CN108287471B - Parameter self-tuning method of MIMO offset format model-free controller based on system error - Google Patents

Parameter self-tuning method of MIMO offset format model-free controller based on system error Download PDF

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CN108287471B
CN108287471B CN201711265766.2A CN201711265766A CN108287471B CN 108287471 B CN108287471 B CN 108287471B CN 201711265766 A CN201711265766 A CN 201711265766A CN 108287471 B CN108287471 B CN 108287471B
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卢建刚
李雪园
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Zhejiang University ZJU
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Abstract

The invention discloses a parameter self-tuning method of an MIMO (multiple input multiple output) bias format model-free controller based on system errors, which is characterized in that a system error set is used as the input of a BP (back propagation) neural network, the BP neural network performs forward calculation and outputs parameters to be tuned of the MIMO bias format model-free controller such as penalty factors and step factors through an output layer, a control algorithm of the MIMO bias format model-free controller is adopted to calculate to obtain a control input vector aiming at a controlled object, the value minimization of a system error function is taken as a target, a gradient descent method is adopted, and the control input is combined to respectively aim at a gradient information set of each parameter to be tuned, so that the system error back propagation calculation is performed, the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated in real time on line, and the parameter self-tuning of the controller based on. The parameter self-tuning method of the MIMO offset format model-free controller based on the system error can effectively overcome the difficulty of on-line tuning of the controller parameters and has good control effect on an MIMO system.

Description

Parameter self-tuning method of MIMO offset format model-free controller based on system error
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of an MIMO partial-format model-free controller based on system errors.
Background
The control problem of MIMO (Multiple Input and Multiple Output) system has been one of the major challenges faced in the field of automation control.
Existing implementations of MIMO controllers include MIMO offset format modeless controllers. The MIMO partial format model-free controller is a novel data driving control method, does not depend on any mathematical model information of a controlled object, only depends on input and output data measured by the MIMO controlled object in real time to analyze and design the controller, is simple and clear in realization, small in calculation burden and strong in robustness, can well control an unknown nonlinear time-varying MIMO system, and has a good application prospect. The theoretical basis of the MIMO offset format model-free controller is proposed by Hou faith and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing company, 2013, page 105) of the union of Hou faith and Jinshangtai, and the control algorithm is as follows:
Figure GDA0001608848100000011
where u (k) is a control input vector at time k, and u (k) is [ u (k) ]1(k),…,umu(k)]TMu is the number of control inputs, Δ u (k) ═ u (k) — u (k-1); e (k) is an error vector at time k, e (k) is [ e1(k),…,emy(k)]TMy is the output number;
Figure GDA0001608848100000012
for the MIMO system pseudo block jacobian matrix estimate at time k,
Figure GDA0001608848100000013
is composed of
Figure GDA0001608848100000014
The ith block (i ═ 1, …, L),
Figure GDA0001608848100000015
is a matrix
Figure GDA0001608848100000016
2 norm of (d); λ is a penalty factor, ρ1,…,ρLL is the control input linearization length constant, step factor.
However, the MIMO offset-format modeless controller needs to rely on empirical knowledge to set the penalty factor λ and the step-size factor ρ in advance before actually putting into service1,…,ρLThe values of the isoparametric parameters have not realized a penalty factor lambda and a step factor rho in the actual application process1,…,ρLAnd (4) performing online self-tuning on the equal parameters. The lack of effective parameter setting means not only makes the use and debugging process of the MIMO partial-format modeless controller time-consuming and labor-consuming, but also can seriously affect the control effect of the MIMO partial-format modeless controller sometimes, and restricts the popularization and application of the MIMO partial-format modeless controller. That is to say: the MIMO offset format modeless controller also needs to solve the problem of online self-tuning parameters in the actual application process.
Therefore, in order to break the bottleneck of restricting the popularization and application of the MIMO partial format model-free controller, the invention provides a parameter self-tuning method of the MIMO partial format model-free controller based on system errors.
