A method for revising performance limits of a network control system based on single-degree-of-freedom controllers

Abstract

The application provides a method for modifying performance limit of a single-degree-of-freedom controller network control system, and relates to the field of network system control, which comprises the following steps: building a single-degree-of-freedom controller network control system under the influence of quantization, obtaining an optimal performance expression of the system, according to the double-coprime decomposition of the system, combining the double-Bezout equation and the Youla parameterized form of the single-degree-of-freedom controller to solve a second expression form of the transfer function of the system, and then obtaining a second optimal tracking performance expression of the system, and based on the all-pass decomposition, H2 space decomposition and internal-external decomposition technology, an explicit expression of the modified performance limit of the system is obtained. The application has the beneficial effects that the problems of the modified tracking performance limit and the modified trade-off performance limit of the system are studied, the tracking performance of the multi-input multi-output discrete network control system is greatly improved, and the influence of the essential characteristics of the controlled object and the communication constraint on the system performance is quantified.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of network system control, and particularly relates to a modified performance limit method of a network control system based on a single-degree-of-freedom controller. BACKGROUND

[0002] Performance analysis method for NCSs with coding and quantization constraints introduces a system model, and studies the tracking performance limit of a network control system with coding constraints and quantization constraints. Network parameters mainly consider the influence of additive white Gaussian noise in a forward channel and coding and decoding, and quantization and bandwidth in a feedback channel. By using spectral decomposition technology, a displayed expression of the tracking performance limit of the system is obtained. Although the coding and decoding and the constraints of noise are considered in the actual communication network, there are still constraints such as packet loss delay, and the quantizer has a higher resolution compared with the uniform quantizer used in the model. The research on the tracking performance limit of the network control system for the model needs to be further deepened.

[0003] Optimal modified tracking performance for MIMO networked control systems with communication constraints introduces a research model, and studies the optimal modified tracking performance of a multiple-input multiple-output (MIMO) network control system with packet loss and bandwidth constraints. Network parameters mainly consider Gaussian white noise and constraints of packet loss and bandwidth. By using spectral decomposition technology, a displayed expression of the modified tracking performance limit of the system is obtained through a modification factor. For the model, although the modification factor is used, the defined modification factor cannot adapt to some more complex network control systems, and the research can be further deepened. SUMMARY

[0004] The present application aims at deepening the research on the tracking performance limit of the network control system by the prior art. The present application provides a modified performance limit method of a network control system based on a single-degree-of-freedom controller, mainly comprising the following steps:

[0005] A network control system based on a single-degree-of-freedom controller under the influence of quantization is built, and an optimal performance expression of the system is obtained;

[0006] According to the double-coprime decomposition of the system, a second expression form of the transfer function of the system is solved by combining a double-Bezout equation and a Youla parameterization form of the single-degree-of-freedom controller, and a second optimal tracking performance expression of the system is obtained.

[0007] Based on all-pass decomposition, H2 space decomposition, partial fraction decomposition technique, the second optimal tracking performance expression of the system is calculated, so as to obtain the explicit expression of the system correction performance limit.

[0008] Further, the system output is the first expression:

[0009]

[0010] Among them, represents the discrete form of the signal , including: : represents the output of the system; n represents the additive white Gaussian noise of the feedforward channel, the mean , the variance , ; u represents the control input of the system; r represents the reference input of the system, and the vector form is represented as: , wherein is a constant unit vector, k represents the time, and the discrete form of the reference input obtained by Z transform is: ; is the output of the system, and the vector form is represented as: , wherein is the relative quantization error probability independent of the system output, which is uniformly distributed on , , , respectively represent the maximum value and the error probability value of the relative quantization error probability, , , E is the mathematical expectation; represents the time delay; is the controlled object.

[0011] The system control input is the second expression:

[0012]

[0013] Among them, K represents a single degree of freedom controller; represents the data packet loss probability in the feedback channel, and the data packet loss in the feedback channel of the system is modeled as: , which is subject to the probability distribution , .

[0014] The system error signal is the third expression:

[0015]

[0016] wherein, is the transfer function of the reference input to the error signal, is the transfer function of the noise signal to the error signal, collectively referred to as the transfer function of the system.

