CN101968629A - PID (Proportional Integral Derivative) control method for elastic integral BP neural network based on RBF (Radial Basis Function) identification - Google Patents

Abstract

A PID control system based on an elastic integral BP neural network identified by RBF, which includes: determining the structure of the BP neural network, determining the initial value; determining the structure of the RBF identification network; sampling; forward calculating the BP network, and calculating the output of the PID control system ; Calculate the RBF identification network; modify the identification network parameters; modify the weighting coefficient of the BP neural network. The advantage of the present invention is that: the BP neural network is combined with the traditional PID control to form an intelligent neural network PID control system. It does not need to establish an accurate mathematical model, it can automatically identify the controlled process parameters, automatically adjust the control parameters, and adapt to the changes of the controlled process parameters. effective measures.

Description

PID control method of elastic integral BP neural network based on RBF identification

【Technical field】：

The invention belongs to the technical field of intelligent control, and relates to a PID control system based on improved parameter setting of BP neural network, in particular to a PID control system based on elastic integral BP neural network identified by RBF. the

【Background technique】:

The adjustment system controlled by proportional, integral and differential is called PID control system for short. It is the most widely used, oldest and most vigorous control method in industrial process control. In the current industrial production, more than 90% of the control systems It is a PID control system. It adopts the method based on the object mathematical model, which has the advantages of simple algorithm, good robustness, high reliability, and good control effect, so it is widely used in industrial control processes, especially for deterministic control systems that can establish accurate mathematical models. For the traditional PID control system, before it is put into operation, in order to obtain a more ideal control effect, three parameters must be adjusted: the proportional coefficient K _P , the integral coefficient K _I , and the differential coefficient K _D . This is because there are various controlled objects in the production department, and they have different requirements on the characteristics of the control system. Control effect, if the control system parameters are not set well, even if the control system itself is very advanced, its control effect will be poor.

With the development of industry, the complexity of the control object is also deepening. Many large-delay, time-varying, nonlinear complex systems, such as temperature control systems, have complex mechanism of the controlled process, high-order nonlinear, slow time-varying , pure hysteresis and other characteristics, the conventional PID control seems helpless; in addition, there are many uncertain factors in the actual production process, such as noise, load vibration and other environmental conditions, process parameters and even model results will change, such as variable structure , variable parameters, nonlinear, time-varying, etc., not only is it difficult to establish an accurate mathematical model of the controlled object, but also the control parameters of the PID control system have a fixed form, which is difficult to adjust online and adapt to changes in the external environment. These make the PID control system in The ideal effect cannot be achieved in practical application, and it is more and more restricted and challenged. the

People have been looking for the adaptive technology of PID control system parameters to meet the control requirements of complex systems. The development of neural network theory makes this idea possible. Artificial neural network (ANN for short) is an adaptive nonlinear dynamic system composed of a large number of simple basic neurons connected to each other. Neural network control can fully and arbitrarily approach any complex nonlinear relationship, has a strong ability to synthesize information, and can learn and adapt to the dynamic characteristics of severely uncertain systems, so it has strong robustness and fault tolerance, and can handle those Processes that are difficult to describe with models and rules have been successfully applied in the control of some uncertain systems. The error backpropagation neural network (referred to as BP network), with its arbitrary nonlinear expression ability, can realize the PID control with the best combination through the learning of system performance. the

【Invention content】：

The purpose of the present invention is to solve the problem that the traditional PID control system is difficult to adjust in real time online due to fixed control parameters, and the robustness is not strong, and it is difficult to adapt to changes in the external environment, and to provide a PID control method based on an elastic integral BP neural network identified by RBF. the

求值，用一个径向基网络即RBF神经网络建立一个被控对象的辨识模型，用此模型去训练BP网络控制系统。 The present invention relates to an improved intelligent PID control method based on BP neural network. The method first proposes an elastic integral PID control algorithm on the basis of variable speed integrals, and then uses BP network to tune PID control, and corrects the time derivative term for the weight value.

