designed; (2) Discretize the state space model to obtain a 2D dynamic model. Specifically, in order to discretize the linear repetitive process of actuator failure, we define (10) Then we get a 2D dynamic model to describe the dynamic behavior of the system. The 2D dynamic model is as follows: (11) in, ,

[0043] , .

[0044] Step S3: Analyze the stability of the control system based on the stability condition and the 2D dynamic model; In an optional embodiment, in this step, the discrete system equation (11) constructed in the previous step is subjected to stability analysis. Given that the necessary and sufficient conditions for the system (11) to be stable along the channel must satisfy the following three conditions: (1). ; (2). ; (3). The transfer function matrix is , , The modulus of all eigenvalues ​​of is strictly less than 1.

[0045] Among them, (1) is used to ensure convergence on the output iteration batch; (2) is used to ensure convergence on the repetition cycle time; (3) is used to ensure convergence on both time and batch.

[0046] Since this embodiment explores the stability in the frequency domain, the following lemma can be introduced as a reference: Transfer function of discrete linear system in frequency domain If there is a symmetric matrix and a matrix of appropriate dimension , so that the inequality: (12) holds, then the following frequency domain inequality also holds , (13) in,

[0047] And the matrix Can be divided into: (14) According to the frequency range It is expressed in the following form: (15) Therefore, for the above-mentioned fault-repeating system (11), the present invention proposes that if there is a positive definite matrix and a matrix of appropriate dimension So that the following linear matrix inequality holds: (16) (17) Then the system output can asymptotically track the expected output signal on both the time axis and the batch axis.

[0048] Because formula (16) is equivalent to (18) Known , so we can deduce , satisfying the stability condition (2) In the frequency domain, equation (12) can be rewritten as (19) It can be expressed as ,in

[0049]

[0050]

[0051] From the projection theorem, we know that if If it is established, then there must exist:

[0052] Therefore, formula (19) still holds , so that it satisfies ,set up:

[0053]

[0054] At this point, the following inequality holds: (20) Known , , if the above formula holds, then Established, available , satisfying stability condition (1); It can be expressed as: (twenty one) Next, applying Schur's complement theorem to equation (21) yields equation (17).

[0055] Since equation (17) holds, equation (21) can be further written as: (twenty two) That is (twenty three) The stability condition (3) is satisfied, so it is proved that the system (11) is stable. This step lays the foundation for the subsequent design of the fault-tolerant controller, because ensuring system stability is the key condition to prevent the system from getting out of control or diverging when a fault occurs.

[0056] Step S4: designing controller parameters of the control system based on the stability of the control system; In an optional embodiment, the control parameters cannot be directly solved due to the coupling between the system parameters. Therefore, this step requires designing the control parameters so that the control parameters can be effectively solved under the premise of ensuring the stability of the system. Specifically, according to the analysis of S3, the control system is stable. Then, based on the projection lemma, there exists

[0057] Make , , , , , it can be deduced (twenty four) Then get .

[0058] Similar to S3, you can get (25) Multiply (25) by Then multiply The transpose of (26) make , known , , where the parameters , formula (26) can be rewritten as (27) make , , , ,satisfy, .

[0059] From step three, we can know

[0060] Established. Multiply the above formula by the front and back and its transpose, we can get (28) make , , , , , .

[0061] Can be launched

[0062] in , , , , , .

[0063] Available ;in , That is (29) Established, the control parameter can be obtained as (30) Step S5: Analyze the robustness of the control system using controller parameters to ensure the robustness of the control system.

[0064] In an optional embodiment, S4 is proposed under very ideal conditions, but in practical applications, accurately building a model of a dynamic system is often a difficult task because there is often uncertainty in the parameters in the system model. This uncertainty will have a negative impact on the performance of the system, causing the system to fail to meet the control requirements and may even cause the system to become unstable. Therefore, this section will analyze the uncertain system.

