CN108107727B - Parameter self-tuning method of MISO (multiple input single output) compact-format model-free controller based on partial derivative information - Google Patents

Abstract

The invention discloses a parameter self-tuning method based on partial derivative information for a MISO compact model-free controller. The partial derivative information set is used as the input of a BP neural network, and the BP neural network performs forward calculation and outputs penalty factors, Step size factor and other parameters of the MISO compact model-free controller to be set, the control algorithm of the MISO compact model-free controller is used to calculate the control input vector for the controlled object, with the goal of minimizing the value of the system error function, the gradient is used. The descending method, combined with the control input, respectively, for the gradient information set of each parameter to be tuned, the system error back-propagation calculation is performed, and the hidden layer weight coefficient and output layer weight coefficient of the BP neural network are updated online in real time, and the controller is based on the partial derivative. Information parameter auto-tuning. The parameter self-tuning method based on the partial derivative information of the MISO compact model-free controller proposed by the invention can effectively overcome the online tuning problem of the controller parameters, and has a good control effect on the MISO system.

Description

Parameter self-tuning method based on partial derivative information for MISO compact model-free controller

technical field

The invention belongs to the field of automatic control, in particular to a parameter self-tuning method based on partial derivative information of a MISO compact model-free controller.

Background technique

The control problem of MISO (Multiple Input and Single Output) system has always been one of the major challenges in the field of automation control.

Existing implementations of MISO controllers include MISO compact model-free controllers. MISO compact model-free controller is a new type of data-driven control method, which does not rely on any mathematical model information of the controlled object, but only relies on the real-time measurement of the input and output data of the MISO controlled object to analyze and design the controller, and The implementation is simple, the computational burden is small, and the robustness is strong. It can also control the unknown nonlinear time-varying MISO system well, and has a good application prospect. The theoretical basis of the MISO compact model-free controller was proposed by Hou Zhongsheng and Jin Shangtai in their co-authored "Model-Free Adaptive Control - Theory and Application" (Science Press, 2013, p. 95). The algorithm is as follows:

为k时刻的MISO系统伪梯度估计值的行矩阵，

为行矩阵

的2范数；λ为惩罚因子，ρ为步长因子。Among them, u(k) is the control input vector at time k, u(k)=[u ₁ (k),...,u _m (k)] ^T , m is the number of control inputs; e(k) is time k systematic error;

is the row matrix of the pseudo-gradient estimates of the MISO system at time k,

is a row matrix

The 2 norm of ; λ is the penalty factor, and ρ is the step factor.

However, the MISO compact model-free controller needs to rely on empirical knowledge to pre-set the values of the penalty factor λ and the step size factor ρ before the actual operation, and the penalty factor λ and the step size have not yet been realized in the actual operation process. Online auto-tuning of parameters such as factor ρ. The lack of effective parameter tuning means not only makes the use and debugging of the MISO compact model-free controller time-consuming and laborious, but also sometimes seriously affects the control effect of the MISO compact model-free controller and restricts the performance of the MISO compact model-free controller. Promote the application. That is to say: the MISO compact model-free controller also needs to solve the problem of online self-tuning parameters in the actual operation process.

Therefore, in order to break the bottleneck restricting the popularization and application of the MISO compact model-free controller, the present invention proposes a parameter self-tuning method of the MISO compact model-free controller based on partial derivative information.

SUMMARY OF THE INVENTION

In order to solve the problems existing in the background art, the purpose of the present invention is to provide a parameter self-tuning method for a MISO compact model-free controller based on partial derivative information.