[0017] The modified trade-off performance index of the system is the fourth expression:

[0018] wherein, is the tracking error vector, the scaling factor , the Z-transform is: .

[0019] Further, substituting the third expression into the fourth expression, according to the Parseval theorem, the first optimal tracking performance expression of the system is the fifth expression:

[0020]

[0021] Further, according to the dual-coprime factorization of the system, combined with the dual-Bezout equation and the Youla parameterization form of the single-input single-output controller, the second expression form of the transfer function of the system is solved, and substituted into the fifth expression to obtain the second optimal tracking performance expression of the system, which is the sixth expression:

[0022] wherein, is a constant expression defined for convenient calculation . represents a stable, regular, real-rational transfer function or matrix set; represents a time constant; is a unit matrix; , , , , , respectively represent zero point factors under the influence of the scaling factor , construct a construction matrix that satisfies the dual-Bezout equation, and the controller transfer function matrix.

[0023] Further, substituting the input, output and additive white Gaussian noise of the feedforward channel of the system into the third expression, the first expression form of the transfer function of the system can be obtained:

[0024]

[0025] .

[0026] ​Further, the second expression of the transfer function of the system is obtained from the first expression of the transfer function of the system, based on the double-coprime factorization of the system, the double-Bezout equation and the Youla parameterization of the single-degree-of-freedom controller.

[0027] The expression of the double-coprime factorization of the system is:

[0028]

[0029] wherein, are the zero and pole factors obtained by left-coprime factorization; are the zero and pole factors obtained by right-coprime factorization.

[0030] The expression of the double-Bezout equation is:

[0031]

[0032] wherein, , , , are the construction matrices for constructing the matrices satisfying the double-Bezout equation.

[0033] The expression of the Youla parameterization of the single-degree-of-freedom controller is:

[0034]

[0035] wherein, denotes the set of controllers.

[0036] Substituting the first expression of the transfer function of the system, the second expression of the transfer function of the system is obtained, and the mathematical expression is:

[0037]

[0038] .

[0039] Further, the steps for calculating the second optimal tracking performance expression based on the all-pass factorization, H2 space factorization and partial fraction factorization technology include: , The seventh and eighth expressions are the split results of the second optimal tracking performance expression;

[0040] The mathematical representation of the seventh expression is as follows:

[0041]

[0042] The mathematical representation of the eighth expression is as follows:

[0043]

[0044] wherein, is a first part of the second optimal tracking performance expression; is a second part of the second optimal tracking performance expression.

[0045] Further, the solving of the seventh expression is specifically:

[0046] For the system, there is a full rank decomposition:

[0047]

[0048] wherein, is a full rank factor, containing non-minimum phase zeros of the controlled object , , is a total number of minimum phase zeros, is a minimum phase factor; The decomposition is: ;

[0049] wherein, denotes a conjugate of is a direction vector of the non-minimum phase zero , is a transpose thereof; , is a vector satisfying the equation , is a transpose of ;

[0050] Based on the decomposition equation, the seventh expression is simplified to obtain a first simplified expression of :

[0051]

[0052] wherein, the other part belongs to , , is a subspace of the Hilbert space; based on the subspace decomposition, the first simplified expression is decomposed to obtain a first decomposition expression of :

[0053] The decomposition step is repeated to finally obtain ;

[0054] ​​is expressed as the ninth expression:

[0055]

[0056] is expressed as the tenth expression:

[0057] .

[0058] Further, the solving process of the ninth expression is as follows:

[0059]

[0060] According to , the partial fraction in the ninth expression is expanded as:

[0061] and the ninth expression is solved as the eleventh expression:

[0062]

[0063] wherein, .

