CN107844051B - Parameter self-tuning method of SISO full-format model-free controller based on system error - Google Patents

Parameter self-tuning method of SISO full-format model-free controller based on system error Download PDF

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CN107844051B
CN107844051B CN201711323736.2A CN201711323736A CN107844051B CN 107844051 B CN107844051 B CN 107844051B CN 201711323736 A CN201711323736 A CN 201711323736A CN 107844051 B CN107844051 B CN 107844051B
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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 full-format model-free controller based on system errors, which utilizes the system errors and function groups thereof as the input of a BP neural network, the BP neural network carries out forward calculation and outputs parameters to be tuned of the SISO full-format model-free controller such as punishment factors, step factors and the like through an output layer, the control algorithm of the SISO full-format model-free controller is adopted for calculation to obtain the control input aiming at a controlled object, the value minimization of the system error function is taken as the target, a gradient descent method is adopted, the gradient information of each parameter to be tuned is respectively aimed at by combining the control input, the system error back propagation calculation is carried out, the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network are updated in real time on line, and the parameter self-tuning of the controller based on the system errors is realized. The parameter self-tuning method of the SISO full-format model-free controller based on the system error can effectively overcome the problem of tuning of the controller parameters and achieve good control effect.

Description

Parameter self-tuning method of SISO full-format model-free controller based on system error
Technical Field
The invention belongs to the field of automatic control, and particularly relates to a parameter self-tuning method of a SISO full-format model-free controller based on system errors.
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) full-format modeless controller is one of the main implementation methods for the modeless controller. The theoretical basis of the SISO full-format model-free controller is proposed by Houzhong and Jinshangtai in the 'model-free adaptive control-theory and application' (scientific publishing agency, 2013, pages 83-84) of the Hedame, and the control algorithm is as follows:
Figure BDA0001503660130000011
wherein u (k) is the control input at time k; Δ u (k) ═ u (k) — u (k-1); Δ y (k) ═ y (k) — y (k-1); e (k) is the system error at time k;
Figure BDA0001503660130000012
is a pseudo-gradient estimate for time k,
Figure BDA0001503660130000013
is composed of
Figure BDA0001503660130000014
The ith component of (i ═ 1, …, Ly + Lu); ly is a control output linearization length constant preset in the SISO full-format model-free controller and is an integer greater than or equal to 1; lu is a control input linearization length constant preset in the SISO full-format model-free controller and is an integer greater than or equal to 1; λ is a penalty factor; rho1,…,ρLy+LuIs the step size factor.
At present, the SISO full-format modeless controller needs to rely on empirical knowledge to set a penalty factor lambda and a step factor rho in advance before actual use1,…,ρLy+LuThe values of the isoparametric parameters have not realized a penalty factor lambda and a step factor rho in the actual application process1,…,ρLy+LuAnd (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 full-format model-free controller time-consuming and labor-consuming, but also can seriously affect the control effect of the SISO full-format model-free controller sometimes, and restricts the popularization and application of the SISO full-format model-free controller.
Therefore, in order to break the bottleneck of restricting the popularization and application of the SISO full-format model-free controller, the invention provides a parameter self-tuning method of the SISO full-format model-free controller based on system errors.
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 full-format model-free controller based on system errors.
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 output linearization length constant Ly of the SISO full-format model-free controller, wherein the Ly is an integer greater than or equal to 1; determining a control input linearization length constant Lu of the SISO full-format model-free controller, wherein the Lu is an integer greater than or equal to 1; SISO full-format modeless controller parameters include a penalty factor λ and a step factor ρ1,…,ρLy+Lu(ii) a Determining parameters to be set of a SISO full-format model-free controller, wherein the parameters to be set of the SISO full-format model-free controller are part or all of the parameters of the SISO full-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLy+LuAny 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 full-format modeless controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;
step (2): 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 (3): taking any one or any combination of the system error and the function group thereof, the system output expected value and the system output actual value obtained by the calculation in the step (2) as the input of the BP neural network;
and (4): based on the input of the BP neural network in the step (3), 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 full-format model-free controller;
and (5): calculating to obtain a control input u (k) of the SISO full-format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO full-format model-free controller based on the system error e (k) obtained in the step (2) and the value of the parameter to be set of the SISO full-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 full-format model-free controller, wherein the specific calculation formula is as follows:
when the parameters to be set of the SISO full-format model-free controller comprise a penalty factor lambda and Lu is 1, the control input u (k) is the gradient information of the penalty factor lambda at the time k:
Figure BDA0001503660130000031
when the parameters to be set of the SISO full-format model-free controller comprise penalty factors lambda and Lu >1, the control input u (k) is the gradient information at the k moment aiming at the penalty factors lambda:
Figure BDA0001503660130000032
when the parameters to be set of the SISO full-format model-free controller contain step length factors rhoiAnd 1 ≦ i ≦ Ly, the control input u (k) is for the step-size factor ρiThe gradient information at time k is:
Figure BDA0001503660130000033
when the parameters to be set of the SISO full-format model-free controller contain step length factors rhoLy+1The control input u (k) is for the step-size factor pLy+1The gradient information at time k is:
Figure BDA0001503660130000034
when the parameters to be set of the SISO full-format model-free controller contain step length factors rhoiAnd i is more than or equal to Ly +2 and less than or equal to Ly + Lu and Lu>1, the control input u (k) is for the step-size factor piThe gradient information at time k is:
Figure BDA0001503660130000041
wherein Δ u (k) (u (k)) -u (k-1), Δ y (k) (y (k)) -y (k-1),
Figure BDA0001503660130000042
is a pseudo-gradient estimate for time k,
Figure BDA0001503660130000043
is composed of
Figure BDA0001503660130000044
The ith component of (i ═ 1, …, Ly + Lu);
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 (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 (2), and repeating the steps (2) to (8).