For this reason, the above-mentioned purpose of the present invention is achieved by the following technical solutions, comprising the following steps:

Step (1): For a MISO (Multiple Input and Single Output) system with m inputs (m is an integer greater than or equal to 2) and 1 output, use a MISO compact format model-free controller for control; The parameters of the MISO compact model-free controller include a penalty factor λ and a step size factor ρ; the parameters to be set for the MISO compact model-free controller are determined, and the parameters to be set for the MISO compact model-free controller are the parameters of the MISO compact model-free controller. Format part or all of the parameters of the model-free controller, including any one or any combination of the penalty factor λ and the step factor ρ; determine the number of input layer nodes, hidden layer nodes, and output layer nodes of the BP neural network, The number of nodes in the output layer is not less than the number of parameters to be set in the MISO compact model-free controller; the weight coefficients of the hidden layer and the weight coefficients of the output layer of the BP neural network are initialized; the initialization set {partial derivative information set} partial derivative information in ;

Step (2): record the current moment as time k;

Step (3): Based on the expected value of the system output and the actual value of the system output, use the system error calculation function to calculate the system error at time k, denoted as e(k);

Step (4): the partial derivative information in the set {partial derivative information set} is used as the input of the BP neural network, the BP neural network performs forward calculation, and the calculation result is output through the output layer of the BP neural network, Obtain the value of the parameter to be tuned in the MISO compact model-free controller;

Step (5): based on the systematic error e(k) obtained in step (3) and the value of the parameters to be set for the MISO compact model-free controller obtained in step (4), adopt the MISO compact model-free controller The control algorithm is calculated to obtain the control input vector u(k)=[u ₁ (k),..., _um (k)] ^T of the MISO compact model-free controller for the controlled object at time k;

Step (6): For the jth control input u _j (k) (1≤j≤m) in the control input vector u(k) obtained in step (5), calculate the jth control input u _j (k) respectively for the gradient information of each of the MISO compact model-free controller parameters to be tuned at time k, the specific calculation formula is as follows:

When a penalty factor λ is included in the to-be-adjusted parameters of the MISO compact model-free controller, the gradient information of the jth control input u _j (k) for the penalty factor λ at time k is:

When the parameters to be set in the MISO compact model-free controller include a step factor ρ, the gradient information of the jth control input u _j (k) at time k for the step factor ρ is:

为k时刻的MISO系统伪梯度估计值的行矩阵，

为行矩阵

的第j个梯度分量估计值，

为行矩阵

的2范数；in,

is the row matrix of the pseudo-gradient estimates of the MISO system at time k,

is a row matrix

The j-th gradient component estimate of ,

is a row matrix

2 norm of ;

The set of all the above-mentioned gradient information is denoted as {gradient information j}, and put into the set {gradient information set};

记为前一时刻的偏导信息

当所述MISO紧格式无模型控制器待整定参数中包含步长因子ρ时则所述{梯度信息j}集合中的梯度信息

记为前一时刻的偏导信息

Record the gradient information in the {gradient information j} set as the partial derivative information at the previous moment in sequence, that is: when the MISO compact model-free controller parameter to be tuned includes a penalty factor λ, the { Gradient information in the set of gradient information j}

Denote the partial derivative information of the previous moment

When the to-be-tuned parameters of the MISO compact model-free controller include a step size factor ρ, then the gradient information in the {gradient information j} set

Denote the partial derivative information of the previous moment

The set of all the above-mentioned partial derivation information is denoted as {partial derivation information j}, and put into the set {partial derivation information set};

For the other m-1 control inputs in the control input vector u(k) obtained in step (5), this step is repeated until the set {gradient information set} contains all {{gradient information 1},... , a set of {gradient information m}}, and the set {partial derivative information set} includes all sets of {{partial derivative information 1},...,{partial derivative information m}}, and then enter step (7);

Step (7): With the goal of minimizing the value of the system error function, the gradient descent method is used, combined with the set {gradient information set} obtained in step (6), the back propagation calculation of the system error is performed, and the BP neural network is updated. The hidden layer weight coefficient and the output layer weight coefficient are used as the hidden layer weight coefficient and the output layer weight coefficient when the BP neural network performs forward calculation at the next moment;

Step (8): After the control input vector u(k) acts on the controlled object, the actual value of the system output of the controlled object at the next moment is obtained, and then returns to step (2), and repeats steps (2) to ( 8).

While adopting the above technical solutions, the present invention can also adopt or combine the following further technical solutions:

The independent variables of the system error calculation function in the step (3) include the expected value of the system output and the actual value of the system output.

