CN107991865B - Decoupling control method for MIMO based on SISO tight format model-free controller and system error - Google Patents

Decoupling control method for MIMO based on SISO tight format model-free controller and system error Download PDF

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CN107991865B
CN107991865B CN201711187307.7A CN201711187307A CN107991865B CN 107991865 B CN107991865 B CN 107991865B CN 201711187307 A CN201711187307 A CN 201711187307A CN 107991865 B CN107991865 B CN 107991865B
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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 decoupling control method of MIMO (Multiple Input and Multiple Output) based on SISO (Single Input and Single Output) compact format model-free controller and system error, which comprises the steps of firstly decomposing an MIMO system into a plurality of SISO (Single Input and Single Output) systems which are mutually coupled according to the coupling characteristic and the tendency characteristic of the MIMO system; the SISO system is controlled by adopting a SISO compact format model-free controller; based on a BP neural network, taking system errors as input, aiming at minimizing a system error function value comprehensively considering the contribution of all SISO system errors, adopting a gradient descent method, combining control input and respectively aiming at gradient information of each parameter to be set of a controller, carrying out system error back propagation calculation, realizing online self-setting of parameters such as penalty factors, step factors and the like of a SISO compact-format model-free controller, and synchronously realizing online decoupling among a plurality of SISO systems. The method provided by the invention can realize a good control effect and is an effective means for solving the control problem of the MIMO system.

Description

Decoupling control method for MIMO based on SISO tight format model-free controller and system error
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a decoupling control method for MIMO based on SISO compact format model-free controller and system error.
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. A typical characteristic of MIMO systems is coupling, that is: a change in one input will tend to change multiple outputs, and an output will also not be affected by only one input; at the same time, however, this coupling in most cases, in particular in the field of industrial process automation, will exhibit a tendency, namely: changes in one input tend to cause a particular output to change significantly while having less effect on other outputs, and one output tends to be significantly affected by a particular input while being less affected by other inputs. The tendency characteristic of the MIMO system provides feasibility for decomposing the MIMO system into a plurality of SISO (Single Input and Single Output) systems; the coupling characteristic of the MIMO system indicates that the SISO systems must synchronously solve the problem of online decoupling among the SISO systems when respectively adopting SISO controllers for control.
There are several implementations of SISO controllers, including SISO compact-format modeless controllers. The SISO compact 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 SISO 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 SISO system, and has a good application prospect. The theoretical basis of the SISO compact-format model-free controller is proposed by Hou Zhong and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing agency, 2013, page 56) of the Hei-Shi, and the control algorithm is as follows:
Figure BDA0001480302290000021
wherein u (k) is the control input at time k; e (k) is the system error at time k;
Figure BDA0001480302290000022
is a pseudo gradient estimation value at the k moment; λ is a penalty factor; ρ is the step factor.
However, the SISO 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 parameters such as the penalty factor λ and the step factor ρ has not been realized in the actual application process. The lack of effective parameter setting means not only makes the using and debugging process of the SISO compact format model-free controller time-consuming and labor-consuming, but also can seriously affect the control effect of the SISO compact format model-free controller sometimes, and restricts the popularization and application of the SISO compact format model-free controller. That is to say: the SISO compact-format model-free controller also needs to solve the problem of online self-tuning parameters in the actual application process.
Therefore, the invention provides a decoupling control method of MIMO based on SISO compact format model-free controller and system error, which can synchronously solve the difficult problem of on-line self-setting parameter of SISO compact format model-free controller and the difficult problem of on-line decoupling between a plurality of SISO systems, and provides a new method for solving the control problem of MIMO system.
Disclosure of Invention
In order to solve the problems in the background art, the present invention provides a decoupling control method for MIMO based on SISO tight format model-less controller and system error.