Disclosure of Invention
In order to solve the problems in the background art, the invention aims to provide a parameter self-tuning method of a MIMO offset format model-less controller based on system errors.
To this end, the above object of the present invention is achieved by the following technical solution, comprising the steps of:
step (1): for a Multiple Input and Multiple Output (MIMO) system having mu inputs (mu is an integer greater than or equal to 2) and my outputs (my is an integer greater than or equal to 2), controlling by using a MIMO offset format modeless controller; determining a control input linearization length constant L of the MIMO offset format modeless controller, wherein L is an integer greater than 1; the MIMO partial format model-less controller parameters comprise a penalty factor lambda and a step factor rho1,…,ρL(ii) a Determining parameters to be set of the MIMO partial-format model-free controller, wherein the parameters to be set of the MIMO partial-format model-free controller are part or all of the parameters of the MIMO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLAny one or any combination of the above; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the MIMO partial-format modeless controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;
step (2): recording the current time as k time;
and (3): based on the jy output expected value and the jy output actual value (jy is more than or equal to 1 and less than or equal to my) of the MIMO system, adopting the jy error calculation function to calculate the jy error at the k moment, and marking the jy error as ejy(k) (ii) a Recording any one or any combination of the jy error and the function set thereof, the jy output expected value and the jy output actual value as a set { error set jy }, and putting the set { system error set }; this step is repeated for the other my-1 outputs of the MIMO system until the set { system error set } contains the set of all { { error set 1}, …, { error set my } } and an error vector e (k) ═ e composed of my errors is obtained at the same time1(k),…,emy(k)]TThen entering the step (4);
and (4): taking the set { system error set } obtained in the step (3) as the input of a BP neural network, carrying out forward calculation on the BP neural network, and outputting a calculation result through an output layer of the BP neural network to obtain a value of a parameter to be set of the MIMO partial-format modeless controller;
and (5): calculating a control input vector u (k) [ u ], [ u ] of the MIMO offset format model-less controller at the time k for the controlled object by adopting a control algorithm of the MIMO offset format model-less controller based on the error vector e (k) obtained in the step (3) and the value of the parameter to be set of the MIMO offset format model-less controller obtained in the step (4)1(k),…,umu(k)]T；
And (6): aiming at the ju control input u in the control input vector u (k) obtained in the step (5)ju(k) (ju is more than or equal to 1 and less than or equal to mu), calculating the ju control input uju(k) Respectively aiming at the gradient information of the parameters to be set of each MIMO offset format model-free controller at the moment k, the specific calculation formula is as follows:
when the parameters to be set of the MIMO offset format model-free controller contain penalty factor lambda, the ju control input uju(k) The gradient information at the k moment for the penalty factor λ is:
Figure GDA0001608848100000031
when the parameter to be set of the MIMO offset format model-free controller contains the step factor rho1Then, the said ju control input uju(k) For the step size factor p1The gradient information at time k is:
Figure GDA0001608848100000041
when the parameter to be set of the MIMO offset format model-free controller contains the step factor rhoiAnd when i is more than or equal to 2 and less than or equal to L, the jth control input uju(k) For the step size factor piThe gradient information at time k is:
Figure GDA0001608848100000042
wherein, Δ uj(k)＝uj(k)-uj(k-1)，
Figure GDA0001608848100000043
For the MIMO system pseudo block jacobian matrix estimate at time k,
Figure GDA0001608848100000044
is composed of
Figure GDA0001608848100000045
The ith block (i ═ 1, …, L),
Figure GDA0001608848100000046
is a matrix
Figure GDA0001608848100000047
The jy th row and the ju th column element,
Figure GDA0001608848100000048
is a matrix
Figure GDA0001608848100000049
2 norm of (d);
the set of all the gradient information is marked as { gradient information ju }, and a set { gradient information set } is put in;
repeating the step for the other mu-1 control inputs in the control input vector u (k) obtained in step (5) until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information mu } }, and then proceeding to step (7);
and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the set { gradient information set } obtained in the step (6) is combined, the backward propagation calculation of the system error is carried out, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated and used as the weight coefficient of the hidden layer and the weight coefficient of the output layer when the BP neural network carries out forward calculation at the later moment;
and (8): and (4) after the control input vector u (k) acts on the controlled object, obtaining my output actual values of the controlled object at the later moment, returning to the step (2), and repeating the step (2) to the step (8).