[0064] Further, the solving process of the tenth expression is as follows:

[0065] Define , substitute into the tenth expression, and obtain the first transformation expression of :

[0066]

[0067] wherein, represents the minimum phase factor, including all stable poles of the controlled object; includes all unstable poles of the controlled object, and is defined as:

[0068]

[0069] wherein, represents the pole factor; is an unstable pole, is the conjugate thereof; is the all-pass factor of the unstable pole, is the direction vector thereof, represents the transpose of ; is a vector satisfying the formula , represents the transpose of ;

[0070] For the all-pass factor , the Z transform expansion is as follows:

[0071]

[0072] wherein, denotes the Z-transform of is an intermediate matrix, is the Z-transform of , is a full- factorization; denotes a construction matrix satisfying the equation

[0073] and further obtaining a second transformation of

[0074]

[0075] wherein, , , denotes , , the inverse Z-transform of denotes a minimum phase factor;

[0076]

[0077]

[0078] substituting the second transformation of obtains a third transformation of :

[0079]

[0080] wherein, is a definition for simplifying the equation

[0081]

[0082] based on a spatial decomposition, , decomposes and obtains a fourth transformation of :

[0083]

[0084] wherein, ,

[0085] designing an optimal controller such that the controller parameters such that the fourth transformation of with the fraction other than 0, at this time , the substituted into the tenth expression, the solution result of the twelfth expression is obtained:

[0086]

[0087] wherein, indicates the definition of the intermediate matrix of the simplified operation, and is defined as:

[0088] .

[0089] Further, the solution result of the seventh expression is obtained as the thirteenth expression by combining the eleventh expression and the twelfth expression:

[0090]

[0091] Further, the solution process of the eighth expression is the same as that of the seventh expression, and the solution result is represented as the fourteenth expression:

[0092]

[0093] wherein, .

[0094] Further, the explicit expression of the system correction performance limit is obtained as the solution result of the second optimal tracking performance expression by combining the thirteenth expression and the fourteenth expression, and is represented as the fifteenth expression:

[0095]

[0096] The technical scheme provided by the application has the beneficial effects that: the application builds a new framework of a single-degree-of-freedom controller network control system under the influence of quantization, with data packet loss, time delay and signal constraints, studies the correction tracking performance limit and the correction trade-off performance limit of the system, designs an optimal controller by using the tools of co-prime decomposition and Youla parameterization, greatly improves the tracking performance of a multi-input multi-output discrete network control system under the premise of ensuring system stability, and obtains the lower bound of the tracking performance of the multi-input multi-output discrete network control system, quantifies the influence of the essential characteristics of the controlled object and the communication constraints on the system performance. BRIEF DESCRIPTION OF DRAWINGS

[0097] The application will be further described below in combination with the drawings and embodiments, and the drawings show:

[0098] Figure 1 is a framework schematic diagram of a single-degree-of-freedom controller network control system in the embodiments of the application;

[0099] Figure 2 is a schematic diagram of a linear two-degree-of-freedom vehicle model in embodiments of the present application;

[0100] Figure 3 is a schematic diagram of the modified tracking performance limit of a networked single-degree-of-freedom system under different outputs and different noises in embodiments of the present application;

[0101] Figure 4 is a schematic diagram of the modified tracking performance limit of a networked two-degree-of-freedom system under different time delays and different lengths in embodiments of the present application. DETAILED DESCRIPTION

[0102] In order to have a more clear understanding of the technical features, objectives and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the accompanying drawings.

[0103] Embodiments of the present application provide a modified performance limit method, device and storage medium based on a single-degree-of-freedom controller network control system.

[0104] Please refer to Figure 1 , Figure 1 is a schematic diagram of a framework of a single-degree-of-freedom controller network control system in embodiments of the present application, and the expressions of various parameters are as follows:

[0105] represents the output of the system.

[0106] n represents the additive white Gaussian noise of the feedforward channel, the mean , and the variance , ;

[0107] u represents the control input of the system.

[0108] r represents the reference input of the system, and the vector form is represented as: wherein is a constant unit vector, k represents the time, and the discrete form of the reference input obtained by Z transform is: .

[0109] is a quantizer, is the quantization of the system output, and the vector form is represented as: wherein is the relative quantization error probability independent of the system output, which is uniformly distributed on , , , respectively represent the maximum value and the error probability value of the relative quantization error probability, 、 , E is mathematical expectation.

[0110] represents time delay.

[0111] is the controlled object.

[0112] Data packet loss in the feedback channel of the system is modeled as: , subject to probability distribution , , represents the data packet loss probability in the feedback channel.

[0113] Subsequently, for the convenience of calculation, represents the discrete form of the signal , including: .