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 MIMO (Multiple Input and Multiple Output) system having mi inputs (mi is an integer greater than or equal to 2) and mo outputs (mo is an integer greater than or equal to 2), selecting one Input of the mi inputs and one Output of the mo outputs to form a SISO (Single Input and Single Output) system; repeating the operation m times (m is more than or equal to 1, m is less than or equal to mi, m is less than or equal to mo, and m is an integer) to form m SISO systems, wherein the input of any one SISO system is not used as the input of other SISO systems, and the output of any one SISO system is not used as the output of other SISO systems; the m SISO systems are controlled by adopting m SISO compact format model-free controllers;
step (2): for the jth (j is more than or equal to 1 and less than or equal to m) SISO compact format no-model controller, the parameters of the jth SISO compact format no-model controller comprise a penalty factor lambdajAnd step size factor ρj(ii) a Determining the parameters to be set of the jth SISO compact format model-free controller, wherein the parameters to be set of the jth SISO compact format model-free controller are part or all of the parameters of the jth SISO compact format model-free controller and contain a penalty factor lambdajAnd step size factor ρjAny 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 jth BP neural network,the number of the output layer nodes is not less than the number of parameters to be set of the jth SISO compact format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of a jth BP neural network; if m is more than or equal to 2, the step is repeatedly executed for other m-1 SISO compact format model-free controllers;
and (3): recording the current time as k time;
and (4): calculating a gradient information set at the k moment;
the j (1 is not less than j and not more than m) th SISO compact format model-free controller comprises the processing steps of (4-1), (4-2), (4-3), (4-4) and (4-5):
the step (4-1) is as follows: based on the output expected value of the jth SISO system and the output actual value of the jth SISO system, adopting the error calculation function of the jth SISO system to calculate the jth SISO system error at the k moment, and recording the jth SISO system error as ej(k)；
The step (4-2) is as follows: recording any one or any combination of the jth SISO system error and the function group thereof, the jth SISO system output expected value and the jth SISO system output actual value obtained by the calculation in the step (4-1) as a set { system error j }, and taking the set { system error j } as the input of a jth BP neural network;
the step (4-3) is as follows: based on the input of the jth BP neural network in the step (4-2), the jth BP neural network performs forward calculation, and a calculation result is output through an output layer of the jth BP neural network to obtain a value of a parameter to be set of the jth SISO tight-format model-free controller;
the step (4-4) is as follows: based on the jth SISO system error e obtained in the step (4-1)j(k) And (4-3) calculating the value of the parameter to be set of the jth SISO tight format model-free controller by adopting the control algorithm of the SISO tight format model-free controller to obtain the control input u of the jth SISO tight format model-free controller at the moment k for the controlled objectj(k)；
The step (4-5) is as follows: based on the control input u obtained in step (4-4)j(k) Calculating said control input uj(k) Respective for jth SISO compact formatGradient information of each parameter to be set of the model controller at the moment k is obtained, and a specific calculation formula of the gradient information is as follows:
when the parameter to be set of the jth SISO compact format model-free controller contains a penalty factor lambdajWhile, the control input uj(k) For the penalty factor lambdajThe gradient information at time k is:
Figure BDA0001480302290000041
when the parameter to be set of the jth SISO compact format model-free controller contains a step factor rhojWhile, the control input uj(k) For the step size factor pjThe gradient information at time k is:
Figure BDA0001480302290000042
wherein,
Figure BDA0001480302290000043
a pseudo gradient estimation value of a jth SISO compact format model-free controller at the moment k;
the set of all the gradient information is marked as { gradient information j }, and a set { gradient information set } is put in;
if m is 1, the gradient information set is unchanged, and then step (5) is carried out;
if m is more than or equal to 2, each SISO compact format model-free controller in the m SISO compact format model-free controllers has the processing procedures of the step (4-1), the step (4-2), the step (4-3), the step (4-4) and the step (4-5); when each of the m SISO compact format modeless controllers has completely performed the processing of step (4-1), step (4-2), step (4-3), step (4-4), and step (4-5), the { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information m } }, and then step (5) is proceeded to;
and (5): aiming at the jth (j is more than or equal to 1 and less than or equal to m) SISO compact-format model-free controller, the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the { gradient information set } obtained in the step (4) is combined, the system error back propagation calculation is carried out, the hidden layer weight coefficient and the output layer weight coefficient of the jth BP neural network are updated to serve as the hidden layer weight coefficient and the output layer weight coefficient when the jth BP neural network carries out forward calculation at the later moment, and meanwhile, if m is more than or equal to 2, the decoupling of the jth SISO compact-format model-free controller and other m-1 SISO compact-format model-free controllers is synchronously realized;
if m is 1, entering the step (6);
if m is more than or equal to 2, repeatedly executing the step aiming at other m-1 SISO compact format model-free controllers until the weight coefficients of the hidden layer and the output layer of all m BP neural networks are updated, and then entering the step (6);
and (6): all m of said control inputs u1(k),…,um(k) And (6) after the action on the controlled object, obtaining all m SISO system output actual values of the controlled object at the later moment, returning to the step (3), and repeating the steps (3) to (6).
