Networked system output tracking control performance method for model uncertainty

Abstract

The invention relates to the field of networked system output tracking control performance, in particular to a networked system output tracking control performance method for model uncertainty. Data packet loss in a communication channel is modeled in a feedback channel of a network control system by using a Bernoulli process and a binary random process, and it is assumed that reference input and channel noise signals of the system are independent identically distributed random processes with non-zero mean values and are mutually independent, and through all-pass decomposition and partial fractional decomposition, the data packet loss in the communication channel is calculated. A system model is deduced by using tools and methods such as a double Bezout equation, a space decomposition technology, a Youla parameterization method of a controller, statistical characteristics of random signals and the like, and finally, an explicit expression of the optimal tracking performance of the system is obtained. According to the method, the problem of OTC performance deterioration possibly caused by data packet loss and additive white Gaussian noise (AWGN) is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of networked system output tracking control, and particularly relates to a networked system output tracking control performance method for model uncertainty. BACKGROUND

[0002] In networked control systems (NCSs), the communication network constraints such as network-induced delay, data packet dropout, noise, etc. can affect the optimal tracking performance (OTP) and even the stability of the system. The existing technology mainly studies the OTP of NCSs considering the data packet dropout and non-zero mean additive white noise (AWN) constraints in the communication network. Based on the single degree of freedom (SDOF) controller and the two degree of freedom (TDOF) controller, the OTP limit explicit expressions of NCSs under the constraints of non-zero mean noise and data packet dropout are obtained by using the coprime factorization and Youla parameterization methods. The results show that the inherent characteristics of the controlled object and the communication parameters of the network channel will affect the OTP of NCSs. Although the existing technology considers the influence of inherent characteristics and communication parameters, it does not consider the output tracking control of discrete networked systems under the erasure channel with model uncertainty. Therefore, it is necessary to optimize the performance of networked control systems under the erasure channel with model uncertainty when there are data packet dropout and noise constraints. SUMMARY

[0003] In order to solve the problems of data packet dropout, noise, etc. in the network, and the existence of model uncertainty in the erasure channel, which can seriously affect the performance and even the stability of the control system, the present application provides a networked system output tracking control performance method for model uncertainty, mainly comprising: S1: for the output tracking control system of the networked system, the data packet dropout process is modeled by using the Bernoulli process; S2: based on the model established in S1, the tracking error of the system is calculated, and then the tracking error performance index is obtained; S3: the transfer function of the system is obtained by double Bezout decomposition and Youla parameterization; S4: the transfer function is coprime decomposed and all-pass decomposed in combination with the tracking error performance index, and the optimal tracking performance explicit expression of the system is obtained.

[0004] A computer device comprising a memory, a processor and a computer program stored in the memory, the processor executing the computer program to implement the steps of the above method.

[0005] A computer readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above method.

[0006] A computer program product comprising computer programs or instructions which, when executed by a processor, implement the steps of the above method.

[0007] The technical scheme provided by the present application has the beneficial effects that the present application mainly discusses the limitations caused by model uncertainty (including channel and controlled object model). Data packet loss and additive white Gaussian noise (AWGN) can cause OTC performance deterioration. To solve this problem, the present application uses Bernoulli process and binary random process to model data packet loss in the communication channel in the feedback channel of the network control system, and assumes that the reference input and channel noise signal of the system are independent and identically distributed random processes with non-zero mean and are independent of each other. Through full-part decomposition, partial fraction decomposition, double Bezout equation, Space decomposition technology, controller Youla parameterization method and statistical characteristics of random signals are used to derive the system model, and finally the optimal tracking performance explicit expression of the system is obtained. The present application considers the erasure channel with model uncertainty and the feedback channel with data packet loss, and establishes a new framework for performance analysis of output tracking control (OTC) of discrete time system (DTSs). The analytical closed-form expression is derived, which reveals the dependence of OTC performance limitation on the non-minimum phase (NMP) zero point, unstable pole and its direction of the controlled object, and the data packet loss probability. BRIEF DESCRIPTION OF DRAWINGS

[0008] The present application will be further described below in conjunction with the drawings and embodiments. In the drawings: Figure 1 is a flowchart of the networked system output tracking control performance method in the embodiment of the present application; Figure 2 is a structure diagram of the output tracking control system of the networked system in the embodiment of the present application; Figure 3 is a schematic diagram of the tracking performance limit of the network control system under the influence of different data packet loss probabilities in the embodiment of the present application. DETAILED DESCRIPTION

[0009] In order to have a clearer understanding of the technical features, objects and effects of the present application, the specific embodiments of the present application will be described in detail with reference to the drawings.

