CN108107722B - Decoupling control method for MIMO based on SISO bias format model-less controller and system error - Google Patents

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

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CN108107722B
CN108107722B CN201711187230.3A CN201711187230A CN108107722B CN 108107722 B CN108107722 B CN 108107722B CN 201711187230 A CN201711187230 A CN 201711187230A CN 108107722 B CN108107722 B CN 108107722B
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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 Multiple Output) based on SISO (Single Input Multiple Output) partial-format model-free controller and system error, which comprises the following steps of firstly decomposing an MIMO system into a plurality of SISO (Single Input 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 partial-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 partial-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 bias format model-less 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 partial-format model-free controllers and 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. 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 biased Format modeless controllers. The SISO bias 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 partial format model-free controller is proposed by Houzhong and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing agency, 2013, page 68) of the Hedame, and the control algorithm is as follows:
Figure BDA0001480215010000021
wherein u (k) is the control input at time k; Δ u (k) ═ u (k) — u (k-1); e (k) is the system error at time k;
Figure BDA0001480215010000022
is a pseudo-gradient estimate for time k,
Figure BDA0001480215010000023
is composed of
Figure BDA0001480215010000024
The ith component of (i ═ 1, …, L); l is a control input linearization length constant and is an integer greater than 1; λ is a penalty factor; rho1,…,ρLIs the step size factor.
However, the SISO biased format modeless controller needs to rely on empirical knowledge to set the penalty factor λ and the step factor ρ in advance before it is actually put into service1,…,ρLNumerical value of isoparametricThe penalty factor lambda and the step factor rho are not realized 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 using and debugging process of the SISO partial format model-free controller time-consuming and labor-consuming, but also can seriously affect the control effect of the SISO partial format model-free controller sometimes, and restricts the popularization and application of the SISO partial format model-free controller. That is to say: the SISO offset 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 partial mode no-model controller and system error, which can synchronously solve the difficult problem of on-line self-tuning parameters of SISO partial mode no-model 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 partial 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 partial-format model-free controllers;
step (2): determining a control input linearization length constant L of the jth (1 ≦ j ≦ m) SISO partial format modeless controllerj，LjIs an integer greater than 1; the jth SISO partial-format modeless controller parameter comprises a penalty factor lambdajAnd step size factor
Figure BDA0001480215010000031
Determining the parameter to be set of the jth SISO partial lattice type modeless controller, wherein the parameter to be set of the jth SISO partial lattice type modeless controller is part or all of the parameter of the jth SISO partial lattice type modeless controller and contains a penalty factor lambdajAnd step size factor
Figure BDA0001480215010000032
Any 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 partial-format modeless 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 partial 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 jth (1 is not less than j and not more than m) SISO partial format modeless controller is provided with the processing of the steps (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 partial-format modeless controller;
the step (4-4) is as follows: based on the system error e of the jth SISO system obtained in the step (4-3) at the moment kj(k) And (4-3) calculating the value of the parameter to be set of the jth SISO partial-format modeless controller obtained in the step (4-3) by adopting the control algorithm of the SISO partial-format modeless controller to obtain the control input u of the jth SISO partial-format modeless controller at the time 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 partial 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 partial-format modeless controller contains a penalty factor lambdajWhile, the control input uj(k) For the penalty factor lambdajThe gradient information at time k is:
Figure BDA0001480215010000041
when the parameter to be set of the jth SISO partial-format modeless controller contains a step factor rhoj,1While, the control input uj(k) For the step size factor pj,1The gradient information at time k is:
Figure BDA0001480215010000042
when the parameter to be set of the jth SISO partial-format modeless controller contains a step factor rhoj,iAnd when i is more than or equal to 2 and less than or equal to L, the control input uj(k) For the step size factor pj,iThe gradient information at time k is:
Figure BDA0001480215010000043
wherein, Δ uj(k)＝uj(k)-uj(k-1)，
Figure BDA0001480215010000051
For the pseudo gradient estimate at time k for the jth SISO partial-format modeless controller,
Figure BDA0001480215010000052
is composed of
Figure BDA0001480215010000053
1, …, Lj)；
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 partial format model-free controller in the m SISO partial 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 partial 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 } comprises the set of all { { gradient information 1}, …, { gradient information m }, and then step (5) is entered;
and (5): aiming at the jth SISO partial-format model-free controller (j is more than or equal to 1 and less than or equal to m), 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 partial-format model-free controller and other m-1 SISO partial-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 partial 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 partial format modeless controllers, the change of the value of j can be sequential value or irregular value, as long as the processing process of each SISO partial format modeless 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 partial format modeless 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 partial format modeless controllers can be carried out according to the requirement.