The system error calculation function in the step (3) adopts e(k)=y ^* (k)-y(k), wherein y ^* (k) is the expected value of the system output set at time k, and y(k ) is the actual value of the system output sampled at time k; or e(k)=y ^* (k+1)-y(k), where y ^* (k+1) is the expected value of the system output at time k+1, y(k) is the actual output value of the system sampled at time k.

The independent variable of the system error function in the step (7) includes any one or any combination of the system error, the expected value of the system output, and the actual value of the system output.

其中，e(k)为系统误差，Δu_j(k)＝u_j(k)-u_j(k-1)，b_j为大于或等于0的常数，1≤j≤m。The systematic error function in the step (7) is

Among them, e(k) is the systematic error, Δu _j (k)=u _j (k)-u _j (k-1), b _j is a constant greater than or equal to 0, 1≤j≤m.

The parameter self-tuning method of the MISO compact model-free controller based on partial derivative information provided by the present invention can achieve a good control effect and effectively overcome the problem that the penalty factor λ and the step size factor ρ need time-consuming and laborious tuning.

Description of drawings

Fig. 1 is the principle block diagram of the present invention;

Fig. 2 is the BP neural network structure schematic diagram that the present invention adopts;

Fig. 3 is a control effect diagram of the two-input single-output MISO system when the penalty factor λ and the step size factor ρ are self-tuning at the same time;

Fig. 4 is the control input diagram of the two-input single-output MISO system when the penalty factor λ and the step size factor ρ are self-tuning at the same time;

Fig. 5 is the change curve of the penalty factor λ when the penalty factor λ and the step size factor ρ are self-tuning at the same time of the two-input single-output MISO system;

Fig. 6 is the change curve of the step factor ρ when the penalty factor λ and the step factor ρ are self-tuning at the same time of the two-input single-output MISO system;

Fig. 7 is a control effect diagram of the two-input single-output MISO system when the penalty factor λ is fixed and the step size factor ρ is self-tuning;

Fig. 8 is a control input diagram of a two-input single-output MISO system when the penalty factor λ is fixed and the step size factor ρ is self-tuning;

Fig. 9 is the change curve of step factor ρ when the penalty factor λ is fixed and the step factor ρ is self-tuning in the two-input single-output MISO system.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

Figure 1 shows the principle block diagram of the present invention. For a MISO system with m inputs (m is an integer greater than or equal to 2) and 1 output, the MISO compact model-free controller is used for control; the parameters of the MISO compact model-free controller include a penalty factor λ and a step factor ρ; determine the parameters to be set of the MISO compact model-free controller, which are part or all of the parameters of the MISO compact model-free controller, including any one or any combination of the penalty factor λ and the step factor ρ; In Figure 1, the parameters to be set for the MISO compact model-free controller are the penalty factor λ and the step size factor ρ; determine the number of input layer nodes, the number of hidden layer nodes, and the number of output layer nodes of the BP neural network, among which the number of output layer nodes Not less than the number of parameters to be set in the MISO compact model-free controller; initialize the hidden layer weight coefficient and output layer weight coefficient of the BP neural network; initialize the partial derivative information in the set {partial derivative information set}.