While adopting the above technical scheme, the present invention can also adopt or combine the following further technical schemes:
the arguments of the jy-th error calculation function in the step (3) include a jy-th expected output value and a jy-th actual output value.
The jy th error calculation function in the step (3) adopts
Figure GDA0001608848100000051
Wherein
Figure GDA0001608848100000052
The jy th expected output value, y, set for time kjy(k) Sampling the jy output actual value at the k moment; or by using
Figure GDA0001608848100000053
Wherein
Figure GDA0001608848100000054
The jy th output expectation value at the time k +1, yjy(k) And outputting the actual value for the jy th output value sampled at the time k.
The jy-th error and the function set thereof in the step (3) include the jy-th error e at the time kjy(k) And the accumulation of the jy error at the time k and all the previous times
Figure GDA0001608848100000055
Jy error e at time kjy(k) First order backward difference e ofjy(k)-ejy(k-1), the jy th error e at time kjy(k) Second order backward difference e ofjy(k)-2ejy(k-1)+ejy(k-2) the jy th error e at time kjy(k) Any one or any combination of high order backward differences.
The independent variable of the system error function in the step (7) comprises any one or any combination of my errors, my output expected values and my output actual values.
Said systematic error function in said step (7) is
Figure GDA0001608848100000056
Wherein e isjy(k) For the jy error, Δ uju(k)＝uju(k)-uju(k-1)，ajyAnd bjuIs a constant greater than or equal to 0, jy is greater than or equal to 1 and less than or equal to my, and ju is greater than or equal to 1 and less than or equal to mu.
The MIMO offset format model-free controller parameter self-tuning method provided by the invention can realize good control effect and effectively overcome penalty factor lambda and step factor rho1,…,ρLThe difficult problem of setting needs time and labor waste.
Drawings
FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic diagram of a BP neural network structure employed in the present invention;
FIG. 3 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3Meanwhile, a 1 st output control effect graph is obtained during self-tuning;
FIG. 4 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3Meanwhile, a control effect graph of the 2 nd output in self-tuning;
FIG. 5 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3Simultaneously self-timing control input diagram;
FIG. 6 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3Meanwhile, self-adjusting a punishment factor lambda change curve;
FIG. 7 shows a two-input two-output MIMO system with penalty factor λ and step size factor ρ1,ρ2,ρ3Step size factor p while self-aligning1,ρ2,ρ3A change curve;
FIG. 8 is a diagram of a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3The 1 st output control effect graph during self-tuning;
FIG. 9 shows a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3The control effect diagram of the 2 nd output during self-tuning;
FIG. 10 is a diagram of a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3A self-timed control input map;
FIG. 11 is a diagram of a two-input two-output MIMO system with a fixed penalty factor λ and a step size factor ρ1,ρ2,ρ3Step factor p at self-alignment1,ρ2,ρ3A curve of variation.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Fig. 1 shows a schematic block diagram of the present invention. For a MIMO system with mu inputs (mu is an integer greater than or equal to 2) and my outputs (my is an integer greater than or equal to 2), adopting a MIMO offset format modeless controller to control; determining a control input linearization length constant L of the MIMO partial-format modeless controller, wherein L is an integer greater than 1; the MIMO partial format model-free controller parameters comprise a penalty factor lambda and a step factor rho1,…,ρL(ii) a Determining parameters to be set of the MIMO partial-format model-free controller, wherein the parameters are part or all of the parameters of the MIMO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLAny one or any combination of the above; in fig. 1, the parameters to be set of the MIMO offset-format modeless controller are penalty factor λ and step factor ρ1,…,ρL(ii) a Determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the MIMO partial format model-free controller; and initializing the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network.