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 BDA0001480215010000061
Wherein
Figure BDA0001480215010000062
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 BDA0001480215010000063
Wherein
Figure BDA0001480215010000064
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 BDA0001480215010000065
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 BDA0001480215010000066
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 partial format model-less controller and the system error can synchronously solve the difficult problem of the on-line self-tuning parameter of the SISO partial 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 ρj,1,ρj,2,ρj,3Meanwhile, 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 ρj,1,ρj,2,ρj,3Meanwhile, 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 ρj,1,ρj,2,ρj,3Simultaneously self-timing control input diagram;
FIG. 6 shows a penalty factor λ for a two-input two-output MIMO systemjAnd step size factor ρj,1,ρj,2,ρj,3Penalty 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 ρj,1,ρj,2,ρj,3Step size factor p while self-aligning1,1,ρ1,2,ρ1,3A change curve;
FIG. 8 shows a penalty factor λ for a two-input two-output MIMO systemjAnd step size factor ρj,1,ρj,2,ρj,3Step size factor p while self-aligning2,1,ρ2,2,ρ2,3A change curve;
FIG. 9 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pj,1,ρj,2,ρj,3Self-timing the control effect graph of the 1 st SISO system;
FIG. 10 is a diagram of a two input two output MIMO system at penaltyPenalty factor lambdajFixed step factor pj,1,ρj,2,ρj,3A control effect graph of the 2 nd SISO system during self-setting;
FIG. 11 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pj,1,ρj,2,ρj,3A self-timed control input map;
FIG. 12 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pj,1,ρj,2,ρj,3Step factor p at self-alignment1,1,ρ1,2,ρ1,3A change curve;
FIG. 13 shows a penalty factor λ for a two-input two-output MIMO systemjFixed step factor pj,1,ρj,2,ρj,3Step factor p at self-alignment2,1,ρ2,2,ρ2,3A change curve;
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 partial-format model-free controllers.
Determining a control input linearization length constant L of the jth (1 ≦ j ≦ m) SISO partial format modeless controllerj，LjIs an integer greater than 1; the jth SISO partial-format modeless controller parameter contains a penalty factor lambdajAnd step size factor
Figure BDA0001480215010000081
Determining a parameter to be set of a jth SISO partial-format modeless controller, wherein the jth SISO partial-format modeless controller is used for setting the parameter to be setThe number is part or all of the jth SISO partial-format modeless controller parameter and comprises a penalty factor lambdajAnd step size factor
Figure BDA0001480215010000082
Any one or any combination of the above; in FIG. 1, the parameter to be set of the jth SISO partial format model-less controller is a penalty factor λjAnd step size factor
Figure BDA0001480215010000083
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 partial-format modeless controller; and initializing the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network. The work described in this paragraph is repeated for the other m-1 SISO partial format modeless controllers.
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 partial 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 BDA0001480215010000093
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 BDA0001480215010000091
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 partial-form modeless controller; then, based on the jth SISO systematic error ej(k) Jth SISO partial format model-free controlThe value of the parameter to be set of the controller is calculated by adopting the control algorithm of the SISO biased format model-free controller to obtain the control input u of the jth SISO biased format model-free controller at the moment k for the controlled objectj(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 bias 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 biased 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 BDA0001480215010000092
The method comprises the steps of minimizing the value of the absolute value. The work described in this paragraph is repeatedly performed for other m-1 SISO partial 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 model control method 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 a decoupling control process of the MIMO based on the SISO bias format model-free controller and system errors 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 can adopt a structure that the hidden layer is a single layer, and can also adopt the hidden layer as a single layerA multi-layer structure. 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 is L in fig. 2)j+ 1). 3 nodes of the input layer, and the jth SISO systematic error ej(k) Accumulation of the jth SISO systematic error
Figure BDA0001480215010000101
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 j SISO bias format model-free controllerjAnd step size factor
Figure BDA0001480215010000102
Respectively correspond to each other. The update process of the hidden layer weight coefficient and the output layer weight coefficient of the jth BP neural network specifically comprises the following steps: 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 BDA0001480215010000103
The method comprises the steps of minimizing the value of the absolute value.