Denote the current time as time k; use the difference between the expected value y ^* (k) of the system output and the actual value y(k) of the system output as the systematic error e(k) at time k; The guided information is used as the input of the BP neural network, and the BP neural network performs forward calculation, and the calculation results are output through the output layer of the BP neural network to obtain the values of the parameters to be tuned for the MISO compact model-free controller; based on the system error e(k ), the value of the parameter to be set in the MISO tight format model-free controller, adopt the control algorithm of the MISO tight format model-free controller, calculate the MISO tight format model-free controller for the control input vector u of the controlled object at time k (k)=[u ₁ (k),..., _um (k)] ^T ; for the j-th control input u _j (k) (1≤j≤m) in the control input vector u(k), calculate The jth control input u _j (k) is respectively the gradient information of each of the MISO compact model-free controller parameters to be tuned at time k, and the set of all the gradient information is recorded as {gradient information j} , put it into the set {gradient information set}; record the gradient information in the {gradient information j} set as the partial derivative information at the previous moment in sequence, and record the set of all the partial derivative information as {partial derivative information information j}, put it into the set {partial derivative information set}; for the other m-1 control inputs in the control input vector u(k), repeat the execution until the set {gradient information set} contains all {{gradients} A set of information 1},...,{gradient information m}}, while the set {partial derivative information set} contains all sets of {{partial derivative information 1},...,{partial derivative information m}}; then, combining The set {gradient information set} aims to minimize the value of the system error function. In Figure 1, the goal is to minimize e ² (k), and the gradient descent method is used to calculate the back propagation of the system error and update the BP neural network. The weight coefficient of the hidden layer and the weight coefficient of the output layer of the network are used as the weight coefficient of the hidden layer and the weight coefficient of the output layer when the BP neural network performs the forward calculation at the next moment; after the control input vector u(k) acts on the controlled object , obtain the actual value of the system output of the controlled object at the next moment, and then repeat the work described in this paragraph to carry out the parameter self-tuning process of the MISO compact model-free controller based on the partial derivative information at the next moment.

分别对应。输出层的节点，与惩罚因子λ和步长因子ρ分别对应。BP 神经网络的隐含层权系数、输出层权系数的更新过程具体为：以系统误差函数的值最小化为目标，图2中以e²(k)最小化为目标，采用梯度下降法，结合所述集合{梯度信息集}，进行系统误差反向传播计算，从而更新BP神经网络的隐含层权系数、输出层权系数。FIG. 2 shows a schematic diagram of the structure of the BP neural network adopted in the present invention. The BP neural network can adopt a single-layer structure or a multi-layer structure. In the schematic diagram of Figure 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 consisting of an input layer, a single-layer hidden layer, and an output layer is adopted, and the number of nodes in the input layer is It is set to m×the number of parameters to be set (the number of parameters to be set in Figure 2 is 2), the number of nodes in the hidden layer is 6, and the number of nodes in the output layer is set as the number of parameters to be set (the number of parameters to be set in Figure 2 is 6) number of 2). The number of nodes in the input layer is divided into m groups, the number of nodes in each group is the number of parameters to be set, and the nodes in the jth group are the same as the partial derivative information in the {partial derivative information j} set.

corresponding respectively. The nodes of the output layer, corresponding to the penalty factor λ and the step size factor ρ, respectively. The update process of the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network is as follows: the goal is to minimize the value of the system error function. In Figure 2, the goal is to minimize e ² (k). Combined with the set {gradient information set}, the system error back-propagation calculation is performed 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 two-input single-output MISO system:

The expected value of the system output y ^* (k) is as follows:

y ^* (k)=(-1) ^round ( ^(k-1)/100 )

In this specific embodiment, m=2.

The BP neural network adopts a three-layer network structure consisting of an input layer, a single-layer hidden layer and an output layer. The number of nodes in the input layer is set to 2×the number of parameters to be set, the number of nodes in the hidden layer is set to 6, and the number of nodes in the output layer is set to 6. The number is set as the number of parameters to be set.

For the above-mentioned specific embodiments, two groups of test verifications have been carried out.

During the first set of experimental verification, the number of input layer nodes of the BP neural network in Figure 2 is preset to 4, and the number of output layer nodes is preset to 2, and the penalty factor λ and the step size factor ρ are simultaneously self-tuning, Figure 3 For the control effect diagram, Figure 4 is the control input diagram, Figure 5 is the change curve of the penalty factor λ, and Figure 6 is the change curve of the step factor ρ. The results show that the method of the present invention can achieve a good control effect by self-tuning the penalty factor λ and the step factor ρ at the same time, and can effectively overcome the problem that the penalty factor λ and the step factor ρ need time-consuming and laborious tuning.

