CN108181808B - System error-based parameter self-tuning method for MISO partial-format model-free controller - Google Patents

Abstract

The invention discloses a parameter self-tuning method based on system error for a MISO partial format model-free controller. The system error set is used as the input of a BP neural network, and the BP neural network performs forward calculation and outputs a penalty factor and a step size through an output layer. The parameters to be set in the MISO partial model-free controller such as factors are calculated using the control algorithm of the MISO partial model-free controller to obtain the control input vector for the controlled object. The objective is to minimize the value of the system error function, and the gradient descent method is used. , and combined with the control input 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, so as to realize the parameters of the controller based on the system error. VDF. The parameter self-tuning method based on the system error of the MISO partial format model-free controller proposed by the invention can effectively overcome the on-line tuning problem of the controller parameters, and has a good control effect on the MISO system.

Description

Systematic Error-Based Parameter Self-tuning Method for MISO Partial Format Model-Free Controller

technical field

The invention belongs to the field of automatic control, and in particular relates to a parameter self-tuning method based on system error of a MISO partial format 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 partial format model-free controllers. MISO partial format 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 input and output data measured in real time by 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 partial 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. 106). The algorithm is as follows:

为k时刻的MISO系统伪分块梯度估计值的行矩阵，

为行矩阵

的第i块行矩阵(i＝1,…,L)，

为行矩阵

的2范数；λ为惩罚因子，ρ₁,…,ρ_L为步长因子，L为控制输入线性化长度常数。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, Δu(k)=u( k)-u(k-1); e(k) is the systematic error at time k;

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

is a row matrix

The i-th row matrix of (i=1,...,L),

is a row matrix

The 2 norm of ; λ is the penalty factor, ρ ₁ ,…,ρ _L is the step factor, and L is the control input linearization length constant.

However, the MISO partial model-free controller needs to rely on empirical knowledge to pre-set the values of the penalty factor λ and the step factor ρ ₁ ,..., ρ _L and other parameters before the actual operation, which has not been realized in the actual operation process. Online self-tuning of parameters such as penalty factor λ and step size factor ρ ₁ ,…,ρ _L. The lack of effective parameter tuning means not only makes the use and debugging process of the MISO partial model-free controller time-consuming and laborious, but also sometimes seriously affects the control effect of the MISO partial model-free controller and restricts the performance of the MISO partial model-free controller. Promote the application. That is to say: the MISO partial format 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 partial model-free controller, the present invention proposes a parameter self-tuning method based on the system error of the MISO partial model-free controller.

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 based on the systematic error of the MISO partial format model-free controller.

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 partial format model-free controller for control; Determine the control input linearization length constant L of the MISO partial model-free controller, where L is an integer greater than 1; the MISO partial model-free controller parameters include a penalty factor λ and a step factor ρ ₁ ,...,ρ _L ; Determine the parameters to be set of the MISO partial format model-free controller, and the parameters to be set of the MISO partial format model-free controller are part or all of the parameters of the MISO partial format model-free controller, including the penalty factor λ and the step size Any one or any combination of factors _{ρ 1} , . The number of parameters to be set in the partial format model-free controller; the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are initialized;

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); the system error and its function group, the system output expected value, the system Output any one or any combination of actual values and put them into the set {system error set};

Step (4): the set {system error set} obtained in step (3) 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 values of the parameters to be tuned in the MISO partial format model-free controller;

Step (5): Based on the systematic error e(k) obtained in step (3) and the values of the parameters to be tuned in the MISO partial model-free controller obtained in step (4), the MISO partial model-free controller is adopted. The control algorithm is calculated to obtain the control input vector u(k)=[u ₁ (k),..., _um (k)] ^T of the MISO partial 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 partial format model-free controller parameters to be tuned at time k, the specific calculation formula is as follows:

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

When the to-be-adjusted parameters of the MISO partial model-free controller include a step factor ρ ₁ , the gradient information of the jth control input u _j (k) for the step factor ρ ₁ at time k is:

When the to-be-tuned parameters of the MISO partial model-free controller include a step size factor ρ _i and 2≤i≤L, the jth control input u _j (k) is at k for the step size factor ρ _i The gradient information at time is:

为k时刻的MISO系统伪分块梯度估计值的行矩阵，

为行矩阵

的第i块行矩阵(i＝1,…,L)，

为行矩阵

的第j个梯度分量估计值，

为行矩阵

的2范数；where Δu _j (k)=u _j (k)-u _j (k-1),

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

is a row matrix

The i-th row matrix of (i=1,...,L),

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};

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},... , the set of {gradient 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.

