Method and system for optimizing tracking performance of networked control system

Abstract

The invention provides a networked control system tracking performance optimization method and system, and relates to communication signal tracking control, and the method comprises the steps: building a two-degree-of-freedom networked control system model; according to the two-degree-of-freedom networked control system model, obtaining an output signal and an error signal of the two-degree-of-freedom networked control system; according to the output signal, co-prime decomposition based on a rational transfer function matrix, a Bezout equation and a Youla parameterization form of a two-degree-of-freedom controller are calculated; the error signal is simplified; calculating an optimal performance expression of the two-degree-of-freedom networked control system model according to the simplified error signal; the optimal performance expression is simplified; calculating an optimal tracking performance expression of the two-degree-of-freedom networked control system model according to the simplified optimal performance expression; and optimizing the tracking performance of the networked control system according to the optimal tracking performance expression of the two-degree-of-freedom networked control system model.

Description

TECHNICAL FIELD

[0001] The present application relates to communication signal tracking control, in particular to a networked control system tracking performance optimization method and system. BACKGROUND

[0002] In the prior art, for example, document 1 [Optimal Tracking Performance Analysis of MIMO Control Systems Under Multiple Constraints] gives a discrete system model, studies the optimal tracking performance of networked control systems under multiple communication constraints, and integrates the communication constraints into the uplink and downlink. The influence of the quantizer is considered in the uplink, and the influence of the codec, additive white Gaussian noise and bandwidth is considered in the downlink. The optimal tracking performance of the system is obtained by designing an optimal two-degree-of-freedom controller. Although the model considers more comprehensive network constraints, the quantizers are all uniform quantizers. The uniform quantizer divides the input signal into equal intervals in the quantization process, which may lead to a low signal-to-noise ratio for high dynamic range signals, especially when some parts of the signal change greatly, distortion may occur.

[0003] For example, document 2 [Tracking and Regulation Performance Limitations of Networked Control Systems Over Erasure Channel With Input Quantization] designs a two-degree-of-freedom system model, and considers the influence of the quantizer, packet loss and Gaussian white noise in the downlink. Based on the frequency domain analysis method, the tracking performance limitation with quantization under the erasure channel is obtained. It can be found that although the accuracy of the quantizer is improved, the quantizer will introduce chattering phenomenon, which can lead to instability of the system and may cause oscillation or other adverse reactions.

[0004] In summary, the prior art generally uses uniform quantizers, which can easily lead to a decrease in signal-to-noise ratio and signal distortion in high dynamic range signal processing. The use of quantizers can introduce chattering phenomenon, which can lead to instability of the system and may cause oscillation or other adverse reactions. SUMMARY

[0005] In order to solve the technical problem that the uniform quantizer is generally used in the prior art, which is easy to cause the signal-to-noise ratio to decrease and the signal to be distorted in high dynamic range signal processing, and the use of the quantizer can introduce the chattering phenomenon, the chattering can cause the system to be unstable, and can cause oscillation or other adverse reactions, the application provides a networked control system tracking performance optimization method and system.

[0006] The technical scheme provided by the embodiment of the application is as follows:

[0007] The first aspect is:

[0008] The networked control system tracking performance optimization method provided by the embodiment of the application comprises:

[0009] S1: establishing a two-degree-of-freedom networked control system model;

[0010] S2: obtaining an output signal and an error signal of the two-degree-of-freedom networked control system according to the two-degree-of-freedom networked control system model;

[0011] S3: calculating the coprime factorization based on a rational transfer function matrix, a Bezout equation and a Youla parameterization form of a two-degree-of-freedom controller according to the output signal of the two-degree-of-freedom networked control system;

[0012] S4: simplifying the error signal of the two-degree-of-freedom networked control system according to the coprime factorization based on the rational transfer function matrix, the Bezout equation and the Youla parameterization form of the two-degree-of-freedom controller;

[0013] S5: calculating an optimal performance expression of the two-degree-of-freedom networked control system model according to the simplified error signal;

[0014] S6: simplifying the optimal performance expression of the two-degree-of-freedom networked control system model;

[0015] S7: calculating an optimal tracking performance expression of the two-degree-of-freedom networked control system model according to the simplified optimal performance expression;

[0016] S8: optimizing the tracking performance of the networked control system according to the optimal tracking performance expression of the two-degree-of-freedom networked control system model.

