CN102141776A - Particle filter and RBF identification-based neural network PID control parameter self-setting method - Google Patents

Abstract

The invention discloses a particle filter and radial basis function (RBF) identification-based neural network proportion integration differentiation (PID) control parameter self-setting method used for a control system, the object model of which is unknown and the interference of which is on-linear and non-Gaussian noise. The method comprises the following steps of: connecting the output of a PID controller and the system output to the input of an RBF neural network identification structure respectively, and connecting a particle filter part between the system output and the RBF neural network identification structure; and filtering the system output by using particle filter to obtain particle filter output, training the RBF neural network by using the difference value of the particle filter output and the RBF neural network output as a target function to obtain the RBF neural network output, then calculating Jacobian information of the system, finally training a neuron by using the deviation signal between the system reference input and the system output as a target function, guiding the neuron by using the Jacobian information, and adjusting the PID controller by a learning algorithm. At the same time of keeping the characteristics of high PID control robustness, good reliability and the like, the method can further improve the dynamic response performance and the interference resistance of the control system.

Description

Neural Network PID Control parameter self-tuning method based on particle filter and RBF identification

Technical field

The present invention is specifically related to a kind of method that is used for the Neural Network PID Control parameter self-tuning, belongs to the control system field, and being used for object model the unknown and disturbing is the control system of non-linear and non-Gaussian noise.

Background technology

In the actual industrial production process, that controlling object often has is non-linear, the time become the interference of various non-linear, non-Gaussian noises in uncertainty and the control procedure, controlling object is difficult to set up precise math model, the parameter self-tuning method is numerous and diverse, and therefore conventional PID controller often is difficult to the control effect that reaches good.

In order to improve the robustness of control accuracy and system, The former Russian scholar has proposed multiplex control system on the basis of control system principle of invariance.The advantage of compound control is to increase substantially tracking accuracy, simultaneously also to not influence of system stability.In negative feed back control system, increase the feedforward compensation element and constitute coupled system.Under nominal case, the set-point response and the load disturbance response of this double-freedom control system are full decoupled, can reach the control performance index of expectation separately by regulating set point tracking control unit and feedforward filter respectively, in the hope of before the adverse effect of disturbing signal, offset the influence of this disturbance to system's output by feedforward.But in real work, can be subjected to the interference of random noise and the variation of external loading unavoidably, cause containing in the control signal high frequency interference, cause precise decreasing and control saturated, therefore, in order to obtain desired signal, get rid of interference noise, just need carry out filtering control signal.

At present, domestic having improved multiplex control system with methods such as EKF, experiment shows, improve multiplex control system later and suppressed system disturbance effectively, promoted dynamic property, but in actual set value trace system, because interference of noise makes target signal to noise ratio very low, EKF commonly used requires the independent or relevant Gaussian noise of noise, has defective in actual applications.Random quantity must satisfy the restriction condition of Gaussian distribution when particle filter (PF) algorithm had been broken away from EKF, provided new thinking for solving non-linear non-Gauss's interference problem.Particle filter is by prediction and upgrade the Bayesian Estimation at random that the sampling set that comes from system's probability density function is similar to nonlinear system, its basic skills is: at first the empirical condition according to the system state vector is distributed in the set that state space produces one group of random sample, supposes to have obtained one group of descriptive system state posterior probability distribution P[x (k) constantly at k | z _k)] sampled value, be designated as x (k, i), i=1 ...., N}, these samples are called particle; According to the observed quantity constantly more weight of new particle and position,, revise initial empirical condition and distribute then, the system state value is predicted by the information of adjusted particle, obtain one group of sampled value x (k+1, i), i=1, ..., N} makes it be similar to P[x (k+1) | z _K+1)].When sample size is very big, just be similar to the real posterior probability density function of state variable.This technology is applicable to the nonlinear stochastic system of any non-Gaussian Background, and precision can be approached optimal estimation, is a kind of effectively nonlinear filtering wave technology.

