CN107942654B - Parameter self-tuning method of SISO offset format model-free controller based on offset information - Google Patents

Parameter self-tuning method of SISO offset format model-free controller based on offset information Download PDF

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CN107942654B
CN107942654B CN201711081060.0A CN201711081060A CN107942654B CN 107942654 B CN107942654 B CN 107942654B CN 201711081060 A CN201711081060 A CN 201711081060A CN 107942654 B CN107942654 B CN 107942654B
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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) bias format model-free controller based on bias information, which comprises the steps of utilizing the bias 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, adopting a gradient descent method with the value of a system error function minimized as a target, 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 an online real-time manner, storing the gradient information as the bias information and taking the bias information as input of the BP neural network at the later moment. The parameter self-tuning method of the SISO partial-format model-free controller based on partial derivative information can effectively overcome the difficult problem of tuning of the controller parameters and achieve good control effect.

Description

Parameter self-tuning method of SISO offset format model-free controller based on offset information
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of a SISO partial mode type 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 the SISO (Single Input and Single Output) biased format modeless controller is one of the main implementation methods for the modeless controller. 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 BDA0001458136740000011
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 BDA0001458136740000012
is a pseudo-gradient estimate for time k,
Figure BDA0001458136740000013
is composed of
Figure BDA0001458136740000014
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.
At present, the SISO partial format model-free controller needs to rely on empirical knowledge to set a penalty factor lambda and a step factor rho in advance before actual use1,…,ρLThe values of the isoparametric parameters have not realized a penalty factor lambda and a step factor rho in the actual application process1,…,ρLAnd (4) performing online self-tuning on the equal parameters. The lack of effective parameter setting means not only makes the 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.
Therefore, in order to break the bottleneck of restricting the popularization and application of the SISO partial format model-free controller, the invention provides a parameter self-tuning method of the SISO partial 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 partial 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): determining a control input linearization length constant L of the SISO partial-format model-free controller, wherein L is an integer greater than 1; SISO partial format model-less controller parameters include penalty factor lambda and step factor rho1,…,ρL(ii) a Determining parameters to be set of a SISO partial-format model-free controller, wherein the parameters to be set of the SISO partial-format model-free controller are part or all of the parameters of the SISO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLAny one or any combination of the above; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO partial 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 partial-format modeless controller;
and (5): calculating to obtain a control input u (k) of the SISO partial format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO partial 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 partial 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 partial-format modeless controller, wherein the specific calculation formula is as follows:
when the parameters to be set of the SISO bias format model-free controller comprise a penalty factor lambda, the control input u (k) is the following gradient information at the moment k for the penalty factor lambda:
Figure BDA0001458136740000031
when the parameters to be set of the SISO partial format model-free controller contain step length factors rho1The control input u (k) is for the step-size factor p1The gradient information at time k is:
Figure BDA0001458136740000032
when the parameters to be set of the SISO partial format model-free controller contain step length factors rhoiAnd 2 ≦ i ≦ L, the control input u (k) for the step size factor ρiThe gradient information at time k is:
Figure BDA0001458136740000033
wherein Δ u (k) u (k-1),
Figure BDA0001458136740000034
is a pseudo-gradient estimate for time k,
Figure BDA0001458136740000035
is composed of
Figure BDA0001458136740000036
The ith component of (i ═ 1, …, L);
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): aiming at the control input u (k) calculated in the step (6) respectivelyGradient information of a parameter to be set of the SISO offset format model-free controller at the moment k is sequentially recorded as offset information of the previous moment, namely: when the parameters to be set of the SISO bias format model-free controller contain a penalty factor lambda, one of the gradient information at the k moment
Figure BDA0001458136740000037
One of the partial derivatives recorded as the previous time
Figure BDA0001458136740000038
When the parameters to be set of the SISO partial format model-free controller contain step length factors rhoiAnd when i is more than or equal to 1 and less than or equal to L, one of gradient information at the k moment
Figure BDA0001458136740000041
One of the partial derivatives recorded as the previous time
Figure BDA0001458136740000042
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 partial-format model-free controller based on partial derivative information can realize good control effect and effectively overcome penalty factor lambda and step factor rho1,…,ρLThe difficult problem of setting needs time and labor waste.
