CN113655715B - Performance optimization method of multi-channel discrete network control system - Google Patents
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Abstract
The invention provides a performance optimization method of a multi-channel discrete network control system, which establishes a multi-channel discrete network control system model, simulates data packet loss by utilizing a binary random process, assumes that channel noise is additive white Gaussian noise and network induced delay is constant delay, and carries out full-pass decomposition, internal and external decomposition and H-pass decomposition on the network induced delay 2 And deducing the control system model by using tools such as a spatial decomposition technology, youla parameterization of a controller and the like to obtain the optimal tracking performance of the control system.
Description
Technical Field
The invention relates to the technical field of network system control, in particular to a performance optimization method of a multi-channel discrete network control system.
Background
A system model is introduced in the literature of Performance limitation of network control systems with network delay and channel noises constraints, and the limit of the tracking Performance of a network control system with dual-channel noise constraint and network induced delay constraint is researched. The network parameters mainly consider network induced delay and additive white gaussian noise in the forward channel and additive white gaussian noise constraints in the feedback channel. And selecting an optimal single-parameter structure by using a spectrum decomposition technology to obtain a display expression of the tracking performance limit of the system. Although the system considers the time delay and the additive white gaussian noise constraint in the forward channel and the feedback channel, in the actual network communication channel, the constraints of packet loss, coding and decoding and the like exist, the network constraint considered by the model is not comprehensive enough, and the research on the tracking performance limit of the model on the network control system needs to be further deepened.
The literature "Optimal Tracking Performance of NCSs with Time-delay and Encoding-decoding Constraints" introduces a more complex research model, and researches the Optimal Performance of a network control system with network-induced delay Constraints, two-channel additive white Gaussian noise Constraints and Encoding and decoding Constraints. The network parameters mainly consider the coding and decoding constraint, the additive white Gaussian noise constraint and the feedback channel in the forward channelNetwork-induced delay constraints and additive white Gaussian noise constraints in the channel, using H 2 Norm and spectrum decomposition technology is used for obtaining a display expression of the tracking performance limit of the system based on an optimal single-parameter structure. For this model, the network constraints to be considered are more complex, but still further studies can be made, for example, to study the influence of packet loss on system tracking performance on this basis.
Disclosure of Invention
One of the main problems solved by the present invention is the problem of how to further optimize the tracking performance of a multiple-input multiple-output discrete network control system.
The invention provides a performance optimization method of a multi-channel discrete network control system, which comprises the following steps: establishing a multi-channel discrete network control system model, wherein system input of the multi-channel discrete network control system model is expressed as a first expression:
wherein,
for the input of a model of a multi-channel discrete network control system, n 1 、n 2 Additive white Gaussian noise in the feedforward path and in the feedback path, A and A -1 Representing the transfer function of encoding and decoding, respectively, z -τ Representing time delay, K being a single degree of freedom controller, parameter d r Representing packet loss, r-is the reference input
Outputting for the system;
the output of the multi-channel discrete network control system model is represented as a second expression:
wherein,
g is a controlled object;
based on the error signal
Is a third expression:
wherein,
is a reference input;
and a tracking performance index J, J being a fourth expression:
where λ is 0 ≦ λ ≦ 1, λ is a trade-off between system tracking error and channel input constraints, Γ is a predefined constraint value for the channel input energy,
represents the energy of the system output signal, an
Representing the energy of the error signal to obtain a first optimal expression of the multi-channel discrete network control system model:
where V is the direction vector of the reference input, z is the transfer function argument, V = diag (β) 1 2 ,...,β m 2 ),W＝diag(γ 1 2 ,...,γ m 2 )，β i 2 、γ i 2 Respectively, additive white Gaussian noise n in channel i 1 、n 2 M is a natural number, T ry Is a reference input
To the system output
The transfer function of (a) is selected,
additive white Gaussian noise for forward channel
To the system output
The transfer function of (a) is selected,
additive white Gaussian noise for feedback channel
To the system output
The transfer function of (a) is selected,
for Q ∈ RH ∞ Representing a stable, regular, real rational transfer function (matrix) set, inf representing an infimum bound;
calculating to obtain reference input based on co-prime decomposition, all-pass decomposition and Youla parameterized form of single-degree-of-freedom controller of rational transfer function matrix
To the system output
Transfer function T of ry Forward channel additive white gaussian noise
To the system output
Transfer function of
Additive white Gaussian noise of sum feedback channel
To the system output
Transfer function of
And, T ry Expressed as a fifth expression:
T n1y expressed as a sixth expression:
where q is the packet loss probability, I is the identity matrix, z -τ Tau is a time delay coefficient of the network;
converting the obtained fifth expression and sixth expression based on the co-prime decomposition of the rational transfer function matrix, the double-Bezout equation and the Youla parameterized form of the single-degree-of-freedom controller to obtain a converted fifth expression:
and the converted sixth expression:
and the converted seventh expression:
and calculating the first optimal expression by utilizing a spatial decomposition technology, and selecting an optimal controller to enable the decomposed expression related to the controller parameters to be 0, so that the optimal tracking performance of the multi-channel discrete network control system model is obtained.