[0114] The method for modifying the performance limit of a network control system based on a single-degree-of-freedom controller according to an embodiment of the application specifically comprises the following steps:

[0115] First, a network control system based on a single-degree-of-freedom controller under quantization is built, and an optimal performance expression of the system is obtained, specifically as follows:

[0116] First, a network control system based on a single-degree-of-freedom controller is built:

[0117] The system output is the first expression:

[0118]

[0119] The system control input is the second expression:

[0120]

[0121] wherein K represents a single-degree-of-freedom controller.

[0122] The system error signal is the third expression:

[0123]

[0124] wherein, is a transfer function from a reference input to an error signal, is a transfer function from a noise signal to an error signal, collectively referred to as a transfer function of the system.

[0125] The modified trade-off performance index of the system is the fourth expression: ;

[0126] wherein, scaling factor for tracking error vector The Z-transform is: .

[0127] Substitute the third expression into the fourth expression, and according to the Parseval theorem, the first optimal tracking performance expression of the system is the fifth expression:

[0128]

[0129] Secondly, according to the dual-coprime factorization of the system, the second expression form of the transfer function of the system is solved by combining the dual-Bezout equation and the Youla parameterization form of the single-input single-output controller, and then the second optimal tracking performance expression of the system is obtained.

[0130] Substitute the input, output and additive white Gaussian noise of the feedforward channel of the system into the third expression, and the first expression form of the transfer function of the system can be obtained:

[0131]

[0132] .

[0133] The second expression form of the transfer function of the system is obtained by adding the dual-coprime factorization of the system based on the rational transfer function matrix, the dual-Bezout equation and the Youla parameterization form of the single-input single-output controller to the first expression form of the transfer function of the system.

[0134] The expression of the dual-coprime factorization of the system is:

[0135]

[0136] wherein, are the zero point factor and the pole factor obtained by left-coprime factorization; are the zero point factor and the pole factor obtained by right-coprime factorization, respectively.

[0137] The expression of the dual-Bezout equation is:

[0138]

[0139] wherein, , , , is the construction matrix for constructing the dual-Bezout equation.

[0140] The expression of the Youla parameterization form of the single-input single-output controller is:

[0141]

[0142] wherein, represents a set of controllers.

[0143] Substitute the first expression of the transfer function of the system, the second expression of the transfer function of the system is obtained, the mathematical expression is:

[0144]

[0145]

[0146] Substitute the fifth expression to obtain the second optimal tracking performance expression of the system as the sixth expression:

[0147] wherein, is a constant expression defined for convenient calculation ; represents a set of stable, regular, real rational transfer functions or matrices; represents a time constant; is a unit matrix; , , , , , respectively represent zero point factors under the influence of scaling factor , construct a construction matrix that satisfies the double Bezout equation, and the controller transfer function matrix.

[0148] Thirdly, based on all-pass decomposition, H2 space decomposition, and partial fraction decomposition technology, the second optimal tracking performance expression of the system is calculated, so that the explicit expression of the system correction performance limit is obtained.

[0149] Define , , the seventh and eighth expressions, and the second optimal tracking performance expression is the splitting result of the second optimal tracking performance expression.

[0150] The mathematical representation of the seventh expression is as follows:

[0151]

[0152] The mathematical representation of the eighth expression is as follows:

[0153]

[0154] wherein, is the first part of the second optimal tracking performance expression; is the second part of the second optimal tracking performance expression.

[0155] The solution of the seventh expression is specifically:

[0156] For the system, there is a full-pass decomposition:

[0157]

[0158] wherein, is a full-pass factor, containing the non-minimum phase zero of the controlled object , , is the total number of minimum phase zeros, is a minimum phase factor; The decomposition is: ;

[0159] wherein, represents the conjugate of is the direction vector of the non-minimum phase zero , is the transpose thereof; , is a vector satisfying the formula , is the transpose of .

[0160] Based on the decomposition formula, the seventh expression is simplified to obtain the first simplified formula of :

[0161]

[0162] wherein, the other part belongs to , , is a subspace of the Hilbert space; based on the space decomposition, the first simplified formula is decomposed to obtain the first decomposition formula of :

[0163] The decomposition step is repeated to finally obtain ;

[0164] is expressed as the ninth expression:

[0165]

[0166] is expressed as the tenth expression:

[0167] .

