CN108107727B - Parameter self-tuning method of MISO (multiple input single output) compact-format model-free controller based on partial derivative information - Google Patents

Parameter self-tuning method of MISO (multiple input single output) compact-format model-free controller based on partial derivative information Download PDF

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CN108107727B
CN108107727B CN201711317223.0A CN201711317223A CN108107727B CN 108107727 B CN108107727 B CN 108107727B CN 201711317223 A CN201711317223 A CN 201711317223A CN 108107727 B CN108107727 B CN 108107727B
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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 a MISO (MISO) compact form model-free controller based on partial derivative information, which comprises the steps of utilizing a partial derivative information set as input of a BP (back propagation) neural network, carrying out forward calculation on the BP neural network, outputting parameters to be tuned of the MISO compact form model-free controller such as penalty factors and step factors through an output layer, calculating a control input vector aiming at a controlled object by adopting a control algorithm of the MISO compact form model-free controller, carrying out system error back propagation calculation aiming at the minimization of a system error function value, adopting a gradient descent method, combining control input and respectively aiming at a gradient information set of each parameter to be tuned, updating a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network in real time on line, and realizing the parameter self-tuning of the controller based on the partial derivative information. The parameter self-tuning method of the MISO compact-format model-free controller based on the partial derivative information can effectively overcome the difficulty of on-line tuning of the controller parameters and has good control effect on the MISO system.

Description

Parameter self-tuning method of MISO (multiple input single output) compact-format model-free controller based on partial derivative information
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of a MISO (multiple input single output) compact-format model-free controller based on partial derivative information.
Background
The control problem of the MISO (Multiple Input and Single Output) system has been one of the major challenges faced in the field of automation control.
Existing implementations of MISO controllers include MISO compact form modeless controllers. The MISO compact-format model-free controller is a novel data-driven control method, does not depend on any mathematical model information of a controlled object, only depends on input and output data measured by the MISO 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 MISO system, and has a good application prospect. The theoretical basis of the MISO compact-format model-free controller is proposed by Houzhong and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing agency, 2013, page 95) of the Hemo, and the control algorithm is as follows:
Figure RE-GDA0001610391230000011
where u (k) is a control input vector at time k, and u (k) is [ u (k) ]1(k),…,um(k)]TM is the number of control inputs; e (k) is the system error at time k;
Figure RE-GDA0001610391230000012
is a row matrix of MISO system pseudo gradient estimates at time k,
Figure RE-GDA0001610391230000013
is a row matrix
Figure RE-GDA0001610391230000014
2 norm of (d); λ is a penalty factor and ρ is a step factor.
However, the MISO compact-format modeless controller needs to set the values of parameters such as the penalty factor λ and the step factor ρ in advance by relying on empirical knowledge before actual application, and online self-tuning of the parameters such as the penalty factor λ and the step factor ρ is not achieved in the actual application process. The lack of effective parameter setting means not only makes the use and debugging process of the MISO compact-format model-free controller time-consuming and labor-consuming, but also can seriously affect the control effect of the MISO compact-format model-free controller sometimes, and restricts the popularization and application of the MISO compact-format model-free controller. That is to say: the MISO compact-format model-free 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 MISO compact-format model-free controller, the invention provides a parameter self-tuning method of the MISO compact-format model-free controller based on partial derivative information.
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 MISO compact-format model-free controller based on partial derivative information.
