CN101900991A - Composite PID (Proportion Integration Differentiation) neural network control method based on nonlinear dynamic factor - Google Patents

Abstract

The invention discloses a composite PID (Proportion Integration Differentiation) neural network control method based on a nonlinear dynamic factor. In the method, creative improved research is carried out on the basis of stabilizing a PID controller based on a dynamic nonlinear factor by adopting a Ziegler-Nichols method abroad, and the defect of learning a mathematical model of a controlled object by confirming a PID gain parameter through utilizing a root locus method according to the Ziegler-Nichols method is effectively overcome. The invention aims to recombine three gain parameters and three factors in the prior art abroad to obtain six weight factors so as to obtain a composite PID neural network control law based on the nonlinear dynamic factor, which has six neural network weight factors, constructs a neural network model according to the nonlinear control law, and trains the weight factors in the composite PID controller based on the nonlinear dynamic factor on line in real time by using a neural network method to realize intelligent control on a nonlinear system. The invention can rapidly and accurately control a nonlinear object and has high robustness.

Description

Composite PID (Proportion Integration Differentiation) neural network control method based on nonlinear dynamic factor

Technical field

The invention belongs to automation field, relate to a kind of will be online from the quelling intelligence control method based on the parameter that the non-linear compound PID arithmetic element of dynamic factor is dissolved into hidden neuron.

Background technology

Ratio, integration, differential (P, I, D) control in deviation are control modes with the longest history, that vitality is the strongest.Although in today that advanced control strategy is promoted gradually, in the control loop that is moving at present, PID controller more than 90%.But, along with the raising of system complex degree and increasing of object uncertain factor, traditional linear PID control is no longer suitable, and nonlinear PID controller can truly reflect the nonlinear relationship between controlled quentity controlled variable and the deviation signal, overcome the shortcoming of linear PID controller to a certain extent, therefore, more and more be controlled the concern on boundary.In recent years, in order to overcome the weakness of conventional PID controllers, the control circle has proposed a large amount of improvement projects that neural network is combined with PID control, thisly neural network and PID are controlled the research that combines has obtained many achievements in research.Such as, with Neural Network Online correction pid parameter, obtained effectively from calm PID type generalized predictive controller; Adopt a neural network that controlled system is carried out identification and prediction, constitute Linear Network with P, I, D parameter as network weight simultaneously and find the solution performance index, obtained a kind of forecast function Neural network PID controller that has as controller; Adopt PID long-range prediction energy function as majorized function, and with the parameter of the online adjustment controller of local recursion's neural network (LCNN), realization non-linearity PID neural network multi-step prediction control algolithm have good adaptive ability and robustness; Adopt Neural Network Online to obtain linear control signal, obtain the nonlinear Control signal to realize nonlinear Control etc. through the Sigmoid functional transformation again from calm pid parameter.

But above method only is confined to adopt auxiliary P, I, the D parameter of choosing or revise conventional PID controllers of neural network, nonlinear Control ability.For this reason, there is the scholar to propose PID neuroid (PIDNN) control method.Its main thought is that linear PID arithmetic element is dissolved in the neural network hidden neuron through after the amplitude limiting processing, has constructed the simple dynamic network of structure, to realize the control of nonlinear system.Yet this method relates in one aspect to two-layer neural network weight adjustment, has the weights coupling phenomenon, thereby algorithm convergence is overflow, calculated amount is bigger, is unfavorable for the real-time control of quick sampling system; On the other hand, this method just is dissolved into linear PID arithmetic element in the neural network hidden neuron through after the amplitude limiting processing, and its nonlinear Control is indifferent.

Summary of the invention

The objective of the invention is: at the deficiencies in the prior art, the compound PID control law of a kind of kinematic nonlinearity has been proposed first, and the compound PID arithmetic element of kinematic nonlinearity is dissolved in the neural network hidden neuron, thereby construct a kind of linear composite PID (Proportion Integration Differentiation) neural network control method based on the dynamic non-factor.This method synthesis the advantage of the theoretical and neural network theory of nonlinear PID controller.