While adopting the above technical scheme, the present invention can also adopt or combine the following further technical schemes:
in the step (4), if m is greater than or equal to 2, the value of j can be changed in any one or between any two of the steps (4-1), (4-2), (4-3), (4-4) and (4-5) or before the step (4-1) or after the step (4-5) to process other SISO tight format model-less controllers, the change of the value of j can be sequential value or irregular value, as long as the processing process of each SISO tight format model-less controller is in the sequence of the step (4-1), (4-2), (4-3), (4-4) and (4-5), and between the two steps of each SISO tight format model-less controller or before the step (4-1) or after the step (4-5), the steps (4-1), (4-2), (4-3), (4-4) and (4-5) of other SISO compact format model-free controllers can be executed according to the needs.
The argument of said jth SISO system error calculation function in said step (4-1) contains a jth SISO system output expected value and a jth SISO system output actual value.
Said j-th SISO system error calculation function in said step (4-1) adopts
Figure BDA0001480302290000061
Wherein
Figure BDA0001480302290000062
Output expectation value, y, of jth SISO system set for time kj(k) Outputting an actual value for the jth SISO system sampled at the k moment; or by using
Figure BDA0001480302290000063
Wherein
Figure BDA0001480302290000064
Output expectation value, y, for the jth SISO system at time k +1j(k) And outputting an actual value for the jth SISO system sampled at the k moment.
The jth SISO system error in the step (4-2) and a function group thereof comprise the jth SISO system error e at the moment kj(k) And the j-th SISO system error at the k time and all the previous times is accumulated
Figure BDA0001480302290000065
The jth SISO system error e at the moment kj(k) First order backward difference e ofj(k)-ej(k-1), the jth SISO system error e at time kj(k) Second order backward difference e ofj(k)-2ej(k-1)+ej(k-2) th SISO system error e at time kj(k) Any one or any combination of high order backward differences.
The argument of the systematic error function in step (5) contains any one or any combination of m SISO systematic errors, m SISO systematic output expected values, and m SISO systematic output actual values.
Said systematic error function in said step (5) is
Figure BDA0001480302290000066
Wherein e isj(k) For the jth SISO systematic error, Δ uj(k)＝uj(k)-uj(k-1)，ajAnd 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 decoupling control method of the MIMO based on the SISO compact format model-less controller and the system error can synchronously solve the difficult problem of the on-line self-setting parameter of the SISO compact format model-less controller and the difficult problem of the on-line decoupling among a plurality of SISO systems, thereby realizing the decoupling control of the MIMO system.
Drawings
FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic structural diagram of the jth BP neural network adopted by the present invention;
FIG. 3 shows a two-input and two-output MIMO system with penalty factor λjAnd step size factor ρjMeanwhile, self-timing the control effect diagram of the 1 st SISO system;
FIG. 4 shows a penalty factor λ for a two-input two-output MIMO systemjAnd step size factor ρjMeanwhile, a control effect diagram of the 2 nd SISO system during self-setting;
FIG. 5 shows a two-input and two-output MIMO system with penalty factor λjAnd step size factor ρjSimultaneously self-timing control input diagram;
FIG. 6 shows a penalty factor λ for a two-input two-output MIMO systemjAnd step size factor ρjPenalty factor lambda while self-aligningjA change curve;
FIG. 7 shows a penalty factor λ for a two-input two-output MIMO systemjAnd step size factor ρjStep size factor p while self-aligningjA change curve;
FIG. 8 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pjSelf-timing the control effect graph of the 1 st SISO system;
FIG. 9 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pjA control effect graph of the 2 nd SISO system during self-setting;
FIG. 10 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pjA self-timed control input map;
FIG. 11 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pjStep factor p at self-alignmentjA 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. Selecting an input and an output according to the coupling characteristic and the tendency characteristic of the MIMO system to form a SISO system, repeating for m times, thereby decomposing the MIMO system into m SISO systems which are mutually coupled, wherein the input of any one SISO system is not used as the input of other SISO systems, and the output of any one SISO system is not used as the output of other SISO systems; the m SISO systems are controlled by m SISO compact format model-free controllers.