[0017] The second aspect is:

[0018] The networked control system tracking performance optimization system provided by the embodiment of the application comprises a memory and one or more processors.

[0019] The memory stores one or more application programs adapted to be executed by the one or more processors to implement the above networked control system tracking performance optimization method.

[0020] The technical scheme provided by the embodiment of the present application has at least the following beneficial effects:

[0021] In the present application, by establishing a two-degree-of-freedom networked control system model, the output signal and the error signal of the two-degree-of-freedom networked control system are obtained, and the uniform quantizer is avoided, which is not easy to cause the signal-to-noise ratio to decrease and the signal to distort in high dynamic range signal processing, the error signal is simplified by calculating the coprime factorization based on the rational transfer function matrix, the Bezout equation and the Youla parameterization form of the two-degree-of-freedom controller, and then the optimal performance expression of the two-degree-of-freedom networked control system model is calculated, and the optimal tracking performance expression of the two-degree-of-freedom networked control system model is calculated by simplifying the optimal performance expression, which avoids the introduction of chattering phenomenon by using the uniform quantizer, and does not cause the system to be unstable, and does not cause oscillation or other adverse reactions. BRIEF DESCRIPTION OF DRAWINGS

[0022] In order to more clearly illustrate the technical scheme in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced below, and obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0023] Figure 1 A flowchart of a networked control system tracking performance optimization method provided by the embodiment of the present application is shown in the figure.

[0024] Figure 2 A block diagram of a two-degree-of-freedom networked control system provided by the embodiment of the present application is shown in the figure.

[0025] Figure 3 An optimal tracking performance diagram under hysteresis quantization provided by the embodiment of the present application is shown in the figure.

[0026] Figure 4 A structure diagram of a networked control system tracking performance optimization system provided by the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0027] The technical scheme in the present application will be described below with reference to the drawings.

[0028] In the embodiments of the present application, the words such as "example", "for example", etc. are used to represent an example, illustration or description. Any embodiment or design scheme described as "example" in the present application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. Rather, the word "example" is intended to present the concept in a specific manner. In addition, in the embodiments of the present application, the meaning expressed by "and / or" can be both, or can be one of the two.

[0029] In order to make the technical problems, technical solutions and advantages to be solved by the present application clearer, the following will be described in detail in combination with the drawings and specific embodiments.

[0030] Referring to the drawings attached to the specification Figure 1 , a flowchart of a networked control system tracking performance optimization method provided by an embodiment of the present application is shown.

[0031] The embodiment of the present application provides a networked control system tracking performance optimization method, which can be realized by a networked control system tracking performance optimization device, which can be a terminal or a server. The processing flow of the networked control system tracking performance optimization method can include the following steps:

[0032] Referring to the drawings attached to the specification Figure 2 , a double-freedom networked control system block diagram provided by an embodiment of the present application is shown.

[0033] S1: Establish a double-freedom networked control system model.

[0034] S2: Obtain an output signal and an error signal of the double-freedom networked control system according to the double-freedom networked control system model.

[0035] The output signal of the double-freedom networked control system is specifically:

[0036] y=G u

[0037] u=K1 r+K2 z -τ [(1+δ) y+u min ]

[0038] δ=(1-ρ) / (1+ρ)

[0039] Wherein, y represents the output signal of the double-freedom networked control system, G represents the transfer function of the controlled object, u represents the input signal of the controlled object, K1 represents the feedforward controller, r represents the input signal of the double-freedom networked control system, K2 represents the feedback controller, z represents the time delay operator, τ represents the time delay constant, δ represents the nonlinear coefficient of the hysteresis quantizer, u min represents the quantization dead zone, and ρ represents the quantization density of the hysteresis quantizer.

[0040] The error signal of the two-degree-of-freedom networked control system is specifically:

[0041] e = r - y

[0042] Wherein, e represents the error signal of the two-degree-of-freedom networked control system.