[0168] ​​The solution process of the eighth expression is as follows:

[0169]

[0170] According to , the partial fraction in the ninth expression is expanded as:

[0171] and the ninth expression is solved as the eleventh expression:

[0172]

[0173] wherein, .

[0174] The solution process of the tenth expression is as follows:

[0175] Define , substitute into the tenth expression, and obtain the first transformation expression of :

[0176]

[0177] wherein, represents the minimum phase factor, which contains all stable poles of the controlled object; contains all unstable poles of the controlled object, and is defined as:

[0178]

[0179] wherein, represents the pole factor; is an unstable pole, is the conjugate thereof; is the all-pass factor of the unstable pole, is the direction vector thereof, represents the transpose of ; is a vector satisfying the formula , represents the transpose of .

[0180] The Z transform expansion of the all-pass factor is as follows:

[0181]

[0182] wherein, represents the Z transform form of ; is an intermediate matrix, is the Z transform form thereof; , for the all-pass factor decomposition formula; denotes the construction matrix satisfying the equation,

[0183] further obtaining the second transformation formula of

[0184]

[0185] wherein, , , denotes , , the inverse transformation form of the Z transform of denotes the minimum phase factor;

[0186]

[0187]

[0188] substituting the second transformation formula of obtains the third transformation formula of :

[0189]

[0190] wherein, is a definition formula for simplifying the formula, defined as:

[0191]

[0192] based on spatial decomposition, , decomposition is performed on , obtaining the fourth transformation formula of :

[0193]

[0194] wherein, ,

[0195] designing an optimal controller, so that the controller parameters so that the fraction other than in the fourth transformation formula of , at this time , substituting into the tenth expression, obtains the solution result of the tenth expression as the twelfth expression:

[0196]

[0197] wherein, The intermediate matrix representing the simplified operation is defined as:

[0198] .

[0199] Combining the eleventh expression and the twelfth expression, we get the solution of the seventh expression, which is the thirteenth expression:

[0200]

[0201] The solution process of the eighth expression is the same as that of the seventh expression, and the solution result is expressed as the fourteenth expression:

[0202]

[0203] in, .

[0204] Combining the thirteenth and fourteenth expressions as the solution results of the second optimal tracking performance expression, we obtain the explicit expression of the system correction performance limit, which is expressed as the fifteenth expression:

[0205]

[0206] In order to verify the effectiveness of the present invention, the obtained theorem is applied to Figure 2 The linear two-degree-of-freedom car model is used as the controlled object in the system, and the performance limit concept is used to study the vehicle's handling stability. The linear two-degree-of-freedom car model regards the vehicle as a rigid body, ignores the car's suspension, and only considers the car's lateral motion (considering the lateral velocity). ) and yaw motion (considering the yaw velocity ),in addition, is the actual steering of the vehicle, The centroid Speed ​​in the axis direction. and From the front wheel to the center of mass, from the rear wheel to the center of mass distance, and and are the lateral deflection forces of the front and rear wheels respectively.

[0207] By derivation, the dynamic differential equation of the vehicle model can be obtained as follows:

[0208]

[0209] in, For the quality of the car; and are the cornering stiffness of the front and rear wheels respectively; the lateral deflection angle of the center of mass is , is the moment of inertia.

[0210] It is arranged that:

[0211] ,

[0212] wherein, are the definition of the simplified formula, and the specific definition is:

[0213] , ,

[0214] , ,

[0215] , ;

[0216] Therefore, taking as input, as output, and discretizing by the forward Euler method, the discrete transfer function of the controlled object can be obtained as:

[0217]

[0218] wherein, , and - transformation form.