While adopting the above technical scheme, the present invention can also adopt or combine the following further technical schemes:
the independent variables of the system error calculation function in the step (2) comprise a system output expected value and a system output actual value.
The systematic error calculation function in the step (2) 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*Expected value of system output at time when (k +1) is k +1And y (k) is a system output actual value sampled at the moment k.
The system error and the function set thereof in the step (3) include the system error e (k) at the time k, and the accumulation of the system errors at the time k and all previous times, that is, the accumulation of the system errors
Figure BDA0001503660130000045
Any one or any combination of first order backward differences e (k) -e (k-1) of the k-time systematic error e (k), second order backward differences e (k) -2e (k-1) + e (k-2) of the k-time systematic error e (k), and high order backward differences of the k-time systematic error e (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 SISO full-format model-free controller parameter self-tuning method based on the system error can realize good control effect and effectively overcome the penalty factor lambda and the step factor rho1,…,ρLy+LuThe 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 output linearization length constant Ly of the SISO full-format model-free controller, wherein the Ly is an integer greater than or equal to 1; determining a control input linearization length constant Lu of the SISO full-format model-free controller, wherein the Lu is an integer greater than or equal to 1; SISO full-format modeless controller parameters include a penalty factor λ and a step factor ρ1,…,ρLy+Lu(ii) a Determining parameters to be set of a SISO full-format model-free controller, wherein the parameters to be set of the SISO full-format model-free controller are part or all of the parameters of the SISO full-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLy+LuAny one or any combination of the above; in FIG. 1, the parameters to be set by the SISO full-format model-less controller are penalty factor λ and step factor ρ1,…,ρLy+Lu(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 full-format modeless 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) The difference between the actual value y (k) and the system output value y (k) is used as the system error at the time kThe difference e (k) is calculated by adding the system error e (k) at time k, and the system errors at time k and all previous times
Figure BDA0001503660130000061
A combination of first-order backward differences e (k) -e (k-1) of the system errors e (k) at the time k is used 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 full-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 full-format model-free controller aiming at the controlled object at the time k by adopting the control algorithm of the SISO full-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, and taking the updated hidden layer weight coefficient and the output layer weight coefficient as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network carries out forward calculation at the later 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 later moment, repeating the process, and performing a parameter self-tuning process of the SISO full-format model-free controller at the later moment based on the system error.
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 is adopted, the number of nodes of the input layer is set to 3, the number of nodes of the hidden layer is 7, and the number of nodes of the output layer is set to the number of parameters to be set (the number of parameters to be set in fig. 2 is Ly + Lu + 1). 3 nodes of the input layer, and the accumulation of the systematic errors e (k) and e (k)
Figure BDA0001503660130000071
First order backward difference of systematic error e (k)The fractions e (k) to e (k-1) correspond to each other. Node of output layer, penalty factor lambda and step factor rho1,…,ρLy+LuRespectively 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) And (3) aiming at the minimization, performing system error back propagation calculation by adopting a gradient descent method and combining control input u (k) respectively aiming at the gradient information of each parameter to be set at the k moment, so as to update the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network.
The following is a specific embodiment of the present invention.
The controlled object is a typical nonlinear system:
Figure BDA0001503660130000072
desired value y of system output*(k) The following were used:
y*(k)＝5sin((k-1)π/50)+2cos((k-1)π/20)
the value of the control output linearization length constant Ly of the SISO full-format modeless controller is usually set according to the complexity of the controlled object and the actual control effect, and is generally between 1 and 5, and an excessively large value causes a large calculation amount, so that 1 or 3 is generally adopted, and Ly is taken as 1 in the specific embodiment; the value of the control input linearization length constant Lu of the SISO full-format modeless controller is also usually set according to the complexity of the controlled object and the actual control effect, and is generally between 1 and 10, where too small will affect the control effect, and too large will result in large calculation amount, so it is usually 2, 3 or 5, and Lu is 2 in this specific embodiment.
In this particular example, a total of two sets of experimental verifications were performed.