[0043] In the present application, the system is divided into two parts, feedforward control and feedback control, making the controller design more flexible, helping to adjust and optimize the system performance at different stages. The model can reveal the interference of time delay and quantizer nonlinearity on the system, which helps to design a more robust controller to ensure the stable operation of the system in practical application. Since the model comprehensively considers complex factors such as time delay and quantization, it can adapt to the actual engineering scenarios such as unstable network environment and limited bandwidth, improving the practicability and reliability of the system.

[0044] S3: According to the output signal of the two-degree-of-freedom networked control system, calculate the coprime factorization based on the rational transfer function matrix, Bezout equation and Youla parameterization form of the two-degree-of-freedom controller.

[0045] It should be noted that coprime factorization is a method of decomposing a complex system into two independent parts. These two parts have no common characteristics (such as zeros or poles) in mathematics, so they are called "coprime". Through coprime factorization, the dynamic characteristics of the system can be described more clearly, and a simpler and clearer basis for controller design is provided.

[0046] It should be noted that the Bezout equation is a mathematical expression describing the relationship between two functions, which can represent how two functions work together to achieve a certain effect. In control systems, the Bezout equation is often used to establish the balance between the controlled object and the controller, providing a stability guarantee for the design of the controller.

[0047] It should be noted that the Youla parameterization form is a flexible controller design method that adjusts system performance by introducing free design parameters. It can optimize the dynamic performance of the system according to the needs of the designer, such as reducing errors and enhancing anti-interference ability, while ensuring the stability of the system. This method greatly simplifies the design process of complex controllers, while improving design efficiency and adaptability.

[0048] In one possible implementation, S3 is specifically:

[0049] According to the following formula, calculate the coprime factorization based on the rational transfer function matrix, Bezout equation and Youla parameterization form of the two-degree-of-freedom controller:

[0050]

[0051] wherein, denotes the first factor of the left coprime factorization, denotes the second factor of the left coprime factorization, N denotes the first factor of the right coprime factorization, D denotes the second factor of the right coprime factorization, Y denotes the first matrix parameter in the Bezout identity, X denotes the second matrix parameter in the Bezout identity, denotes the second matrix parameter in the Bezout identity of the left coprime factorization, denotes the first matrix parameter in the Bezout identity of the left coprime factorization, I denotes the identity matrix, RH ∞ denotes the set of all stable, regular and real-rational transfer functions, κ denotes the set of all controllers that can stabilize the networked control system, K denotes the transfer function of the two-degree-of-freedom controller, R denotes the first control parameter of the two-degree-of-freedom controller that is free to design, Q denotes the second control parameter of the two-degree-of-freedom controller that is free to design.

[0052] In the present application, by restricting the controller design within the set RH ∞ , it is ensured that the designed controller can stabilize the networked control system, and the robustness is guaranteed even in complex network environment. The Youla parameterization form allows the introduction of two free design parameters Q and R, making the design of the controller more flexible. By coprime factorization and Bezout identity, the complex controller design problem is decomposed into an easily handled mathematical form, thus greatly simplifying the solution process of the controller.

[0053] S4: simplifying the error signal of the two-degree-of-freedom networked control system according to the coprime factorization based on the rational transfer function matrix, the Bezout identity and the Youla parameterization form of the two-degree-of-freedom controller.

[0054] In one possible implementation, S4 is specifically:

[0055] Simplifying the error signal of the two-degree-of-freedom networked control system according to the following formula:

[0056]

[0057] wherein e denotes the error signal of the two-degree-of-freedom networked control system.

[0058] In the present application, by simplifying, the error signal can be decomposed into parts related to system dynamics, controller design parameters (Q and R), and network constraints (time delay and quantizer nonlinearity), making the source and influencing factors of the error more intuitive. After simplifying the error signal, it can be clear which parts can be optimized by controller design (parameters Q and R) and which parts are limited by network time delay and quantizer nonlinearity, so as to improve the system performance in a targeted manner. Through simplification, the error signal is transformed into a standard mathematical form, facilitating further performance index calculation and theoretical analysis.

[0059] S5: According to the simplified error signal, calculate the optimal performance expression of the two-degree-of-freedom networked control system model.