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FIG. 1 is a functional block diagram of the present invention;
FIG. 2 is a schematic diagram of a BP neural network structure employed in the present invention;
FIG. 3 shows penalty factor λ and step size factor ρ1,ρ2,ρ3Meanwhile, self-setting a timing control effect graph;
FIG. 4 shows penalty factor λ and step size factor ρ1,ρ2,ρ3Simultaneously self-timing control input diagram;
FIG. 5 shows penalty factor λ and step size factor ρ1,ρ2,ρ3Meanwhile, self-adjusting a punishment factor lambda change curve;
FIG. 6 shows penalty factor λ and step size factor ρ1,ρ2,ρ3Step size factor p while self-aligning1,ρ2,ρ3A change curve;
FIG. 7 shows a penalty factor λ fixed and a step size factor ρ1,ρ2,ρ3A self-timing control effect graph;
FIG. 8 shows a penalty factor λ fixed and a step size factor ρ1,ρ2,ρ3A self-timed control input map;
FIG. 9 shows a penalty factor λ fixed and a step size factor ρ1,ρ2,ρ3Step factor p at self-alignment1,ρ2,ρ3A curve of variation.
Detailed Description
The invention is further described with reference to the following figures and specific examples.
Fig. 1 shows a schematic block diagram of the present invention. Determining a control input linearization length constant L of the SISO partial-format model-free controller, wherein L is an integer greater than 1; SISO partial format model-less controller parameters include penalty factor lambda and step factor rho1,…,ρL(ii) a Determining parameters to be set of a SISO partial-format model-free controller, wherein the parameters to be set of the SISO partial-format model-free controller are part or all of the parameters of the SISO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLAny one or any combination of the above; in FIG. 1, the parameters to be set by the SISO partial-format model-less controller are penalty factor λ and step factor ρ1,…,ρL(ii) a Determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO partial 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 a calculation result is output through an output layer to obtain a value of a parameter to be set of the SISO partial-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 biased format model-free controller aiming at the controlled object at the time k by adopting the control algorithm of the SISO biased 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 target, updating hidden layer weight coefficient and output layer weight coefficient of BP neural network, and using as BP neural network at later timeHidden layer weight coefficient and output layer weight coefficient in forward calculation; information of gradient
Figure BDA0001458136740000061
Partial derivative information recorded as previous time in sequence
Figure BDA0001458136740000062
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 partial format model-free controller at the next moment based on 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 L +1), 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 L + 1). Node of input layer, and partial derivative information
Figure BDA0001458136740000063
Respectively correspond to each other. Node of output layer, penalty factor lambda and step factor rho1,…,ρLRespectively correspond to each other. The update process of the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network specifically comprises the following steps: targeting the minimization of the value of the systematic error function, denoted by e in FIG. 22(k) Minimizing to obtain target, gradient descent method combined with control input u (k) for penalty factor lambda and step size factor rho1,…,ρLAnd (4) carrying out system error back propagation calculation on the gradient information at the moment k, 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 BDA0001458136740000071
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 embodiment, the control input linearization length constant L for the SISO partial mode-less controller is preset to 3.
In this particular example, a total of two sets of experimental verifications were performed.
When the first group of tests verifies, the number of nodes of the input layer and the number of nodes of the output layer of the BP neural network in the graph 2 are preset to be 4, and a penalty factor lambda and a step factor rho are set1,ρ2,ρ3Performing simultaneous self-tuning, controlling effect diagram, controlling input diagram, punishment factor lambda change curve and step factor rho1,ρ2,ρ3The variation curves are shown in fig. 3, 4, 5 and 6, respectively. The result shows that the method of the invention carries out the punishment factor lambda and the step factor rho1,ρ2,ρ3The method has the advantages of realizing good control effect by carrying out self-tuning at the same time, and effectively overcoming the penalty factor lambda and the step factor rho1,ρ2,ρ3The difficult problem of setting needs time and labor waste.