In the second group of test verification, the number of input layer nodes of the BP neural network in Figure 2 is preset to 2, and the number of output layer nodes is preset to 1. First, the penalty factor λ is fixed as the penalty value for the first group of test verification. The average value of the factor λ, and then the step factor ρ is self-tuning, Figure 7 is the control effect diagram, Figure 8 is the control input diagram, and Figure 9 is the step size factor ρ variation curve. The results also show that the method of the present invention can achieve a good control effect by self-tuning the step factor ρ when the penalty factor λ is fixed, and can effectively overcome the problem of time-consuming and laborious tuning of the step factor ρ.

-y(k)；对上述具体实施例的被控对象而言，采用上述不同的系统误差计算函数，都能够实现良好的控制效果。It should be particularly pointed out that, in the above specific embodiment, the difference between the expected system output value y ^* (k) and the actual system output value y(k) is taken as the system error e(k), that is, e(k)=y ^* (k)-y(k), which is only a method in the system error calculation function; it is also possible to combine the expected system output value y ^* (k+1) at time k+1 with the actual value y output by the system at time k The difference between (k) is used as the systematic error e(k), that is, e(k)=y ^* (k+1)-y(k); the systematic error calculation function can also use the independent variable to include the expected value of the system output and the Other calculation methods for outputting the actual value, for example,

-y(k); For the controlled object of the above-mentioned specific embodiment, good control effects can be achieved by using the above-mentioned different system error calculation functions.

其中，Δu_j(k)＝u_j(k)-u_j(k-1)，b_j为大于或等于0的常数，1≤j≤m；显然，当b_j均等于0时，系统误差函数仅考虑了e²(k)的贡献，表明最小化的目标是系统误差最小，也就是追求精度高；而当b_j大于0时，系统误差函数同时考虑e²(k)的贡献和

的贡献，表明最小化的目标在追求系统误差小的同时，还追求控制输入变化小，也就是既追求精度高又追求操纵稳。对上述具体实施例的被控对象而言，采用上述不同的系统误差函数，都能够实现良好的控制效果；与系统误差函数仅考虑e²(k)贡献时的控制效果相比，在系统误差函数同时考虑e²(k)的贡献和

的贡献时其控制精度略有降低而其操纵平稳性则有提高。It should be particularly pointed out that, in the above-mentioned specific embodiment, when the value of the system error function is minimized to update the hidden layer weight coefficient and the output layer weight coefficient of the BP neural network, the system error function adopts e. ² (k), which is only one function in the system error function; the system error function can also use any one of the independent variables including the system error, the expected value of the system output, the actual value of the system output, or any combination of other function, for example, the systematic error function uses (y ^* (k)-y(k)) ² or (y ^* (k+1)-y(k)) ² , which is another way of using e ² (k) A functional form; as another example, the systematic error function takes

Among them, Δu _j (k)=u _j (k)-u _j (k-1), b _j is a constant greater than or equal to 0, 1≤j≤m; obviously, when both b _j are equal to 0, the systematic error The function only considers the contribution of e ² (k), indicating that the goal of minimization is to minimize the systematic error, that is, to pursue high precision; and when b _j is greater than 0, the systematic error function considers the contribution of e ² (k) and

The contribution of , shows that the goal of minimization is to pursue small system error and small change of control input, that is, to pursue both high precision and stable operation. For the controlled object of the above-mentioned specific embodiment, using the above ^- mentioned different system error functions, all can achieve good control effect; The function considers both the contribution of e ² (k) and

When the contribution of , its control accuracy is slightly reduced and its handling stability is improved.

等参数。Finally, it should be particularly pointed out that the parameters to be set for the MISO compact model-free controller include any one or any combination of the penalty factor λ and the step factor ρ; At the same time, the penalty factor λ and the step factor ρ are self-tuning at the same time. In the second group of test verification, the penalty factor λ is fixed and the step factor ρ is self-tuning. In practical application, the parameters to be tuned can also be selected according to the specific situation. any combination of Say, depending on the situation, may also include a row matrix of pseudo-gradient estimates for the MISO system

and other parameters.

The above-mentioned specific embodiments are used to explain the present invention, are only preferred embodiments of the present invention, rather than limit the present invention, within the spirit of the present invention and the protection scope of the claims, any modification, equivalent replacement, Improvements and the like all fall within the protection scope of the present invention.

