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

Abstract

The invention relates to a PID (Proportional Integral Derivative) control method for an elastic integral BP neural network based on RBF (Radial Basis Function) identification, which comprises the following steps: determining the structure of the BP neural network and determining an initial value; determining the structure of an RBF identification network; sampling; positively calculating the BP network and calculating the output of a PID control system; calculating the RBF identification network; revising the parameters of the identification network; and revising the weighting coefficient of the BP netural network. The invention has the advantages that the BP neural network is combined with the traditional PID control to form an intelligent neural network PID control system; no accurate mathematical model is required to be established; the change of the parameters of the controlled course, the parameters of the automatic setting control and the parameters of adapting to the controlled course can be automatically identified; and the method is an effective measure for solving the problems of difficult parameter setting, no real-time parameter adjustment and weak robustness of the traditional PID control system.

Description

PID control method based on the elasticity integration BP neural network of RBF identification

[technical field]:

The invention belongs to field of intelligent control technology, relate to a kind of PID control system, especially based on the PID control system of the elasticity integration BP neural network of RBF identification based on BP neural network modified parameter tuning.

[background technology]:

In proportion, the regulating system controlled of integration and differential abbreviates the PID control system as, be most widely used general, with the longest history in the industrial process control, the control mode that vitality is the strongest, in present commercial production, the control system more than 90% is the PID control system.Its adopts the method based on mathematical model of controlled plant, and advantage is that algorithm is simple, robustness good and reliability is high, controls respond wellly, so is widely used in industrial control process, is particularly useful for setting up the deterministic control system of mathematical models.For the traditional PID control system, before it is put into operation, expect comparatively ideal control effect, three parameters of must having adjusted earlier: scale-up factor K _P, integral coefficient K _I, differential coefficient K _DThis is because in the production division various controlled devices are arranged, they have different requirements to the characteristic of control system, the purpose of adjusting is exactly to manage to make the characteristic of control system to work good with controlled device, so that obtain the Optimal Control effect, if the control system parameter tuning is bad, even control system itself is very advanced, its control effect also can be very poor.

Along with industrial expansion, the complexity of controlling object is also in continuous intensification, many large time delay, the time become, nonlinear complication system, as temperature control system, controlled process mechanism complexity has high-order nonlinear, characteristics such as changes when slow, pure hysteresis, and conventional PID controls and seems powerless; In addition, exist many uncertain factors in the actual production process, as under noise, load vibration and some other environmental baseline, procedure parameter even model result all can change, as become structure, variable element, non-linear, time and become etc., not only be difficult to set up the controll plant precise math model, and the controlled variable of PID control system has fixed form, be difficult for online adjustment, be difficult to adapt to the variation of external environment, these make the PID control system can not reach desirable effect in actual applications, more and more are restricted and challenge.

People are seeking the adaptive technique of PID control system parameter always, and to adapt to the control requirement of complication system, the development of neural network theory makes this imagination become possibility.Artificial neural network (be called for short ANN) is to be interconnected and the self-adaptation nonlinear dynamic system that constitutes by a large amount of simple basic neurons.ANN (Artificial Neural Network) Control can fully at random be approached the nonlinear relationship of any complexity, has very strong informix ability, can learn and adapt to the dynamic perfromance of serious uncertain system, so very strong robustness and fault-tolerance are arranged, can handle those and be difficult to process, successful Application in the control of some uncertain systems with model and rule description.Error back propagation neural network (be called for short BP network), any non-linear expression's ability that is had, study that can the way system performance realizes having the PID control of best of breed.

[summary of the invention]:

The present invention seeks to solve the traditional PID control system because controlled variable is fixed, it is not strong to be difficult for online in real time adjustment and robustness, is difficult to adapt to the problem that external environment changes, and a kind of PID control method of the elasticity integration BP neural network based on the RBF identification is provided.

What the present invention relates to is a kind of modified intelligent PID control method based on the BP neural network, and this method at first proposes elasticity integral PID control algorithm on the basis of speed change integration, use BP network Tuning PID Controller then, derivative term during at the weights correction

Evaluation, with one radially the base net network be the identification model that the RBF neural network is set up a controlled device, go the BP network control system with this model.

The PID control system based on the elasticity integration BP neural network of RBF identification that invention provides 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 w of each layer weighting coefficient _Ij ⁽²⁾(0) and w _Li ⁽³⁾(0), 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.

BP neural network structure described in the 1st step adopts three layers of BP neural network simple in structure.

The corresponding selected controlled system running status amount of the input layer of described BP neural network, 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.

RBF identification network utilization cmos circuit described in the 2nd step is realized; 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.

Elasticity integration control algorithm described in the 4th step proposes on speed change integral algorithm basis, and 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;

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.

