CN108073072B - Parameter self-tuning method of SISO (Single input Single output) compact-format model-free controller based on partial derivative information - Google Patents

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

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CN108073072B
CN108073072B CN201711081072.3A CN201711081072A CN108073072B CN 108073072 B CN108073072 B CN 108073072B CN 201711081072 A CN201711081072 A CN 201711081072A CN 108073072 B CN108073072 B CN 108073072B
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卢建刚
李雪园
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Zhejiang University ZJU
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Abstract

The invention discloses a parameter self-tuning method of a SISO (Single input Single output) compact-format model-free controller based on partial derivative information, which comprises the steps of utilizing the partial derivative information as input of a BP (back propagation) neural network, carrying out forward calculation on the BP neural network, outputting parameters to be tuned of controllers such as penalty factors and step length factors through an output layer, adopting a control algorithm of the controllers to calculate control input aiming at a controlled object, calculating gradient information of the control input respectively aiming at each parameter to be tuned, minimizing a value of a system error function as a target, adopting a gradient descent method, combining the gradient information to carry out system error back propagation calculation, updating a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network in real time on line, storing the gradient information as partial derivative information and using the gradient information as input of the BP neural network at the later moment. The parameter self-tuning method of the SISO compact-format model-free controller based on the partial derivative information can effectively overcome the difficult problem of tuning of the controller parameters and realize good control effect.