[0060] In the present application, the optimal performance expression clearly indicates the theoretical limit of the system tracking performance, providing a quantitative standard for evaluating the maximum tracking capability of the system under various constraints (such as time delay, quantizer nonlinearity, etc.). By calculating the optimal performance expression, it can be clear which factors affect the system performance, and a clear goal is provided for controller design and optimization, i.e. how to approach the optimal performance.

[0061] In one possible implementation, S5 specifically includes sub-steps S501 to S502:

[0062] S501: Calculate the tracking performance index.

[0063] In one possible implementation, S501 specifically is:

[0064] According to the following formula, calculate the tracking performance index:

[0065]

[0066] where J() represents the tracking performance index, l represents the trade-off factor between channel input energy constraint and tracking error, E{} represents the expectation operator, represents the original error signal, |||2 represents the two-norm, represents the actual output signal of the two-degree-of-freedom networked control system, Π represents the upper bound of the channel input energy.

[0067] In the present application, the tracking performance index considers the constraints of tracking error and channel input energy through the trade-off factor. This trade-off enables the system design to achieve the best compromise between the two, meeting the needs of practical applications. By calculating the tracking performance index, the key factors affecting the system performance can be identified, providing a clear goal for designing and optimizing the controller, such as how to adjust parameters Q, R to minimize the error or energy consumption.

[0068] S502: Calculate the optimal performance expression of the two-degree-of-freedom networked control system model according to the tracking performance index and the simplified error signal.

[0069] In a possible implementation, S502 specifically comprises:

[0070] The optimal performance expression of the two-degree-of-freedom networked control system model is calculated according to the following formula:

[0071]

[0072] wherein J * represents the optimal performance expression of the two-degree-of-freedom networked control system model, represents a first performance part related to the tracking error, represents a second performance part related to the quantizer nonlinearity and the channel time delay, inf represents the lower limit, and υ represents the weight vector of the input signal.

[0073] In the present application, the theoretical optimal tracking performance of the system can be quantitatively determined through the optimal performance expression, and the optimal performance that the system can achieve under the constraints of network time delay, quantizer nonlinearity, etc. is revealed. By explicitly determining the optimal performance of the system, an accurate optimization target can be provided for the controller design, i.e. how to adjust the parameters to approach the performance limit and reduce the tracking error and energy consumption. Through the optimal performance expression, the performance bottleneck of the system can be identified, such as the non-minimum phase zero point, unstable pole or network nonlinearity, etc., thereby helping to develop compensation strategies to improve performance.

[0074] S6: Simplify the optimal performance expression of the two-degree-of-freedom networked control system model.

[0075] In a possible implementation, S6 specifically comprises:

[0076] The first performance part and the second performance part in the optimal performance expression of the two-degree-of-freedom networked control system model are simplified respectively:

[0077]

[0078] wherein n z represents the number of non-minimum phase zero points, s k represents the kth non-minimum phase zero point, represents the conjugate transpose vector of the direction of the kth non-minimum phase zero point, H represents the conjugate transpose symbol, h represents the frequency domain transfer function, e jθ represents the angle representation of the jth complex number in polar coordinates, θ represents the angle, n p represents the number of unstable poles, represents the conjugate pole of the kth unstable pole, p represents the conjugate pole of the l-th unstable pole. l This represents the l-th unstable pole. ψ is the conjugate transpose of the direction of the k-th unstable pole. k-1 Let ψ be the product matrix of k-1 unstable poles. l-1 Let ω represent the product matrix of l-1 unstable poles. l Indicates the direction of the l-th unstable pole. ω represents the conjugate transpose of the direction of the l-th unstable pole. k Let s represent the k-th unstable pole. l This represents the l-th non-minimum phase zero. H represents the conjugate pole of the k-th non-minimum phase zero. k H represents the compensation matrix associated with the k-th non-minimum phase zero. l ξ represents the compensation matrix associated with the l-th non-minimum phase zero. l Indicates the direction of the l-th non-minimum phase zero. G represents the direction conjugate transpose vector of the l-th non-minimum phase zero. l This represents a portion of the all-pass matrix associated with the l-th non-minimum phase zero. Let B represent the cumulative performance matrix associated with all unstable poles, and let B represent the all-pass factor of the second factor D after right coprime decomposition and all-pass decomposition.