For the jth (j is more than or equal to 1 and less than or equal to m) SISO compact format no-model controller, the parameters of the jth SISO compact format no-model controller comprise a penalty factor lambdajAnd step size factor ρj(ii) a Determining the parameters to be set of the jth SISO compact format model-free controller, wherein the parameters to be set of the jth SISO compact format model-free controller are part or all of the parameters of the jth SISO compact format model-free controller and contain a penalty factor lambdajAnd step size factor ρjAny one or any combination of the above; in FIG. 1, the parameter to be set of the jth SISO tight format model-less controller is a penalty factor λjAnd step size factor ρj(ii) a Determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of a jth BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the jth SISO compact-format model-free controller; and initializing the hidden layer weight coefficient and the output layer weight coefficient of the jth BP neural network. Repeat execution of the instructions described in this paragraph for the other m-1 SISO compact Format modeless controllersAnd (6) working.
The current time is denoted as time k.
Aiming at the jth (j is more than or equal to 1 and less than or equal to m) SISO compact-format modeless controller, firstly, the actual output value y of the system is obtained through samplingj(k) Outputting the expected value of the system
Figure BDA0001480302290000081
And the system outputs the actual value yj(k) The difference is used as the j-th SISO system error e at the k timej(k) (ii) a Then the jth SISO system error e at the k momentj(k) And the j-th SISO system error at the k time and all the previous times is accumulated
Figure BDA0001480302290000082
The jth SISO system error e at the moment kj(k) First order backward difference e ofj(k)-ej(k-1) as an input to the jth BP neural network; performing forward calculation on the jth BP neural network, and outputting a calculation result through an output layer of the jth BP neural network to obtain a value of a parameter to be set of the jth SISO compact-format model-free controller; then, based on the jth SISO systematic error ej(k) And calculating the value of the parameter to be set of the jth SISO compact-format model-free controller by adopting the control algorithm of the SISO compact-format model-free controller to obtain the control input u of the jth SISO compact-format model-free controller aiming at the controlled object at the moment kj(k) (ii) a Calculating a control input uj(k) And respectively aiming at the gradient information of each parameter to be set of the jth SISO compact-format model-free controller at the moment k, marking the set of all the gradient information as { gradient information j }, and putting the set { gradient information set }. The work described in this paragraph is repeated for the other m-1 SISO compact format modeless controllers, such that the { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information m } }.
The systematic error function in FIG. 1, which comprehensively considers the contributions of all m SISO systematic errors, is targeted for the minimization of the value of the systematic error function
Figure BDA0001480302290000091
The method comprises the steps of minimizing the value of the absolute. The work described in this paragraph is repeatedly performed for other m-1 SISO compact-format modeless controllers until the hidden layer weight coefficients and the output layer weight coefficients of all m BP neural networks are updated.
All m of said control inputs u1(k),…,um(k) And after the control device acts on the controlled object, obtaining all m SISO system output actual values of the controlled object at the later moment, returning to the paragraph of [ recording the current moment as the k moment ], and starting the decoupling control process of the MIMO based on the SISO tight format model-free controller and the system error at the later moment.
FIG. 2 shows the structure diagram of the jth (j is more than or equal to 1 and less than or equal to m) BP neural network adopted by the invention. The jth BP neural network may adopt a structure in which the hidden layer is a single layer, or may adopt a structure in which the hidden layer is a multilayer. In the schematic diagram of fig. 2, for the sake of simplicity, the jth 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 3, the number of nodes of the hidden layer is set to 6, and the number of nodes of the output layer is set to the number of parameters to be set (the number of parameters to be set in fig. 2 is 2). 3 nodes of the input layer, and the jth SISO systematic error ej(k) Accumulation of the jth SISO systematic error
Figure BDA0001480302290000092
Jth SISO systematic error ej(k) First order backward difference e ofj(k)-ej(k-1) correspond to each other. Node of output layer, penalty factor lambda of jth SISO tight format model-free controllerjAnd step size factor ρjRespectively correspond to each other. Hidden layer weight coefficient of jth BP neural networkThe updating process of the weight coefficient of the output layer is specifically as follows: the systematic error function in FIG. 2, which comprehensively considers the contributions of all m SISO systematic errors, is targeted for the minimization of the value of the systematic error function
Figure BDA0001480302290000101
The method comprises the steps of minimizing the value of the absolute.
