A servo system fault reconstruction method based on adaptive PI sliding mode observer

Abstract

The application discloses a servo system fault reconstruction method based on an adaptive PI sliding mode observer, and is used for solving the problem of high-frequency chattering of a reconstruction signal or inaccurate fault restoration caused by dependence of a traditional fault reconstruction method based on a sliding mode observer on prior information such as a fault boundary. The reconstruction method replaces a discontinuous term in a traditional sliding mode observer with an adaptive PI function to construct an observer, establishes a dimension-increased state space model of a servo control system containing a fault, converts a sensor fault into an actuator fault form, designs an adaptive PI sliding mode observer and solves related gain parameters, and reconstructs fault information by using the observer. The application does not require any prior fault information, has no limitation on the amplitude of a fault signal, can accurately restore various fault signals, avoids high-frequency chattering, and is suitable for fault diagnosis of servo systems in fields such as robots, numerical control machine tools, aerospace, etc.

Description

Technical Field

[0001] This invention relates to the field of servo system fault diagnosis and reconfiguration technology, and in particular to a servo system fault reconfiguration method based on an adaptive PI sliding mode observer. Background Technology

[0002] Servo systems play a crucial role in modern industrial control, and are widely used in robotics, CNC machine tools, aerospace, and other fields. A servo system failure can lead to a decline in the performance of the entire control system or even its complete failure, causing serious losses. To maintain stable and reliable operation, it is essential to be able to obtain real-time fault information, including the magnitude, type, and severity of the fault.

[0003] Currently, fault reconstruction techniques are widely used to obtain fault information. Fault reconstruction is a technique that estimates fault signals based on the system's mathematical model and the state variables affected by the fault. It not only determines whether the system is faulty, but also, through analysis of the reconstructed signal, provides information such as the type of fault, its magnitude, and the potential severity of damage to the system. Among the many fault reconstruction methods, a typical approach is the sliding mode observer-based fault reconstruction method. This method leverages the invariance of a sliding mode observer to external disturbances after entering the sliding mode, and directly reconstructs the fault signal using the concept of equivalent fault injection.

[0004] When using a conventional sliding mode observer for fault reconstruction, a prerequisite is that the boundaries of the fault signal must be known. The discontinuity switching gain of the sliding mode observer must be set to be greater than the upper boundary of the fault signal for the state error signal to eventually enter the sliding surface and thus accurately reconstruct the fault signal. However, in actual systems, the fault boundaries are often unknown. To ensure that the state error signal eventually enters the sliding surface, the discontinuity switching gain is often estimated and set to a large value. As a result, when the fault is small, the reconstructed signal will produce high-frequency chattering, and when the fault boundary value is greater than the discontinuity switching gain, the reconstructed signal cannot accurately reproduce the fault signal. Summary of the Invention

[0005] This invention proposes a servo system fault reconstruction method based on an adaptive PI sliding mode observer. By changing the gain setting method when the control system uses a sliding mode observer for fault reconstruction, it solves the problem that traditional sliding mode observer-based methods require prior information such as fault boundaries. This method does not require any prior fault information and achieves accurate reconstruction of fault information in linear control systems.

[0006] The servo system fault reconstruction method based on an adaptive PI sliding mode observer according to embodiments of the present invention includes: A new state vector is formed by fusing the servo system state vector and the sensor measurement filter vector, and an extended state space model is established based on the new state vector. Based on the aforementioned dimensionality-enhanced state-space model, a sliding mode observer is designed, and an adaptive PI sliding mode observer is constructed by replacing the discontinuous switching terms in the sliding mode observer with an adaptive PI function. The structure of the adaptive PI function is as follows: , In the formula, For integral gain, For any given non-zero proportional gain; Output the estimation error; Adaptive adjustment is performed based on the following formula: , In the formula, It is a positive number; The sensor fault signal is reconstructed based on the adaptive PI sliding mode observer.

[0007] According to some embodiments of the present invention, the reconstruction of the sensor fault signal based on the adaptive PI sliding mode observer includes: Design a coordinate transformation matrix T such that the system matrix of the product of the new state vectors in the increased-dimensional state-space model is... The system matrix of the multiplication of regulator input vectors satisfy: In the formula, It is a stable matrix; Based on the multiplication term of the sensor fault function in the augmented state-space model, T is used. Perform the transformation to obtain the matrix. , It is a non-singular fault distribution matrix; The reconstructed sensor fault signal value is: .