[0079] The frequency domain transfer function is specifically:

[0080] Where, ψ k-1 Specifically: b l σ represents the matrix associated with the l-th unstable pole. l This represents the vector associated with the l-th unstable pole. This represents the conjugate transpose of the vector associated with the l-th unstable pole.

[0081] Where, ψ l-1 Specifically: b k σ represents the matrix associated with the k-th unstable pole. k This represents the vector associated with the k-th unstable pole. This represents the conjugate transpose of the vector associated with the k-th unstable pole.

[0082] Among them, H k Specifically:

[0083] Among them, H l Specifically:

[0084] where G l Specifically,

[0085] where, Specifically,

[0086] Specifically, first calculate

[0087] N = LN0by all-pass decomposition, where N0represents the minimum phase part of N, which contains the non-minimum phase zero point z k , k = 1, 2, …, n z , and the direction vector of which is ξ k , and the repetition of the non-minimum phase zero point z k is 1, L can be decomposed as where L k represents the all-pass factor L related to the kth non-minimum phase zero point, and the orthogonal complement matrix χ k of the kth non-minimum phase zero point satisfies k Simplifying, we have:

[0088]

[0089] In the above equation, H2represents the Hardy space, ⊥ represents the orthogonal operation, and a suitable control parameter Q can be selected to make Then:

[0090]

[0091] After calculation, we have:

[0092] Therefore where

[0093] Define the inner-outer factorization where Υ i ∈ RH ∞ represents the inner factor, and Υ o ∈ RH ∞ represents the outer factor, so we have:

[0094]

[0095] Since Υ o is right invertible, we have Then: ​

[0096] wherein,

[0097] Further, the same way is used to calculate to obtain:

[0098]

[0099] wherein p k , k = 1, 2, …, n p is an unstable pole of the object, and the direction vector is ω k , W k represents any matrix satisfying the equation k , and

[0100] In the present application, through all-pass decomposition and inner-outer factorization, the limiting effect of non-minimum phase zero, unstable pole and other factors on system performance is clarified, which helps to understand how these factors affect the tracking performance of the system. Through step-by-step simplification, concise expressions related to design parameters are obtained, which helps to accurately optimize different parts (such as tracking error or network constraints) in subsequent controller design. Through the simplification and decomposition of the influence of unstable poles and non-minimum phase zeros, it is ensured that the system can still achieve optimal tracking performance when facing these adverse factors, thereby improving the stability and robustness of the system.

[0101] S7: According to the simplified optimal performance expression, the optimal tracking performance expression of the two-degree-of-freedom networked control system model is calculated.

[0102] In one possible implementation, S7 is specifically:

[0103] According to the first performance part and the second performance part in the simplified optimal performance expression, the optimal tracking performance expression of the two-degree-of-freedom networked control system model is calculated:

[0104]

[0105] wherein, ​An optimal tracking performance expression of a two-degree-of-freedom networked control system model is provided. In the present application, the optimal tracking performance expression reveals the theoretical limit tracking performance of the system under the constraints of time delay, quantizer nonlinearity (such as quantization dead zone, quantization density), etc., and provides a quantifiable standard for the tracking accuracy of the system. The expression directly links the tracking performance of the system to the network parameters (such as quantizer characteristics, time delay) and the dynamic characteristics of the controlled object (such as non-minimum phase zero, unstable pole), which helps to understand how these factors affect the tracking performance. By calculating the optimal tracking performance expression, an explicit optimization benchmark can be provided for controller design, making the goal of controller parameter design clearer, so as to approach the performance limit.

[0106] S8: According to the optimal tracking performance expression of the two-degree-of-freedom networked control system model, the tracking performance of the networked control system is optimized.

[0107] In the present application, by using the optimal tracking performance expression, the controller design parameters that minimize the system tracking error and optimize energy utilization can be found, so as to achieve the best tracking performance of the system. The optimal tracking performance expression provides an explicit performance standard, quantifies the optimization goal of the system, and makes the controller design process more targeted and directional. In the networked control system, there are bandwidth, energy and other resource constraints. Through optimization, the present application can achieve the best balance between tracking accuracy and energy input constraints, and ensure efficient operation of the system under resource constraints.