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 Single Output (MISO) system with m inputs (m is an integer greater than or equal to 2) and 1 Output, adopting a MISO compact format model-free controller for control; the MISO compact-format model-free controller parameters comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a MISO (multiple input single output) compact-format model-free controller, wherein the parameters to be set of the MISO compact-format model-free controller are part or all of the parameters of the MISO compact-format model-free controller and comprise any one or any combination of a punishment factor lambda and a step factor rho; 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 MISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; initializing partial derivative information in a set { partial derivative information set };
step (2): recording the current time as k time;
and (3): calculating to obtain a system error at the k moment by adopting a system error calculation function based on the system output expected value and the system output actual value, and recording as e (k);
and (4): taking the partial derivative information in the set { partial derivative information set } as the input of a BP (back propagation) 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 MISO (single input single output) compact-format model-free controller;
and (5): calculating and obtaining a control input vector u (k) [ [ u (k) of the MISO tight format model-free controller at the time k for the controlled object by adopting a control algorithm of the MISO tight format model-free controller based on the system error e (k) obtained in the step (3) and the value of the parameter to be set of the MISO tight format model-free controller obtained in the step (4)1(k),…,um(k)]T；
And (6): aiming at the jth control input u in the control input vector u (k) obtained in the step (5)j(k) (j is more than or equal to 1 and less than or equal to m), calculating the jth control input uj(k) Respectively aiming at the gradient information of the parameters to be set of each MISO compact-format model-free controller at the moment k, the specific calculation formula is as follows:
when the parameters to be set of the MISO compact-format model-free controller contain penalty factor lambda, the jth control input uj(k) The gradient information at the k moment for the penalty factor λ is:
Figure RE-GDA0001610391230000031
when the parameters to be set of the MISO compact-format model-free controller contain the step factor rho, the jth control input uj(k) The gradient information at the k moment for the step factor ρ is:
Figure RE-GDA0001610391230000032
wherein the content of the first and second substances,
Figure RE-GDA0001610391230000033
is a row matrix of MISO system pseudo gradient estimates at time k,
Figure RE-GDA0001610391230000034
is a row matrix
Figure RE-GDA0001610391230000035
The j-th gradient component estimate of (a),
Figure RE-GDA0001610391230000036
is a row matrix
Figure RE-GDA0001610391230000037
2 norm of (d);
the set of all the gradient information is marked as { gradient information j }, and a set { gradient information set } is put in;
recording the gradient information in the { gradient information j } set as partial derivative information of the previous moment in sequence, namely: when the parameters to be set of the MISO compact-format model-free controller contain penalty factor lambda, the gradient information in the { gradient information j } set
Figure RE-GDA0001610391230000041
Recording as partial derivative information of previous time
Figure RE-GDA0001610391230000042
When the parameters to be set of the MISO compact-format model-free controller contain the step factor rho, the gradient information in the set of the gradient information j is obtained
Figure RE-GDA0001610391230000043
Recording as partial derivative information of previous time
Figure RE-GDA0001610391230000044
The set of all the partial derivative information is marked as { partial derivative information j }, and the set { partial derivative information set } is put into;
repeating the step for the other m-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 m } }, and the set { partial derivative information set } contains the set of all { { partial derivative information 1}, …, { partial derivative information m } }, 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 a system output actual value 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 independent variables of the system error calculation function in the step (3) comprise a system output expected value and a system output actual value.
The systematic error calculation function in the step (3) adopts e (k) y*(k) -y (k), wherein y*(k) The system output expected value is set for the time k, and y (k) is the system output actual value obtained by sampling at the time k; or using e (k) ═ y*(k +1) -y (k), wherein y*And (k +1) is a system output expected value at the moment of k +1, and y (k) is a system output actual value obtained by sampling at the moment of k.
The independent variable of the system error function in the step (7) comprises any one or any combination of a system error, a system output expected value and a system output actual value.
Said systematic error function in said step (7) is
Figure RE-GDA0001610391230000051
Wherein e (k) is the systematic error, Δ uj(k)＝uj(k)-uj(k-1)，bjIs a constant greater than or equal to 0, and j is greater than or equal to 1 and less than or equal to m.
The parameter self-tuning method of the MISO compact-format model-free controller based on the partial derivative information can achieve good control effect and effectively overcome the problem that the penalty factor lambda and the step factor rho need to be time-consuming and labor-consuming to be tuned.
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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 is a control effect diagram of a two-input single-output MISO system when a penalty factor lambda and a step factor rho are self-timed at the same time;
FIG. 4 is a control input diagram for a two-input single-output MISO system with simultaneous self-timing of penalty factor λ and stride factor ρ;
FIG. 5 is a change curve of penalty factor λ for a two-input single-output MISO system when penalty factor λ and step-size factor ρ are self-aligned simultaneously;
FIG. 6 is a change curve of the step factor rho of a two-input single-output MISO system when the penalty factor lambda and the step factor rho are self-aligned simultaneously;
FIG. 7 is a graph of the control effect of a two-input single-output MISO system when the penalty factor λ is fixed and the step-size factor ρ is self-setting;
FIG. 8 is a control input diagram for a two-input single-output MISO system with a fixed penalty factor λ and a self-setting step size factor ρ;
FIG. 9 is a plot of the change in stride factor ρ for a two-input single-output MISO system with a fixed penalty factor λ and self-adjusting stride factor ρ.