时刻系统误差e(k)的一阶后向差分e(k)-e(k-1)、 k时刻系统误差e(k)的二阶后向差分e(k)-2e(k-1)+e(k-2)、k时刻系统误差e(k)的高阶后向差分的任意之一或任意种组合。The systematic error and its function group in the step (3) include the systematic error e(k) at time k, the accumulation of systematic errors at time k and all previous times, namely:

The first-order backward difference e(k)-e(k-1) of the systematic error e(k) at time k, the second-order backward difference e(k)-2e(k-1) of the systematic error e(k) at time k +e(k-2), any one or any combination of the higher-order backward difference of the systematic error e(k) 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 partial model-free controller based on the system error provided by the present invention can achieve a good control effect and effectively overcome the time-consuming and laborious tuning of the penalty factor λ and the step factor ρ ₁ ,..., ρ _L. problem.

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 factors ρ ₁ , ρ ₂ , and ρ ₃ are simultaneously self-tuning;

Fig. 4 is the control input diagram of the two-input single-output MISO system when the penalty factor λ and the step size factors ρ ₁ , ρ ₂ , and ρ ₃ are simultaneously self-tuning;

Fig. 5 is the change curve of the penalty factor λ when the penalty factor λ and the step size factors ρ ₁ , ρ ₂ , ρ ₃ are simultaneously self-tuning in the two-input single-output MISO system;

Fig. 6 is the change curve of step factor ρ ₁ , ρ ₂ , ρ ₃ when the penalty factor λ and step factor ρ ₁ , ρ ₂ , ρ ₃ are self-tuning at the same time in 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 factors ρ ₁ , ρ ₂ , ρ ₃ are self-tuning;

Fig. 8 is the control input diagram of the two-input single-output MISO system when the penalty factor λ is fixed and the step size factors ρ ₁ , ρ ₂ , ρ ₃ are self-tuning;

Fig. 9 is the change curve of the step size factors ρ ₁ , ρ ₂ , ρ ₃ when the penalty factor λ is fixed and the step size factors ρ ₁ , ρ ₂ , ρ ₃ are 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 partial model-free controller is used for control; the control input linearization length constant L of the MISO partial model-free controller is determined , _L is an integer greater than 1; the parameters of the MISO partial model-free controller include a penalty factor λ and a step factor ρ ₁ , . Part or all of the parameters of the model-free controller in the format, including any one or any combination of the penalty factor λ and the step factor ρ ₁ ,...,ρ _L ; in Figure 1, the parameters to be tuned for the MISO partial model-free controller is the penalty factor λ and the step size factor ρ ₁ ,...,ρ _L ; determine the number of nodes in the input layer, the number of nodes in the hidden layer, and the number of nodes in the output layer of the BP neural network, wherein the number of nodes in the output layer is not less than the MISO partial format model-free The number of parameters to be set by the controller; the weight coefficient of the hidden layer and the weight coefficient of the output layer of the BP neural network are initialized.

时刻系统误差e(k)的一阶后向差分e(k)-e(k-1)的组合，放入集合{系统误差集}；将集合{系统误差集}作为BP神经网络的输入，BP神经网络进行前向计算，计算结果通过BP神经网络的输出层输出，得到MISO偏格式无模型控制器待整定参数的值；基于所述系统误差e(k)、所述MISO偏格式无模型控制器待整定参数的值，采用MISO偏格式无模型控制器的控制算法，计算得到MISO偏格式无模型控制器针对被控对象在k时刻的控制输入向量u(k)＝[u₁(k),…,u_m(k)]^T；针对控制输入向量u(k)中的第j个控制输入u_j(k) (1≤j≤m)，计算所述第j个控制输入u_j(k)分别针对各个所述MISO偏格式无模型控制器待整定参数在k时刻的梯度信息，并将全部所述梯度信息的集合记为{梯度信息j}，放入集合{梯度信息集}；针对控制输入向量u(k)中的其他m-1个控制输入，重复执行直至集合{梯度信息集}包含全部{{梯度信息1},…,{梯度信息m}}的集合；随后，结合所述集合{梯度信息集}，以系统误差函数的值最小化为目标，图1中以e²(k)最小化为目标，采用梯度下降法，进行系统误差反向传播计算，更新BP神经网络的隐含层权系数、输出层权系数，作为后一时刻BP 神经网络进行前向计算时的隐含层权系数、输出层权系数；控制输入向量u(k)作用于被控对象后，得到被控对象在后一时刻的系统输出实际值，然后重复执行本段落所述的工作，进行后一时刻的MISO偏格式无模型控制器基于系统误差的参数自整定过程。Record the current time as time k; use the difference between the expected value of the system output y ^* (k) and the actual value of the system output y(k) as the systematic error e(k) at time k, and then use the system error at time k e(k) , the accumulation of systematic errors at time k and all previous times is