[0108] Reference is made to the accompanying drawings Figure 3 , which shows the optimal tracking performance graph under hysteresis quantization provided by the present application.

[0109] In one possible implementation, the transfer function model of the controlled object is considered as follows:

[0110]

[0111] From the model, it is known that it contains a non-minimum phase zero point z = 1.2, whose direction is η = (0, 0, 1) T , contains an unstable pole p = k (|k| > 1), whose direction is w = (0, 1, 0) T , and the input signal vector is selected as

[0112] The effects of channel input energy constraints, quantization dead zone and quantization density on the optimal tracking performance of the networked control system are shown in Figure 3The results show that the quantization dead zone is positively correlated with the lower bound of tracking performance. That is, the larger the quantization dead zone, the worse the tracking performance. In addition, the results show that a smaller value of delta corresponds to a higher quantization density, which can improve the tracking performance. Finally, the results show that allowing a larger energy input channel is beneficial to improving the tracking performance of the networked control system.

[0113] The technical scheme provided by the embodiment of the application has at least the following beneficial effects:

[0114] In the application, by establishing a two-degree-of-freedom networked control system model, the output signal and the error signal of the two-degree-of-freedom networked control system are obtained, and the use of a uniform quantizer is avoided, which is not easy to cause the signal-to-noise ratio to decrease and the signal to distort in high dynamic range signal processing. The error signal is simplified by calculating the coprime factorization based on the rational transfer function matrix, the Bezout equation and the Youla parameterization form of the two-degree-of-freedom controller, and then the optimal performance expression of the two-degree-of-freedom networked control system model is calculated. The optimal tracking performance expression of the two-degree-of-freedom networked control system model is calculated by simplifying the optimal performance expression, which avoids the introduction of chattering phenomenon caused by the use of the quantizer, does not cause the system to be unstable, and does not cause oscillation or other adverse reactions.

[0115] Reference is made to the accompanying drawings Figure 4 The accompanying drawings show a structure schematic diagram of a networked control system tracking performance optimization system provided by the application.

[0116] The application further provides a networked control system tracking performance optimization system 30, comprising a memory 303 and one or more processors 301.

[0117] The memory 303 stores one or more application programs, and the one or more application programs are adapted to be executed by the one or more processors 301 to implement the networked control system tracking performance optimization method of the method embodiment.

[0118] The networked control system tracking performance optimization system 30 comprises a processor 301 and a memory 303. The processor 301 and the memory 303 are connected, for example, through a bus 302.

[0119] The structure of the networked control system tracking performance optimization system 30 does not constitute a limitation on the embodiments of the application.

[0120] The processor 301 can be a CPU, a general-purpose processor, a DSP, an ASIC, an FPGA, or other programmable logic device, a transistor logic device, a hardware component, or any combination thereof. It can implement or execute various exemplary logical blocks, modules, and circuits described in conjunction with the present disclosure. The processor 301 can also be a combination that implements a computing function, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, and the like.

[0121] The bus 302 can include a path for transmitting information between the above-mentioned components. The bus 302 can be a PCI bus or an EISA bus, etc. The bus 302 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, only one thick line is shown in the figure, but it does not mean that there is only one bus or one type of bus.

[0122] The memory 303 can be a ROM or other type of static storage device that can store static information and instructions, a RAM or other type of dynamic storage device that can store information and instructions, an EEPROM, a CD-ROM or other optical disk storage, an optical disk storage (including a compact disk, a laser disk, an optical disk, a digital versatile disk, a Blu-ray disk, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and capable of being accessed by a computer, but not limited thereto.

[0123] It should be noted that the networked control system tracking performance optimization system 30 can implement the networked control system tracking performance optimization method described above, and can achieve the same or similar technical effects. To avoid repetition, the present application will not be described again.