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 BDA0001480302290000102
Figure BDA0001480302290000103
Figure BDA0001480302290000104
Figure BDA0001480302290000105
y1(k)＝x11(k)
y2(k)＝x21(k)
where a (k) is 1+0.1sin (2k pi/1500), and b (k) is 1+0.1cos (2k pi/1500).
Desired value y of system output*(k) The following were used:
Figure BDA0001480302290000106
Figure BDA0001480302290000107
in this embodiment, the MIMO system is decomposed into 2 SISO systems (m is 2) coupled to each other according to the coupling characteristic and the tendency characteristic of the MIMO system: the input of the 1 st SISO System is u1(k) Output is y1(k) (ii) a The input to the 2 nd SISO system is u2(k) Output is y2(k) In that respect The 2 SISO systems are controlled using 2 SISO compact-format modeless controllers. The 1 st BP neural network and the 2 nd BP neural network both adopt 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 3, 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 parameters to be set of respective controllers.
For the above specific examples, two sets of experimental verification were performed.
When the first group of experiments verify that the number of output layer nodes of the BP neural network in FIG. 2 is 2, and the penalty factor lambda of the 2 SISO compact-format model-free controllersjAnd step size factor ρjPerforming the simultaneous self-tuning, fig. 3 is a control effect diagram of the 1 st SISO system, fig. 4 is a control effect diagram of the 2 nd SISO system, fig. 5 is a control input diagram, fig. 6 is a penalty factor lambdajThe variation curve, FIG. 7, is the step factor ρjA curve of variation. The result shows that the method designs 2 SISO compact format model-free controllers and combines the penalty factor lambda of the BP neural network to each SISO compact format model-free controllerjAnd step size factor ρjAnd the simultaneous self-tuning is carried out, so that a good control effect can be realized, and the decoupling control of the MIMO system is realized.
In the second set of experimental verification, the number of output layer nodes of the BP neural network in fig. 2 is 1, and first 2 penalty factors λ are calculatedjRespectively fixing the values as a first group of punishment factors lambda during test verificationjIs equal to 1,2, and then step size factor p for 2 SISO tight format modeless controllersjSelf-tuning is performed, and FIG. 8 is the firstControl effect diagram of 1 SISO system, FIG. 9 is control effect diagram of 2 th SISO system, FIG. 10 is control input diagram, FIG. 11 is step factor ρjA curve of variation. The result shows that the method of the invention has a penalty factor lambdajWhen in fixation, 2 SISO compact format model-free controllers are designed and combined with the step factor rho of the BP neural network to each SISO compact format model-free controllerjThe self-tuning is carried out, so that a good control effect can be realized, and the decoupling control of the MIMO system is realized.
It should be particularly noted that in the above-described embodiments, the j-th (1. ltoreq. j. ltoreq.m) SISO system output is output with a desired value
Figure BDA0001480302290000111
With the j-th SISO system output actual value yj(k) The difference is taken as the jth SISO system error ej(k) That is to say
Figure BDA0001480302290000112
Figure BDA0001480302290000113
One method of calculating a function for only the jth SISO system error; the output expectation value of the jth SISO system at the moment k +1 can also be output
Figure BDA0001480302290000114
The j th SISO system at the time of k outputs an actual value yj(k) The difference is taken as the jth SISO system error ej(k) That is to say
Figure BDA0001480302290000115
The jth SISO system error calculation function may also use other calculation methods where the arguments include a desired jth SISO system output value and an actual jth SISO system output value, such as, for example,
Figure BDA0001480302290000121
for the controlled objects of the above embodiments, good control can be achieved by using the different system error calculation functionsAnd (5) effect.