Technical scheme of the present invention is: adopt a kind of improvement project of the calm PID controller based on the kinematic nonlinearity factor of Ziegler-Nichols method to carry out further improvement research according to external pertinent literature, effectively avoided utilizing root-locus technique to determine that the gain parameter needs of PID know the drawback of the mathematical model of controlled device according to the Ziegler-Nichols method.The present invention is intended to the training of neural net method real-time online based on each gain parameter and coefficient in the compound PID controller of the kinematic nonlinearity factor, to realize the Based Intelligent Control of nonlinear system.

Further, specifically be divided into following steps:

(1) according to abroad based on the PID control law of the kinematic nonlinearity factor by launching to become compound PID control law based on the kinematic nonlinearity factor;

(2) according to the mathematical model based on the compound PID control law of nonlinear dynamic factor of structure, 1 dynamic linear proportional and 1 kinematic nonlinearity proportional, 1 dynamic linear integral and 1 kinematic nonlinearity integral, 1 dynamic linear differential term and 1 kinematic nonlinearity differential term are dissolved in the hidden neuron 6 dynamic operation unit totally, the kinematic nonlinearity composite PID (Proportion Integration Differentiation) neural network controller model that structure has traditional PI D essential characteristic, as shown in Figure 1;

(3) selected neural network learning rate by the initial value of the given at random weights coefficient of related request of each weights coefficient in the dynamic non-linear compound PID control law, has been avoided given by rule of thumb initial value;

(4) adopt gradient descent method online in real time to upgrade neural network weight, obtain the control signal of controlled device, to realize the online in real time Based Intelligent Control of non-linear object.

Advantage of the present invention is: simple in structure, exempt from model prediction, calculated amount little, be convenient to unknown object and be difficult to modeling the time become the nonlinear Control of Object with Time Delay.

Description of drawings

Fig. 1 is based on the composite PID (Proportion Integration Differentiation) neural network control system schematic diagram of nonlinear dynamic factor.

Embodiment

The present invention is further illustrated with reference to the accompanying drawings below.

1. based on the compound PID arithmetic element of nonlinear dynamic factor

In recent years, at Ziegler-Nichols method quelling PID controller a kind of improvement project has been proposed abroad, promptly

$\left\{\begin{array}{c}{K}_p^m\left(k\right)=K_p(1+k_1|\mathrm{\α}\left(k\right)\left|\right)\\ K_i^m\left(k\right)=K_i(0.3+k_2\mathrm{\α}\left(k\right))\\ K_d^m\left(k\right)=K_d(1+k_3|\mathrm{\α}\left(k\right)\left|\right)\end{array}\right.---\left(1\right)$

Wherein, k ₁=k ₂=1, k ₃=12;

The main innovation of formula (1) is during the gain that nonlinear dynamic factor α (k) is incorporated into PID is adjusted, and with the calm gain parameter K of PID of Ziegler-Nichols method _p, K _iAnd K _dBut, need know the mathematical model of controlled device with the gain parameter of the calm PID of Ziegler-Nichols method, and utilize root-locus technique to determine gain parameter.The present invention has done further research on the basis of formula (1), be intended to strengthen versatility with each gain parameter and coefficient in the neural net method real-time online training type (1).