[0008] According to some embodiments of the present invention, the fused servo system state vector and sensor measurement filter vector form a new state vector, and based on the new state vector, an extended state space model is established, including: Constructing a state-space model: Formula 1, Where t is the system runtime. This represents the system state vector belonging to the n-dimensional real vector space. The derivative of the system state vector; This represents the regulator input vector belonging to the m-dimensional real vector space; The function represents the system output vector of the sensor measurement, which belongs to the p-dimensional real vector space. Represents a bounded but unknown sensor fault function; , , All are system matrices, namely, an n x n real matrix, an n x m real matrix, and a p x n real matrix, respectively. Let be the fault matrix, and let be a real matrix with p rows and q columns, satisfying . C is a full-rank row matrix; A filter is used to filter the system output vector measured by the sensor; the filtering method of the filter is as follows: Formula 2, in, The filtered value of the system output vector measured by the sensor. for derivative, Choose it as a stable matrix; Define the new state vector as: Formula 3, By combining Equations 1-3, an increased-dimensional state-space model can be established.

[0009] This invention also proposes a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the servo system fault reconstruction method based on an adaptive PI sliding mode observer as described above.

[0010] This invention also proposes a computer-readable storage medium storing an information transmission implementation program. When the program is executed by a processor, it implements the steps of the servo system fault reconstruction method based on an adaptive PI sliding mode observer as described above.

[0011] This invention also proposes a computer program product, including a computer program that, when executed by a processor, implements the steps of the servo system fault reconstruction method based on an adaptive PI sliding mode observer as described above.

[0012] This invention uses an adaptive PI function to replace the discontinuities in the sliding mode observer, based on the conventional sliding mode observer fault reconstruction method, to design an adaptive PI sliding mode observer for fault reconstruction. By using this method, no prior information about the fault is needed when designing the observer, and the fault signal can be accurately estimated.

[0013] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0014] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of the embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1 This is a flowchart of a servo system fault reconstruction method based on an adaptive PI sliding mode observer in an embodiment of the present invention. Detailed Implementation

[0015] Exemplary embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art. Furthermore, in some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0016] The core of this invention is to replace the discontinuities in a traditional sliding mode observer with an adaptive PI function, thus constructing an adaptive PI sliding mode observer. The goal is achieved through three key steps: system modeling, observer design, and fault reconstruction. The specific process is as follows: Figure 1 As shown, it includes the following steps: Step S1: Establish an augmented model of the servo control system with faults; For servo control systems with sensor malfunctions, a state-space model is used for modeling. The original state-space model of the system is as follows: Formula 1, Where t is the system runtime. This represents the system state vector belonging to the n-dimensional real vector space. The derivative of the system state vector; This represents the regulator input vector belonging to the m-dimensional real vector space; The function represents the system output vector of the sensor measurement, which belongs to the p-dimensional real vector space. Represents a bounded but unknown sensor fault function; , , All are system matrices, namely, an n x n real matrix, an n x m real matrix, and a p x n real matrix, respectively. Let be the fault matrix, and let be a real matrix with p rows and q columns, satisfying . C is a full-rank row matrix; To convert sensor faults into actuator fault forms that are easier to reconfigure, the sensor measurement value Y(t) is filtered. The filter is designed as follows: Formula 2, in, The filtered value of the system output vector measured by the sensor. for derivative, Choose it as a stable matrix; Define the new state vector as: Formula 3, By combining equations 1-3, we can establish an increased-dimensional state-space model: Formula 4, In the formula, I P (The identity matrix).

[0017] In the augmented system represented by the new state-space equations, the faults of the original system's sensors are transformed into the faults of the new system's actuators. Therefore, through coordinate transformation, the sensor faults and actuator faults of the control system have the same form and can be reconstructed using the same reconstruction method.

[0018] Step S2: Design an adaptive PI sliding mode observer; Based on the augmented system state-space model obtained in step S1, an adaptive PI sliding mode observer is designed, with the following expression: Formula 5, in, For linear feedback gain matrix, The sliding mode gain matrix is... To output the estimation error, and They are respectively The estimated value.

[0019] The PI function used to replace the switching function in the designed adaptive PI sliding mode observer has the following structure: Formula 6, In the formula, k i For integral gain, k p For any given non-zero proportional gain; e y (t) Output the estimation error; To ensure the stability of the observer and the asymptotic reachability of the sliding surface, the following design and solution are required: By comparing formulas 4 and 5, the dynamic equations for the state estimation error and the error are defined as follows: Formula 7, Represents a bounded but unknown sensor fault function; Define the sliding surface as: , formula 8, The sliding surface is the set (a hyperplane) of error vectors e that satisfy the condition that "the product of the design matrix Ca and the state estimation error vector e is zero".

[0020] The necessary and sufficient condition for the state error system shown in Equation 7 to reach the sliding surface defined in Equation 8 within a finite time is that the system matrix satisfies the following assumptions: Condition 1: Formula 9, In the formula, Rank() is the rank function; Condition 2: The invariant zeros of lie in the left half of the complex space.