[0065] This step considers the linear repeated process with norm uncertainty: (31) in , , , represents the admissible norm bounded uncertainty, satisfying: (32) in , , , represents a known matrix, represents an uncertain disturbance, satisfying: (33) The state space model of the repetitive process of the controlled system can be obtained as follows: (34) , , , , For a repetitive system with nondeterministic faults (34), for any , if there exists a matrix , the reversible matrix , and the matrix , , , , , , scalar , So that the following linear matrix inequality holds: (35) (36) in , , , , , , , , , , , , Then, the system (34) is stable in the entire operating frequency range. The gain matrix of the update law of iterative learning fault-tolerant control is as follows: (37) According to step 3, after adding uncertainty, we can deduce: (38) We can get: (39) Formula (39) can be rewritten as (40) According to Schur's complement theorem, we can get (41) (42) Multiply the left-hand side matrix of inequality (42) by the diagonal matrix , we can get equation (35), and similarly we can get equation (36).

[0066] Example 2 In order to verify the stability of the system dynamic fault-tolerant control method for actuator failure proposed in Example 1, this embodiment experimentally verifies the method proposed in Example 1 on a high-precision two-dimensional machining platform. Figure 3 As shown, it is ensured that the design method is not only feasible in theory, but also can meet the needs of industrial manufacturing processes in practical applications.

[0067] Next, we will conduct an in-depth analysis and study of the X-axis and Y-axis transfer functions in the system. The system is discretized into the sampling time: (43) Assume that the operating frequency range of the system is divided into three frequency bands: low, medium and high as shown in Table 1: Table 1

[0068] That is , during the iteration process, the system has an actuator failure, and the failure coefficient . Figure 5 The spectrum of the desired trajectory is shown in Figure 2. The effective harmonic range of the reference trajectory varies in the low frequency range, which means that the motion of the system is more significant in the low frequency range, so .

[0069] The fault-tolerant control effect can be achieved by using the model and Therefore, through steps four to six, the dynamic fault-tolerant controller of the x-axis can be obtained as follows:

[0070] Similarly, the dynamic fault-tolerant controller of the y-axis can be obtained:

[0071] Control effect such as Figure 4 As shown in Figure 2, through the continuous iterative process, it can be observed that as the number of iterations increases, the actual output trajectory of the system gradually begins to be consistent with the expected trajectory.

[0072] At the same time, the system can be tested for uncertainty, such as Figure 6As shown in the figure, in the initial stage, due to the existence of random errors and initial deviations, the actual output trajectory may be significantly different from the desired trajectory. However, through the adaptive ability of the dynamic iterative learning control system, as the number of iterations increases, the system gradually adjusts itself to correct the errors and deviations, thereby achieving an actual output trajectory that is closer to the desired trajectory. This experimental result further verifies the superior performance of the control method proposed in this paper. Figure 7 By comparing the convergence of the random uncertainty test, it can be concluded that all four cases converge.

[0073] Example 3 like Figure 2 As shown, an embodiment of the present invention further provides a system dynamic fault-tolerant control system for actuator failure, comprising: The first building module is used to build a state space model of actuator failure in the control system; A second building module: used for building a control law and a 2D dynamic model of the control system according to the state space model, wherein the control law is based on a dynamic iterative learning update law, the control law is used to control an input vector of an actuator, and the control law is used to ensure that the control system operates stably when an actuator fails; A first analysis module: used for analyzing the stability of the control system according to the stability condition and the 2D dynamic model; Design module: used for designing controller parameters of the control system based on the stability of the control system; The second analysis module is used to analyze the robustness of the control system using the controller parameters to ensure the robustness of the control system.

[0074] The system proposed in this embodiment is based on the method proposed in Embodiment 1. It can be understood that the options involved in Embodiment 1 are also applicable in this embodiment, so they will not be described in detail.

[0075] Example 4 The embodiment of the present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer-stored program is executed by a processor, the system dynamic fault-tolerant control method for actuator failure is implemented.

[0076] In summary, the embodiments of the present invention provide a system dynamic fault-tolerant control method, system and storage medium for actuator failures, which optimizes the iterative controller parameters by establishing a control system control law based on a dynamic iterative learning update law, ensures that the actuator can achieve accurate tracking and stable control of the system output in a fault environment, effectively reduces the impact of uncertainty in the control system on the performance, improves the robustness and stability of the control system, and ensures the continuity of the system.

[0077] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention. These improvements and substitutions should also be regarded as the scope of protection of the present invention.