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 BDA0001480215010000104
Figure BDA0001480215010000111
Figure BDA0001480215010000112
Figure BDA0001480215010000113
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 BDA0001480215010000114
Figure BDA0001480215010000115
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)。
The 2 SISO systems are controlled by 2 SISO partial format model-free controllers. Control input linearization Length constant L for SISO biased Format modeless controllerjThe value of (2) is usually set in accordance with the complexity of the controlled object and the actual control effect, and is usually between 1 and 10, and too small will affect the control effect, and too large will result in a large amount of calculation, so 3 or 5 is usually adopted. In this particular embodiment, the control inputs of the 2 SISO partial-format modeless controllers linearize the length constant LjAre all taken to be 3, i.e. L1＝L2＝3。
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.
During the first group of test verification, the number of output layer nodes of the BP neural network in FIG. 2 is 4, and the penalty factor lambda of the 2 SISO partial-format model-free controllersjAnd step size factor ρj,1,ρj,2,ρj,3Performing 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 ρ1,1,ρ1,2,ρ1,3The variation curve, FIG. 8, is the step factor ρ2,1,ρ2,2,ρ2,3A curve of variation. The result shows that the method designs 2 SISO partial format model-free controllers and combines the penalty factor lambda of the BP neural network to each SISO partial format model-free controllerjAnd step size factor ρj,1,ρj,2,ρj,3And 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.
When the second group of experiments verify that the number of output layer nodes of the BP neural network in FIG. 2 is 3, firstly, 2 penalty factors lambda are addedjRespectively 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 partial format modeless controllersj,1,ρj,2,ρj,3Performing self-tuning, wherein FIG. 9 is a control effect graph of the 1 st SISO system, FIG. 10 is a control effect graph of the 2 nd SISO system, FIG. 11 is a control input graph, and FIG. 12 is a step factor ρ1,1,ρ1,2,ρ1,3The variation curve, FIG. 13, is the step factor ρ2,1,ρ2,2,ρ2,3A curve of variation. The results show that the inventionIn a penalty factor lambdajWhen in fixation, 2 SISO partial format model-free controllers are designed and combined with the step length factor rho of each SISO partial format model-free controller of the BP neural networkj,1,ρj,2,ρj,3The 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 BDA0001480215010000121
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 BDA0001480215010000122
Figure BDA0001480215010000123
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 BDA0001480215010000124
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 BDA0001480215010000125
The jth SISO system error calculation function may also use other calculation methods where the arguments include a jth SISO system output expected value and a jth SISO system output actual value, such as, for example,
Figure BDA0001480215010000131
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 BP neural network is defined as the jth (1. ltoreq. j. ltoreq.m)The input j-th SISO system error and the function set thereof select the j-th SISO system error ej(k) Accumulation of jth SISO systematic errors
Figure BDA0001480215010000132
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 BDA0001480215010000133
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 BDA0001480215010000134
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.