Further, calculating the first optimal expression using a spatial decomposition technique includes:
definition of
Is an eighth expression:
definition of
Is a ninth expression:
definition of
A tenth expression:
wherein,
as a first part of the first optimal expression,
as a second part of the first optimal expression
In the third part of the first optimal expression, Q is a single degree of freedom controller parameter,
to conform to the double Bezout equation
And belong to RH ∞ Is determined by the matrix of the first and second matrices,
is the factor of the controlled object obtained by left co-prime decomposition, N is the factor of the controlled object obtained by right co-prime decomposition, and q is a constant.
Further, the computing the first optimal expression using a spatial decomposition technique further includes computing J 1 * ：
N is a factor obtained by right cross-prime decomposition of the controlled object and comprises all zero points of the controlled object, and the expression of N is an eleventh expression:
N＝L z N m ，
wherein L is z The non-minimum phase zero point z of the controlled object is included as an all-pass factor i ,i＝1,2,...,N z ，N m The non-minimum phase factor comprises all minimum phase zeros of the controlled object;
L z decomposed into a twelfth expression:
wherein s is i Is a non-minimum phase zero point and,
for its conjugate zero, z is the transfer function argument,
according to the eleventh expression and the twelfth expression, simplifying the eighth expression to obtain a first simplified expression:
further, for the first simplified expression, defining f expression as a thirteenth expression:
wherein f is a self-defined function about a non-minimum phase zero;
then the first simplified equation is converted into a second simplified equation according to the thirteenth expression:
further, due to
Then there is a third simplified expression based on the spatial decomposition technique:
definition of
And
is provided with
Expressed as a fourteenth expression:
wherein f is -1 Is the inverse of the above-mentioned self-defined function;
calculating out
There is a sixteenth expression according to cauchy theorem:
wherein s is j Is another non-minimum phase zero, dz is the calculus sign;
substituting the sixteenth expression into the fourteenth expression to obtain a seventeenth expression:
wherein H is a conjugate transpose;
then calculate
From the all-pass decomposition formula:
M＝B p M m ，
wherein B is p The all-pass factor includes all unstable poles p of the controlled object i ,i＝1,2,...,N p ；
B p Decomposed into an eighteenth expression:
wherein M is m For the minimum phase factor, all stable poles, N, of the controlled object are included p Number of unstable poles, p j For the jth unstable pole, the number,
is the conjugation thereof;
the fifteenth expression is thus simplified to:
wherein,
is the whole flux factor B p The inverse of (a) is,
is composed of
A minimum phase part obtained by full-pass decomposition;
there is a nineteenth expression based on the partial fraction decomposition:
wherein, a i Is an expression for the pole of instability, and
substituting the nineteenth expression into the simplified fifteenth expression to obtain a twentieth expression:
wherein R is 1 (s)、R 2 (s) are all RH ∞ ，
Is an unstable pole p i Conjugation of (1);
because:
then based on the spatial decomposition technique to obtain
The twenty-first expression of (1):
further, the selecting the optimal controller so that the decomposed expression related to the controller parameter is 0, thereby obtaining the optimal tracking performance of the multi-channel discrete network control system model includes:
selecting an appropriate controller parameter Q such that
Then it is possible to obtain:
and because
And the double Bezout equation yields:
therefore, it is not only easy to use
Further simplified to a twenty-second expression:
and calculating according to the twenty-second expression to obtain a twenty-third expression:
further obtain
A twenty-fourth expression:
further, calculating
And
method and calculation of
The method of (1), wherein, after the calculation
Expressed as a twenty-fifth expression:
wherein, t(s) i )＝(s i ) τ N m (s i )M -1 (s i )，t(s i ) H Is t(s) i ) Conjugate transpose of(s) j )＝(s j ) τ N m (s j )M -1 (s j )，
For the variance of additive white gaussian noise in the forward channel i,
w i is zero point s i In the direction of (a) of (b),
is a conjugate transpose thereof, wherein e j Is a unit vector with the jth element being 1;
and after calculation
Expressed as a twenty-sixth expression:
wherein,
in order to be a conjugate thereof,
l(p i ) H in order to be a conjugate transpose thereof,
O m (p j ) Substituting the minimum phase part obtained by the encoder through all-pass decomposition into the unstable pole p j As a result of (a) the process of (b),
is its inverse, L -1 (p j ) Substituting the instability pole p for the twelfth expression j Inverse of the result of (2), gamma i 2 For the variance of additive white gaussian noise in the feedback channel i,
η i is an unstable pole p i In the direction of (a) of (b),
transpose it conjugately, wherein e j Is a unit vector with the jth element being 1.