Description

Parameter self-tuning method of SISO (Single input Single output) compact-format model-free controller based on partial derivative information
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of a SISO (SISO) compact-format model-free controller based on partial derivative information.
Background
The model-free controller is a novel data-driven control method, does not depend on any mathematical model information of a controlled object, only depends on input and output data measured by the 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 system, and has a good application prospect.
There are various implementation methods for the modeless controller, wherein a SISO (Single Input and Single Output) compact-format modeless controller is one of the main implementation methods for the modeless controller. 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 BDA0001458129520000011
wherein u (k) is the control input at time k; e (k) is the system error at time k;
Figure BDA0001458129520000012
is a pseudo gradient estimation value at the k moment; λ is a penalty factor; ρ is the step factor.
At present, the numerical values of parameters such as a penalty factor lambda, a step factor rho and the like are required to be set in advance by an SISO (SISO) compact-format model-free controller before actual application, and online self-tuning of the parameters such as the penalty factor lambda, the step factor rho and the like is not 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.
Therefore, in order to break the bottleneck of restricting the popularization and application of the SISO compact format model-free controller, the invention provides a parameter self-tuning method of the SISO compact format model-free controller based on partial derivative information.
Disclosure of Invention
In order to solve the problems in the background art, the invention aims to provide a parameter self-tuning method of a SISO (SISO) compact format model-free controller based on partial derivative information.
To this end, the above object of the present invention is achieved by the following technical solution, comprising the steps of:
step (1): parameters of the SISO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a SISO (system-in-process) compact-format model-free controller, wherein the parameters to be set of the SISO compact-format model-free controller are part or all of the parameters of the SISO compact-format model-free controller and comprise any one or any combination of a punishment factor lambda and a step factor rho; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;
step (2): initializing partial derivative information of the previous moment as the input of a BP neural network;
and (3): recording the current moment as k moment, and calculating by adopting a system error calculation function to obtain a system error of the k moment based on a system output expected value and a system output actual value, and recording as e (k);
and (4): based on the input of the BP neural network, the BP neural network carries out forward calculation, and the calculation result is output through an output layer to obtain the value of the parameter to be set of the SISO compact-format model-free controller;
and (5): calculating to obtain a control input u (k) of the SISO compact format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO compact format model-free controller based on the system error e (k) obtained in the step (3) and the value of the parameter to be set of the SISO compact format model-free controller obtained in the step (4);
and (6): based on the control input u (k) obtained in the step (5), calculating gradient information of the control input u (k) at the moment k for parameters to be set of each SISO compact-format model-free controller, wherein the specific calculation formula is as follows:
when the parameters to be set of the SISO compact-format model-free controller contain a penalty factor lambda, the control input u (k) is the following gradient information at the moment k for the penalty factor lambda:
Figure BDA0001458129520000031
when the parameter to be set of the SISO compact-format model-free controller contains a step factor rho, the control input u (k) is that the gradient information of the step factor rho at the k moment is:
Figure BDA0001458129520000032
wherein the content of the first and second substances,
Figure BDA0001458129520000033
is a pseudo gradient estimation value at the k moment;
and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the gradient information obtained in the step (6) is combined, the system error back propagation calculation is carried out, and the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated to be used as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network carries out forward calculation at the later moment;
and (8): and (3) recording the gradient information of the parameters to be set of each SISO compact-format model-free controller at the time k, which is obtained by calculation in the step (6), of the control input u (k) as the partial derivative information of the previous time in sequence, namely: when the parameters to be set of the SISO compact-format model-free controller contain a penalty factor lambda, one of the gradient information at the k moment
Figure BDA0001458129520000034
One of the partial derivatives recorded as the previous time
Figure BDA0001458129520000035
When the parameters to be set of the SISO compact-format model-free controller contain the step factor rho, one of the gradient information at the k moment
Figure BDA0001458129520000036
One of the partial derivatives recorded as the previous time
Figure BDA0001458129520000037
The partial derivative information of the previous moment is used as the input of the BP neural network when the BP neural network carries out forward calculation at the next moment;
and (9): and (e) after the control input u (k) acts on the controlled object, obtaining a system output actual value of the controlled object at the later moment, returning to the step (3), and repeating the steps (3) to (9).
While adopting the above technical scheme, the present invention can also adopt or combine the following further technical schemes:
the independent variables of the system error calculation function in the step (3) comprise a system output expected value and a system output actual value.
The systematic error calculation function in the step (3) adopts e (k) y*(k) -y (k), wherein y*(k) The system output expected value is set for the time k, and y (k) is the system output actual value obtained by sampling at the time k; or using e (k) ═ y*(k +1) -y (k), wherein y*And (k +1) is a system output expected value at the moment of k +1, and y (k) is a system output actual value obtained by sampling at the moment of k.
The independent variable of the system error function in the step (7) comprises any one or any combination of a system error, a system output expected value and a system output actual value.
The system error function in the step (7) is e2(k)+ωΔu2(k) Where e (k) is a systematic error, Δ u (k) -u (k-1), and ω is a constant equal to or greater than 0.
The parameter self-tuning method of the SISO compact-format model-free controller based on the partial derivative information can achieve good control effect and effectively overcome the problem that a penalty factor lambda and a step factor rho need to be time-consuming and labor-consuming to perform tuning.
Drawings
FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic diagram of a BP neural network structure employed in the present invention;
FIG. 3 is a diagram illustrating the effect of the control of the simultaneous self-timing of the penalty factor λ and the step factor ρ;
FIG. 4 is a control input diagram for the simultaneous self-timing of penalty factor λ and step-size factor ρ;
FIG. 5 is a plot of the change in penalty factor λ when the penalty factor λ and the step size factor ρ are self-aligned simultaneously;
FIG. 6 is a plot of the change in the step size factor ρ for a simultaneous self-alignment of the penalty factor λ and the step size factor ρ;
FIG. 7 is a graph of the control effect when the penalty factor λ is fixed and the step factor ρ is self-timed;
FIG. 8 is a control input plot with a penalty factor λ fixed and a step factor ρ self-timed;
FIG. 9 is a plot of the change in the step size factor ρ with the penalty factor λ fixed and the step size factor ρ self-aligned.