Evaluate, use a radial basis network (RBF neural network) to establish an identification model of the controlled object, and use this model to train the BP network control system.

The PID control system of the elastic integral BP neural network based on RBF identification provided by the invention comprises the following steps:

1. Determine the number of input layer nodes M and the number of hidden layer nodes Q of the three-layer BP neural network, and give the initial value w _ij ⁽²⁾ (0) and w _li ⁽³⁾ (0) of the weighting coefficients of each layer , select the learning rate η and the inertia coefficient α, and the calculation times k=1 at this time;

2. Determine the number of input nodes m and the number of hidden layer nodes s of the RBF identification network, and give the center vector C _j (0) of the hidden layer nodes, the initial value b _j (0) of the base broadband parameter, and the initial value of the weight coefficient w _j (0), learning rate ρ, inertia coefficient γ, calculation times k=1, this network is used to establish the identification model of the controlled object, so as to dynamically observe the sensitivity of the output of the controlled object to the control input, and provide it to the BP neural network ;

3. Obtain the input value r(k) and output value y(k) of the three-layer BP neural network by sampling, and calculate the error e(k) at this moment;

4. Forward calculation of the input and output of neurons in each layer of BP neural network, the three output values of the output layer of BP neural network are the three adjustable parameters K _P , _KI , K _D of the PID control system; given Deviation threshold ε, calculate the PID output u(k) according to the elastic integral control algorithm, and subtract it from the last u(k-1) to get Δu(k), which is sent to the control object and RBF identification network to generate the controlled object output y(k);

The 5th, calculate the input and output of each layer neuron of RBF identification network according to the forward calculation formula of RBF identification network, the output of RBF identification network is vector group y _m (k), m is the number of output values;

Sixth, use the iterative algorithm of the RBF identification network to correct the output weight coefficient of the identification network, the center vector of the hidden layer node and the base width parameter of the hidden layer node;

The 7th, use the iterative algorithm of BP neural network to revise the weighting coefficient of BP neural network, make calculation times k=k+1, return to step 3, continue to execute in order, stop when the error reaches the requirement. the

The BP neural network structure described in the first step adopts a three-layer BP neural network with a simple structure. the

The input layer node of the BP neural network corresponds to the selected controlled system operating state quantity, the integral function of the output layer neuron is a non-negative Sigmoid function, and the activation function of the hidden layer neuron is a positive and negative symmetric Sigmoid function. the

The RBF identification network described in the second step is implemented using CMOS circuits; the input voltage signal is converted into a current signal through a transconductance amplification system, and then the radial basis can be obtained as a Gauss-like function through an absolute value circuit and a root mean square circuit The input of the generation circuit, the output of the Gauss-like function generation circuit is the output of the RBF neuron. the

The elastic integral control algorithm described in the fourth step is proposed on the basis of the variable speed integral algorithm, and the specific content is:

u(k)=u(k-1)+

K _p {[e(k)-e(k-1)]+K ₁ f(|e(k)|)*e(k)+K _D [e(k)-2e(k-1)+e (k-2)]}

是一个系数，其取值规则为： u(k) and u(k-1) are the output values of the kth and k-1th operations of PID respectively; e(k), e(k-1) and e(k-2) are the BP neural The error values of the kth, k-1th and k-2th operations in the network; K _P , K _I , and K _D are the three parameters of the PID control system;

is a coefficient, and its value rule is:

When |e(k)|≤ε, $f\left(\right|e\left(k\right)\left|\right)=\frac{e-\left|e\left(k\right)\right|}{e};$

ε为第4步给出的偏差门限，即当系统偏差超出偏差门限值ε时，引入非线性减指数函数的目的是使积分项即使在偏差较大时仍然起一定的作用，偏差越大，积分作用越弱。 When |e(k)|＞ε,

ε is the deviation threshold given in step 4, that is, when the system deviation exceeds the deviation threshold ε, the purpose of introducing a nonlinear subtractive exponential function is to make the integral term still play a certain role even when the deviation is large, and the larger the deviation , the weaker the integral effect.

