CN105487379A - Prediction function control method for coking heating furnace oxygen content - Google Patents

Abstract

The invention discloses a prediction function control method for coking heating furnace oxygen content. The prediction function control method comprises steps of modeling for an industrial process through the substantial data collected during the industrial process, dividing the model into a linear part and a non-linear part, using a counterpropagation nerve network to perform modeling on the non-linear portion, using a traditional linear two-point method to perform modeling on the linear part, using the prediction function control method to perform rolling optimization on the established model, and returning the feedback of correction so as to determine the control variable outputted at the next moment. The invention uses the prediction function, which, compared with the traditional PID control, can more effectively improve the dynamic performance and stability of the system.

Description

A kind of predictive functional control algorithm of coking heater oxygen content

Technical field

The invention belongs to technical field of automation, relate to a kind of predictive functional control algorithm of coking heater oxygen content.

Background technology

Coking plays an important role in the economy promoting petrochemical industry.In the control system of coke furnace, the control of oxygen content is a very important problem, and it directly can have influence on indoor pressure, the temperature etc. of radiation.Due to the overall flow that coke-fired furnace, distillation column and coke drum are mutually mutual.The volume of gaseous state oil is in a distillation column closely-related with the circulating temperature flowing into oil in coke-fired furnace, but the content of the temperature of oil on oxygen has direct impact.Oil temperature remaining in coke-fired furnace and the coking rate in coke drum also affect the consumption being sent to fuel needed in stove, and these factors are also maintained close ties with the content of oxygen.Interference in process, the delay of time, non-linear effects the oxygen content in coke-fired furnace, thus the switch that result in coke drum makes process occur a lot of periodic concussions.Non-linear just because of during the course, complicated dynamic and the interference of variable, so general PID controller is also difficult to the content of oxygen to control a setting value.Although Model Predictive Control (DMC) has applied in industrial process widely, the challenge in coke oven has limited applicability and the efficiency of DMC control.Although multi-model strategy and nonlinear control can be adopted, but multi-model strategy needs a large amount of operations and tests widely, this causes control performance greatly to depend on the form of operation, for nonlinear Control, have enough effective nonlinear models and the best practice of corresponding nonlinear model, this be also industrial faced by a great problem.

When occur in industrial flow very complicated nonlinear time, it is extremely important that the data of industrial process but manifest.Can pass through the dynamic model of valid data process of establishing a large amount of in industry, thus the structure obtaining model carrys out the controller of design ideal.There is the research of association area, but also occurred that a large amount of difficult problem etc. is to be solved.Such as, have many model parameters to need identification and the interference of model to be that predicted value trends towards through negative feedback infinite.

Summary of the invention

The present invention is directed to the deficiencies in the prior art, propose a kind of data structuring model applies to oxygen content in coking heater control method in conjunction with Predictive function control design.The advantage of this control method is make use of black box principle in industry and carrys out CONTROLLER DESIGN, effectively can utilize linear control method.This control method compared with traditional PID method, improves the anti-interference in process in the application of reality.

First the present invention is that a large amount of data by collecting in industrial process carry out modeling to industrial process, model is seen as linear processes two parts form, then utilize reverse transmittance nerve network (BPNN) to carry out modeling to non-linear partial respectively, utilize traditional linear two-point method to carry out modeling to linear segment.Utilize the method for Predictive function control (PFC) to carry out rolling optimization, feedback compensation to the model established, thus determine the control variable that subsequent time exports.

Technical scheme of the present invention is by data acquisition Modling model, utilizes the prediction mechanism of Predictive function control, constantly carries out rolling optimization determination controlled volume.The method obviously can improve dynamic property and the stability of system.