The combination of the first-order backward difference e(k)-e(k-1) of the systematic error e(k) at time is put into the set {systematic error set}; the set {systematic error set} is used as the input of the BP neural network, 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 set for the MISO partial model-free controller; based on the system error e(k), the MISO partial model-free model The value of the parameters to be tuned by the controller, the control algorithm of the MISO partial model-free controller is used to calculate the control input vector u(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 j-th control input u _j (k) For each of the gradient information of the parameters to be set in the MISO partial model-free controller at time k, denote the set of all the gradient information as {gradient information j}, and put it into the set {gradient 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 sets of {{gradient information 1},...,{gradient information m}}; then, Combined with the set {gradient information set}, the goal is 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 The weight coefficient of the hidden layer and the weight coefficient of the output layer of the neural 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 forward calculation at the next moment; the control input vector u(k) acts on the controlled object Then, the actual value of the system output of the controlled object at the next moment is obtained, and then the work described in this paragraph is repeated to carry out the parameter self-tuning process of the MISO partial model-free controller based on the system error at the next moment.

系统误差e(k)的一阶后向差分e(k)-e(k-1)分别对应。输出层的节点，与惩罚因子λ和步长因子ρ₁,…,ρ_L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 3, the number of hidden layer nodes is set to 6, and the number of output layer nodes is set to the number of parameters to be set (the number of parameters to be set in Figure 2 is L+1). The 3 nodes of the input layer, the accumulation of the systematic error e(k) and the systematic error

The first-order backward differences e(k)-e(k-1) of the systematic error e(k) correspond respectively. The nodes of the output layer correspond to the penalty factor λ and the step size factor ρ ₁ ,...,ρ _L 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 value of the control input linearization length constant L of the MISO partial model-free controller is usually set according to the complexity of the controlled object and the actual control effect. It is generally between 1 and 10. If it is too small, it will affect the control effect. The assembly leads to a large amount of calculation, so generally 3 or 5 are often taken, and L is taken as 3 in this specific embodiment.

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 3, the number of nodes in the hidden layer is set to 6, and the number of nodes in the output layer is set to be set. number of parameters.

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

In the first set of test verification, the number of output layer nodes of the BP neural network in Figure 2 is preset to 4, and the penalty factor λ and the step size factors ρ ₁ , ρ ₂ , ρ ₃ are simultaneously self-tuning, and Figure 3 shows the control effect. Fig. 4 is the control input diagram, Fig. 5 is the change curve of the penalty factor λ, and Fig. 6 is the change curve of the step factor ρ ₁ , ρ ₂ , ρ ₃ . The results show that the method of the present invention can achieve a good control effect by simultaneously self-tuning the penalty factor λ and the step size factors ρ ₁ , ρ ₂ , ρ ₃ , and can effectively overcome the penalty factor λ and the step size factor ρ ₁ , ρ ₂ , ρ ₃ need to be time-consuming and laborious to tune.

During the verification of the second set of experiments, the number of nodes in the output layer of the BP neural network in Figure 2 is 3. First, the penalty factor λ is fixed as the average value of the penalty factor λ in the verification of the first set of experiments, and then the step size factor ρ ₁ , ρ ₂ , ρ ₃ perform self-tuning, Fig. 7 is the control effect diagram, Fig. 8 is the control input diagram, and Fig. 9 is the change curve of the step factor ρ ₁ , ρ ₂ , ρ ₃ . The results also show that when the penalty factor λ is fixed, the method of the present invention can achieve a good control effect by self-tuning the step size factors ρ ₁ , ρ ₂ , ρ ₃ , and can effectively overcome the step size factors ρ ₁ , ρ ₂ , ρ ₃ is a time-consuming and laborious problem to tune.

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,

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.