It should also be particularly noted that in the above-described embodiment, the jth SISO system error e, which is the jth (1 ≦ j ≦ m) BP neural network input, and its function set, is selectedj(k) Accumulation of jth SISO systematic errors
Figure BDA0001480302290000122
Jth SISO systematic error ej(k) First order backward difference e ofj(k)-ej(k-1) a combination of only one of said jth SISO system error and its function set; the jth SISO system error and its function set may also include other combinations, for example, the jth SISO system error ej(k) Accumulation of the jth SISO systematic error
Figure BDA0001480302290000123
Jth SISO systematic error ej(k) First order backward difference e ofj(k)-ej(k-1), jth SISO System error ej(k) Second order backward difference e ofj(k)-2ej(k-1)+ej(k-2), jth SISO System error ej(k) Any one or any combination of third or fourth or higher order backward difference, etc. For the controlled object of the above embodiment, the above different system errors and their function sets are used, such as the jth SISO system error ej(k) Accumulation of the jth SISO systematic error
Figure BDA0001480302290000124
Jth SISO systematic error ej(k) First order backward difference e ofj(k)-ej(k-1), jth SISO System error ej(k) Second order backward difference e ofj(k)-2ej(k-1)+ejThe combination of (k-2) (in this case, the number of input layer nodes of the jth BP neural network is preset to 4), can achieve a good control effect.
More particularly, it should be noted that in the above-described embodiment, the jth BP neural network is updated with the goal of minimizing the value of the systematic error functionWhen the weight coefficient of the hidden layer and the weight coefficient of the output layer of the network are calculated, the system error function adopts the system error function comprehensively considering the contribution of all m SISO system errors
Figure BDA0001480302290000125
Only one of the systematic error functions; the systematic error function can also be any other function with independent variables including any one or any combination of m SISO systematic errors, m SISO system output expected values, and m SISO system output actual values, for example, the systematic error function can be
Figure BDA0001480302290000131
Or
Figure BDA0001480302290000132
That is to say by using
Figure BDA0001480302290000133
Another functional form of (1); as another example, the systematic error function employs
Figure BDA0001480302290000134
Wherein e isj(k) For the jth SISO systematic error, Δ uj(k)＝uj(k)-uj(k-1)，ajAnd 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 bjEqual to 0, the systematic error function only takes into account
Figure BDA0001480302290000135
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 is simultaneously considered
Figure BDA0001480302290000136
Are made a contribution to
Figure BDA0001480302290000137
Indicates that the minimized target is pursuingThe system error is small, and the control input change is small, namely, the precision is high and the operation is stable. 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 BDA0001480302290000138
Compared with the control effect during contribution, the system error function is considered simultaneously
Figure BDA0001480302290000139
Are made a contribution to
Figure BDA00014803022900001310
The contribution of (1) is that the control precision is slightly reduced and the operation stability is improved.
It should be further noted that the method for executing the step (4-1) to the step (4-5) may be a method for waiting for one SISO compact format modeless controller to finish the execution from the step (4-1) to the step (4-5) and then starting to execute another SISO compact format modeless controller from the step (4-1) to the step (4-5); a method of waiting for more than 1 and less than m SISO compact form modeless controllers to complete the execution of the step (4-1) and then starting to execute other SISO compact form modeless controllers from the step (4-1) to the step (4-5) after the completion of the execution of the step (4-5); it is also possible to employ a method in which all m SISO compact format modeless controllers perform all of the steps (4-1) to all of the steps (4-5).