Step of the present invention is as follows:

1. set up the model of controlled device

1-1. due to the model of controlled device be enough become by linear processes two parts, so following form can be described as:

y(k)＝y _L(k)+y _NL(k)(1)

Wherein y _lk () is the output of linear model under step response, y _nLk () passes through y _l(k) and y (k) | _i, (i=1,2 ..., N) between the nonlinear model determined of deviation, y (k) | _i, (i=1,2 ..., N) and be the output of controlled device y (k) in i moment real process, N is the sampled point number exported.

The linear segment of 1-2. model can be obtained by step response, and y (t) is the actual output of model, and y (∞) is that the stable state of model exports, U ₀it is the enlargement factor of input signal.The y (t) exported can use form state, the gain of model can be expressed as

According to the feature of model process, the linear segment of whole model can be described as first order modeling and add delay component or second-order model delay component.Choosing linear model is following form:

$G\left(s\right)=\frac{{\mathrm{Ke}}^{-\mathrm{\τ}s}}{Ts+1}---\left(2\right)$

Therefore y ^*t () can be described by mode below.

$y^{*}\left(t\right)=\left\{\begin{array}{cc}0& t<\mathrm{\&tau;}\\ 1-e^{-\frac{t-\mathrm{\&tau;}}{T}}& t\&GreaterEqual;\mathrm{\&tau;}\end{array}\right.---\left(3\right)$

Wherein get y ^*(t ₁)=0.39, y ^*(t ₂)=0.63, t ₂>t ₁> τ, delay time T and response time T can obtain:

T＝2(t ₂-t ₁)

(4)

τ＝2t ₁-t ₂

Non-linear partial in 1-3. model can be obtained by step below:

If wherein y _li(k) (i=1,2 ..., N) and be y _lk () is in the value of corresponding time point.The y of non-linear partial in model _nLk (), is made by BPNN value minimum value, model is as follows:

$y_{NL}\left(k\right)=g\{\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g\&lsqb;w2(i,1)u(k-d-1)+w2(i,2)y(k-1)\&rsqb;\}---\left(5\right)$

Wherein w ₂(i, j) (j=1,2), w ₃i () is the connection weight of neural network power link layer, I is the number of output node, and g (x) activation function can be chosen as g (x)=1/ (1+e ^-x), the delay link in model is equivalent to d=τ/T _s.By sampling time T _s, be expressed as following form by after the model discretize of controlled device:

y(k)＝α ₁y(k-1)+β ₀u(k-d-1)+y _NL(k)(6)

Wherein α ₁, β ₀it is coefficient corresponding in equation.

2. PREDICTIVE CONTROL function (PFC) Controller gain variations:

2-1. the prediction of output

If:

$\mathrm{\&theta;}\left(k\right)=\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g\&lsqb;w2(i,1)u(k-d-1)+w2(i,2)y(k-1)\&rsqb;---\left(7\right)$

In order to predict the result of future course, can g (θ (k)) and respectively at central point θ ₀with carry out linearization process and can obtain following equation:

$\begin{array}{c}g\left(\mathrm{\&theta;}\right(k\left)\right)=g\left({\mathrm{\&theta;}}_0\right)+g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)\&lsqb;\mathrm{\&theta;}\left(k\right)-{\mathrm{\&theta;}}_0\&rsqb;+\mathrm{\&epsiv;}\left(\mathrm{\&phi;}\right(k\left)\right)\\ =g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)\mathrm{\&theta;}\left(k\right)+g\left({\mathrm{\&theta;}}_0\right)-g^{\&prime;}\left({\mathrm{\&theta;}}_0\right){\mathrm{\&theta;}}_0+\mathrm{\&epsiv;}\left(\mathrm{\&phi;}\right(k\left)\right)\end{array}---\left(9\right)$

Wherein φ (k)=[u (k-d-1), y _m(k-1)] ^t, ε and it is nonlinear function.