[0021] For a system that satisfies the assumptions, design a coordinate transformation matrix T to perform a linear coordinate transformation on the state vector of the original system. This gives the system matrix the following form in the new coordinate system: Formula 10, in, For a stable matrix, It is an identity matrix.

[0022] Fault input matrix: , Formula 11, Here, F1 is a non-singular matrix.

[0023] Based on this, the gain matrix of the sliding mode observer can be obtained as follows: Formula 12, in, This is a custom stability matrix.

[0024] k p For a PI function proportional gain, for any given non-zero proportional gain value, there exists a corresponding integral gain k. i Ensure that the sliding surface shown in Equation 8 is asymptotically reachable after replacing the switching term with a PI function. Integral gain k i The calculation method is as follows: , Formula 13, in, It is a positive number.

[0025] Step S3: Accurate reconstruction of fault information; The sensor fault information is reconstructed using the adaptive PI sliding mode observer designed in step S2. The sensor fault reconstruction method is as follows: , Formula 14, in, Let f(t) be the reconstructed value of the fault signal. This formula can be used to accurately estimate the fault information of the servo system. y The calculation requires the use of G in Formula 12. l and G n .

[0026] This invention uses an adaptive PI function to replace the discontinuity terms of the traditional sliding mode observer, which can achieve accurate reconstruction of the fault signal without any prior fault information (such as fault boundaries), thus solving the problem of dependence on prior information in traditional methods. There are no limitations on the amplitude of the fault signal. Whether it is a minor fault or a major fault, the fault signal can be accurately restored, avoiding the high-frequency jitter or reconstruction distortion problems caused by improper gain settings in traditional methods. By transforming sensor faults into actuator faults through coordinate transformation, a unified reconstruction of sensor and actuator faults is achieved, thus broadening the applicability of the method.

[0027] It should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0028] Those skilled in the art will understand that the steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular hardware and software combination.

Claims

1. A servo system fault reconstruction method based on an adaptive PI sliding mode observer, characterized in that, include: A new state vector is formed by fusing the servo system state vector and the sensor measurement filter vector, and an extended state space model is established based on the new state vector. Based on the aforementioned dimensionality-enhanced state-space model, a sliding mode observer is designed, and an adaptive PI sliding mode observer is constructed by replacing the discontinuous switching terms in the sliding mode observer with an adaptive PI function. The structure of the adaptive PI function is as follows: ， In the formula, For integral gain, For any given non-zero proportional gain; Output the estimation error; Adaptive adjustment is performed based on the following formula: ， In the formula, It is a positive number; The sensor fault signal is reconstructed based on the adaptive PI sliding mode observer.

2. The method as described in claim 1, characterized in that, The reconstruction of the sensor fault signal based on the adaptive PI sliding mode observer includes: Design a coordinate transformation matrix T such that the system matrix of the product of the new state vectors in the increased-dimensional state-space model is... The system matrix of the multiplication of regulator input vectors satisfy: In the formula, It is a stable matrix; Based on the multiplication term of the sensor fault function in the augmented state-space model, T is used. Perform the transformation to obtain the matrix. , It is a non-singular fault distribution matrix; The reconstructed sensor fault signal value is: 。 3. The method as described in claim 1, characterized in that, The fused servo system state vector and sensor measurement filter vector form a new state vector, and based on the new state vector, an extended-dimensional state space model is established, including: Constructing a state-space model: Official 1, Where t is the system runtime. This represents the system state vector belonging to the n-dimensional real vector space. The derivative of the system state vector; This represents the regulator input vector belonging to the m-dimensional real vector space; The function represents the system output vector of the sensor measurement, which belongs to the p-dimensional real vector space. Represents a bounded but unknown sensor fault function; , , All are system matrices, namely, an n x n real matrix, an n x m real matrix, and a p x n real matrix, respectively. Let be the fault matrix, and let be a real matrix with p rows and q columns, satisfying . C is a full-rank row matrix; A filter is used to filter the system output vector measured by the sensor; the filtering method of the filter is as follows: Official 2, in, The filtered value of the system output vector measured by the sensor. for derivative, Choose it as a stable matrix; Define the new state vector as: Official 3, By combining Equations 1-3, an increased-dimensional state-space model can be established.

4. A computer device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the servo system fault reconfiguration method based on an adaptive PI sliding mode observer as described in claim 1, 2, or 3.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores an implementation program for information transmission, which, when executed by a processor, implements the steps of the servo system fault reconstruction method based on an adaptive PI sliding mode observer as described in claim 1, 2, or 3.

6. A computer program product, characterized in that, The system includes a computer program that, when executed by a processor, implements the steps of the servo system fault reconstruction method based on an adaptive PI sliding mode observer as described in claim 1, 2, or 3.

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