In the control method that application RBF (radial basis function) neural network realization pid parameter is adjusted,, determine the structure of RBF network, i.e. neuronic number in network input layer, hidden layer and the output layer at first according to input, the output number of system.Three of general selection identification network are input as: u (k), and y (k), y (k-1), wherein u (k) represents the control signal of k PID controller output constantly, the output signal of etching system during y (k) expression k, the output signal of etching system when y (k-1) represents k-1.The target function of adjusting of neural network is: The reference of etching system input adopted the gradient descent method can obtain three parameter k of PID then when wherein r (k) represented k _p, k _iAnd k _dAdjustment amount, thereby realize adjusting of pid parameter.

Adopt RBF neural network tuned proportion integration differentiation pid parameter, simple in structure, and the RBF network has the high and stronger adaptive ability of precision to Nonlinear Systems Identification, but this method is controlled the interference of various non-linear non-Gaussian noises in the process easily, thereby the identification precision of RBF network is produced bigger influence; Though and particle filter can be eliminated the influence of noise to system control performance, the parameter that it can't identification PID controller.

Summary of the invention

The objective of the invention is at object model the unknown and interference in the prior art for non-linear, the control system of non-Gaussian noise and propose a kind of Neural Network PID Control parameter self-tuning method based on particle filter (PF) and RBF (radial basis function) identification, particle filter and RBF neural network are combined, adopt particle filter to handle the original advantage of non-linear non-Gauss's time-varying system parameter estimation and state filtering problem, and adopt the RBF neural network that Nonlinear Systems Identification is had the high and strong characteristics of adaptive ability of precision, improve the performance index and the antijamming capability of control system better.

Technical scheme of the present invention is to adopt following steps: 1) output of the Neuron PID controller in the system is connected the controlling object input, with output of PID controller and the output y of system _OutConnect the input of RBF neural network structure identification respectively, the output y of system _OutAnd connection particle filter part between the RBF neural network structure identification; 2) adopt particle filter that system is exported y _OutCarry out filtering, obtain particle filter output y _e, particle filter is exported y _eWith RBF neural network output y _mThe value e that subtracts each other ₂=y _e-y _mAs objective function training RBF neural network, obtain RBF neural network identification output y _m(k); 3) in conjunction with RBF neural network identification output y _m(k) Jacobi's information of computing system

U (k) is the control signal of PID controller output, y _Out(k) be the control signal of system's output; 4) system reference is imported r _InWith the output y of system _OutBetween deviation signal e ₁As objective function training neuron, use Jacobi's information guiding neuron is adjusted the PID controller by learning algorithm these 3 parameters of scale-up factor, integration time constant and derivative time constant.

The invention has the beneficial effects as follows: the present invention obtains accurate Jacobi's information by particle filter and RBF System Discrimination, be that controlling object is exported the sensitivity information to the control input, solve single neuron PID and control owing to the unknown of Jacobi's information, substitute the coarse problem of bringing of calculating of calculating with sign function; When keeping characteristics such as PID control robustness height and good reliability, further improved the dynamic response performance and the antijamming capability of control system.

Description of drawings

Below in conjunction with the drawings and specific embodiments the present invention is described in further detail:

Fig. 1 is based on the pid parameter of particle filter and RBF from adjusting structural representation.

Embodiment

Referring to Fig. 1, at first set up control system structure as shown in Figure 1, the method for building up of this structure is: original control system is that the output of the PID controller in the system is connected the controlling object input, the present invention increases RBF neural network structure identification and particle filter part on original Neuron PID controller basis.The output of Neuron PID controller and the output of system are connected the input of RBF neural network structure identification respectively, particle filter partly is connected between the output and RBF neural network structure identification of system, and the input signal of RBF neural network is the control signal u (k) of PID controller output and the output y of system _OutUtilize the output y of particle filter to system _OutCarry out filtering, the output that obtains filtering is y as a result _eWith the output of particle filter y as a result _eOutput y with the RBF neural network _mSubtract each other, i.e. e ₂=y _e-y _m, it as objective function training RBF neural network, is obtained the identification output y of RBF neural network _mBack (dotted line among Fig. 1 is the System Discrimination process) calculates Jacobi's information of system

Be the sensitivity information of controlling object output to the control input.Utilize system reference input r _InWith the output y of system _OutBetween deviation signal e ₁As objective function training neuron, and adjust neuronic weight coefficient in conjunction with the Jacobi information that the identification of RBF network obtains, promptly use Jacobi's information guiding neuron (ANN) and adjust 3 parameters of PID controller by learning algorithm, thereby obtain 3 parameters of PID controller, i.e. scale-up factor K _P, integration time constant T _IWith derivative time constant T _D