Claims (3)

1. The parameter self-tuning method of the MISO compact-format model-free controller based on the partial derivative information is characterized by comprising the following steps of:

   step (1): for a Multiple Input and Single Output (MISO) system with m inputs (m is an integer greater than or equal to 2) and 1 Output, adopting a MISO compact format model-free controller for control; the MISO compact-format model-free controller parameters comprise a penalty factor lambda and a step factor rho; determining parameters to be set of a MISO (multiple input single output) compact-format model-free controller, wherein the parameters to be set of the MISO compact-format model-free controller are part or all of the parameters of the MISO 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 MISO compact-format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network; initializing partial derivative information in a set { partial derivative information set };

   step (2): recording the current time as k time;

   and (3): calculating to obtain a system error at the k moment by adopting a system error calculation function based on the system output expected value and the 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): taking the partial derivative information in the set { partial derivative information set } as the input of a BP (back propagation) neural network, carrying out forward calculation on the BP neural network, and outputting a calculation result through an output layer of the BP neural network to obtain a value of a parameter to be set of the MISO (single input single output) compact-format model-free controller;

   and (5): calculating and obtaining a control input vector u (k) [ [ u (k) of the MISO tight format model-free controller at the time k for the controlled object by adopting a control algorithm of the MISO tight 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 MISO tight format model-free controller obtained in the step (4)₁(k),…,u_m(k)]^T；

   And (6): aiming at the jth control input u in the control input vector u (k) obtained in the step (5)_j(k) (j is more than or equal to 1 and less than or equal to m), calculating the jth control input u_j(k) Respectively aiming at the gradient information of the parameters to be set of each MISO compact-format model-free controller at the moment k, the specific calculation formula is as follows:

   when the parameters to be set of the MISO compact-format model-free controller contain penalty factor lambdaThen, the jth control input u_j(k) The gradient information at the k moment for the penalty factor λ is:

   

   when the parameters to be set of the MISO compact-format model-free controller contain the step factor rho, the jth control input u_j(k) The gradient information at the k moment for the step factor ρ is:

   

   wherein,

   

   is a row matrix of MISO system pseudo gradient estimates at time k,

   

   is a row matrix

   

   The j-th gradient component estimate of (a),

   

   is a row matrix

   

   2 norm of (d);

   the set of all the gradient information is marked as { gradient information j }, and a set { gradient information set } is put in;

   recording the gradient information in the { gradient information j } set as partial derivative information of the previous moment in sequence, namely: when the parameters to be set of the MISO compact-format model-free controller contain penalty factor lambda, the gradient information in the { gradient information j } set

   

   Recording as partial derivative information of previous time

   

   When the parameters to be set of the MISO compact-format model-free controller contain the step factor rho, the gradient information in the set of the gradient information j is obtained

   

   Recording as partial derivative information of previous time

   

   The set of all the partial derivative information is marked as { partial derivative information j }, and the set { partial derivative information set } is put into;

   repeating the step for the other m-1 control inputs in the control input vector u (k) obtained in step (5) until the set { gradient information set } contains the set of all { { gradient information 1}, …, { gradient information m } }, and the set { partial derivative information set } contains the set of all { { partial derivative information 1}, …, { partial derivative information m } }, and then proceeding to step (7);

   and (7): the value minimization of a system error function is taken as a target, a gradient descent method is adopted, the set { gradient information set } obtained in the step (6) is combined, the backward propagation calculation of the system error is carried out, and the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are updated and used as the weight coefficient of the hidden layer and the weight coefficient of the output layer 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 (4) after the control input vector 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 step (2) to the step (8).
2. 2. The MISO compact format model-free control of claim 1The parameter self-tuning method based on the partial derivative information is characterized in that the system 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.
3. 3. The MISO compact format model-less controller parameter self-tuning method of claim 1, wherein the systematic error function in step (7) is

   

   Wherein e (k) is the systematic error, Δ u_j(k)＝u_j(k)-u_j(k-1)，b_jIs a constant greater than or equal to 0, and j is greater than or equal to 1 and less than or equal to m.

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