Further, obtaining an optimal performance expression of the multi-channel discrete network control system model according to the twenty-fourth expression, the twenty-fifth expression and the twenty-sixth expression is as follows:
the invention establishes a multi-channel discrete network control system model, simulates data packet loss by utilizing a binary random process, assumes that channel noise is additive white Gaussian noise, and network-induced delay is constant time delay and is realized by all-pass decomposition, inside and outside decomposition and H 2 Spatial decomposition technique and Youla parameterization of controllerThe model of the multi-channel discrete network control system is deduced, and the optimal tracking performance of the control system is obtained.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description, serve to explain the principles of the invention.
Fig. 1 is a schematic diagram of a model of a mimo discrete network control system according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of tracking performance limits under different time delays in the embodiment of the present invention.
Fig. 3 is a schematic diagram of the tracking performance limit under different packet loss probabilities in the embodiment of the present invention.
Detailed Description
Various exemplary embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that: the relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise.
Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description.
The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments and the accompanying drawings.
Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate.
In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
In a first embodiment, as shown in fig. 1, a multiple-input multiple-output discrete network control system is provided, and for the network system, an optimization method of a multiple-channel discrete network control system is provided:
firstly, establishing a multi-input multi-output discrete network control system model, wherein the input of the multi-channel discrete network control system model is expressed as a formula (1):
wherein,
for the input of a model of a multi-channel discrete network control system, n 1 、n 2 Respectively, additive white Gaussian noise in and in the feedforward path, A -1 Representing transfer functions of encoding and decoding, respectively, z -τ Representing time delay, K being a controller with single degree of freedom, parameter d r Which represents a loss of a data packet,
is a reference input
Is output for the system;
the output of the multi-channel discrete network control system model is expressed as a formula:
wherein,
g is a controlled object;
based on the error signal
The expression of (c) is:
wherein,
is a reference input;
and tracking performance index J, the expression of J is:
where λ is 0 ≦ λ ≦ 1, λ is a trade-off between system tracking error and channel input constraints, Γ is a predefined constraint value for the channel input energy,
represents the energy of the system output signal, an
Representing the energy of the error signal to obtain an optimal expression of the multi-channel discrete network control system model:
where V is the directional vector of the reference input, z is the transfer function argument, V = diag (β) 1 2 ,...,β m 2 ),W＝diag(γ 1 2 ,...,γ m 2 )，β i 2 、γ i 2 Respectively, additive white Gaussian noise n in channel i 1 、n 2 M is a natural number, T ry Is a reference input
To the system output
Transfer function of (2), T n1y Additive white Gaussian noise for forward channel
To the system output
The transfer function of (a) is selected,
additive white Gaussian noise for feedback channel
To the system output
The transfer function of (a) is selected,
for Q ∈ RH ∞ Representing a stable, regular, real rational transfer function (matrix) set, inf representing an infimum bound;
reference input is calculated based on co-prime decomposition and all-pass decomposition of rational transfer function matrix and Youla parameterization form of single-degree-of-freedom controller
To the system output
Transfer function T of ry Forward channel additive white gaussian noise
To the system output
Transfer function T of n1y And feedback channel additive white Gaussian noise
To the system output
Transfer function of
And, T ry The expression of (a) is:
T n1y the expression of (c) is:
T n2y the expression of (a) is:
where q is the packet loss probability, I is the identity matrix, z -τ Tau is a time delay coefficient of the network;
converting the obtained formulas (6) - (7) based on the co-prime decomposition of the rational transfer function matrix, the double Bezout equation and the Youla parameterization form of the single-degree-of-freedom controller to obtain a converted expression:
and the converted sixth expression:
and the converted seventh expression:
then, the optimal expression (5) is calculated by using a spatial decomposition technology:
definition of
Is expressed as:
definition of
Is expressed as:
definition of
Is expressed as:
wherein,
for the first part of the optimal expression,
for the second part of the optimal expression,
is a third part of the optimal expression, the optimal expression being a combination of the three parts, and wherein Q is a single degree of freedom controller parameter,
to conform to the double Bezout equation
And belong to RH ∞ Is determined by the matrix of the first and second matrices,
is the factor of the controlled object obtained by left co-prime decomposition, N is the factor of the controlled object obtained by right co-prime decomposition, and q is a constant.