[0124] The technical scheme provided by the embodiment of the present application has at least the following beneficial effects:

[0125] In the present application, by establishing a two-degree-of-freedom networked control system model, the output signal and the error signal of the two-degree-of-freedom networked control system are obtained, avoiding the use of uniform quantizers, which can not easily lead to a decrease in signal-to-noise ratio and signal distortion in high dynamic range signal processing. The error signal is simplified by calculating the coprime factorization based on the rational transfer function matrix, the Bezout equation, and the Youla parameterization form of the two-degree-of-freedom controller, and then the optimal performance expression of the two-degree-of-freedom networked control system model is calculated. The optimal tracking performance expression of the two-degree-of-freedom networked control system model is calculated by simplifying the optimal performance expression. The use of the uniform quantizer avoids the introduction of chattering phenomenon, does not cause the instability of the system, and does not cause oscillation or other adverse reactions.

[0126] The application further provides a computer readable storage medium, which stores a computer program capable of being loaded and executed by a processor to track performance optimization method of the networked control system.

[0127] The above merely provides a specific embodiment of the application, but the protection scope of the application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the application, which should be covered in the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

[0128] The following points need to be explained:

[0129] (1) The attached drawings of the embodiments of the application only involve the structures involved in the embodiments of the application, and other structures can refer to the general design.

[0130] (2) In order to be clear, the thickness of the layer or area is enlarged or reduced in the drawings used for describing the embodiments of the application, that is, the drawings are not drawn according to the actual proportion. It can be understood that when an element such as a layer, a film, an area or a substrate is referred to as being located on or under another element, the element can be directly located on or under another element or there can be an intermediate element.

[0131] (3) In the case of no conflict, the embodiments of the application and the features in the embodiments can be combined with each other to obtain new embodiments.

[0132] The above merely provides a specific embodiment of the application, but the protection scope of the application is not limited thereto, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A method for optimizing the tracking performance of a networked control system, characterized in that, include: S1: Establish a two-degree-of-freedom networked control system model; S2: Based on the two-degree-of-freedom networked control system model, obtain the output signal and error signal of the two-degree-of-freedom networked control system; S3: Based on the output signal of the two-degree-of-freedom networked control system, calculate the coprime decomposition of the rational transfer function matrix, the Bezout equation, and the Youla parameterization of the two-degree-of-freedom controller; S4: Simplify the error signal of the two-degree-of-freedom networked control system based on the coprime decomposition of the rational transfer function matrix, the Bezout equation, and the Youla parameterization of the two-degree-of-freedom controller. S5: Based on the simplified error signal, calculate the optimal performance expression of the two-degree-of-freedom networked control system model; S6: Simplify the optimal performance expression of the two-degree-of-freedom networked control system model; S7: Based on the simplified optimal performance expression, calculate the optimal tracking performance expression of the two-degree-of-freedom networked control system model; S8: Optimize the tracking performance of the networked control system based on the optimal tracking performance expression of the two-degree-of-freedom networked control system model.

2. The method for optimizing the tracking performance of a networked control system according to claim 1, characterized in that, The output signal of the two-degree-of-freedom networked control system is specifically: y = Gu u = K1r + K2z -τ [(1 + δ)y + u min ] δ=(1-ρ) / (1+ρ) Where y represents the output signal of the two-degree-of-freedom networked control system, G represents the transfer function of the controlled object, u represents the input signal of the controlled object, K1 represents the feedforward controller, r represents the input signal of the two-degree-of-freedom networked control system, K2 represents the feedback controller, z represents the time delay operator, τ represents the time delay constant, δ represents the nonlinear coefficient of the hysteresis quantizer, and u min ρ represents the quantization dead zone, and ρ represents the quantization density of the hysteresis quantizer. The error signal of the two-degree-of-freedom networked control system is specifically as follows: e = ry Where e represents the error signal of the two-degree-of-freedom networked control system.

3. The method for optimizing the tracking performance of a networked control system according to claim 1, characterized in that, Specifically, S3 is: Calculate the coprime decomposition of the rational transfer function matrix, the Bezout equation, and the Youla parameterization of the two-degree-of-freedom controller using the following formulas: in, Indicates the first factor after left coprime decomposition. Let N represent the second factor after left coprime decomposition, D represent the first factor after right coprime decomposition, Y represent the first matrix parameter in the Bezout equation, and X represent the second matrix parameter in the Bezout equation. This represents the second matrix parameter in the Bezout equation after left coprime decomposition. Let I represent the first matrix parameter in the Bezout equation after left coprime decomposition, and let RH represent the identity matrix. ∞ Let κ represent the set of all stable, regular, and real rational transfer functions, let K represent the set of all controllers that can make the networked control system stable, let R represent the first control parameter of the two-degree-of-freedom controller, and let Q represent the second control parameter of the two-degree-of-freedom controller.