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

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

$\mathrm{\Δ}{w}_{\mathrm{li}}^3\left(k\right)=\mathrm{\η}{\mathrm{\δ}}_l^{\left(3\right)}{O}_i^{\left(2\right)}\left(k\right)+\mathrm{\α\Δ}{w}_{\mathrm{li}}^{\left(3\right)}(k-1)$

${\mathrm{\δ}}_i^{\left(3\right)}=e\left(k\right)\mathrm{sgn}\left(\frac{\∂y\left(k\right)}{\∂\mathrm{\Δu}\left(k\right)}\right)\frac{\∂\mathrm{\Δu}\left(k\right)}{\∂O_l^{\left(3\right)}\left(k\right)}g\left({\mathrm{net}}^{\left(3\right)}\left(k\right)\right)$

(l＝1，2，3)

It is the weight coefficient correction of the k time computing 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 network the k time.

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

The weight coefficient learning algorithm of hidden layer is:

$\mathrm{\Δ}{w}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=\mathrm{\η}{\mathrm{\δ}}_i^{\left(2\right)}{O}_j^{\left(1\right)}\left(k\right)+\mathrm{\α\Δ}{w}_{\mathrm{ij}}^{\left(2\right)}(k-1)$

${\mathrm{\δ}}_i^{\left(2\right)}=f^{\′}\left({\mathrm{net}}_i^{\left(2\right)}\left(k\right)\right)\underset{l=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\δ}}_l^{\left(3\right)}{w}_{\mathrm{li}}^{\left(3\right)}\left(k\right)$

(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.

Principle of work of the present invention:

PID control system based on the BP neural network is made up of the PID control system and the BP neural network of classics, its basic thought is an expression ability of utilizing the self-learning function and the nonlinear function of neural network, defer to certain optimum index, the parameter of online adjustment PID control system, make it to adapt to the variation of object parameters and structure and the variation of input reference signal, and can resist the influence of external disturbance, reach target with good robustness.

The initial weight of BP neural network

With

Choose the performance impact of control system very big.Because system is non-linear, initial value to study whether reach local minimum, whether can restrain and the length relation of training time very big.If initial weight is too big, make that input and the n after the weighting dropped on the saturation region of S type activation function, thereby cause its derivative f (s) very little, and in calculating the weights correction formula because δ ∞ f (n), when f (n) → o, δ → 0 is arranged then, this makes Δ w _Ij→ 0, adjustment process almost is deadlocked.So general hope always all approaches 0 through each the neuronic input value after the initial weighting, can guarantee that like this each neuronic weights can both change maximum part at their S type activation function and regulate.

Advantage of the present invention and good effect:

The present invention combines the BP neural network with traditional PID control, constitute intelligent Neural Network PID Control System.It need not set up precise math model, can automatically identification controlled process parameter, the automatic adjusting controlled variable, adapt to the variation of controlled process parameter, be solve the traditional PID control systematic parameter adjust difficulty, can not adjust parameter and the not strong effective measures of robustness in real time.

[description of drawings]:

Fig. 1 is the PID control system structural representation based on the elasticity integration BP neural network of RBF identification.

(1) elasticity integral PID control system: directly controlled device is carried out closed-loop control, and the online adjustment mode of parameter.

(2) neural network: according to system running state, regulate the parameter of PID control system,, make three adjustable parameters of output layer neural network output state corresponding to the PID control system in the hope of reaching the optimization of certain performance index.Self study, weighting coefficient adjustment by neural network, make the PID control system of neural network output corresponding to certain optimal control law.

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

Radially base net network RBF neural network has been set up the identification model of a controlled device, goes the BP network control system with this model.

Fig. 3 is the single model of single RBF neural network in " based on the PID control system of the elasticity integration BP neural network of RBF identification ".

Fig. 4 is the 2*3 combination RBF neural network model in " based on the PID control system of the elasticity integration BP neural network of RBF identification ".

Fig. 5 is that the 2*3 combination RBF neural network CMOS in " based on the PID control system of the elasticity integration BP neural network of RBF identification " realizes.

Fig. 6 is the system construction drawing of controlled system-circuit among the present invention's related " based on PID control device of the elasticity integration BP neural network of RBF identification ".ROM27OS is as the storer of control program, and whole procedure is 1K message block (a two-symbol message block); Two PIA give fixed temperature by the data of ADC (analog-digital converter) respectively as IO interface, temperature is carried out number show and duty is shown; PTM (programmable timer module) is with 128 five equilibriums, and as the SCR trigger pulse output of control heating wire input, by transistor, pulse transformer triggers controllable silicon; The precision of ADC is 12 bits, during full scale (FFF (H)), is input as 50mv (thermoelectrical potential that is equivalent to 1232.4 ° of nichrome alumino-nickel couples, 1 figure place are equivalent to 0.3C °).

Fig. 7 is the flow process of utilization this method control circuit among the present invention's related " based on PID control device of the elasticity integration BP neural network of RBF identification ".