At first formula (1) is expanded into

$\left\{\begin{array}{c}{K}_p^m\left(k\right)=K_p+K_p{k}_1\left|\mathrm{\α}\left(k\right)\right|\\ K_i^m\left(k\right)={0.3K}_i+{K_{i}k}_2\mathrm{\α}\left(k\right)\\ K_d^m\left(k\right)=K_d+K_d{k}_3\left|\mathrm{\α}\left(k\right)\right|\end{array}\right.---\left(2\right)$

If w ₁=K _p, w ₂=K _pk ₁, w ₃=0.3K _i, w ₄=K _ik ₂, w ₅=K _d, w ₆=K _dk ₃, then formula (2) becomes

$\left\{\begin{array}{c}{K}_p^m\left(k\right)=w_1+w_2\left|\mathrm{\α}\left(k\right)\right|\\ K_i^m\left(k\right)=w_3+w_4\mathrm{\α}\left(k\right)\\ K_d^m\left(k\right)=w_5+w_6\left|\mathrm{\α}\left(k\right)\right|\end{array}\right.---\left(3\right)$

Each coefficient w shown in the formula (3) in the gain function ₁, w ₂, w ₃, w ₄, w ₅, w ₆Can be by the training of neural net method online in real time, thereby the online in real time that realizes the non-linearity PID gain is calm, this control to nonlinear and time-varying system is particularly important, needing with the calm PID gain parameter of Ziegler-Nichols method can effectively avoid the difficult problem of known controlled device mathematical model.According to external existing result of study: k ₁=k ₂=1, k ₃=12, therefore, give each coefficient w in the gain function shown in the fixed pattern (3) at random ₁, w ₂, w ₃, w ₄, w ₅, w ₆Initial value the time, should satisfy constraint condition: w ₁=w ₂＞0,0＜w ₃＜w ₄, 0＜w ₅＜w ₆

2. based on the compound PID neuroid controller of nonlinear dynamic factor

As everyone knows, conventional digital PID control law is

$u\left(k\right)=k_{p}e\left(k\right)+k_i\underset{m=0}{\overset{k}{\mathrm{\Σ}}}e\left(m\right)+k_d\mathrm{\Δe}\left(k\right)---\left(4\right)$

The gain of three kinematic nonlinearities in the formula (3) is substituted three linear gains in the formulas (4), can get non-linear, digital PID control law and be:

$u\left(k\right)=[w_1+w_2|\mathrm{\α}\left(k\right)\left|\right]e\left(k\right)+[w_3+w_4\mathrm{\α}\left(k\right)]\underset{m=0}{\overset{k}{\mathrm{\Σ}}}e\left(m\right)+[w_5+w_6|\mathrm{\α}\left(k\right)\left|\right]\mathrm{\Δe}\left(k\right)---\left(5\right)$

By formula (5) as can be known, in fact this control law has kept the essential characteristic of traditional PI D, different is: this control law is composited 6 dynamic operation unit by 1 dynamic linear proportional and 1 kinematic nonlinearity proportional, 1 dynamic linear integral and 1 kinematic nonlinearity integral, 1 dynamic linear differential term and 1 kinematic nonlinearity differential term totally, therefore be a compound PID control law of Nonlinear Dynamic, promptly be composited by a dynamic linear PID and a kinematic nonlinearity PID.Can construct the compound PID neuroid of Nonlinear Dynamic controller model as shown in Figure 1 according to formula (5), wherein

S _I1=s (k), S _I2=α (k) s (k),

And

Neural network output, promptly controlled device is input as

$u\left(k\right)=[w_1+w_2|\mathrm{\α}\left(k\right)\left|\right]\hat{e}\left(k\right)+[w_3+w_4\mathrm{\α}\left(k\right)]s\left(k\right)+[w_5+w_6|\mathrm{\α}\left(k\right)\left|\right]\mathrm{\Δ}\hat{e}\left(k\right)---\left(6\right)$

3. based on the compound PID neuroid right value update algorithm of nonlinear dynamic factor

(1) the definition error function is

e(k)＝r(k)-y(k) (7)

(2) the definition performance index are

$J=\frac{1}{2}\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{\hat{e}}^2(k+1)---\left(8\right)$

Wherein,

$\hat{e}(k+1)=S_e\left(e(k+1)\right),e(k+1)=r(k+1)-y(k+1)---\left(9\right)$

(3) adopt the gradient descent method, neural network weight more new formula is

$w_j^{k+1}=w_j^k-\mathrm{\μ}\frac{\∂J}{\∂w_j^k}---\left(10\right)$

Can get by formula (6), (8), (9):