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 MISO system with m inputs (m is an integer greater than or equal to 2) and 1 output, adopting a MISO compact format model-free controller for control; the MISO compact-format model-free controller parameters comprise a penalty factor lambda and a step factor rho; determining parameters to be set of the MISO tight-format model-free controller, wherein the parameters are part or all of the parameters of the MISO tight-format model-free controller and comprise any one or any combination of a penalty factor lambda and a step factor rho; in fig. 1, parameters to be set by the MISO compact-format model-less controller are a penalty factor λ and a step factor ρ; 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 MISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; the partial derivatives in the set { partial derivatives set } are initialized.
Recording the current time as k time; outputting the system to a desired value y*(k) Taking the difference with the system output actual value y (k) as the system error e (k) at the time k; taking partial derivative information in the set { partial derivative information set } as 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 MISO compact-format model-free controller; based on the system error e (k) and the value of the parameter to be set of the MISO tight format model-free controller, calculating to obtain a control input vector u (k) ═ u (u) of the MISO tight format model-free controller at the time k for the controlled object by adopting a control algorithm of the MISO tight format model-free controller1(k),…,um(k)]T(ii) a For the jth control input u in the control input vector u (k)j(k) (j is more than or equal to 1 and less than or equal to m), calculating the jth control input uj(k) Respectively aiming at gradient information of parameters to be set of each MISO compact-format model-free controller at the moment k, recording a set of all the gradient information as { gradient information j }, and putting the set { gradient information set }; sequentially recording the gradient information in the { gradient information j } set as partial derivative information of a previous moment, recording the set of all the partial derivative information as { partial derivative information j }, and putting the set { partial derivative information set }; repeating the execution for the other m-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 m } }, while the set { partial derivative information set } contains the set of all { { partial derivative information 1}, …, { partial derivative information m } }; subsequently, the set { gradient information set } is combined, targeted at the minimization of the value of the systematic error function, denoted e in fig. 12(k) Minimizing as a target, performing system error back propagation calculation by adopting a gradient descent method, updating a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network, and taking the updated hidden layer weight coefficient and the output layer weight coefficient as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network performs forward calculation at the later moment; after the control input vector u (k) acts on the controlled object,and obtaining a system output actual value of the controlled object at the later moment, then repeatedly executing the work in the paragraph, and carrying out a parameter self-tuning process of the MISO compact-format model-free controller at the later moment based on the partial derivative information.
Fig. 2 shows a schematic structural diagram of the BP neural network adopted in the present invention. The BP neural network may have a structure in which the hidden layer is a single layer, or may have a structure in which the hidden layer is a plurality of layers. In the schematic diagram of fig. 2, for the sake of simplicity, the BP neural network adopts a structure in which the 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, the number of nodes of the input layer is set to mx the number of parameters to be set (in fig. 2, the number of parameters to be set is 2), the number of nodes of the hidden layer is 6, and the number of nodes of the output layer is set to the number of parameters to be set (in fig. 2, the number of parameters to be set is 2). The number of nodes of the input layer is divided into m groups, the number of nodes of each group is the number of parameters to be set, and the number of nodes of the jth group and the partial derivative information in the { partial derivative information j } set
Figure RE-GDA0001610391230000071
Respectively correspond to each other. And the nodes of the output layer correspond to the penalty factor lambda and the step factor rho respectively. 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: targeting the minimization of the value of the systematic error function, denoted by e in FIG. 22(k) And (4) minimizing to a target, and performing system error back propagation calculation by adopting a gradient descent method and combining the set { gradient information set }, so as to update the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network.
The following is a specific embodiment of the present invention.
The controlled object is a typical nonlinear two-input single-output MISO system:
Figure RE-GDA0001610391230000072
desired value y of system output*(k) The following were used:
y*(k)＝(-1)round((k-1)/100)
in this particular embodiment, m is 2.