Decomposing the optimal expression into three parts, respectively calculating the values of the three parts, firstly calculating
N is a factor obtained by right-side co-prime decomposition of the controlled object and comprises all zeros of the controlled object, and the expression of N is as follows:
N＝L z N m (15)，
wherein L is z The non-minimum phase zero point z of the controlled object is included as an all-pass factor i ,i＝1,2,...,N z ，N m The non-minimum phase factor contains all minimum phase zeros of the controlled object;
L z the decomposition is into the expression:
wherein s is i Is a non-minimum phase zero point and,
for its conjugate zero, z is the transfer function argument,
according to the formulas (15) - (16), simplifying the optimal expression to obtain a first simplified expression:
for the first simplified form, the expression of the function f defining the non-minimum phase zero is:
wherein f is a self-defined function about a non-minimum phase zero;
then according to said (18), the first normalization equation can be converted to a second normalization equation:
due to the fact that
Then equation (19) is further simplified based on the spatial decomposition technique:
for ease of calculation, define
And
is provided with
Expressed as:
wherein f is -1 Is the inverse of the above-mentioned self-defined function;
computing
According to the cauchy theorem, the method comprises the following steps:
wherein s is j Is another non-minimum phase zero, dz is the calculus sign;
substituting the (23) into the (21) to obtain:
wherein H is a conjugate transpose.
Then calculate
From the all-pass decomposition formula:
M＝B p M m (25)，
wherein B is p The all-pass factor includes all unstable poles p of the controlled object i ,i＝1,2,…,N p ；
B p The decomposition is as follows:
wherein M is m The minimum phase factor includes all unstable poles of the controlled object, N p For unstable pole bits, p j Is the jth unstable pole, p j Is the conjugation thereof;
thus simplifying to obtain:
wherein,
is the whole flux factor B p The inverse of (a) is,
is composed of
A minimum phase part obtained by full-pass decomposition;
based on partial fraction decomposition:
wherein, a i Is an expression for the pole of instability, and
substituting the (28) into the (27) after the simplification to obtain:
wherein R is 1 (s)、R 2 (s) are all RH ∞ ，
Is an unstable pole p i Conjugation of (1);
and because:
then based on the spatial decomposition technique to obtain
Expression (c):
finally, selecting the optimal controller to enable a part of expressions related to the controller parameters in the decomposed formula to be 0, thereby obtaining the optimal tracking performance of the multi-channel discrete network control system model, wherein the calculation step comprises the following steps:
selecting an appropriate controller parameter Q such that:
then it is possible to obtain:
and because of
And the double Bezout equation yields:
therefore, it is not only easy to use
Further simplifying as follows:
the following are obtained through simple calculation:
according to the calculated above
And
expressions (24) and (35), to obtain
Comprises the following steps:
calculating out
And
method and calculation of
In the same way, wherein, after calculation
Expressed as:
wherein, t(s) i )＝(s i ) τ N m (s i )M -1 (s i )，t(s i ) H Is t(s) i ) Conjugate transpose of (1), t(s) j )＝(s j ) τ N m (s j )M -1 (s j )，
For the variance of additive white gaussian noise in the forward channel i,
w i is zero point s i In the direction of (a) of (b),
transpose it conjugately, wherein e j Is a unit vector with the jth element being 1;
and after calculation
Expressed as:
wherein,
in order to be a conjugate thereof,
l(p i ) H is a conjugate transpose of the above-mentioned materials,
O m (p j ) Substituting the minimum phase part obtained by the encoder through all-pass decomposition into the unstable pole p j As a result of (a) the result of (b),
to its inverse, L -1 (p j ) Substituting the instability pole p for the twelfth expression j Inverse of the result of (1), γ i 2 To feed back the variance of additive white gaussian noise in channel i,
η i is an unstable pole p i In the direction of (a) of (b),
is a conjugate transpose thereof, wherein e j Is a unit vector with the jth element being 1.