$\frac{\∂J}{\∂w_j^k}=-\hat{e}(k+1)y_u\frac{\∂u\left(k\right)}{\∂w_j^k}---\left(11\right)$

Can get respectively by formula (6)

$\frac{\∂J}{\∂w_1^k}=-\hat{e}(k+1)\hat{e}\left(k\right)y_u,$ $\frac{\∂J}{\∂w_2^k}=-\hat{e}(k+1)\left|\mathrm{\α}\left(k\right)\right|\hat{e}\left(k\right)y_u,$ $\frac{\∂J}{\∂w_3^k}=-\hat{e}(k+1)s\left(k\right)y_u$

$\frac{\∂J}{\∂w_4^k}=-\hat{e}(k+1)\mathrm{\α}\left(k\right)s\left(k\right)y_u,$ $\frac{\∂J}{\∂w_5^k}=-\hat{e}(k+1)\mathrm{\Δ}\hat{e}\left(k\right)y_u,$ $\frac{\∂J}{\∂w_6^k}=-\hat{e}(k+1)\left|\mathrm{\α}\left(k\right)\right|\mathrm{\Δ}\hat{e}\left(k\right)y_u$

Therefore, can get the right value update formula by formula (10) is

$w_1^{k+1}=w_1^k+\mathrm{\μ}\hat{e}(k+1)\hat{e}\left(k\right)y_u;$ $w_2^{k+1}=w_2^k+\mathrm{\μ}\hat{e}(k+1)\left|\mathrm{\α}\left(k\right)\right|\hat{e}\left(k\right)y_u$

$w_3^{k+1}=w_3^k+\mathrm{\μ}\hat{e}(k+1)s\left(k\right)y_u;$ $w_4^{k+1}=w_4^k+\mathrm{\μ}\hat{e}(k+1)\mathrm{\α}\left(k\right)s\left(k\right)y_u$

$w_5^{k+1}=w_5^k+\mathrm{\μ}\hat{e}(k+1)\mathrm{\Δ}\hat{e}\left(k\right)y_u;$ $w_6^{k+1}=w_6^k+\mathrm{\μ}\hat{e}(k+1)\left|\mathrm{\α}\left(k\right)\right|\mathrm{\Δ}\hat{e}\left(k\right)y_u$

Wherein, 0＜μ＜1 is a learning rate,

4. the further discussion of right value update algorithm

By above-mentioned right value update formula as can be known,

With

All with to export y (k+1) (unknown) future of system relevant, thereby can make the neural network weight training dyscalculia occur.Domestic and international many scholars adopt the identification Method of controlled device to solve this dyscalculia, still, caused also that calculated amount is big, another problem of real-time difference, and for time-varying system, Model Distinguish are unrealistic.For this reason, the present invention proposes the effective ways that solve this dyscalculia, have versatility.

(1) well-known, if algorithm is a convergent, then must have:

Therefore, as long as satisfy condition:

Can guarantee that algorithm is a convergent.Can establish in view of the above:

And 0＜β＜1.Because β can remedy by learning rate μ, therefore, β can be lain among the learning rate μ.

(2) if substitute with sign function

Also be fully feasible.Because positive and negative the direction that the decision weights change of its symbol, the size of its numerical value only influences the pace of change of weights, and the weights pace of change also can be remedied by learning rate μ.If establish

${\hat{y}}_u\left(k\right)=\left\{\begin{array}{cc}\mathrm{sign}\left[\frac{y\left(k\right)-y(k-1)}{u(k-1)-u(k-2)}\right],& u(k-1)\≠u(k-2)\\ \mathrm{sign}[y\left(k\right)-y(k-1)],& u(k-1)=u(k-2)\end{array}\right.---\left(12\right)$