The iterative algorithm 1 of the middle BP neural network described in the 7th step is:

The weight coefficient learning algorithm of the output layer of BP neural network is:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&Delta;\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&Delta;\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; net</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

(l=1, 2, 3)

为第k次运算BP神经网络输出层神经元i的权系数修正量；η为学习速率； 为输出层的局部梯度； 

为隐层中神经元i的激活值，α是动量项，通常是正数；net⁽³⁾(k)输出层网络第k次的输入值。 

For the kth operation BP neural network output layer neuron i weight coefficient correction; η is the learning rate; is the local gradient of the output layer;

is the activation value of neuron i in the hidden layer, α is the momentum item, usually a positive number; net ⁽³⁾ (k) the input value of the kth time of the output layer network.

The iterative algorithm 2 of the middle BP neural network described in the 7th step is:

The weight coefficient learning algorithm of the hidden layer is:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; net</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>$

(i=1,2,...Q) 

g(□)=g(x)(1-g(x)), f'(□)=(1-f ² (x))/2

为隐层神经元j第k次运算的权系数修正量；η为学习速率； 

为隐层的局部梯度； 

为网络输入层中神经元j的激活值，α是动量项，通常是正数； 

隐层第k次的神经元i的输入值。 

is the correction value of the weight coefficient of the kth operation of the hidden layer neuron j; η is the learning rate;

is the local gradient of the hidden layer;

is the activation value of neuron j in the network input layer, α is a momentum item, usually a positive number;

The input value of the kth neuron i in the hidden layer.

Working principle of the present invention:

The PID control system based on BP neural network is composed of the classic PID control system and BP neural network. The basic idea is to use the self-learning function of the neural network and the representation ability of nonlinear functions, and follow certain optimal indicators to adjust the PID control online. The parameters of the system can adapt to the changes of the parameters and structure of the controlled object and the change of the input reference signal, and can resist the influence of external disturbances to achieve the goal of good robustness. the

和 

的选取对控制系统的性能影响很大。由于系统是非线性的，初始值对学习是否达到局部最小、是否能够收敛以及训练时间的长短关系 很大。如果初始权值太大，使得加权之后的输入和n落在了S型激活函数的饱和区，从而导致其导数f(s)非常小，而在计算权值修正公式中，因为δ∞f(n)，当f(n)→o时，则有δ→0，这使得Δw_ij→0，调节过程几乎停顿下来。所以，一般总是希望经过初始加权后的每个神经元的输入值都接近于0，这样可以保证每个神经元的权值都能够在它们的S型激活函数变化最大之处进行调节。 The initial weight of BP neural network

and

The selection of , has a great influence on the performance of the control system. Since the system is nonlinear, the initial value has a great relationship with whether the learning reaches the local minimum, whether it can converge and the length of the training time. If the initial weight is too large, the weighted input and n fall into the saturation region of the S-type activation function, resulting in a very small derivative f(s), and in the calculation of the weight correction formula, because δ∞f( n), when f(n)→o, then there is δ→0, which makes Δw _ij →0, and the adjustment process almost comes to a standstill. Therefore, it is generally hoped that the input value of each neuron after the initial weighting is close to 0, so as to ensure that the weight of each neuron can be adjusted where their S-type activation function changes the most.