Above-mentioned application particle filter is to the output y of control system _OutThe method of carrying out filtering is as follows:

The basic skills of particle filter is: by seeking one group of random sample of propagating to probability density function p (x in state space _k| z _k) be similar to, replace integral operation with sample average, thus the minimum variance estimate of the state of acquisition, and these samples promptly are called " particle ".The employing mathematical linguistics is described below: for stochastic process stably, the posterior probability density of etching system is p (x when supposing k-1 _K-1| z _K-1), choose n random sample point according to certain principle, after k obtains metrical information constantly, to upgrade through state and time, the posterior probability density of n particle can be approximately p (x _k| z _k).Along with the increase of particle filter number, the probability density function of particle approaches the probability density function of state gradually, and particle filter estimates promptly to have reached the effect of optimum Bayesian Estimation, and its filter step is as follows:

Step 1: initialization: when establishing moment k=0,

I=1,2 ..., N; From p (x _k| x _K-1, y _k) in randomly draw n sample (particle); Wherein, x ₀The state vector of representing 0 o'clock etching system, x _kThe state vector of etching system during expression k, y _kThe output of etching system during expression k, the state priori conditions probability of p (g) expression system,

Expression k=0 is i the sample (particle) of state vector constantly, and its weights are

Step 2: corresponding sample p (x is calculated in pointwise _k| y _K-1) and p (x _k| y _k) sampled value;

Step 3: utilize Formula is calculated the weights of corresponding sample, and it is carried out normalization; Be k i particle of state vector constantly

Weights.

Step 4: calculate new particle collection, according to

Formula resampling N time obtains δ (g) represents Dirac function.

Step 5: output result: state estimation: Variance is estimated:

Expression k is the estimated value of state vector constantly, P _kIt is its corresponding variance.

Step 6:k → k+1 returns step 3 circulation then, until end, finishes the output y to control system _Out, the output result who obtains particle filter is y _e

Jacobi's information of aforesaid system

Computing method as follows:

Determined the identification performance index function of RBF neural network before this, in the System Discrimination structure, the input vector of RBF neural network is X=[x ₁, x ₂... x _n] ^T, establish the radially basic H=[h of RBF neural network ₁, h ₂... h _j... h _m] ^T, wherein radially basic h _jSelect the gaussian basis function: J=1,2 ... m, wherein || g|| represents norm, and exp (g) represents exponential function.The center vector of j node of RBF neural network is: C _j=[c _J1, c _J2... c _Ji... c _Jn] ^T, i=1,2 ... n.If the sound stage width vector of RBF neural network is: B=[b ₁, b ₂... b _m] ^T, b wherein ₁Be the sound stage width degree parameter of node j, and be number greater than zero.The weight of RBF neural network is: W=[w ₁, w ₂... w _j... w _m] ^T, then the identification performance index function of RBF neural network is:

$J=\frac{1}{2}{e}_2\left(k\right)=\frac{1}{2}(y_e\left(k\right)-y_m\left(k\right)),$

Y wherein _eBe the output result of particle filter, y _m(k) be the identification output of RBF neural network.

Then, take the gradient descent method, the iterative algorithm of output power, node sound stage width and node center parameter is as follows:

w _j(k)＝w _j(k-1)+η(y _e(k)-y _m(k))h _j+α(w _j(k-1)-w _j(k-2))

$\mathrm{\Δ}{b}_j=(y_e\left(k\right)-y_m\left(k\right)w_j{h}_j\frac{{\left|\right|X-C_j\left|\right|}^2}{b_j^3}$

b _j(k)＝b _j(k-1)+ηΔb _j+α(b _j(k-1)-b _j(k-2))，

$\mathrm{\Δ}{c}_{\mathrm{ji}}=(y_e\left(k\right)-y_m\left(k\right))w_j\frac{x_j-c_{\mathrm{ji}}}{b_j^2}$

c _ji(k)＝c _ji(k-1)+ηc _ji+α(c _ji(k-1)-c _ji(k-2))

Wherein, η is a learning rate, and α is a factor of momentum.