Then above-mentioned right value update formula can be rewritten as

$\left\{\begin{array}{c}{w}_1^{k+1}=w_1^k+\mathrm{\μ}{\hat{e}}^2\left(k\right){\hat{y}}_u\\ w_2^{k+1}=w_2^k+\mathrm{\μ}{\hat{e}}^2\left(k\right)\left|\mathrm{\α}\left(k\right)\right|{\hat{y}}_u\\ w_3^{k+1}=w_3^k+\mathrm{\μ}\hat{e}\left(k\right)s\left(k\right){\hat{y}}_u\\ w_4^{k+1}=w_4^k+\mathrm{\μ}\hat{e}\left(k\right)s\left(k\right)\mathrm{\α}\left(k\right){\hat{y}}_u\\ w_5^{k+1}=w_5^k+\mathrm{\μ}\hat{e}\left(k\right)\mathrm{\Δ}\hat{e}\left(k\right){\hat{y}}_u\\ w_6^{k+1}=w_6^k+\mathrm{\μ}\hat{e}\left(k\right)\mathrm{\Δ}\hat{e}\left(k\right)\left|\mathrm{\α}\left(k\right)\right|{\hat{y}}_u\end{array}\right.---\left(13\right)$

Wherein, β has lain among the learning rate μ.

(3) oscillatory occurences to occur in order effectively avoiding causing in the neural metwork training process, usually weights to be carried out normalized, promptly because of weights are excessive

$w_j^{k+1}=w_j^{k+1}/\underset{i=1}{\overset{6}{\mathrm{\Σ}}}\left|w_i^{k+1}\right|,(j=\mathrm{1,2},\·\·\·,6)---\left(14\right)$

By formula (12)～formula (13) as can be known, the calculating of weights is only relevant with u (k-2) with current or historical input r (k), r (k-1) and output y (k), y (k-1) and historical control signal u (k-1), thereby efficiently solves the difficult problem of weights calculating.The Nonlinear Dynamic composite PID (Proportion Integration Differentiation) neural network controller of the present invention research only relates to multiplication and additive operation, calculate simple, calculated amount is little, is convenient to practical application, being convenient to especially with the dsp chip is the realization of non-linear composite PID (Proportion Integration Differentiation) neural network controller of core.

Claims (6)

1. one kind is utilized neural network to calm based on the method for the compound PID controller parameter of nonlinear dynamic factor, it is characterized in that, abroad three gain parameters of the prior art and three coefficients reconfigure and obtain six weights coefficients, thereby the structure thought of nonlinear pid controller gain parameter has been proposed, derive non-linear compound PID control law formula, be neural network model with non-linear compound PID control law formula then, with six coefficients in the non-linear compound PID control law formula is the neural metwork training weights, draws the control signal of non-linear controlled device by Neural Network Online training in real time.

2. method according to claim 1 is characterized in that, described system is a nonlinear system.

3. method according to claim 1 is characterized in that, the control law of described system is non-linear compound PID control law.

4. method according to claim 1 is characterized in that, the non-linear compound PID control law of described system is composited by a dynamic linear PID and a kinematic nonlinearity PID.

5. method according to claim 1, it is characterized in that, described neural network is three layers of BP neural network, input layer and output layer are respectively a neuron, hidden layer comprises six neurons, is respectively two linearities and non-linear ratio's neuron, two linearities and non-linear integral neuron and two linearities and non-linear differential neuron.

6. method according to claim 1 is characterized in that, specifically is divided into following steps:

(1) is neural network model with non-linear compound PID control law formula, is the weights of neural network with each coefficient in the non-linear compound PID control law formula, and provides the initial value of weights coefficient, selected learning rate.

(2) export as train samples with the desired output and the reality of system, with the desired output error signal that output produces with reality input signal as neural network after amplitude limiting processing, with the control signal of neural network output as non-linear controlled device.

(3) train in real time by Neural Network Online, draw non-linear compound PID control law, non-linear controlled device is implemented online in real time control.

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