[0010] Embodiment 1 The embodiment of the present application provides a single-input single-output discrete-time networked system output tracking control performance method based on a single degree of freedom controller under an erasure channel with additive white Gaussian noise (AWGN) process model uncertainty and a feedback channel with packet loss, as shown in the flowchart Figure 1 . The method comprises the following steps:​ S1: For the output tracking control system of networked systems, Bernoulli process is used to model the data packet loss process; S2: Based on the model established in S1, the tracking error of the system is calculated, and then the tracking error performance index is obtained; S3: The transfer function of the system is obtained through double Bezout decomposition and Youla parameterization; S4: Combined with the tracking error performance index, the transfer function is subjected to coprime decomposition and all-pass decomposition, and the optimal tracking performance explicit expression of the system is obtained.

[0011] The output tracking control system of networked systems is shown in Figure 2 , represents the additive white Gaussian noise in the feedback channel, represents the reference input of the additive white Gaussian noise random process, and is set , is transformed into . and are the control input and system output respectively, is a single degree of freedom controller, represents the nominal model of the channel filter, represents the channel model uncertainty, represents the nominal model of the noise spectrum factor, represents the noise spectrum factor uncertainty, represents the nominal model of the controlled object, represents the controlled object uncertainty.

[0012] The data packet loss is modeled as a Bernoulli packet loss process, and the data packet loss is represented by the parameter , and its probability distribution function is , where is the probability of data loss. In this example, Figure 1 there is packet loss in the negative feedback link of , and the probability is directly used for calculation.

[0013] The tracking error of the system is .

[0014] In the tracking performance limit analysis process, it is assumed that the signals of each channel are independent of each other, and the symbol is used to represent the transformed form of the signal . It is assumed that the nominal controlled object has different non-minimum phase (NMP) zeros ;​ two distinct unstable poles , and each pole has multiplicity one. Moreover, any NMP zero is not equal to any unstable pole.

[0015] tracking error performance index , is the variance of the tracking error . , where is the variance of .

[0016] Let , have the double Bezout identity , according to the theorem of double Bezout decomposition, where and contain all zeros of , and contain all poles, and , is the set of all stable, proper, rational transfer functions (matrices).

[0017] Youla parameterization of SISO controller: .

[0018] Based on coprime factorization of system graph where , , there are , . And there are , , . denotes the channel model uncertainty, denotes the plant uncertainty. can be derived from coprime factorization , , is the minimum phase part of , is the minimum phase part of .

[0019] By double Bezout decomposition and Youla parameterization, the transfer function , . Then the tracking performance limit can be written as where denotes the reference input of additive white Gaussian noise random process.

[0020] For the convenience of calculation, make , .

[0021] The following calculations :

[0022] definition ,in, Include All stable poles in the part, all-pass factor Defined as , It is the extreme point conjugate, Here is the direction vector of the unstable pole. for The conjugate transpose of . Is to make The matrix, yes The conjugate transpose of . It includes all the unstable poles of the controlled object. .

[0023] but

[0024] In the formula, for The decomposition is as follows:

[0025] in , for The j-th component of the decomposition, To be Substitute The result after that, for The reverse, .

[0026] make According to the theorem, we have equation 1: ,when There is a second formula: Subtracting equation 2 from equation 1, we get... Therefore, ,but because , ,in and If two subspaces are mutually orthogonal in a Hilbert space, then based on space decomposition techniques, we have:

[0027] Selecting appropriate controller parameters such that where is the minimum phase part of

[0028] By calculation then

[0029] Again, by the double Bezout identity and then so that

[0030] then

[0031] The following calculations :

[0032] where can be decomposed as where is the time delay of , , denotes the noise spectral factor uncertainty, is the inverse of , It is important to note that belongs to the delay-antistable part, where the superscript k represents the accumulation to the kth, so can be rewritten as

[0033] where is the conjugate of is the conjugate of and is the time delay of is the number of non-minimum phase zeros.

[0034] then

[0035] where ,​​​​​​ , Thus,

[0036] In the formula,

[0037]

[0038]

[0039] Selecting appropriate controller parameters , So that

[0040] Thus,

[0041] So the tracking error performance limit expression is obtained as: .