[embodiment]:

Embodiment 1:

A kind of PID control method of the elasticity integration BP neural network based on the RBF identification (see Fig. 1, Fig. 2), this method may further comprise the steps:

(1) determines the structure of BP network, and provide the initial value of each layer weighting coefficient

With

Selected learning rate η and inertial coefficient α, k=1;

(2) determine input node and number m, the hidden node number 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, k=1;

(3) sampling obtains y (k), r (k), calculates e (k);

(4) forward calculates the neuronic input of BP each layer of network, output, and the output of BP output layer is three adjustable parameters of PID control; Give the threshold value ε that deviates,, and be merged into Δ u (k) with the u (k-1) of last time and send into controlling object and RBF identification network, produce the output y (k) of controlling object according to the output u (k) of elasticity integration control algorithm computation PID control system;

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

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

(7) with the iterative algorithm correction BP network weight coefficient of BP network, make k=k+1, return step (3), continue to carry out in order.

The network structure of BP employing three-layer neural network simple in structure in the above-mentioned said step (1) needs input layer to count M and hidden layer node is counted Q.

The corresponding selected system running state amount of above-mentioned said step (1) input node, output node is three adjustable parameters of corresponding PID control system respectively, the neuronic integral function of output layer is got non-negative Sigmoid function, and the Sigmoid function of the desirable positive and negative symmetry of excitation function of hidden layer neuron.

The RBF identification network can use cmos circuit to realize in the above-mentioned said step (2).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.

Elasticity integration control algorithm refers in the above-mentioned said step (4):

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)]}

The value rule of coefficient f (| e (k) |) 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 predetermined deviation thresholding.

The elasticity integration proposes on speed change integral algorithm basis in the above-mentioned said step (4), when system deviation exceeds threshold value ε, introduce a nonlinear exponential function that subtracts, when deviation is big even purpose is that integral is still play a part is certain, deviation is big more, and integral action is weak more.

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

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

$\mathrm{\Δ}{w}_{\mathrm{li}}^3\left(k\right)=\mathrm{\η}{\mathrm{\δ}}_l^{\left(3\right)}{O}_i^{\left(2\right)}\left(k\right)+\mathrm{\α\Δ}{w}_{\mathrm{li}}^{\left(3\right)}(k-1)$

${\mathrm{\δ}}_i^{\left(3\right)}=e\left(k\right)\mathrm{sgn}\left(\frac{\∂y\left(k\right)}{\∂\mathrm{\Δu}\left(k\right)}\right)\frac{\∂\mathrm{\Δu}\left(k\right)}{\∂O_l^{\left(3\right)}\left(k\right)}g\left({\mathrm{net}}^{\left(3\right)}\left(k\right)\right)$

(l＝1，2，3)

The weight coefficient learning algorithm of hidden layer is:

$\mathrm{\Δ}{w}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=\mathrm{\η}{\mathrm{\δ}}_i^{\left(2\right)}{O}_j^{\left(1\right)}\left(k\right)+\mathrm{\α\Δ}{w}_{\mathrm{ij}}^{\left(2\right)}(k-1)$

${\mathrm{\δ}}_i^{\left(2\right)}=f^{\′}\left({\mathrm{net}}_i^{\left(2\right)}\left(k\right)\right)\underset{l=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\δ}}_l^{\left(3\right)}{w}_{\mathrm{li}}^{\left(3\right)}\left(k\right)$

(i＝1，2，...Q)

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

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:

$\mathrm{\Δ}{w}_{\mathrm{li}}^3\left(k\right)=\mathrm{\η}{\mathrm{\δ}}_l^{\left(3\right)}{O}_i^{\left(2\right)}\left(k\right)+\mathrm{\α\Δ}{w}_{\mathrm{li}}^{\left(3\right)}(k-1)$

${\mathrm{\δ}}_i^{\left(3\right)}=e\left(k\right)\mathrm{sgn}\left(\frac{\∂y\left(k\right)}{\∂\mathrm{\Δu}\left(k\right)}\right)\frac{\∂\mathrm{\Δu}\left(k\right)}{\∂O_l^{\left(3\right)}\left(k\right)}g\left({\mathrm{net}}^{\left(3\right)}\left(k\right)\right)$

(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:

$\mathrm{\Δ}{w}_{\mathrm{ij}}^{\left(2\right)}\left(k\right)=\mathrm{\η}{\mathrm{\δ}}_i^{\left(2\right)}{O}_j^{\left(1\right)}\left(k\right)+\mathrm{\α\Δ}{w}_{\mathrm{ij}}^{\left(2\right)}(k-1)$

${\mathrm{\δ}}_i^{\left(2\right)}=f^{\′}\left({\mathrm{net}}_i^{\left(2\right)}\left(k\right)\right)\underset{l=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\δ}}_l^{\left(3\right)}{w}_{\mathrm{li}}^{\left(3\right)}\left(k\right)$

(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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