Can be obtained further by above-mentioned expression formula:

Can be found by above formula relevant to future anticipation moieties into close, that therefore a higher-order function can be ignored.Thus following form can be obtained:

$\begin{array}{c}{y}_m\left(k\right)={\mathrm{\&alpha;}}_1{y}_m(k-1)+{\mathrm{\&beta;}}_{0}u(k-d-1)\\ +\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right)\&lsqb;w2(i,1)u(k-d-1)+w2(i,2)y(k-1)\&rsqb;+C\end{array}---\left(12\right)$

Wherein $C=\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)\&lsqb;g\left({\mathrm{\&theta;}}_{i0}\right)-g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right){\mathrm{\&theta;}}_{i0}\&rsqb;+g\left({\mathrm{\&theta;}}_0\right)-g^{\&prime;}\left({\mathrm{\&theta;}}_0\right){\mathrm{\&theta;}}_0$ Be a constant term, following equation can be obtained:

y(k)＝a ₁y(k-1)+b ₀u(k-d-1)+C(13)

Wherein $\begin{array}{c}{a}_1={\mathrm{\&alpha;}}_1+\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right)w2(i,2)\\ b_1={\mathrm{\&beta;}}_1+\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right)w2(i,1)\end{array}---\left(14\right)$

2-2. carries out difference operator Δ=1-z by above formula (13) two ends ^-1conversion, after difference, the output of model is y _m(k), the following result of its form:

y _m(k)＝A ₁y _m(k-1)+A ₂y _m(k-2)+B _1,0Δu(k-d-1)(15)

Wherein A ₁=1+a ₁, A ₂=-a ₁, B _1,0=b ₀.

2-3. utilizes the modelling pfc controller of above formula (15), it can be divided into three parts.Part I is y _past(k+d+p) it is determined by the input and output in past, and Part II is G _pu _pdecided by the present and following input quantity, Part III be predicated error it be decided by feedback error wherein in the tangible k moment, the spatial choice of anticipation function is N _y:

$\begin{array}{c}\hat{y}(k+d+p/k)=y_{past}(k+d+p)+G_p{U}_p+\&lsqb;y\left(k\right)-\hat{y}\left(k\right)\&rsqb;\\ p=1,2,\mathrm{...},N_y\end{array}---\left(16\right)$

Wherein U _p=(Δ u (k), Δ u (k+1) ..., Δ u (k+p-1)) ^t

$\begin{array}{c}{G}_p=\left[\begin{array}{cccc}{B}_{1,0}& & & \\ B_{2,0}& B_{1,0}& 0& \\ \mathrm{...}& \mathrm{...}& & \\ B_{p,0}& B_{p-1,0}& \mathrm{...}& B_{1,0}\end{array}\right]\\ B_{k,0}=b_{k-1}+\underset{j=1}{\overset{k-1}{\&Sigma;}}{A}_j{B}_{k-j,0},k=2,\mathrm{3...},p\end{array}---\left(17\right)$

In the strategy of PREDICTIVE CONTROL, controlled quentity controlled variable is the connection that is closely related with the characteristic sum initial set value of systematic procedure.

$u(k+i)=\underset{j=1}{\overset{M}{\&Sigma;}}{\mathrm{\&lambda;}}_j{f}_j\left(i\right)---\left(18\right)$

Wherein λ _jweight coefficient, f _ji () is the value of basis function at sampling instant i, M is basis function

y _ref(k+d)＝y(k)

(19)

y _ref(k+d+p)＝μ ^py(k)+(1-μ ^p)y _s

p＝1,2,…,N _y

Wherein μ is smoothing factor, y _sit is setting value

2-4. optimality criterion is as follows:

$J=min{\left(y_{ref}\right(k+d+N_y)-\hat{y}(k+d+N_y/k\left)\right)}^2---\left(20\right)$

Thus obtain controlling increment, calculate the controlled quentity controlled variable in k moment:

$\begin{array}{c}\mathrm{\&Delta;}u\left(k\right)=\left(y_{ref}\right(k+d+N_y)-y_{past}(k+d+N_y)-y(k)+\hat{y}(k\left)\right)/B_{N_y,0}\\ u\left(k\right)={\mathrm{\&lambda;}}_1=u(k-1)+\mathrm{\&Delta;}u\left(k\right)\end{array}---\left(21\right)$

The controlled quentity controlled variable obtained is acted on controlled device by 2-5., by the time repeats step 2-2 to step 2-4 during subsequent time and continues controlled quentity controlled variable u (k+1) cycling successively solving controlled device.