Advantages and positive effects of the present invention:

The invention combines BP neural network with traditional PID control to form an intelligent neural network PID control system. It does not need to establish an accurate mathematical model, it can automatically identify the controlled process parameters, automatically adjust the control parameters, and adapt to the changes of the controlled process parameters. effective measures. the

[Description of drawings]:

Figure 1 is a schematic diagram of the PID control system based on the elastic integral BP neural network identified by RBF. the

(1) Elastic integral PID control system: direct closed-loop control of the controlled object, and online parameter adjustment. the

(2) Neural network: adjust the parameters of the PID control system according to the operating state of the system in order to achieve the optimization of a certain performance index, so that the output state of the output layer neural network corresponds to the three adjustable parameters of the PID control system. Through the self-learning of the neural network and the adjustment of the weighting coefficient, the output of the neural network corresponds to a PID control system of an optimal control law. the

Fig. 2 is the elastic integral PID control structure based on BP and RBF neural network in "PID control system of elastic integral BP neural network based on RBF identification". the

The radial basis network (RBF) neural network establishes an identification model of the controlled object, and uses this model to train the BP network control system. the

Fig. 3 is a single model of a single RBF neural network in "PID control system based on elastic integral BP neural network identified by RBF". the

Figure 4 is the 2*3 combined RBF neural network model in "PID control system based on elastic integral BP neural network identified by RBF". the

Figure 5 is the CMOS implementation of the 2*3 combined RBF neural network in "PID control system based on elastic integral BP neural network identified by RBF". the

Fig. 6 is a system structure diagram of the controlled system-circuit in the "PID control device based on elastic integral BP neural network identified by RBF" of the present invention. ROM27OS is used as the memory of the control program, and the whole program is 1K information group (binary information group); two PIAs are used as input and output interfaces to respectively set the temperature through the data of the ADC (Analog to Digital Converter), digitally display the temperature and The working status is displayed; PTM (programmable timer module) is attached with 128 equal parts, which are used as the SCR trigger pulse output to control the input of the heating wire, and the SCR is triggered by the transistor and the pulse transformer; the accuracy of the ADC is 12 bits, and the full scale ( FFF(H)), the input is 50mv (equivalent to the thermoelectric potential of the nickel-chromium-nickel-aluminum thermocouple 1232.4°, 1 digit is equivalent to 0.3C°). the

FIG. 7 is a flow chart of using this method to control the circuit in the "PID control device based on elastic integral BP neural network identified by RBF" of the present invention. the

【Detailed ways】:

Example 1:

A kind of PID control method (see Fig. 1, Fig. 2) of the elastic integral BP neural network based on RBF identification, this method comprises the following steps:

和 

选定学习速率η和惯性系数α，k＝1； (1) Determine the structure of the BP network, and give the initial value of the weighting coefficient of each layer

and

Select learning rate η and inertia coefficient α, k=1;

(2) Determine the input nodes and the number m of the RBF identification network, the number s of hidden layer nodes, and give the center vector C _j (0) of the hidden layer nodes, the initial value b _j (0) of the base broadband parameter, and the initial weight coefficient Value w _j (0), learning rate ρ, inertia coefficient γ, k=1;

(3) Sampling to get y(k), r(k), and calculate e(k);

(4) Forward calculation of the input and output of neurons in each layer of the BP network, the output of the BP output layer is the three adjustable parameters of the PID control; the deviation threshold ε is given, and the PID control system is calculated according to the elastic integral control algorithm The output u(k), and combined with the last u(k-1) into Δu(k) is sent to the control object and RBF identification network to generate the output y(k) of the control object;

(5) Calculate the input and output of neurons in each layer of the RBF identification network according to the forward calculation formula of RBF, and the output of the identification network is y _m (k);

(6) Use the RBF iterative algorithm to modify the identification network output weight coefficient, hidden layer node center vector, and hidden layer node base width parameters;

(7) Use the iterative algorithm of the BP network to correct the weight coefficient of the BP network, set k=k+1, return to step (3), and continue to execute in sequence. the

The network structure of BP in the above-mentioned step (1) adopts a three-layer neural network with a simple structure, which requires the number M of input layer nodes and the number Q of hidden layer nodes. the

The above-mentioned step (1) input node corresponds to the selected system operating state quantity, and the output node corresponds to the three adjustable parameters of the PID control system, the integral function of the output layer neurons is a non-negative Sigmoid function, and the hidden layer The activation function of neurons can be positive and negative symmetrical Sigmoid function. the