The optimal performance expression of the multi-channel discrete network control system model obtained according to the formulas (36) to (38) is as follows:
the invention utilizes a binary random process to simulate the data packet loss, assumes that the channel noise is additive white Gaussian noise, and the network induced delay is a constant delay which is decomposed through full-pass decomposition, internal and external decomposition and H 2 And the model is deduced by using tools such as a spatial decomposition technology, youla parameterization of a controller and the like, so that the optimal tracking performance of the system is obtained.
Compared with the prior art, the invention has the advantages that: 1. comprehensively considering multiple communication constraints of double-channel additive white Gaussian noise, data packet loss, communication time delay and coding and decoding, and establishing a network control system model under the multiple communication constraints; 2. an optimal controller is designed by utilizing tools such as cross-prime decomposition, youla parameterization and the like, and the tracking performance of the multi-input multi-output discrete network control system is greatly improved on the premise of ensuring the stability of the system; 3. through the frequency domain H 2 The optimal control method obtains the infimum boundary of the tracking performance of the multi-input multi-output discrete network control system, and deeply reveals the internal relation between the performance of the network control system and various communication constraints on the basis of the prior art.
The following experimental data demonstrate the outstanding optimization effect that this embodiment can produce:
considering a discrete multi-input multi-output controlled object, a transfer function matrix model of the controlled object is as follows:
from the transfer function matrix, it contains a non-minimum phase zero z = k, and its output zero direction is η = (1, 0) T Comprising an unstable pole p =2, with the pole direction ω = (0, 1) T Defining the input vector as v = (1, 0) T And (3) selecting:
then:
selecting:
then there are:
we can get from the controlled object model:
when the temperature is higher than the set temperature
0.2, 0.5 and 0.8 respectively, then the performance is goodThe limiting expression:
the limit of the tracking performance of the mimo discrete network control system under different delay constraints is shown in fig. 2, and by comparing the tracking performance when T =0.2, T =0.5 and T =0.8, it can be seen that the larger the delay parameter in the feedback channel of the mimo network control system is, the worse the performance of the discrete mimo network control system is. And as can be seen from fig. 2, when the unstable pole of the controlled object is sufficiently close to the non-minimum phase zero, the tracking performance of the discrete multiple-input multiple-output network control system may be deteriorated sharply. As can be seen from fig. 3, the tracking performance becomes worse as the packet loss probability increases.
The above description is only exemplary of the present invention and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and scope of the present invention should be included in the present invention.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising a," "8230," "8230," or "comprising" does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.
Claims (8)
1. A performance optimization method for a multi-channel discrete network control system is characterized by comprising the following steps:
establishing a multi-channel discrete network control system model, wherein system input of the multi-channel discrete network control system model is expressed as a first expression:
wherein,
system input, n, for a model of a multi-channel discrete network control system 1 、n 2 Additive white Gaussian noise in the feedforward path and in the feedback path, A and A -1 Representing the transfer function of encoding and decoding, respectively, z -τ Representing time delay, K is a single degree of freedom controller, parameter d r Which represents a loss of a data packet,
for the purpose of reference input, the system is,
outputting for the system;
the output of the multi-channel discrete network control system model is represented as a second expression:
wherein,
g is a controlled object;
based on the error signal
Is a third expression:
wherein,
is a reference input;
and a tracking performance index J, J being a fourth expression:
where λ is 0 ≦ λ ≦ 1, λ is a trade-off between system tracking error and channel input constraints, Γ is a predefined constraint value for the channel input energy,
represents the energy of the system output signal, an
Representing the energy of the error signal to obtain a first optimal expression of the multi-channel discrete network control system model:
where V is the directional vector of the reference input, z is the transfer function argument, V = diag (β) 1 2 ,...,β m 2 ),W＝diag(γ 1 2 ,...,γ m 2 )，β i 2 、γ i 2 Are respectively additive white Gaussian noise n in the channel i 1 、n 2 I =1, 2.. The m, m is a positive integer, T ry Is a reference input
To the system output
The transfer function of (a) is set,
additive white Gaussian noise for forward channel
To the system output
The transfer function of (a) is set,
additive white Gaussian noise for feedback channel
To the system output
The transfer function of (a) is selected,
Q∈RH ∞ representing a stable, regular, real rational transfer function or matrix set, inf representing an infimum boundary;
calculating to obtain reference input based on co-prime decomposition, all-pass decomposition and Youla parameterized form of single-degree-of-freedom controller of rational transfer function matrix
To the system output
Transfer function T of ry Forward channel additive white gaussian noise
To the system output
Transfer function of
Additive white Gaussian noise of sum feedback channel
To the system output
Transfer function of
And, T ry Expressed as a fifth expression:
where q is the packet loss probability, I is the identity matrix, z -τ Tau is a time delay coefficient for network time delay;
converting the obtained fifth expression and sixth expression based on the co-prime decomposition of the rational transfer function matrix, the double-Bezout equation and the Youla parameterized form of the single-degree-of-freedom controller to obtain a converted fifth expression:
and the converted sixth expression:
and the converted seventh expression:
and calculating the first optimal expression by utilizing a spatial decomposition technology, and selecting an optimal controller to enable the expression related to the controller parameters after decomposition to be 0, thereby obtaining the optimal tracking performance of the multi-channel discrete network control system model.
2. The method of claim 1, wherein computing the first optimal expression using a spatial decomposition technique comprises:
definition of
Is an eighth expression:
definition of
Is a ninth expression:
definition of
A tenth expression:
wherein,
as a first part of the first optimal expression,
as a second part of the first optimal expression
In a third part of the first optimal expression, Q is a single degree of freedom controller parameter,
to conform to the double Bezout equation
And belong to RH ∞ Is determined by the matrix of the first and second matrices,
is the factor of the controlled object obtained by left co-prime decomposition, N is the factor of the controlled object obtained by right co-prime decomposition, and q is a constant.
3. The method of claim 2, wherein said computing said first optimal expression using a spatial decomposition technique further comprises computing a first optimal expression for a multi-channel discrete network control system
N is a factor obtained by right coprime decomposition of the controlled object and comprises all zeros of the controlled object, and N is expressed as an eleventh expression:
N＝L z N m ，
wherein L is z The non-minimum phase zero point z of the controlled object is included as an all-pass factor i ,i＝1,2,...,N z ，N m The non-minimum phase factor contains all minimum phase zeros of the controlled object;
L z decomposed into a twelfth expression:
wherein s is i Is a non-minimum phase zero point and,
for its conjugate zero, z is the transfer function argument,
according to the eleventh expression and the twelfth expression, simplifying the eighth expression to obtain a first simplified expression:
4. the method as claimed in claim 3, wherein for the first simplified expression, f is defined as a thirteenth expression:
wherein f is a self-defined function about a non-minimum phase zero;
then the first simplified equation is converted into a second simplified equation according to the thirteenth expression:
5. the method of claim 4, wherein the performance of the multi-channel discrete network control system is optimized due to
Then there is a third simplified expression based on the spatial decomposition technique:
definition of
And
is provided with
Expressed as a fourteenth expression:
wherein f is -1 Is the inverse of the above self-defined function;
computing
There is a sixteenth expression according to cauchy theorem:
wherein s is j Is another non-minimum phase zero, dz is the calculus sign;
substituting the sixteenth expression into the fourteenth expression to obtain a seventeenth expression:
wherein H is conjugate transpose;
then calculate
From the all-pass decomposition formula:
M＝B p M m ，
wherein B is p The all-pass factor includes all unstable poles p of the controlled object i ,i＝1,2,...,N p ；B p Decomposed into an eighteenth expression:
wherein M is m The minimum phase factor includes all unstable poles, N, of the controlled object p Number of unstable poles, p j For the jth unstable pole, the number,