4. The method for optimizing the tracking performance of a networked control system according to claim 3, characterized in that, Specifically, S4 is: The error signal of the two-degree-of-freedom networked control system is simplified according to the following formula: Where e represents the error signal of the two-degree-of-freedom networked control system.

5. The method for optimizing the tracking performance of a networked control system according to claim 1, characterized in that, S5 specifically includes: S501: Calculates tracking performance metrics; S502: Based on the tracking performance index and the simplified error signal, calculate the optimal performance expression of the two-degree-of-freedom networked control system model.

6. The method for optimizing the tracking performance of a networked control system according to claim 5, characterized in that, Specifically, S501 is: Calculate the tracking performance metrics using the following formula: Where J() represents the tracking performance metric, E{} represents the trade-off between channel input energy constraints and tracking error, and E{} represents the expectation operator. Let ||||2 represent the original error signal, and ||||2 represent the L2 norm. Π represents the actual output signal of the two-degree-of-freedom networked control system, and Π represents the upper bound of the channel input energy.

7. The method for optimizing the tracking performance of a networked control system according to claim 6, characterized in that, Specifically, S502 is as follows: Calculate the optimal performance expression of the two-degree-of-freedom networked control system model according to the following formula: Among them, J * This represents the optimal performance expression for a two-degree-of-freedom networked control system model. This represents the first performance component related to tracking error. The second performance part is related to the quantizer nonlinearity and channel delay, where inf represents the infimum and υ represents the weight vector of the input signal.

8. The method for optimizing the tracking performance of a networked control system according to claim 7, characterized in that, Specifically, S6 is: The first and second performance parts in the optimal performance expression of the two-degree-of-freedom networked control system model are simplified respectively: Where, n z s represents the number of non-minimum phase zeros. k This represents the k-th non-minimum phase zero. The conjugate transpose vector of the direction of the k-th non-minimum phase zero, H represents the sign of the conjugate transpose, h represents the frequency domain transfer function, and e jθ Let θ represent the angle of the j-th complex number in polar coordinates, where θ represents the angle, and n p Indicates the number of unstable poles. This represents the conjugate pole of the k-th unstable pole. p represents the conjugate pole of the l-th unstable pole. l This represents the l-th unstable pole. ψ is the conjugate transpose of the direction of the k-th unstable pole. k-1 Let ψ be the product matrix of k-1 unstable poles. l-1 Let ω represent the product matrix of l-1 unstable poles. l Indicates the direction of the l-th unstable pole. ω represents the conjugate transpose of the direction of the l-th unstable pole. k Let s represent the k-th unstable pole. l This represents the l-th non-minimum phase zero. H represents the conjugate pole of the k-th non-minimum phase zero. k H represents the compensation matrix associated with the k-th non-minimum phase zero. l ξ represents the compensation matrix associated with the l-th non-minimum phase zero. l Indicates the direction of the l-th non-minimum phase zero. G represents the direction conjugate transpose vector of the l-th non-minimum phase zero. l This represents a portion of the all-pass matrix associated with the l-th non-minimum phase zero. Let B represent the cumulative performance matrix associated with all unstable poles, and let B represent the all-pass factor of the second factor D after right coprime decomposition and all-pass decomposition.

9. The method for optimizing the tracking performance of a networked control system according to claim 8, characterized in that, Specifically, S7 is: Based on the first and second performance parts in the simplified optimal performance expression, calculate the optimal tracking performance expression of the two-degree-of-freedom networked control system model: in, This represents the optimal tracking performance expression for a two-degree-of-freedom networked control system model.

10. A networked control system tracking performance optimization system, characterized in that, include: Memory and one or more processors; The memory stores one or more application programs, which are adapted to be executed by the one or more processors to implement the networked control system tracking performance optimization method according to any one of claims 1 to 9.

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