The RBF identification network in the above-mentioned step (2) can be realized by using a CMOS circuit. The input voltage signal is converted into a current signal through the transconductance amplification system, and then the radial basis can be obtained through the absolute value circuit and the root mean square circuit as the input of the Gauss-like function generation circuit, and the output of the Gauss-like function generation circuit is the RBF nerve element output. the

The elastic integral control algorithm in the above-mentioned step (4) refers to:

u(k)=u(k-1)+

K _p {[e(k)-e(k-1)]+K ₁ f(|e(k)|)*e(k)+K _D [e(k)-2e(k-1)+e (k-2)]}

The value rule of coefficient f(|e(k)|) is:

When |e(k)|≤ε, $f\left(\right|e\left(k\right)\left|\right)=\frac{e-\left|e\left(k\right)\right|}{e};$

ε为预定的偏差门限。 When |e(k)|＞ε,

ε is a predetermined deviation threshold.

The elastic integral in the above-mentioned step (4) is proposed on the basis of the variable speed integral algorithm. When the system deviation exceeds the threshold value ε, a non-linear subtractive exponential function is introduced to make the integral term even when the deviation is large. It still plays a certain role when the deviation is larger, and the integral effect is weaker. the

The iterative algorithm of the BP network in the above-mentioned step (7):

The weight coefficient learning algorithm of the output layer of BP neural network is:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&Delta;u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>\frac{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&Delta;u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; net</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

(l=1, 2, 3)

The weight coefficient learning algorithm of the hidden layer is:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&alpha;\&Delta;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; net</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; li</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>$

(i=1,2,...Q) 

g(□)=g(x)(1-g(x)), f′(□)=(1-f ² (x))/2.

Claims (6)

1. PID control method based on the elasticity integration BP neural network of RBF identification is characterized in that this method may further comprise the steps:

1st, the input layer of determining three layers of BP neural network is counted M and hidden layer node is counted Q, and provides the initial value of each layer weighting coefficient

With

Selected learning rate η and inertial coefficient α, calculation times k=1 at this moment;

2nd, determine input number of nodes m, the number of hidden nodes s of RBF identification network, and provide the center vector C of hidden node _j(0), the initial value b of sound stage width band parameter _j(0), weight coefficient initial value w _j(0), learning rate ρ, inertial coefficient γ, calculation times k=1, this network is used to set up the identification model of controlled device, so that dynamic observe the sensitivity of the output of controlling object to the control input, offers the BP neural network;

3rd, sampling obtains input value r (k), the output valve y (k) of three layers of BP neural network, calculates this moment error e (k);

4th, forward calculates the neuronic input of BP each layer of neural network, output, and three output valves of BP neural network output layer are three adjustable parameter K of PID control system _P, K _I, K _DGive the threshold value ε that deviates,, and subtract each other with the u (k-1) of last time and to obtain Δ u (k) and send into controlling object and RBF identification network, produce the output y (k) of controlled device according to the output u (k) of elasticity integration control algorithm computation PID;

5th, calculate the neuronic input and output of RBF each layer of identification network according to the forward computing formula of RBF identification network, the RBF identification network is output as Vector Groups y _m(k), m is the output valve number;

6th, export weight coefficient, the center vector of hidden node and the sound stage width parameter of hidden node with the iterative algorithm correction identification network of RBF identification network;

7th, use the weighting coefficient of the iterative algorithm correction BP neural network of BP neural network, make calculation times k=k+1, returned for the 3rd step, continue to carry out in order, stop when error reaches requirement.

2. PID control system according to claim 1, the corresponding selected controlled system running status amount of input layer that it is characterized in that the BP neural network described in the 1st step, the neuronic integral function of output layer is got non-negative Sigmoid function, and the excitation function of hidden layer neuron is got the Sigmoid function of positive and negative symmetry.