Recording the current timeIs the k moment; output the jy th expected value
Figure GDA0001608848100000071
And the jy th output actual value yjy(k) The difference is used as the jy error e at the k timejy(k) (ii) a The jy th error ejy(k) And the accumulation of the jy error at the time k and all the previous times
Figure GDA0001608848100000072
Jy error e at time kjy(k) First order backward difference e ofjy(k)-ejy(k-1) the combination is marked as a set { error group jy }, and is put into the set { system error set }; for the other my-1 outputs of the MIMO system, the process is repeated until the set { system error set } contains the set of all { { error group 1}, …, { error group my } } and an error vector e (k) ═ e is obtained at the same time, the error vector is composed of my errors1(k),…,emy(k)]T(ii) a Then, the set { system error set } is used as the input of a BP neural network, the BP neural network carries out forward calculation, and a calculation result is output through an output layer of the BP neural network to obtain the value of a parameter to be set of the MIMO partial-format model-free controller; based on the error vector e (k) and the value of the parameter to be set of the MIMO offset format model-free controller, the control algorithm of the MIMO offset format model-free controller is adopted to calculate and obtain a control input vector u (k) ═ u of the MIMO offset format model-free controller at the time k for the controlled object1(k),…,umu(k)]T(ii) a For the jth control input u in the control input vector u (k)ju(k) Calculating said ju-th control input uju(k) Respectively aiming at gradient information of parameters to be set of each MIMO partial-format model-free controller at the time k, marking the set of all the gradient information as { gradient information ju }, and putting the set { gradient information set }; repeating the execution for the other mu-1 control inputs in the control input vector u (k) until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information mu } }; subsequently, in combination with the set { gradient information set }, the system of comprehensively considering all my error contributions in fig. 1 is targeted at minimizing the value of the systematic error functionIntegral error function
Figure GDA0001608848100000081
The value of (1) is minimized as a target, a gradient descent method is adopted to carry out system error back propagation calculation, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated to be used as the weight coefficient of the hidden layer and the weight coefficient of the output layer when the BP neural network carries out forward calculation at the later moment; and after the control input vector u (k) acts on the controlled object, my output actual values of the controlled object at the later moment are obtained, then the work in the paragraph is repeatedly executed, and the parameter self-tuning process of the MIMO offset format model-free controller at the later moment based on the system error is carried out.
FIG. 2 is a schematic diagram of a BP neural network structure adopted by the present invention, wherein the BP neural network may adopt a structure in which a hidden layer is a single layer or a structure in which hidden layers are multiple layers, for simplicity, the BP neural network adopts a structure in which a hidden layer is a single layer, that is, a three-layer network structure composed of an input layer, a single-layer hidden layer and an output layer is adopted, the number of nodes of the input layer is set to be 3 × my, the number of nodes of the hidden layer is set to be 8, the number of nodes of the output layer is set to be the number of parameters to be set (the number of the parameters to be set is L +1 in FIG. 2), the number of nodes of the input layer is divided into my groups, each group includes 3 nodes, wherein the 3 nodes of the jy group and an error e in a set { error group jy }, and the 3 nodes ofjy(k) Accumulation of errors
Figure GDA0001608848100000082
Error ejy(k) First order backward difference e ofjy(k)-ejy(k-1) correspond to each other. Node of output layer, penalty factor lambda and step factor rho1,…,ρLRespectively correspond to each other. The update process of the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network specifically comprises the following steps: the value of the systematic error function is minimized, and the systematic error function comprehensively considering all the my error contributions is shown in FIG. 2
Figure GDA0001608848100000083
Is minimized to obtain a target value by gradient descent methodAnd combining the set { gradient information set }, and performing system error back propagation calculation, thereby updating the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network.