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. Parameters of the SISO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a SISO (system-in-process) compact-format model-free controller, wherein the parameters to be set of the SISO compact-format model-free controller are part or all of the parameters of the SISO compact-format model-free controller and comprise any one or any combination of a punishment factor lambda and a step factor rho; in fig. 1, the parameters to be set by the SISO compact-format model-less controller are penalty factor λ and step factor ρ; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; the current time is recorded as the time k, firstly, the system output actual value y (k) is obtained through sampling, and the system output expected value y*(k) Taking the difference with the system output actual value y (k) as the system error e (k) at the time k, and then taking the partial derivative information at the previous time as the input of the BP neural network; the BP neural network carries out forward calculation, and the calculation result is output through an output layer to obtain the value of the parameter to be set of the SISO compact-format model-free controller; then, based on the value of the system error e (k) and the value of the parameter to be set, calculating to obtain the control input u (k) of the SISO compact format model-free controller aiming at the controlled object at the time k by adopting the control algorithm of the SISO compact format model-free controller; then calculating to obtain gradient information of control input u (k) at the time k aiming at each parameter to be set; combining the gradient information, targeting a value minimization of the systematic error function, denoted e in fig. 12(k) Minimizing as a target, updating the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network,the weight coefficients are used as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network carries out forward calculation at the later moment; information of gradient
Figure BDA0001458129520000051
Partial derivative information recorded as previous time in sequence
Figure BDA0001458129520000052
The partial derivative information of the previous moment is used as the input of the BP neural network when the BP neural network carries out forward calculation at the next moment; and (c) after the control input u (k) acts on the controlled object, obtaining a system output actual value of the controlled object at the next moment, repeating the process, and performing a parameter self-tuning process of the SISO compact format model-free controller at the next moment based on the partial derivative information.
Fig. 2 shows a schematic structural diagram of the BP neural network adopted in the present invention. The BP neural network may have a structure in which the hidden layer is a single layer, or may have a structure in which the hidden layer is a plurality of layers. In the schematic diagram of fig. 2, for the sake of simplicity, the BP neural network adopts a structure in which the hidden layer is a single layer, that is, a three-layer network structure composed of an input layer, a single-layer hidden layer, and an output layer, the number of nodes of the input layer is set as the number of parameters to be set (in fig. 2, the number of parameters to be set is 2), the number of nodes of the hidden layer is 6, and the number of nodes of the output layer is set as the number of parameters to be set (in fig. 2, the number of parameters to be set is 2). 2 nodes of the input layer, and partial derivative information
Figure BDA0001458129520000061
Respectively correspond to each other. The 2 nodes of the output layer correspond to the penalty factor λ and the step factor ρ, respectively. The update process of the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network specifically comprises the following steps: targeting the minimization of the value of the systematic error function, denoted by e in FIG. 22(k) And (3) minimizing to a target, and performing system error back propagation calculation by combining a gradient descent method and control input u (k) according to the gradient information of the penalty factor lambda and the step factor rho at the k moment, so as to update the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network.
The following is a specific embodiment of the present invention.
The controlled object is a typical nonlinear system:
Figure BDA0001458129520000062
desired value y of system output*(k) The following were used:
y*(k)＝5sin((k-1)π/50)+2cos((k-1)π/20)
in this particular example, a total of two sets of experimental verifications were performed.
During the first group of experimental verification, the number of input layer nodes and the number of output layer nodes of the BP neural network in fig. 2 are preset to be 2, the penalty factor λ and the step factor ρ are self-tuned simultaneously, and a control effect graph, a control input graph, a change curve of the penalty factor λ and a change curve of the step factor ρ are respectively shown in fig. 3, fig. 4, fig. 5 and fig. 6. The result shows that the method can realize good control effect by self-setting the penalty factor lambda and the step factor rho at the same time, and can effectively overcome the problem that the penalty factor lambda and the step factor rho need to be time-consuming and labor-consuming to set.
During the second group of test verification, firstly, the penalty factor lambda is fixedly valued as the average value of the penalty factor lambda during the first group of test verification, the number of input layer nodes and the number of output layer nodes of the BP neural network in the graph 2 are preset to be 1, then the step factor rho is self-adjusted, and a control effect graph, a control input graph and a step factor rho change curve are respectively shown in the graphs 7, 8 and 9. The result also shows that the method can realize good control effect by self-tuning the step factor rho when the penalty factor lambda is fixed, and can effectively overcome the problem that the step factor rho needs to be time-consuming and labor-consuming to be tuned.
It should be noted that in the above-described embodiment, the system is output with the desired value y*(k) The difference with the actual system output value y (k) is used as the system error e (k), i.e. e (k) y*(k) -y (k), only one method of calculating a function for the systematic error; the expected value y of the system output at the moment k +1 can also be used*The difference between (k +1) and the actual system output value y (k) at time k is taken as the system error e (k), i.e. e (k) y*(k +1) -y (k); the system error calculation function may also employ other calculation methods where the independent variables include a desired system output value and an actual system output value, for example,
Figure BDA0001458129520000071
Figure BDA0001458129520000072
for the controlled object of the above embodiment, good control effects can be achieved by using the different system error calculation functions.
It should be noted that, in the above specific embodiment, the input of the BP neural network includes the partial derivative information at the previous time, but is not limited to the partial derivative information at the previous time, and for example, according to the specific situation, the input may also include information such as a desired value of system output, an actual value of system output, and the like.
More particularly, in the above embodiment, when the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated with the goal of minimizing the value of the systematic error function, the systematic error function adopts e2(k) Only one of said systematic error functions; the system error function may also be other functions with independent variables including any one or any combination of system error, system output expected value and system output actual value, for example, the system error function may be (y)*(k)-y(k))2Or (y)*(k+1)-y(k))2I.e. using e2(k) Another functional form of (1); as another example, the systematic error function takes e2(k)+ωΔu2(k) Wherein Δ u (k) -u (k-1), ω is a constant greater than or equal to 0; it is clear that the systematic error function only considers e when ω equals 02(k) The contribution of (1) shows that the aim of minimization is to minimize the system error, namely pursuing high precision; and when omega is greater than 0, the system error function considers e simultaneously2(k) Sum of contribution of (1) and Δ u2(k) Tribute (a Chinese character)This document shows that the aim of minimization is to achieve a low variation of the control input, i.e. both high precision and stable handling, while at the same time achieving a low system error. For the controlled object of the above embodiment, good control effect can be achieved by adopting the different system error functions; considering only e with the systematic error function2(k) Control effects in contribution to the system error function while considering e2(k) Sum of contribution of (1) and Δ u2(k) The contribution of (1) is that the control precision is slightly reduced and the operation stability is improved.
Finally, it should be particularly pointed out that the parameters to be set by the SISO compact-format model-free controller include any one or any combination of a penalty factor λ and a step factor ρ; in the above specific embodiment, the penalty factor λ and the step factor ρ realize simultaneous self-tuning during the first set of test verification, and the penalty factor λ is fixed and the step factor ρ realizes self-tuning during the second set of test verification; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor rho is fixed, and the penalty factor lambda realizes self-setting; in addition, the parameters to be set by the SISO compact-format modeless controller include, but are not limited to, a penalty factor λ and a step factor ρ, and may further include, for example, a pseudo-gradient estimation value according to the specific situation
Figure BDA0001458129520000081
And the like.
The above-described embodiments are intended to illustrate the present invention, but not to limit the present invention, and any modifications, equivalents, improvements, etc. made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.