When the first group of experiments verify, the number of output layer nodes of the BP neural network in FIG. 2 is preset to be 4, and a penalty factor lambda and a step factor rho are calculated1,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 the output layer of the BP neural network in the graph 2 is 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,ρ3Self-tuning is carried out, 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 BDA0001503660130000081
-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 also be noted that in the above embodiment, the systematic error e (k), the accumulation of systematic errors, and the set of functions thereof, are selected as inputs to the BP neural network
Figure BDA0001503660130000082
The combination of the first order backward differences e (k) -e (k-1) of the systematic errors e (k) is only one combination of the systematic errors and their function groups; the set of systematic errors and their functions may also include other combinations, e.g. systematic errors e (k), the accumulation of systematic errors i.e. the accumulation of systematic errors
Figure BDA0001503660130000083
Any one or any combination of first order backward differences e (k) -e (k-1) of the systematic error e (k), second order backward differences e (k) -2e (k-1) + e (k-2) of the systematic error e (k), third or fourth or higher order backward differences of the systematic error e (k), and the like. For the controlled object of the above embodiment, the above different system errors and their function sets are adopted, such as the system error e (k), and the accumulation of the system error is
Figure BDA0001503660130000091
The first-order backward difference e (k) -e (k-1) of the system error e (k) and the second-order backward difference e (k) -2e (k-1) + e (k-2) of the system error e (k) (at this time, the number of nodes of the input layer of the BP neural network is preset to be 4), and good control effect can be realized.
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) In addition toA functional form; 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) 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 full-format model-free controller include a penalty factor λ and a step factor ρ1,…,ρLy+LuAny 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 full-format model-free 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 BDA0001503660130000101
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. A parameter self-tuning method of a SISO full-format model-free controller based on system errors is characterized by comprising the following steps:
    step (1): determining a control output linearization length constant Ly of the SISO full-format model-free controller, wherein the Ly is an integer greater than or equal to 1; determining a control input linearization length constant Lu of the SISO full-format model-free controller, wherein the Lu is an integer greater than or equal to 1; SISO full-format modeless controller parameters include a penalty factor λ and a step factor ρ1,…,ρLy+Lu(ii) a Determining parameters to be set of a SISO full-format model-free controller, wherein the parameters to be set of the SISO full-format model-free controller are part or all of the parameters of the SISO full-format model-free controller and comprise a penalty factor lambda and a step factor rho1,…,ρLy+LuAny 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 full-format modeless controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;
    step (2): 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 (3): taking any one or any combination of the system error and the function group thereof, the system output expected value and the system output actual value obtained by the calculation in the step (2) as the input of the BP neural network;
    and (4): based on the input of the BP neural network in the step (3), 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 full-format model-free controller;
    and (5): calculating to obtain a control input u (k) of the SISO full-format model-free controller at the time k for the controlled object by adopting a control algorithm of the SISO full-format model-free controller based on the system error e (k) obtained in the step (2) and the value of the parameter to be set of the SISO full-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 full-format model-free controller, wherein the specific calculation formula is as follows:
    when the parameters to be set of the SISO full-format model-free controller comprise a penalty factor lambda and Lu is 1, the control input u (k) is the gradient information of the penalty factor lambda at the time k:
    Figure FDA0002197556040000021
    when the parameters to be set of the SISO full-format model-free controller comprise penalty factors lambda and Lu >1, the control input u (k) is the gradient information at the k moment aiming at the penalty factors lambda:
    Figure FDA0002197556040000022
    when the parameters to be set of the SISO full-format model-free controller contain step length factors rhoiAnd 1 ≦ i ≦ Ly, the control input u (k) is for the step-size factor ρiThe gradient information at time k is:
    Figure FDA0002197556040000023
    when the parameters to be set of the SISO full-format model-free controller contain step length factors rhoLy+1For the step-size factor, the control input u (k)ρLy+1The gradient information at time k is:
    Figure FDA0002197556040000031
    when the parameters to be set of the SISO full-format model-free controller contain step length factors rhoiAnd i is more than or equal to Ly +2 and less than or equal to Ly + Lu and Lu>1, the control input u (k) is for the step-size factor piThe gradient information at time k is:
    Figure FDA0002197556040000032
    wherein Δ u (k) (u (k)) -u (k-1), Δ y (k) (y (k)) -y (k-1),
    Figure FDA0002197556040000033
    is a pseudo-gradient estimate for time k,
    Figure FDA0002197556040000034
    is composed of
    Figure FDA0002197556040000035
    The ith component of (i ═ 1, …, Ly + Lu);
    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 (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 (2), and repeating the steps (2) to (8).
  2. 2. Root of herbaceous plantThe SISO full format model-less controller systematic error based parameter self-tuning method of claim 1, wherein the systematic error calculation function in step (2) employs 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 full-format model-free controller parameter self-tuning method of claim 1, wherein the system error and its function set in step (3) comprises the system error e (k) at time k, and the accumulation of the system errors at time k and all previous times
    Figure FDA0002197556040000041
    Any one or any combination of first order backward differences e (k) -e (k-1) of the k-time systematic error e (k), second order backward differences e (k) -2e (k-1) + e (k-2) of the k-time systematic error e (k), and high order backward differences of the k-time systematic error e (k).
  4. 4. The SISO full format model-less controller systematic error based parameter self-tuning method of claim 1, wherein the systematic error function in 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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