The following is a specific embodiment of the present invention.
The controlled object is a typical nonlinear two-input and two-output MIMO system:
Figure GDA0001608848100000084
Figure GDA0001608848100000085
Figure GDA0001608848100000091
Figure GDA0001608848100000092
y1(k)＝x11(k)
y2(k)＝x21(k)
where α (k) ═ 1+0.1sin (2k pi/1500) and β (k) ═ 1+0.1cos (2k pi/1500).
Desired value y of system output*(k) The following were used:
Figure GDA0001608848100000093
Figure GDA0001608848100000094
in this particular embodiment, mu-my-2.
The value of the control input linearization length constant L of the MIMO offset-format modeless controller is usually set according to the complexity of the controlled object and the actual control effect, and is generally between 1 and 10, and too small value will affect the control effect, and too large value will result in large calculation amount, so 3 or 5 is usually adopted, and L is 3 in this specific embodiment.
The BP neural network adopts a three-layer network structure consisting of an input layer, a single-layer hidden layer and an output layer, the number of nodes of the input layer is set to be 6, the number of nodes of the hidden layer is set to be 8, and the number of nodes of the output layer is set to be the number of parameters to be set.
For the above specific examples, two sets of experimental verification were performed.
When the first group of experiments verify, the number of output layer nodes of the BP neural network in FIG. 2 is preset to be 4, and a penalty factor lambda and a step factor rho are calculated1,ρ2,ρ3Performing the simultaneous self-tuning, wherein FIG. 3 is a control effect graph of the 1 st output, FIG. 4 is a control effect graph of the 2 nd output, FIG. 5 is a control input graph, FIG. 6 is a penalty factor lambda variation curve, and FIG. 7 is a step factor rho1,ρ2,ρ3A curve of variation. The result shows that the method of the invention carries out the punishment factor lambda and the step factor rho1,ρ2,ρ3The method has the advantages of realizing good control effect by carrying out self-tuning at the same time, and effectively overcoming the penalty factor lambda and the step factor rho1,ρ2,ρ3The difficult problem of setting needs time and labor waste.
When the second group of tests verify, the number of output layer nodes of the BP neural network in the graph 2 is 3, firstly, the penalty factor lambda is fixedly valued as the average value of the penalty factor lambda when the first group of tests verify, and then the step factor rho is subjected to1,ρ2,ρ3Performing self-tuning, wherein FIG. 8 is a control effect graph of the 1 st output, FIG. 9 is a control effect graph of the 2 nd output, FIG. 10 is a control input graph, and FIG. 11 is a step factor ρ1,ρ2,ρ3A curve of variation. The results also show that the method of the invention is implemented by applying the step factor rho when the penalty factor lambda is fixed1,ρ2,ρ3Self-tuning is carried out, good control effect can be realized, and the step factor rho can be effectively overcome1,ρ2,ρ3The difficult problem of setting needs time and labor waste.
It should be noted that, in the above-described embodiment, the jy-th output expectation value is set
Figure GDA0001608848100000101
And the jy th output actual value yjy(k) The difference is used as the jy error e at the k timejy(k) That is to say
Figure GDA0001608848100000102
One method of calculating a function for only said jy-th error; the jy th output expectation value at the time k +1
Figure GDA0001608848100000103
And the jy output y at time kjy(k) The difference is used as the jy error ejy(k) That is to say
Figure GDA0001608848100000104
The jy-th error calculation function may also use other calculation methods in which the arguments include the jy-th expected output value and the jy-th actual output value, for example,
Figure GDA0001608848100000105
for the controlled object of the above embodiment, good control effects can be achieved by using the different system error calculation functions.