When the second group of tests are verified, the penalty factor lambda is firstly fixed to be the average value of the penalty factor lambda when the first group of tests are verified, the number of nodes of an input layer and the number of nodes of an output layer of the BP neural network in the graph 2 are preset to be 3, and then the step factor rho is subjected to1,ρ2,ρ3Self-tuning, control effect diagram, control input diagram, step factor rho1,ρ2,ρ3The change curves are shown in fig. 7, 8, and 9, respectively. The results also show that the method of the invention is implemented by applying the step factor rho when the penalty factor lambda is fixed1,ρ2,ρ3To carry outSelf-tuning, good control effect can be realized, and the step factor rho can be effectively overcome1,ρ2,ρ3The difficult problem of setting needs time and labor waste.
It should be noted that in the above-described embodiment, the 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 BDA0001458136740000081
-y (k); 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, a system errorDifference function employing 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) The contribution of (1) indicates that the goal of minimization is to pursue small system errors and small control input variation, namely to pursue both high precision and stable steering. For the controlled object of the above embodiment, good control effect can be achieved by adopting the different system error functions; considering only 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 noted that the parameters to be set by the SISO partial-format modeless controller include a penalty factor λ and a step factor ρ1,…,ρLAny one or any combination of the above; in the above specific embodiment, the first set of trial validations is performed with a penalty factor λ and a step-size factor ρ1,ρ2,ρ3Realizes the simultaneous self-tuning, the punishment factor lambda is fixed and the step factor rho is adopted during the verification of the second group of tests1,ρ2,ρ3Self-tuning is realized; in practical application, any combination of parameters to be set can be selected according to specific conditions, for example, the step factor ρ1,ρ2Fixed penalty factor lambda, step factor rho3Self-tuning is realized; in addition, the parameters to be set by the SISO partial-format modeless controller include, but are not limited to, a penalty factor λ and a step factor ρ1,…,ρLFor example, the pseudo gradient estimation value can be included according to the specific situation
Figure BDA0001458136740000091
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 partial format model-free controller based on partial derivative information is characterized by comprising the following steps:
    step (1): determining a control input linearization length constant L of the SISO partial-format model-free controller, wherein L is an integer greater than 1; SISO partial format model-less controller parameters include penalty factor lambda and step factor rho1,…,ρL(ii) a Determining parameters to be set of a SISO partial-format model-free controller, wherein the parameters to be set of the SISO partial-format model-free controller are part or all of the parameters of the SISO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLAny one or any combination of the above; determining the number of input layer nodes, the number of hidden layer nodes and the number of output layer nodes of the BP neural network, wherein the number of the output layer nodes is not less than the number of parameters to be set of the SISO partial 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 partial-format modeless controller;
    and (5): calculating to obtain a control input u (k) of the SISO partial format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO partial 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 partial 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 partial-format modeless controller, wherein the specific calculation formula is as follows:
    when the parameters to be set of the SISO bias format model-free controller comprise a penalty factor lambda, the control input u (k) is the following gradient information at the moment k for the penalty factor lambda:
    Figure FDA0002197585500000021
    when the parameters to be set of the SISO partial format model-free controller contain step length factors rho1The control input u (k) is for the step-size factor p1The gradient information at time k is:
    Figure FDA0002197585500000022
    when the parameters to be set of the SISO partial format model-free controller contain step length factors rhoiAnd 2 ≦ i ≦ L, the control input u (k) for the step size factor ρiThe gradient information at time k is:
    Figure FDA0002197585500000023
    wherein Δ u (k) u (k-1),
    Figure FDA0002197585500000024
    is a pseudo-gradient estimate for time k,
    Figure FDA0002197585500000025
    is composed of
    Figure FDA0002197585500000026
    The ith component of (i ═ 1, …, L);
    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 bias 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 bias information of the previous time in sequence, namely: when the parameters to be set of the SISO bias format model-free controller contain a penalty factor lambda, one of the gradient information at the k moment
    Figure FDA0002197585500000031
    One of the partial derivatives recorded as the previous time
    Figure FDA0002197585500000032
    When the parameters to be set of the SISO partial format model-free controller contain step length factors rhoiAnd when i is more than or equal to 1 and less than or equal to L, one of gradient information at the k moment
    Figure FDA0002197585500000033
    One of the partial derivatives recorded as the previous time
    Figure FDA0002197585500000034
    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 partial 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 partial format model-less controller 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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