It should be more particularly noted that, in the above-described specific embodiment, when the implicit layer weight coefficients and the output layer weight coefficients of the jth 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 comprehensively considering the contribution of all m SISO systematic errorsFunction(s)
Figure BDA0001480215010000135
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 BDA0001480215010000141
Or
Figure BDA0001480215010000142
That is to say by using
Figure BDA0001480215010000143
Another functional form of (1); as another example, the systematic error function employs
Figure BDA0001480215010000144
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 BDA0001480215010000145
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 BDA0001480215010000146
Are made a contribution to
Figure BDA0001480215010000147
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. Controlled for the above-described embodimentsFor an object, the different system error functions can achieve good control effect; considering only the systematic error function
Figure BDA0001480215010000148
Compared with the control effect during contribution, the system error function is considered simultaneously
Figure BDA0001480215010000149
Are made a contribution to
Figure BDA00014802150100001410
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 biased format modeless controller to finish the execution from the step (4-1) to the step (4-5) and then starting to execute another SISO biased 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 biased format modeless controllers to complete the steps from all the steps (4-1) to (4-5), and then starting to execute other SISO biased format modeless controllers from the steps (4-1) to (4-5); it is also possible to use the method in which all m SISO partial 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 ≦ j ≦ m) SISO partial format modeless controller contains a penalty factor λjAnd step size factor
Figure BDA00014802150100001411
Any 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 ρj,1,ρj,2,ρj,3Realizes the simultaneous self-tuning and the punishment factor lambda in the second group of test verificationjFixed step factor pj,1,ρj,2,ρj,3Self-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 ρj,1,ρj,2Fixed and penalty factor lambdajAnd step size factor ρj,3Self-tuning is realized; in addition, the SISO partial-format modeless controller has to set parameters including, but not limited to, a penalty factor λjAnd step size factor
Figure BDA0001480215010000151
For example, pseudo-gradient estimation values may also be included, as the case may be
Figure BDA0001480215010000152
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 bias 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 partial-format model-free controllers;
    step (2): for the jth SISO partial format modeless controller, where j is greater than or equal to 1 and less than or equal to mDetermining the control input linearization length constant Lj，LjIs an integer greater than 1; the jth SISO partial-format modeless controller parameter comprises a penalty factor lambdajAnd step size factor
    Figure FDA0002552731900000011
    Determining the parameter to be set of the jth SISO partial lattice type modeless controller, wherein the parameter to be set of the jth SISO partial lattice type modeless controller is part or all of the parameter of the jth SISO partial lattice type modeless controller and contains a penalty factor lambdajAnd step size factor
    Figure FDA0002552731900000012
    Any 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 partial-format modeless 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 partial 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 partial format model-free controller, wherein j is more than or equal to 1 and less than or equal to m, the method comprises the following 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) (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 partial-format modeless controller;
    the step (4-4) is as follows: based on the system error e of the jth SISO system obtained in the step (4-3) at the moment kj(k) And (4-3) calculating the value of the parameter to be set of the jth SISO partial-format modeless controller obtained in the step (4-3) by adopting the control algorithm of the SISO partial-format modeless controller to obtain the control input u of the jth SISO partial-format modeless controller at the time 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 partial 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 partial-format modeless controller contains a penalty factor lambdajWhile, the control input uj(k) For the penalty factor lambdajThe gradient information at time k is:
    Figure FDA0002552731900000021
    when the parameter to be set of the jth SISO partial-format modeless controller contains a step factor rhoj,1While, the control input uj(k) For the step size factor pj,1The gradient information at time k is:
    Figure FDA0002552731900000031
    when the parameter to be set of the jth SISO partial format model-free controller comprisesStep factor ρj,iAnd when i is more than or equal to 2 and less than or equal to L, the control input uj(k) For the step size factor pj,iThe gradient information at time k is:
    Figure FDA0002552731900000032
    wherein, Δ uj(k)＝uj(k)-uj(k-1)，
    Figure FDA0002552731900000033
    For the pseudo gradient estimate at time k for the jth SISO partial-format modeless controller,
    Figure FDA0002552731900000034
    is composed of
    Figure FDA0002552731900000035
    Wherein i ═ 1, …, Lj)；
    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 partial format model-free controller in the m SISO partial 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 partial 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 } comprises the set of all { { gradient information 1}, …, { gradient information m }, and then step (5) is entered;
    and (5): aiming at the jth SISO partial-format modeless 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 partial-format modeless controller and other m-1 SISO partial-format modeless 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 partial 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 model-less controller and the systematic error is performed by using the jth SISO systematic error calculation function
    Figure FDA0002552731900000041
    Wherein
    Figure FDA0002552731900000042
    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 FDA0002552731900000043
    Wherein
    Figure FDA0002552731900000044
    Is k +1Output expectation value, y, of the jth SISO systemj(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 FDA0002552731900000045
    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 FDA0002552731900000046
    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 *
郭代银;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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