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 2 multiplied by the number of parameters to be set, the number of nodes of the hidden layer is set to be 6, and the number of nodes of the output layer is set to be the number of the parameters to be set.
For the above specific examples, two sets of experimental verification were performed.
During the first group of experimental verification, the number of nodes of the input layer of the BP neural network in fig. 2 is preset to 4, the number of nodes of the output layer is preset to 2, and the penalty factor λ and the step factor ρ are self-tuned simultaneously, fig. 3 is a control effect diagram, fig. 4 is a control input diagram, fig. 5 is a change curve of the penalty factor λ, and fig. 6 is a change curve of the step factor ρ. The result shows that the method can realize good control effect by self-setting the penalty factor lambda and the step factor rho at the same time, and can effectively overcome the problem that the penalty factor lambda and the step factor rho need to be time-consuming and labor-consuming to set.
During the second group of test verification, the number of nodes of the input layer of the BP neural network in fig. 2 is preset to 2, the number of nodes of the output layer is preset to 1, the penalty factor λ is firstly fixed to be the average value of the penalty factor λ during the first group of test verification, then the step factor ρ is self-tuned, fig. 7 is a control effect diagram, fig. 8 is a control input diagram, and fig. 9 is a step factor ρ change curve. The result also shows that the method can realize good control effect by self-tuning the step factor rho when the penalty factor lambda is fixed, and can effectively overcome the problem that the step factor rho needs to be time-consuming and labor-consuming to be tuned.
It should be noted that in the above-described embodiment, the system is output with the desired value y*(k) The difference with the actual system output value y (k) is used as the system error e (k), i.e. e (k) y*(k) -y (k), only one method of calculating a function for the systematic error; the expected value y of the system output at the moment k +1 can also be used*The difference between (k +1) and the actual system output value y (k) at time k is taken as the system error e (k), i.e. e (k) y*(k +1) -y (k); the system error calculation functionOther methods of calculating the arguments, including desired and actual system output values, may also be used, for example,
Figure RE-GDA0001610391230000081
-y (k); for the controlled object of the above embodiment, good control effects can be achieved by using the different system error calculation functions.
More particularly, in the above 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 adopts e2(k) Only one of said systematic error functions; the system error function may also be other functions with independent variables including any one or any combination of system error, system output expected value and system output actual value, for example, the system error function may be (y)*(k)-y(k))2Or (y)*(k+1)-y(k))2I.e. using e2(k) Another functional form of (1); as another example, a systematic error function is employed
Figure RE-GDA0001610391230000082
Wherein, Δ uj(k)＝uj(k)-uj(k-1)，bjIs a constant greater than or equal to 0, j is greater than or equal to 1 and less than or equal to m; obviously, when bjAll equal to 0, the systematic error function only takes into account e2(k) The contribution of (1) shows that the aim of minimization is to minimize the system error, namely pursuing high precision; when b isjWhen the error is larger than 0, the system error function considers e2(k) Are made a contribution to
Figure RE-GDA0001610391230000091
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; and system error functionNumber only considering e2(k) Control effects in contribution to the system error function while considering e2(k) Are made a contribution to
Figure RE-GDA0001610391230000092
The contribution of (1) is that the control precision is slightly reduced and the operation stability is improved.