3. PID control system according to claim 1 is characterized in that the RBF identification network described in the 2nd step uses cmos circuit to realize; Change input voltage signal into current signal by the mutual conductance amplification system, can obtain radially basic input as class Gauss function generating circuit by absolute value circuit and root mean square circuit then, the output of class Gauss function generating circuit is the neuronic output of RBF.

4. PID control system according to claim 1 is characterized in that the elasticity integration control algorithm described in the 4th step proposes on speed change integral algorithm basis, particular content is:

u(k)＝u(k-1)+

K _p{[e(k)-e(k-1)]+K ₁f(|e(k)|)*e(k)+K _D[e(k)-2e(k-1)+e(k-2)]}

U (k) and u (k-1) are respectively the output valve of the k time and the k-1 time computing of PID; E (k), e (k-1) and e (k-2) are respectively the error amount of the k time, the k-1 time and the k-2 time computing in the BP neural network; K _P, K _I, K _DThree parameters for the PID control system; F (| e (k) |) be a coefficient, its value rule is:

When | e (k) | during≤ε, $f\left(\right|e\left(k\right)\left|\right)=\frac{e-\left|e\left(k\right)\right|}{e};$

When | e (k) | during＞ε,

ε is the 4th deviation thresholding that provides of step, promptly when system deviation exceeds deviation threshold value ε, is that integral is still play a part greatly the time in deviation is certain even introduce the non-linear purpose that subtracts exponential function, and deviation is big more, and integral action is weak more.

5. PID control system according to claim 1 is characterized in that the iterative algorithm 1 of the BP neural network described in the 7th step is:

The weight coefficient learning algorithm of BP neural network output layer is:

$\mathrm{\&Delta;}{w}_{\mathrm{li}}^3\left(k\right)=\mathrm{\&eta;}{\mathrm{\&delta;}}_l^{\left(3\right)}{O}_i^{\left(2\right)}\left(k\right)+\mathrm{\&alpha;\&Delta;}{w}_{\mathrm{li}}^{\left(3\right)}(k-1)$

${\mathrm{\&delta;}}_i^{\left(3\right)}=e\left(k\right)\mathrm{sgn}\left(\frac{\&PartialD;y\left(k\right)}{\&PartialD;\mathrm{\&Delta;u}\left(k\right)}\right)\frac{\&PartialD;\mathrm{\&Delta;u}\left(k\right)}{\&PartialD;O_l^{\left(3\right)}\left(k\right)}g\left({\mathrm{net}}^{\left(3\right)}\left(k\right)\right)$

(l＝1，2，3)

Weight coefficient correction for the k time computing of BP neural network output layer neuron i; η is a learning rate;

Partial gradient for output layer;

Be the activation value of neuron i in the hidden layer, α is a momentum term, normally positive number; Net ⁽³⁾(k) input value of output layer the k time.

6. PID control system according to claim 1 is characterized in that the iterative algorithm 2 of the BP neural network described in the 7th step is:

The weight coefficient learning algorithm of hidden layer is:

$\mathrm{\&Delta;}{w}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=\mathrm{\&eta;}{\mathrm{\&delta;}}_i^{\left(2\right)}{O}_j^{\left(1\right)}\left(k\right)+\mathrm{\&alpha;\&Delta;}{w}_{\mathrm{ij}}^{\left(2\right)}(k-1)$

${\mathrm{\&delta;}}_i^{\left(2\right)}=f^{\&prime;}\left({\mathrm{net}}_i^{\left(2\right)}\left(k\right)\right)\underset{l=1}{\overset{3}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_l^{\left(3\right)}{w}_{\mathrm{li}}^{\left(3\right)}\left(k\right)$

(i＝1，2，...Q)

g(□)＝g(x)(1-g(x))，f′(□)＝(1-f ²(x))/2

Weight coefficient correction for the k time computing of hidden neuron j; η is a learning rate;

Partial gradient for hidden layer;

Be the activation value of neuron j in the network input layer, α is a momentum term, normally positive number;

The input value of the neuron i that hidden layer is the k time.

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