The identification of RBF neural network is output as: y _m(k)=w ₁h ₁+ w ₂h ₂+ ...+w _mh _m

Jacobi's information can be obtained by following formula:

X wherein ₁=u (k), y _OutBe system's output, y _Out(k) be the control signal of system's output, u (k) is the control signal of PID controller output, y _m(k) be the output of RBF neural network identification.

Aforementioned applications Jacobi's information guiding neuron (ANN among Fig. 1) is as follows by the method for 3 parameters of learning algorithm adjustment PID controller:

The Neuron PID controller adopts iterative algorithm to adjust weight coefficient, and algorithm has simple in structure, and reaction is fast, and it is good that signal changes adaptability, characteristics such as strong robustness, and control algolithm and learning algorithm are:

$u\left(k\right)=u(k-1)+K\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{w^{\′}}_i\left(k\right)x_i\left(k\right)$

${w^{\′}}_i\left(k\right)=w_i\left(k\right)/\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\left|w_i\left(k\right)\right|;$

$E\left(k\right)=\frac{1}{2}{e}_1^2\left(k\right)=\frac{1}{2}{(r_{\mathrm{in}}\left(k\right)-y_{\mathrm{out}}\left(k\right))}^2$

$\mathrm{\Δ}{w}_i\left(k\right)=-\mathrm{\η}\frac{\∂E}{\∂w_i}=-\mathrm{\η}\frac{\∂E}{\∂y_{\mathrm{out}}}\frac{\∂y_{\mathrm{out}}}{\∂u}\frac{\∂u}{\∂w_i}=\mathrm{\η}{e}_1\left(k\right)\frac{\∂y_{\mathrm{out}}}{\∂u}{x}_i\left(k\right);$

w _i(k)＝w _i(k-1)+Δw _i(k)

Wherein

e ₁(k) expression k neuronic input signal of the moment, i.e. system reference input r _InWith the output y of system _OutBetween deviation signal, the control signal of u (k) expression k PID controller output constantly, w _i(k) (i=1,2,3) are neuronic 3 weight coefficients, corresponding to 3 parameters in the PID controller, i.e. and ratio, differential, integral coefficient, Δ w _i(k) be the weight coefficient adjustment amount,

Be Jacobi's information of controlled device, obtain by particle filter and RBF neural network identification.η is a learning of neuron speed, and K is the neuron scale-up factor, and the K value is selected extremely important, and K is big more, and then rapidity is good more, but overshoot is big, even may make system's instability.When the controlled device time delay increased, the K value must reduce, to guarantee system stability.The K value selects too small meeting to make system's rapidity variation.

Claims (2)

1. Neural Network PID Control parameter self-tuning method based on particle filter and RBF identification is characterized in that adopting following steps:

1) output of the Neuron PID controller in the system is connected the controlling object input, with output of PID controller and the output y of system _OutConnect the input of RBF neural network structure identification respectively, the output y of system _OutAnd connection particle filter part between the RBF neural network structure identification;

2) adopt particle filter that system is exported y _OutCarry out filtering, obtain particle filter output y _e, particle filter is exported y _eWith RBF neural network output y _mThe value e that subtracts each other ₂=y _e-y _mAs objective function training RBF neural network, obtain RBF neural network identification output y _m(k);

3) in conjunction with RBF neural network identification output y _m(k) Jacobi's information of computing system

U (k) is the control signal of PID controller output, y _Out(k) be the control signal of system's output;

4) system reference is imported r _InWith the output y of system _OutBetween deviation signal e ₁As objective function training neuron, use Jacobi's information guiding neuron is adjusted the PID controller by learning algorithm these 3 parameters of scale-up factor, integration time constant and derivative time constant.

2. the Neural Network PID Control parameter self-tuning method based on particle filter and RBF identification according to claim 1 is characterized in that: step 2) described to the output y of system _OutThe method of carrying out filtering comprises the steps:

A) randomly draw n sample constantly at k=0, the sampled value of corresponding sample is calculated in pointwise;

B) calculate the weights of corresponding sample and it is carried out normalization;

C) resampling is N time;

D) output state is estimated and the variance estimation;

E) circulation k → k+1 obtains particle filter output y until end _e

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