Claims

1. A system dynamic fault-tolerant control method for actuator failure, characterized in that: The method comprises the following steps: Establish state-space models of actuator failures in control systems; Constructing a control law and a 2D dynamic model of the control system according to the state space model, wherein the control law is based on a dynamic iterative learning update law, the control law is used to control an input vector of an actuator, and the control law is used to ensure that the control system operates stably when an actuator fails; Analyzing the stability of the control system based on stability conditions and the 2D dynamic model; Designing controller parameters of the control system based on the stability of the control system; The robustness of the control system is analyzed using the controller parameters to ensure the robustness of the control system.

2. A system dynamic fault-tolerant control method for actuator failure according to claim 1, characterized in that: The establishing of the state space model of the actuator fault in the control system specifically includes: (1) Construct an initial state space model of the actuator in the control system that repeatedly executes batch processing over a period of time. type; (2) Establish a fault model when the actuator fails. The actuator failures include three types: Conditions: no failure, complete failure and partial failure; (3) Establishing the state space model based on the initial state space model and the fault model.

3. A system dynamic fault-tolerant control method for actuator failure according to claim 2, wherein Characteristically, the initial state space model is as follows: in, , and The control system is The state vector, input vector, and output vector of each run, , , and are the parameter matrices of the corresponding dimensions of the system, is the time period, To run the batch.

4. A system dynamic fault-tolerant control method for actuator failure according to claim 2, wherein The characteristic is that The fault model established when the actuator fails is as follows: in, The first A signal is a variable that has a fault. is the controlled sequence of the control system, is the failure coefficient when the actuator fails, satisfy: If the actuator fails, then ; If the actuator fails completely, then ; If the actuator fails partially, .

5. A system dynamic fault-tolerant control method for actuator failure according to claim 2, characterized in that: The state space model is as follows: 。 6. A system dynamic fault-tolerant control method for actuator failure according to claim 1, characterized in that: The control law and 2D dynamic model of the control system are constructed according to the state space model, including: (1) Establish a dynamic iterative learning update law, which is used to update the correction value of the control system. as follows: ； (2) Based on the dynamic iterative learning update law, the control law of the control system is constructed, and the control law is as follows: ； (3) Discretize the state space model to obtain a 2D dynamic model, which is as follows: in, ， ， 。 7. A system dynamic fault-tolerant control method for actuator failure according to claim 6, characterized in that: The establishing of the dynamic iterative learning update law comprises: (1) Establishing an output tracking error based on a control target, wherein the control target is that under the permissible condition of an actuator failure, the trajectory output by the control system is close to the desired trajectory, and the output tracking error The calculation method is as follows: in, is the expected trajectory, is the trajectory of the control system output, that is, the output vector; (2) Define an operator, the operator as follows: The operator is used to represent along Direction error; (3) Establish the internal state equation of the controller based on the output tracking error and the operator , as follows: in, , and They are all gain matrices of the internal state equations of the controller to be designed; (4) Constructing a dynamic iterative learning update law based on the output tracking error, the operator and the internal state equation.

8. A system dynamic fault-tolerant control method for actuator failure according to claim 1, characterized in that: The stability conditions include: , used to ensure convergence on the output iteration batch; , which is used to ensure the convergence of the repetition cycle time; the transfer function matrix is , , , , which is used to ensure convergence in both time and batch.

9. A system dynamic fault-tolerant control system for actuator failure, the system being based on a system dynamic fault-tolerant control method for actuator failure according to any one of claims 1 to 8, comprising: The first building module is used to build a state space model of actuator failure in the control system; A second building module: used for building a control law and a 2D dynamic model of the control system according to the state space model, wherein the control law is based on a dynamic iterative learning update law, the control law is used to control an input vector of an actuator, and the control law is used to ensure that the control system operates stably when an actuator fails; A first analysis module: used for analyzing the stability of the control system according to the stability condition and the 2D dynamic model; Design module: used for designing controller parameters of the control system based on the stability of the control system; The second analysis module is used to analyze the robustness of the control system using the controller parameters to ensure the robustness of the control system.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer stored program is executed by the processor, a system dynamic fault-tolerant control method for actuator failure as described in any one of claims 1 to 8 is implemented.

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