Finally, it should be particularly pointed out that the parameters to be set of the MISO compact-format model-free controller include any one or any combination of a penalty factor λ and a step factor ρ; in the above specific embodiment, the penalty factor λ and the step factor ρ realize simultaneous self-tuning during the first set of test verification, and the penalty factor λ is fixed and the step factor ρ realizes self-tuning during the second set of test verification; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor rho is fixed, and the penalty factor lambda realizes self-setting; in addition, parameters to be set by the MISO tight format model-free controller include, but are not limited to, a penalty factor λ and a step factor ρ, and for example, a row matrix of the MISO system pseudo-gradient estimation value may be further included according to specific situations
Figure RE-GDA0001610391230000093
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 (3)

  1. The parameter self-tuning method of the MISO compact-format model-free controller based on the partial derivative information is characterized by comprising the following steps of:
    step (1): for a Multiple Input and Single Output (MISO) system with m inputs (m is an integer greater than or equal to 2) and 1 Output, adopting a MISO compact format model-free controller for control; the MISO compact-format model-free controller parameters comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a MISO (multiple input single output) compact-format model-free controller, wherein the parameters to be set of the MISO compact-format model-free controller are part or all of the parameters of the MISO compact-format model-free controller and comprise any one or any combination of a punishment factor lambda and a step factor rho; 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 MISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; initializing partial derivative information in a set { partial derivative information set };
    step (2): recording the current time as k time;
    and (3): calculating to obtain a system error at the k moment by adopting a system error calculation function based on the system output expected value and the system output actual value, and recording as e (k); the independent variables of the system error calculation function comprise a system output expected value and a system output actual value;
    and (4): taking the partial derivative information in the set { partial derivative information set } as the input of a BP (back propagation) 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 MISO (single input single output) compact-format model-free controller;
    and (5): calculating and obtaining a control input vector u (k) [ [ u (k) of the MISO tight format model-free controller at the time k for the controlled object by adopting a control algorithm of the MISO tight format model-free controller based on the system error e (k) obtained in the step (3) and the value of the parameter to be set of the MISO tight format model-free controller obtained in the step (4)1(k),…,um(k)]T；
    And (6): aiming at the jth control input u in the control input vector u (k) obtained in the step (5)j(k) (j is more than or equal to 1 and less than or equal to m), calculating the jth control input uj(k) Respectively aiming at the gradient information of the parameters to be set of each MISO compact-format model-free controller at the moment k, the specific calculation formula is as follows:
    when the parameters to be set of the MISO compact-format model-free controller contain penalty factor lambdaThen, the jth control input uj(k) The gradient information at the k moment for the penalty factor λ is:
    Figure FDA0002208655440000021
    when the parameters to be set of the MISO compact-format model-free controller contain the step factor rho, the jth control input uj(k) The gradient information at the k moment for the step factor ρ is:
    Figure FDA0002208655440000022
    wherein the content of the first and second substances,
    Figure FDA0002208655440000023
    is a row matrix of MISO system pseudo gradient estimates at time k,
    Figure FDA0002208655440000024
    is a row matrix
    Figure FDA0002208655440000025
    The j-th gradient component estimate of (a),
    Figure FDA0002208655440000026
    is a row matrix
    Figure FDA0002208655440000027
    2 norm of (d);
    the set of all the gradient information is marked as { gradient information j }, and a set { gradient information set } is put in;
    recording the gradient information in the { gradient information j } set as partial derivative information of the previous moment in sequence, namely: when the parameters to be set of the MISO compact-format model-free controller contain penalty factor lambda, the gradient information in the { gradient information j } set
    Figure FDA0002208655440000028
    Recording as partial derivative information of previous time
    Figure FDA0002208655440000029
    When the parameters to be set of the MISO compact-format model-free controller contain the step factor rho, the gradient information in the set of the gradient information j is obtained
    Figure FDA00022086554400000210
    Recording as partial derivative information of previous time
    Figure FDA00022086554400000211
    The set of all the partial derivative information is marked as { partial derivative information j }, and the set { partial derivative information set } is put into;
    repeating the step for the other m-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 m } }, and the set { partial derivative information set } contains the set of all { { partial derivative information 1}, …, { partial derivative information m } }, 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 a system error, a system output expected value and a system output actual value;
    and (8): and (4) after the control input vector u (k) acts on the controlled object, obtaining a system output actual value 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 MISO compact format model-free control of claim 1The parameter self-tuning method based on the partial derivative information is characterized in that the system error calculation function in the step (3) adopts e (k) y*(k) -y (k), wherein y*(k) The system output expected value is set for the time k, and y (k) is the system output actual value obtained by sampling at the time k; or using e (k) ═ y*(k +1) -y (k), wherein y*And (k +1) is a system output expected value at the moment of k +1, and y (k) is a system output actual value obtained by sampling at the moment of k.
  3. 3. The MISO compact format model-less controller parameter self-tuning method of claim 1, wherein the systematic error function in step (7) is
    Figure FDA0002208655440000031
    Wherein e (k) is the systematic error, Δ uj(k)＝uj(k)-uj(k-1)，bjIs a constant greater than or equal to 0, and j is greater than or equal to 1 and less than or equal to m.
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