[0219] For a networked control system based on a single degree of freedom controller, different axle speeds and channel noise are selected, and the simulation results of Figure 3 can be obtained based on the method of the application. It can be seen that when the vehicle speed is faster, the system correction performance limit is larger, which indicates that the maneuverability of the vehicle is worse. Similarly, when the noise interference in the channel is larger, the correction performance limit of the system is larger, and the tracking performance of the system gradually deteriorates, so the speed of the vehicle and the noise interference in the channel are negatively related to the system performance. For a networked control system based on a double degree of freedom controller, different network-induced time delays 0.2, 0.4, 0.6 respectively, and different lengths of the center of mass to the front axle can be selected to obtain the simulation results as shown in Figure 4 It can be seen that the larger the network-induced time delay in the channel , the worse the performance of the system, and the network-induced time delay will deteriorate the tracking performance of the networked control system. For the properties of the vehicle itself, such as the length ​​, also affects the control performance of the system. This is because its own properties change the zero and pole points of the control object, thereby affecting the system performance. This is reflected in the display expression of the performance limit, proving the feasibility of the present invention. Figure 4 It can be seen that in different network induced delays Down has different optimal values, specifically, when hour, ,when hour, ,when hour, .

[0220] The key technical points of this scheme are: using binary random process to simulate packet loss, assuming that the channel noise is additive white Gaussian noise, the network induced delay is a constant delay, using logarithmic quantizer, and proposing discrete time correction performance index in order to more reasonably measure the system performance, and using frequency domain analysis and controller Youla parameterization method, combined with full-pass decomposition, internal and external decomposition, Spatial decomposition techniques are used to derive explicit expressions for the system's modified performance limits.

[0221] The beneficial effects of the present invention are as follows: the present invention builds a new framework for a network control system based on a single-degree-of-freedom controller under the influence of quantization, with data packet loss, time delay and signal constraints, and studies the problems of the system's corrected tracking performance limit and corrected trade-off performance limit; an optimal controller is designed using tools such as coprime decomposition and Youla parameterization, which greatly improves the tracking performance of a multi-input multi-output discrete network control system while ensuring system stability; the lower bound of the tracking performance of the multi-input multi-output discrete network control system is obtained, and the influence of the essential characteristics of the controlled object and communication constraints on the system performance is quantified.

[0222] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for correcting performance limits of a network control system based on a single degree of freedom controller, characterized in that: The specific steps include: Build a network control system based on a single degree of freedom controller under the influence of logarithmic quantization, specifically: The system output is the first expression: in, Indicates signal The discrete form of include: ; Represents the output of the system; n Represents the additive white Gaussian noise of the feedforward channel, with mean ,variance , represents the variance of c channels; ; u represents the control input of the system; r represents the reference input of the system, and the vector form is expressed as: ,in, is a constant unit vector, k Represents the moment, and the Z transform obtains the discrete form of the reference input: ; is the logarithmic quantization of the system output, expressed in vector form as: ,in, is the relative quantization error probability independent of the system output, Evenly distributed on , 、 Represent the maximum value and error probability value of relative quantization error probability, respectively. 、 , E is the mathematical expectation; represents the time delay; For the accused; The system control input is the second expression: Where K represents a single degree of freedom controller; represents the probability of data packet loss in the feedback channel. The data packet loss in the feedback channel of the system is modeled as: , obeys the probability distribution , ; The system error signal is expressed as the third expression: in, is the transfer function from reference input to error signal, is the transfer function from noise signal to error signal, collectively referred to as the transfer function of the system; The modified trade-off performance index of the system is expressed as the fourth expression: ; in, is the tracking error vector, the scaling factor , the Z transform is: ; Substituting the third expression into the fourth expression, according to Parseval's theorem, we can obtain the first optimal tracking performance expression of the system as the fifth expression: in For the controller collection, is the seventh expression; and is the eighth expression; According to the dual coprime decomposition of the system, the second expression of the system's transfer function is solved by combining the dual Bezout equation and the Youla parameterized form of the single-degree-of-freedom controller. Substituting it into the fifth expression, the second optimal tracking performance expression of the system is obtained as the sixth expression: in, Constants defined for ease of calculation ; represents a stable, regular, real rational transfer function or set of matrices; represents the time constant; is the identity matrix; and Represents the scaling factor The zero-point factor under the influence of and Indicates the construction matrix that satisfies the double Bezout equation. represents the controller transfer function matrix; In the scaling factor Extreme factors under influence; The second optimal tracking performance expression of the system is calculated based on full-pass decomposition, H2 space decomposition and partial fraction decomposition techniques, thereby obtaining an explicit expression of the system's corrected performance limit.