Claims (3)

  1. A parameter self-tuning method of a SISO compact format model-free controller based on partial derivative information is characterized by comprising the following steps:
    step (1): parameters of the SISO compact format model-free controller comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a SISO (system-in-process) compact-format model-free controller, wherein the parameters to be set of the SISO compact-format model-free controller are part or all of the parameters of the SISO compact-format model-free controller and comprise any one or any combination of a punishment factor lambda and a step factor rho; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;
    step (2): initializing partial derivative information of the previous moment as the input of a BP neural network;
    and (3): recording the current moment as k moment, and calculating by adopting a system error calculation function to obtain a system error of the k moment based on a system output expected value and a system output actual value, and recording as e (k); the independent variables of the system error calculation function comprise a system output expected value and a system output actual value;
    and (4): based on the input of the BP neural network, the BP neural network carries out forward calculation, and the calculation result is output through an output layer to obtain the value of the parameter to be set of the SISO compact-format model-free controller;
    and (5): calculating to obtain a control input u (k) of the SISO compact format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO compact format model-free controller based on the system error e (k) obtained in the step (3) and the value of the parameter to be set of the SISO compact format model-free controller obtained in the step (4);
    and (6): based on the control input u (k) obtained in the step (5), calculating gradient information of the control input u (k) at the moment k for parameters to be set of each SISO compact-format model-free controller, wherein the specific calculation formula is as follows:
    when the parameters to be set of the SISO compact-format model-free controller contain a penalty factor lambda, the control input u (k) is the following gradient information at the moment k for the penalty factor lambda:
    Figure FDA0002197391480000021
    when the parameter to be set of the SISO compact-format model-free controller contains a step factor rho, the control input u (k) is that the gradient information of the step factor rho at the k moment is:
    Figure FDA0002197391480000022
    wherein the content of the first and second substances,
    Figure FDA0002197391480000023
    is a pseudo gradient estimation value at the k moment;
    and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the gradient information obtained in the step (6) is combined, the system error back propagation calculation is carried out, and the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated to be used as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network carries out forward calculation at the later moment; the independent variable of the system error function comprises any one or any combination of a system error, a system output expected value and a system output actual value;
    and (8): and (3) recording the gradient information of the parameters to be set of each SISO compact-format model-free controller at the time k, which is obtained by calculation in the step (6), of the control input u (k) as the partial derivative information of the previous time in sequence, namely: when the parameters to be set of the SISO compact-format model-free controller contain a penalty factor lambda, one of the gradient information at the k moment
    Figure FDA0002197391480000024
    One of the partial derivatives recorded as the previous time
    Figure FDA0002197391480000025
    When the parameters to be set of the SISO compact-format model-free controller contain the step factor rho, one of the gradient information at the k moment
    Figure FDA0002197391480000026
    One of the partial derivatives recorded as the previous time
    Figure FDA0002197391480000027
    The partial derivative information of the previous moment is used as the input of the BP neural network when the BP neural network carries out forward calculation at the next moment;
    and (9): and (e) after the control input u (k) acts on the controlled object, obtaining a system output actual value of the controlled object at the later moment, returning to the step (3), and repeating the steps (3) to (9).
  2. 2. The SISO tight format model-less controller parameter self-tuning method of claim 1, wherein the systematic error calculation function in step (3) adopts e (k) -y*(k) -y (k), wherein y*(k) The system output expected value is set for the time k, and y (k) is the system output actual value obtained by sampling at the time k; or using e (k) ═ y*(k +1) -y (k), wherein y*And (k +1) is a system output expected value at the moment of k +1, and y (k) is a system output actual value obtained by sampling at the moment of k.
  3. 3. The SISO compact format model-less controller partial derivative information based parameter self-tuning method of claim 1, wherein the systematic error function in the step (7) is e2(k)+ωΔu2(k) Where e (k) is a systematic error, Δ u (k) -u (k-1), and ω is a constant equal to or greater than 0.
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