系统误差e(k)的一阶后向差分e(k)-e(k-1) 的组合，仅为其中一种组合；所述集合{系统误差集}还可以采用其他组合，举例来说，为系统误差e(k)、系统误差的累积即

系统误差e(k)的一阶后向差分e(k)-e(k-1)、系统误差e(k)的二阶后向差分e(k)-2e(k-1)+e(k-2)、系统误差e(k)的三阶或四阶或更高阶的后向差分等函数的任意之一或任意种组合。对上述具体实施例的被控对象而言，采用上述不同的集合{系统误差集}，都能够实现良好的控制效果。It should also be specially pointed out that, in the above-mentioned specific embodiment, as the set {systematic error set} of the input of the BP neural network, the systematic error e(k), the accumulation of the systematic error are selected.

The combination of the first-order backward difference e(k)-e(k-1) of the systematic error e(k) is only one of the combinations; the set {systematic error set} can also adopt other combinations, for example , is the accumulation of systematic error e(k), systematic error namely

The first-order backward difference e(k)-e(k-1) of the systematic error e(k), the second-order backward difference e(k)-2e(k-1)+e( k-2), any one or any combination of the third-order or fourth-order or higher-order backward difference and other functions of the systematic error e(k). For the controlled object of the above-mentioned specific embodiment, using the above-mentioned different sets {system error sets}, a good control effect can be achieved.

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 partial model-free controller include any one or any combination of the penalty factor λ and the step factor ρ ₁ , . . . , ρ _L ; in the above specific embodiment , the penalty factor λ and the step size factors ρ ₁ , ρ ₂ , ρ ₃ achieve simultaneous self-tuning in the first group of test verifications, while the penalty factor λ is fixed and the step size factors ρ ₁ , ρ ₂ , ρ ₃ when the second group of tests is verified. Self _- tuning is realized; in practical application, any combination _of parameters to be _tuned can be selected according to the specific situation. tuning; in addition, the parameters to be tuned for the MISO partial model-free controller, including but not limited to the penalty factor λ and the step size factor ρ ₁ ,...,ρ _L , for example, according to the specific situation, can also include the MISO system pseudo-blocking row matrix of gradient estimates

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 (4)

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

   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, adopting a MISO partial format model-free controller for control; determining a control input linearization length constant L of the MISO partial format model-free controller, wherein L is an integer greater than 1; the MISO partial format model-less controller parameters comprise a penalty factor lambda and a step factor rho₁,…,ρ_L(ii) a Determining parameters to be set of the MISO partial-format model-free controller, wherein the parameters to be set of the MISO partial-format model-free controller are part or all of the parameters of the MISO partial-format model-free controller and comprise a penalty factor lambda and a step factor rho₁,…,ρ_LAny 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 MISO partial format model-free controller; initializing a hidden layer weight coefficient and an output layer weight coefficient of the BP neural network;

   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); putting any one or any combination of the system error and the function set thereof, the system output expected value and the system output actual value into a set { a system error set }; 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 set { system error set } obtained in the step (3) 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 partial-format model-free controller;

   and (5): calculating a control input vector u (k) [ [ u ] of the MISO partial-format model-free controller at the time k for the controlled object by adopting a control algorithm of the MISO 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 MISO partial-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 partial-format model-free controller at the moment k, the specific calculation formula is as follows:

   when the parameters to be set of the MISO partial-format model-free controller contain penalty factor lambda, 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 partial-format model-free controller contain step-size factors rho₁Then, the jth control input u_j(k) For the step size factor p₁The gradient information at time k is:

   

   when the parameters to be set of the MISO partial-format model-free controller contain step-size factors rho_iAnd when i is more than or equal to 2 and less than or equal to L, the jth control input u_j(k) For the step size factor p_iThe gradient information at time k is:

   

   wherein, Δ u_j(k)＝u_j(k)-u_j(k-1)，

   

   A row matrix of MISO system pseudo-block gradient estimates at time k,

   

   is a row matrix

   

   The ith block row matrix of (i ═ 1, …, L),

   

   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;

   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 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 biased format modeless controller of claim 1, wherein said systematic error calculation function in said step (3) 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 MISO partial-format model-less controller parameter self-tuning method according to claim 1, wherein the set of the systematic errors and their functions in the step (3) includes the systematic error e (k) at time k, and the accumulation of the systematic errors at time k and all the previous times

   

   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 MISO biased format modeless controller of claim 1, wherein said systematic error function in said step (7) is a systematic error based parameter self-tuning method

   

   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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