It should also be noted that in the above-described embodiment, the set jy of errors contains the error ejy(k) Accumulation of errors
Figure GDA0001608848100000106
Error ejy(k) First order backward difference e ofjy(k)-ejy(k-1), which is only one type of combination; the set jy of errors may also take other types of combinations, including, for example, error ejy(k) Accumulation of errors
Figure GDA0001608848100000107
Error ejy(k) First order backward difference e ofjy(k)-ejy(k-1), error ejy(k) Second order backward difference e ofjy(k)-2ejy(k-1)+ejy(k-2), error ejy(k) Any one or any combination of third or fourth or higher order backward difference, etc. For the controlled object of the above embodiment, a good control effect can be achieved by using the different set { error group jy }.
It should be more particularly noted that, in the above specific embodiment, when the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated with the goal of minimizing the value of the systematic error function, the systematic error function employs the systematic error function comprehensively considering all the my error contributions
Figure GDA0001608848100000111
Only one of the systematic error functions; the system error function may also adopt other functions of which the independent variables comprise any one or any combination of my errors, my expected output values and my actual output values, for example, the system error function adopts
Figure GDA0001608848100000112
Or
Figure GDA0001608848100000113
That is to say by using
Figure GDA0001608848100000114
Another functional form of (1); as another example, the systematic error function employs
Figure GDA0001608848100000115
Wherein e isjy(k) For the jy error, Δ uju(k)＝uju(k)-uju(k-1)，ajyAnd bjuIs a constant greater than or equal to 0, jy is greater than or equal to 1 and less than or equal to my, and ju is greater than or equal to 1 and less than or equal to mu; obviously, when bjuEqual to 0, the systematic error function only takes into account
Figure GDA0001608848100000116
Indicates that the objective of minimization is system errorThe difference is minimum, namely the pursuit precision is high; when b isjuWhen the error is larger than 0, the system error function is simultaneously considered
Figure GDA0001608848100000117
Are made a contribution to
Figure GDA0001608848100000118
The contribution of (1) indicates that the goal of minimization is to pursue small system errors and small control input variation, namely to pursue both high precision and stable steering. For the controlled object of the above embodiment, good control effect can be achieved by adopting the different system error functions; considering only the systematic error function
Figure GDA0001608848100000119
Compared with the control effect during contribution, the system error function is considered simultaneously
Figure GDA00016088481000001110
Are made a contribution to
Figure GDA00016088481000001111
The contribution of (1) is that the control precision is slightly reduced and the operation stability is improved.
Finally, it should be noted that the parameters to be set of the MIMO partial-format modeless controller include a penalty factor λ and a step factor ρ1,…,ρLAny one or any combination of the above; in the above specific embodiment, the first set of trial validations is performed with a penalty factor λ and a step-size factor ρ1,ρ2,ρ3Realizes the simultaneous self-tuning, the punishment factor lambda is fixed and the step factor rho is adopted during the verification of the second group of tests1,ρ2,ρ3Self-tuning is realized; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor ρ1,ρ2Fixed penalty factor lambda, step factor rho3Self-tuning is realized; in addition, the MIMO off-grid modeless controller has parameters to be tuned, including but not limited to penaltiesFactor λ and step factor ρ1,…,ρLFor example, according to specific situations, the method can also comprise the estimated value of the pseudo block Jacobian matrix of the MIMO system
Figure GDA0001608848100000121
And the like.
The above-described embodiments are intended to illustrate the present invention, but not to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.