Finally, it should be noted that the parameter to be set by the jth (1. ltoreq. j. ltoreq.m) SISO compact-format model-less controller contains a penalty factor lambdajAnd step size factor ρjAny one or any combination of the above; in the above embodiment, the first set of trial-and-error penalties is a factor λjAnd step size factor ρjRealizes the simultaneous self-tuning and the punishment factor lambda in the second group of test verificationjFixed step factor pjSelf-tuning is realized; in practical applicationIn the process, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor rhojFixed and penalty factor lambdajSelf-tuning is realized; in addition, the parameters to be set by the SISO compact-format model-free controller include, but are not limited to, a penalty factor lambdajAnd step size factor ρjFor example, the pseudo gradient estimation value can be included according to the specific situation
Figure BDA0001480302290000141
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. The decoupling control method of MIMO based on SISO tight format model-free controller and system error is characterized by comprising the following steps:
    step (1): for a MIMO (Multiple Input and Multiple Output) system with mi inputs and mo outputs, where mi is an integer greater than or equal to 2 and mo is an integer greater than or equal to 2, selecting one Input of the mi inputs and one Output of the mo outputs to form a SISO (Single Input and Single Output) system; repeating the operation m times, wherein m is more than or equal to 1, m is less than or equal to mi, m is less than or equal to mo, and m is an integer, so as to form m SISO systems, wherein the input of any one SISO system is not used as the input of other SISO systems, and the output of any one SISO system is not used as the output of other SISO systems; the m SISO systems are controlled by adopting m SISO compact format model-free controllers;
    step (2): aiming at the jth SISO compact format model-free controller, wherein j is more than or equal to 1 and less than or equal to m, and the parameters of the jth SISO compact format model-free controller comprise a penalty factor lambdajAnd step size factor ρj(ii) a Determining the parameters to be set of the jth SISO compact format model-free controller, wherein the jth SISO compact format model-free controller has noThe parameters to be set by the model controller are part or all of the j-th SISO compact format model-free controller parameters and contain a penalty factor lambdajAnd step size factor ρjAny 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 a jth BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the jth SISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of a jth BP neural network; if m is more than or equal to 2, the step is repeatedly executed for other m-1 SISO compact format model-free controllers;
    and (3): recording the current time as k time;
    and (4): calculating a gradient information set at the k moment;
    for the jth SISO compact format model-less controller, wherein j is more than or equal to 1 and less than or equal to m, the processing of the step (4-1), the step (4-2), the step (4-3), the step (4-4) and the step (4-5) is as follows:
    the step (4-1) is as follows: based on the output expected value of the jth SISO system and the output actual value of the jth SISO system, adopting the error calculation function of the jth SISO system to calculate the jth SISO system error at the k moment, and recording the jth SISO system error as ej(k) (ii) a The independent variables of the jth SISO system error calculation function comprise a jth SISO system output expected value and a jth SISO system output actual value;
    the step (4-2) is as follows: recording any one or any combination of the jth SISO system error and the function group thereof, the jth SISO system output expected value and the jth SISO system output actual value obtained by the calculation in the step (4-1) as a set { system error j }, and taking the set { system error j } as the input of a jth BP neural network;
    the step (4-3) is as follows: based on the input of the jth BP neural network in the step (4-2), the jth BP neural network performs forward calculation, and a calculation result is output through an output layer of the jth BP neural network to obtain a value of a parameter to be set of the jth SISO tight-format model-free controller;
    the step (4-4) is as follows: based on the jth SISO system error e obtained in the step (4-1)j(k) The jth SI obtained in the step (4-3)The value of the parameter to be set of the SO compact-format model-free controller is calculated by adopting the control algorithm of the SISO compact-format model-free controller to obtain the control input u of the jth SISO compact-format model-free controller at the moment k for the controlled objectj(k)；
    The step (4-5) is as follows: based on the control input u obtained in step (4-4)j(k) Calculating said control input uj(k) Respectively aiming at the gradient information of each parameter to be set of the jth SISO compact-format model-free controller at the moment k, wherein the specific calculation formula of the gradient information is as follows:
    when the parameter to be set of the jth SISO compact format model-free controller contains a penalty factor lambdajWhile, the control input uj(k) For the penalty factor lambdajThe gradient information at time k is:
    Figure FDA0002534722680000021
    when the parameter to be set of the jth SISO compact format model-free controller contains a step factor rhojWhile, the control input uj(k) For the step size factor pjThe gradient information at time k is:
    Figure FDA0002534722680000031
    wherein,
    Figure FDA0002534722680000032
    a pseudo gradient estimation value of a jth SISO compact format model-free controller at the moment k;
    the set of all the gradient information is marked as { gradient information j }, and a set { gradient information set } is put in;
    if m is 1, the gradient information set is unchanged, and then step (5) is carried out;
    if m is more than or equal to 2, each SISO compact format model-free controller in the m SISO compact format model-free controllers has the processing procedures of the step (4-1), the step (4-2), the step (4-3), the step (4-4) and the step (4-5); when each of the m SISO compact format modeless controllers has completely performed the processing of step (4-1), step (4-2), step (4-3), step (4-4), and step (4-5), the { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information m } }, and then step (5) is proceeded to;
    and (5): aiming at the jth SISO compact-format model-free controller, wherein j is more than or equal to 1 and less than or equal to m, the minimization of the value of a system error function is taken as a target, a gradient descent method is adopted, the { gradient information set } obtained in the step (4) is combined, the system error back propagation calculation is carried out, the hidden layer weight coefficient and the output layer weight coefficient of the jth BP neural network are updated to serve as the hidden layer weight coefficient and the output layer weight coefficient when the jth BP neural network carries out forward calculation at the later moment, and meanwhile, if m is more than or equal to 2, the decoupling of the jth SISO compact-format model-free controller and other m-1 SISO compact-format model-free controllers is synchronously realized; the independent variable of the system error function comprises any one or any combination of m SISO system errors, m SISO system output expected values and m SISO system output actual values;
    if m is 1, entering the step (6);
    if m is more than or equal to 2, repeatedly executing the step aiming at other m-1 SISO compact format model-free controllers until the weight coefficients of the hidden layer and the output layer of all m BP neural networks are updated, and then entering the step (6);
    and (6): all m of said control inputs u1(k)，…，um(k) And (6) after the action on the controlled object, obtaining all m SISO system output actual values of the controlled object at the later moment, returning to the step (3), and repeating the steps (3) to (6).
  2. 2. The method of claim 1, wherein the step (4-1) of decoupling the MIMO SISO-based compact-format model-less controller from systematic errors employs the jth SISO systematic error computation function
    Figure FDA0002534722680000041
    Wherein
    Figure FDA0002534722680000042
    Output expectation value, y, of jth SISO system set for time kj(k) Outputting an actual value for the jth SISO system sampled at the k moment; or by using
    Figure FDA0002534722680000043
    Wherein
    Figure FDA0002534722680000044
    Output expectation value, y, for the jth SISO system at time k +1j(k) And outputting an actual value for the jth SISO system sampled at the k moment.
  3. 3. The method as claimed in claim 1, wherein the j-th SISO systematic error and its function set in step (4-2) comprises the j-th SISO systematic error e at time kj(k) And the j-th SISO system error at the k time and all the previous times is accumulated
    Figure FDA0002534722680000045
    The jth SISO system error e at the moment kj(k) First order backward difference e ofj(k)-ej(k-1), the jth SISO system error e at time kj(k) Second order backward difference e ofj(k)-2ej(k-1)+ej(k-2) th SISO system error e at time kj(k) Any one or any combination of high order backward differences.
  4. 4. The method of claim 1, wherein the systematic error function in step (5) is selected from the group consisting of
    Figure FDA0002534722680000046
    Wherein e isj(k) For the jth SISO systematic error, Δ uj(k)＝uj(k)-uj(k-1)，ajAnd 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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Citations (6)

* 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
CN1274435A (en) * 1997-10-06 2000-11-22 美国通控集团公司 Model-free adaptive process control
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
CN103399487A (en) * 2013-07-30 2013-11-20 东北石油大学 Nonlinear MIMO (multiple input multiple output) system-based decoupling control method and device
CN105676632A (en) * 2016-01-26 2016-06-15 沈阳化工大学 Model-free adaptive optimized control method for PVC polymerization process

Patent Citations (6)

* 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
CN1274435A (en) * 1997-10-06 2000-11-22 美国通控集团公司 Model-free adaptive process control
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
CN103399487A (en) * 2013-07-30 2013-11-20 东北石油大学 Nonlinear MIMO (multiple input multiple output) system-based decoupling control method and device
CN105676632A (en) * 2016-01-26 2016-06-15 沈阳化工大学 Model-free adaptive optimized control method for PVC polymerization process

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Neural-net-based model-free self-tuning controller with on-line self-learning ability for industrial furnace;Mingwang Zhao;《1994 Proceedings of IEEE International Conference on Control and Applications 》;20020806;全文 *
无模型控制器参数学习步长和惩罚因子的整定研究;马平;《仪器仪表学报》;20080430;第29卷(第4期);全文 *
无模型自适应控制参数整定方法研究;郭代银;《中国优秀硕士学位论文全文数据库信息科技辑》;20150215(第2期);全文 *

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