is the conjugation thereof;
the fifteenth expression is thus simplified to:
wherein,
is the whole flux factor B p The reverse of (c) is true,
is composed of
A minimum phase part obtained by full-pass decomposition;
there is a nineteenth expression based on the partial fraction decomposition:
wherein, a i Is an expression for an unstable pole, and
R 1 ∈RH ∞ ，
substituting the nineteenth expression into the simplified fifteenth expression to obtain a twentieth expression:
wherein R is 1 (s)、R 2 (s) are all RH ∞ ，
Is an unstable pole p i Conjugation of (1);
because:
then based on the spatial decomposition technique to obtain
The twenty-first expression of (1):
6. the method as claimed in claim 2, wherein the selecting the optimal controller such that the decomposed expression related to the controller parameter is 0 to obtain the optimal tracking performance of the model of the multi-channel discrete network control system comprises:
selecting a controller parameter Q such that
Then it is possible to obtain:
and because of
And the double Bezout equation yields:
therefore, it is possible to
Further simplified to a twenty-second expression:
calculating to obtain a twenty-third expression according to the twenty-second expression:
further obtain
A twenty-fourth expression:
7. the method of claim 6, wherein the calculating comprises calculating a performance optimization function for the multi-channel discrete network control system
And
method and calculation of
The method of (1), wherein, after the calculation
Expressed as a twenty-fifth expression:
wherein, t(s) i ) H Is t(s) i ) Conjugate transpose of (1), t(s) i )＝(s i ) τ N m (s i )M -1 (s i )，
For the variance of additive white gaussian noise in the forward channel i,
w i is zero point s i In the direction of (a) of (b),
is a conjugate transpose thereof, wherein e j Is a unit vector with the jth element being 1;
and after calculation
Expressed as a twenty-sixth expression:
wherein,
in order to be a conjugate thereof,
l(p i ) H is a conjugate transpose of the above-mentioned materials,
O m (p j ) Substituting the minimum phase part obtained by the encoder through all-pass decomposition into the unstable pole p j As a result of (a) the process of (b),
is its inverse, L -1 (p j ) Substituting the instability pole p for the twelfth expression j Inverse of the result of (1), γ i 2 To feed back the variance of additive white gaussian noise in channel i,
η i is an unstable pole p i In the direction of (a) of (b),
is a conjugate transpose thereof, wherein e j Is a unit vector with the jth element being 1.
8. The method for optimizing the performance of the multi-channel discrete network control system according to claim 7, wherein the obtaining of the optimal performance expression of the multi-channel discrete network control system model according to the twenty-fourth expression, the twenty-fifth expression and the twenty-sixth expression is as follows:
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6161209A (en) * | 1997-03-28 | 2000-12-12 | Her Majesty The Queen In Right Of Canada, As Represented By The Minister Of Industry Through The Communications Research Centre | Joint detector for multiple coded digital signals |
| CN101155083A (en) * | 2006-09-27 | 2008-04-02 | 中兴通讯股份有限公司 | Network state estimation method based on packet loss rate |
| CN107168053A (en) * | 2017-05-04 | 2017-09-15 | 南京理工大学 | A kind of finite field filter design method with stochastic filtering change in gain |
| CN109039508A (en) * | 2018-09-30 | 2018-12-18 | 上海科梁信息工程股份有限公司 | Wireless multipath fading channel simulator system and method |
| CN112904271A (en) * | 2021-03-03 | 2021-06-04 | 西北大学 | Fourth-order cumulant DOA estimation method based on co-prime array and augmented extended array |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6161209A (en) * | 1997-03-28 | 2000-12-12 | Her Majesty The Queen In Right Of Canada, As Represented By The Minister Of Industry Through The Communications Research Centre | Joint detector for multiple coded digital signals |
| CN101155083A (en) * | 2006-09-27 | 2008-04-02 | 中兴通讯股份有限公司 | Network state estimation method based on packet loss rate |
| CN107168053A (en) * | 2017-05-04 | 2017-09-15 | 南京理工大学 | A kind of finite field filter design method with stochastic filtering change in gain |
| CN109039508A (en) * | 2018-09-30 | 2018-12-18 | 上海科梁信息工程股份有限公司 | Wireless multipath fading channel simulator system and method |
| CN112904271A (en) * | 2021-03-03 | 2021-06-04 | 西北大学 | Fourth-order cumulant DOA estimation method based on co-prime array and augmented extended array |
Non-Patent Citations (2)
| Title |
|---|
| GIS技术在电信固网拓展应用中的研究;李刚等;《四川大学学报（工程科学版）》;20070531;第39卷;第303-307页 * |
| Tunable bandpass filters with constant absolute bandwidth and high linearity;Feng Lin Yu等;《2012 International Conference on Microwave and Millimeter Wave Technology (ICMMT)》;20120705;第1-3页 * |
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