Claims (4)

  1. A parameter self-tuning method of an MIMO offset format model-free controller based on system errors is characterized by comprising the following steps:
    step (1): for a Multiple Input and Multiple Output (MIMO) system with mu inputs and my outputs, wherein mu is an integer greater than or equal to 2, and my is an integer greater than or equal to 2, the MIMO system is controlled by a MIMO offset format modeless controller; determining a control input linearization length constant L of the MIMO offset format modeless controller, wherein L is an integer greater than 1; the MIMO partial format model-less controller parameters comprise a penalty factor lambda and a step factor rho1,…,ρL(ii) a Determining parameters to be set of the MIMO partial-format model-free controller, wherein the parameters to be set of the MIMO partial-format model-free controller are part or all of the parameters of the MIMO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLAny one or any combination of the above; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the MIMO partial-format modeless controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;
    step (2): recording the current time as k time;
    and (3): based on the jy output expected value and the jy output actual value of the MIMO system,wherein jy is more than or equal to 1 and less than or equal to my, and the jy error at the k moment is calculated by adopting the jy error calculation function and is marked as ejy(k) (ii) a The independent variables of the jy error calculation function comprise the jy output expected value and the jy output actual value; recording any one or any combination of the jy error and the function set thereof, the jy output expected value and the jy output actual value as a set { error set jy }, and putting the set { system error set }; this step is repeated for the other my-1 outputs of the MIMO system until the set { system error set } contains the set of all { { error set 1}, …, { error set my } } and an error vector e (k) ═ e composed of my errors is obtained at the same time1(k),…,emy(k)]TThen entering the step (4);
    and (4): taking the set { system error set } obtained in the step (3) as the input of a BP neural network, carrying out forward calculation on the BP neural network, and outputting a calculation result through an output layer of the BP neural network to obtain a value of a parameter to be set of the MIMO partial-format modeless controller;
    and (5): calculating a control input vector u (k) [ u ], [ u ] of the MIMO offset format model-less controller at the time k for the controlled object by adopting a control algorithm of the MIMO offset format model-less controller based on the error vector e (k) obtained in the step (3) and the value of the parameter to be set of the MIMO offset format model-less controller obtained in the step (4)1(k),…,umu(k)]T；
    And (6): aiming at the ju control input u in the control input vector u (k) obtained in the step (5)ju(k) Wherein ju is not less than 1 and not more than mu, calculating the ju control input uju(k) Respectively aiming at the gradient information of the parameters to be set of each MIMO offset format model-free controller at the moment k, the specific calculation formula is as follows:
    when the parameters to be set of the MIMO offset format model-free controller contain penalty factor lambda, the ju control input uju(k) The gradient information at the k moment for the penalty factor λ is:
    Figure FDA0002553118620000021
    when the parameter to be set of the MIMO offset format model-free controller contains the step factor rho1Then, the said ju control input uju(k) For the step size factor p1The gradient information at time k is:
    Figure FDA0002553118620000022
    when the parameter to be set of the MIMO offset format model-free controller contains the step factor rhoiAnd when i is more than or equal to 2 and less than or equal to L, the jth control input uju(k) For the step size factor piThe gradient information at time k is:
    Figure FDA0002553118620000023
    wherein, Δ uj(k)＝uj(k)-uj(k-1)，
    Figure FDA0002553118620000031
    For the MIMO system pseudo block jacobian matrix estimate at time k,
    Figure FDA0002553118620000032
    is composed of
    Figure FDA0002553118620000033
    Wherein i is (1, …, L),
    Figure FDA0002553118620000034
    is a matrix
    Figure FDA0002553118620000035
    The jy th row and the ju th column element,
    Figure FDA0002553118620000036
    is a matrix
    Figure FDA0002553118620000037
    2 norm of (d);
    the set of all the gradient information is marked as { gradient information ju }, and a set { gradient information set } is put in;
    repeating the step for the other mu-1 control inputs in the control input vector u (k) obtained in step (5) until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information mu } }, and then proceeding to step (7);
    and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the set { gradient information set } obtained in the step (6) is combined, the backward propagation calculation of the system error is carried out, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated and used as the weight coefficient of the hidden layer and the weight coefficient of the output layer when the BP neural network carries out forward calculation at the later moment; the independent variable of the system error function comprises any one or any combination of my errors, my output expected values and my output actual values;
    and (8): and (4) after the control input vector u (k) acts on the controlled object, obtaining my output actual values of the controlled object at the later moment, returning to the step (2), and repeating the step (2) to the step (8).