2. A method for correcting performance limits of a network control system based on a single degree of freedom controller according to claim 1, characterized in that: Substituting the additive Gaussian white noise of the system's input, output, and feedforward channel into the third expression, we obtain the first expression of the system's transfer function: 。 3. A method for correcting performance limits of a network control system based on a single degree of freedom controller as claimed in claim 2, characterized in that: The second expression form of the transfer function of the system is obtained by adding the system double coprime decomposition based on the rational transfer function matrix, the double Bezout equation and the Youla parameterization form of the single degree of freedom controller to the first expression form of the transfer function of the system; The expression of the double coprime decomposition of the system is: in, are the zero-point factors and extreme factors obtained by left coprime decomposition; are the zero-point factors and extreme factors obtained by right coprime decomposition respectively; The double Bezout equation is expressed as: in, 、 、 、 To construct a matrix that satisfies the double Bezout equation; The Youla parameterized form of the single degree of freedom controller is expressed as: in, Represents a collection of controllers; Substituting the first expression of the system's transfer function into the second expression of the system's transfer function, the mathematical expression is: 。 4. A method for correcting performance limits of a network control system based on a single degree of freedom controller as claimed in claim 3, characterized in that: The steps of calculating the second optimal tracking performance expression of the system based on full-pass decomposition, H2 space decomposition, and partial fraction decomposition technology include: defining 、 The seventh and eighth expressions are the split results of the second optimal tracking performance expression; The mathematical representation of the seventh expression is as follows: The mathematical representation of the eighth expression is as follows: in, is the first part of the second optimal tracking performance expression; is the second part of the second optimal tracking performance expression.

5. A method for correcting performance limits of a network control system based on a single degree of freedom controller as claimed in claim 4, characterized in that: The solution of the seventh expression is: For the system, there is a full-pass decomposition: in, is the all-pass factor, including the non-minimum phase zero of the controlled object , , is the total number of non-minimum phase zeros, is the minimum phase factor; Breaks down to: ； in, express conjugation of; Non-minimum phase zero The direction vector, Transpose it; 、 For satisfaction vector, for Transpose; based on Decomposition, simplify the seventh expression, and we get The first simplified form of is: in, , the rest belongs to , 、 is a subspace of the Hilbert space; Expressed as a constant unit vector; based on Spatial decomposition decomposes the first simplified formula to obtain The first decomposition of: Repeat the decomposition steps and finally get ; Expressed as the ninth expression: Expressed as the tenth expression: 。 6. A method for correcting performance limits of a network control system based on a single degree of freedom controller as claimed in claim 5, characterized in that: The solution process of the ninth expression is as follows: according to , expand the partial fraction in the ninth expression into: , and then solve the ninth expression to get the eleventh expression: in, .

7. A method for correcting performance limits of a network control system based on a single degree of freedom controller as claimed in claim 6, characterized in that: The solution process of the tenth expression is as follows: definition , substituting into the tenth expression, we get The first transformation of: in, Represents the minimum phase factor, which includes all the stable poles of the controlled object; The all-pass factor that includes all unstable poles of the controlled object is defined as: in, represents the extreme factor; is the unstable point, for its conjugation; is the all-pass factor of the unstable pole, is its direction vector, express The transpose of For satisfaction vector, express The transpose of For the all-pass factor The Z transform expansion is as follows: in, express The Z transform form of for The inverse of the Z transform form; is the intermediate matrix, is its Z-transform form; 、 is the full-pass factorization formula; represents the construction matrix that satisfies the equation; Then get The second transformation of: in, 、 、 express 、 、 The inverse transform form of the Z transform; Indicates that Substituting into the minimum phase factor middle; Indicates that Substitute into the all-pass factor middle; Substitution The second transformation of The third transformation of: in, The definition used to simplify the formula is: based on Spatial decomposition, , ,right Decompose it and get The fourth transformation formula is: in, , Design an optimal controller so that the controller transfer function matrix , making In the fourth transformation formula The fractions other than ,Will Substitute into and get the solution of the tenth expression as the twelfth expression: in, The intermediate matrix representing the simplified operation is defined as: 。 8. A method for correcting performance limits of a network control system based on a single degree of freedom controller according to claim 7, characterized in that: Combining the eleventh expression and the twelfth expression, we get the solution of the seventh expression, which is the thirteenth expression:

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