[0042] Experimental data and conclusions: Consider a discrete multi-input multi-output controlled object, and its transfer function matrix model is

[0043] Obviously, the controlled object is right-reversible, and contains an unstable pole When , there is a non-minimum phase (NMP) zero point . The coprime factorization of can be obtained as: ,

[0044] Further all-pass factorization of is performed, and is obtained. According to the results obtained in the embodiments, the tracking performance limit expression of the model can be calculated as: .

[0045] According to the above expression, the tracking performance limit of the network control system under the influence of different data packet loss probabilities is obtained, and the relationship between the tracking performance limit and the non-minimum phase zero point is shown in Figure 3 . The application solves the problem that data packet loss and additive white Gaussian noise (AWGN) can cause OTC performance deterioration.

[0046] Embodiment 2 A computer device comprising a memory, a processor and a computer program stored on the memory, the processor executing the computer program to implement the steps of the above method.

[0047] Embodiment 3 A computer readable storage medium storing a computer program which, when executed by a processor, implements the steps of the above method.

[0048] Embodiment 4 A computer program product comprising a computer program or instructions which, when executed by a processor, implements the steps of the above method.

[0049] The above description is merely the preferred embodiments of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A networked system output tracking control performance method with model uncertainty, characterized in that, S1: for the output tracking control system of the networked system, a Bernoulli process is used to model the data packet loss process; S2: based on the model established in S1, the tracking error of the system is calculated, and then the tracking error performance index is obtained; S3: the transfer function of the system is obtained through double Bezout decomposition and Youla parameterization; S4: combined with the tracking error performance index, the transfer function is subjected to coprime factorization and all-pass factorization to obtain the optimal tracking performance explicit expression of the system.

2. The model uncertainty, networked system output tracking control performance method according to claim 1, characterized in that, In S1, the established model is: The probability distribution function thereof is , wherein is the probability of data loss occurring, denotes data packet loss.

3. The model uncertainty, networked system output tracking control performance method according to claim 1, wherein, In S2, the tracking error of the system is wherein, denotes a reference input of an additive white Gaussian noise random process, is the system output.

4. The model uncertainty, networked system output tracking control performance method according to claim 3, wherein, In S2, the tracking error performance indicator , is the variance of the tracking error .

5. The model uncertainty, networked system output tracking control performance method according to claim 1, wherein, In S3, the transfer function is: ， ， wherein , is a transfer function obtained by double Bezout decomposition and Youla parameterization, is the probability of data loss occurrence, Q denotes the controller parameters, denotes the inverse of , denotes all the zeros of , denotes all the poles of , and: ， ， ， ， ， and comprise all zeros of and comprise all poles of , , denotes a nominal model of a channel filter, denotes a channel model uncertainty, denotes a nominal model of a noise spectral factor, denotes a noise spectral factor uncertainty, denotes a nominal model of a controlled plant, denotes a controlled plant uncertainty.

6. The model uncertainty, networked system output tracking control performance method, as recited in claim 1, wherein In S4, the optimal tracking performance explicit expression is: wherein denotes the probability of data loss, , denotes two different poles, denotes the number of unstable poles, is the direction vector of the unstable pole , is the conjugate transpose of , is the direction vector of the unstable pole , is the conjugate transpose of , is the variance of , denotes the additive white Gaussian noise in the feedback channel, , is the j-th component of the decomposition , is the result of plugging into , is the inverse of , is the conjugate transpose of , is the conjugate transpose of , denotes the number of non-minimum phase zeros, is the inverse of , denotes the nominal model of the channel filter, denotes the nominal model of the noise spectral factor, denotes the conjugate of , denotes a non-minimum phase zero, is the conjugate of , is the conjugate of , is the conjugate of , and are: ， ， is: denotes the inverse of denotes the uncertainty in the channel model, denotes the noise spectral factor uncertainty of denotes the conjugate of denotes the noise spectral factor uncertainty of denotes the inverse of denotes the uncertainty in the channel model.

7. A computer apparatus comprising a memory, a processor, and a computer program stored on the memory, wherein the computer program, when executed by the processor, causes the processor to perform the method of any one of claims 1 to 6. A processor executes a computer program to implement the steps of the networked system output tracking control performance method with model uncertainty according to claims 1-6.

8. A computer-readable storage medium, characterized in that, A computer program is stored, which, when executed by a processor, implements the steps of the networked system output tracking control performance method with model uncertainty according to claims 1-6.

9. A computer program product, characterised in that, A computer program or instructions are included, which, when executed by a processor, implement the steps of the networked system output tracking control performance method with model uncertainty according to claims 1-6.

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