  2. 2. The method of claim 1, wherein the jy-th error calculation function in step (3) employs a system error-based parameter self-tuning method for the MIMO offset-format modeless controller
    Figure FDA0002553118620000038
    Wherein
    Figure FDA0002553118620000039
    The jy th expected output value, y, set for time kjy(k) Sampling the jy output actual value at the k moment; or by using
    Figure FDA00025531186200000310
    Wherein
    Figure FDA00025531186200000311
    The jy th output expectation value at the time k +1, yjy(k) And outputting the actual value for the jy th output value sampled at the time k.
  3. 3. The method of claim 1, wherein the jy-th error and the function thereof in the step (3) comprise the jy-th error e at time kjy(k) And the accumulation of the jy error at the time k and all the previous times
    Figure FDA0002553118620000041
    Jy error e at time kjy(k) First order backward difference e ofjy(k)-ejy(k-1), the jy th error e at time kjy(k) Second order backward difference e ofjy(k)-2ejy(k-1)+ejy(k-2) the jy th error e at time kjy(k) Any one or any combination of high order backward differences.
  4. 4. The MIMO offset format modeless controller of claim 1, wherein the systematic error function in step (7) is
    Figure FDA0002553118620000042
    Wherein e isjy(k) For the jy error, Δ uju(k)＝uju(k)-uju(k-1)，ajyAnd bjuIs a constant greater than or equal to 0, jy is greater than or equal to 1 and less than or equal to my, and ju is greater than or equal to 1 and less than or equal to mu.
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CN109814388B (en) * 2019-02-01 2021-01-05 浙江大学 Parameter self-tuning MISO different-factor offset format model-free control method
CN109581864A (en) * 2019-02-01 2019-04-05 浙江大学 The inclined format non-model control method of the different factor of the MIMO of parameter self-tuning
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CN109581865B (en) * 2019-02-01 2020-12-22 浙江大学 MISO different-factor partial-format model-free control method
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CN109581992B (en) * 2019-02-01 2020-12-22 浙江大学 Parameter self-tuning MISO different-factor full-format model-free control method
CN109634109A (en) * 2019-02-01 2019-04-16 浙江大学 The inclined format non-model control method of the different factor of MIMO
CN109634108A (en) * 2019-02-01 2019-04-16 浙江大学 The different factor full format non-model control method of the MIMO of parameter self-tuning
CN109814379A (en) * 2019-02-01 2019-05-28 浙江大学 The different factor full format non-model control method of MIMO
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Family Cites Families (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5513098A (en) * 1993-06-04 1996-04-30 The Johns Hopkins University Method for model-free control of general discrete-time systems
US6055524A (en) * 1997-10-06 2000-04-25 General Cybernation Group, Inc. Model-free adaptive process control
CN101349893B (en) * 2007-07-18 2011-03-16 太极光控制软件（北京）有限公司 Forecast control device of adaptive model
CN101957598A (en) * 2010-09-26 2011-01-26 上海电力学院 Gray model-free control method for large time lag system
CN102033492A (en) * 2010-12-29 2011-04-27 国核电力规划设计研究院 Linear neuron on-line learning adaptive control method and controller for passive system
CN103064292A (en) * 2013-01-15 2013-04-24 镇江市江大科技有限责任公司 Biological fermentation adaptive control system and control method based on neural network inverse
CN103399487B (en) * 2013-07-30 2015-10-21 东北石油大学 A kind of decoupling control method based on non-linear multiple-input, multiple-output mimo system and device thereof
CN105676632A (en) * 2016-01-26 2016-06-15 沈阳化工大学 Model-free adaptive optimized control method for PVC polymerization process
CN107023825B (en) * 2016-08-31 2019-01-22 西安艾贝尔科技发展有限公司 Fluidized-bed combustion boiler control and combustion optimizing system
CN107065572A (en) * 2017-06-07 2017-08-18 海南大学 A kind of mixed control method of the unknown time delays of two-output impulse generator NDCS

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