Beneficial effect of the present invention is as follows:

The present invention is based on being simple step response model and non-linear partial by model decomposition complicated in industry, the PREDICTIVE CONTROL utilizing neural network to carry out comprehensive nonlinear system combines with Predictive function control, reduces the complicacy of system architecture, alleviates the burden of computing.The local linear that make use of nonlinear activation function represents, multistep nonlinear prediction is converted to the multi-step linear prediction form of a series of simple, intuitive.Utilize Predictive function control to control than traditional PID, more effectively can improve dynamic property and the stability of system, and in applying to the arranging of industrial control unit (ICU).

Embodiment

For oxygen content control procedure in coking heater stove:

1. set up the model of coking heater

1-1. enough becomes because the oxygen content in coking furnace can be described as linear processes two parts, so can obtain following expression-form:

y(k)＝y _L(k)+y _NL(k)(1)

Wherein y _lk () is the output of model under step response, y _nLk () passes through y _l(k) and y (k) | _i, (i=1,2 ..., N) between the nonlinear block determined of deviation, y (k) | _i, (i=1,2 ..., N) and be that controlled device exports the output of y (k) in i moment real process, N is the sampled point number exported.

The linear segment of 1-2. model can be obtained by step response, and y (t) is the actual output of model, and y (∞) is that the stable state of model exports, U ₀it is the enlargement factor of input signal.The y (t) exported can use form state, the gain of model can be expressed as

According to the feature of model process, the linear segment of whole model can be described as first order modeling and add delay component or second-order model delay component.We choose linear model is following form:

$G\left(s\right)=\frac{{\mathrm{Ke}}^{-\mathrm{\&tau;}s}}{Ts+1}---\left(2\right)$

Therefore y ^*t () can be described by mode below.

$y^{*}\left(t\right)=\left\{\begin{array}{cc}0& t<\mathrm{\&tau;}\\ 1-e^{-\frac{t-\mathrm{\&tau;}}{T}}& t\&GreaterEqual;\mathrm{\&tau;}\end{array}\right.---\left(3\right)$

Wherein get y ^*(t ₁)=0.39, y ^*(t ₂)=0.63, t ₂>t ₁> τ, delay time T and response time T can obtain:

T＝2(t ₂-t ₁)

(4)

τ＝2t ₁-t ₂

Non-linear partial in 1-3. model can be obtained by step below:

If wherein y _li(k) (i=1,2 ..., N) and be y _lk () is in the value of corresponding time point.The y of non-linear partial in model _nLk (), can pass through reverse transmittance nerve network (BPNN) and make value minimum, model is as follows:

$y_{NL}\left(k\right)=g\{\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g\&lsqb;w2(i,1)u(k-d-1)+w2(i,2)y(k-1)\&rsqb;\}---\left(5\right)$

Wherein w ₂(i, j) (j=1,2), w ₃i () is the connection weight of neural network power link layer, I is the number of output node, and g (x) activation function can be chosen as g (x)=1/ (1+e ^-x), the delay link in model is equivalent to d=τ/T _s.By sampling time T _s, be expressed as following form by after the model discretize of controlled device:

y(k)＝α ₁y(k-1)+β ₀u(k-d-1)+y _NL(k)(6)

Wherein α ₁, β ₀it is coefficient corresponding in equation.

2. the concrete grammar of Predictive function control (PFC) Controller gain variations:

The 2-1. prediction of output:

If:

$\mathrm{\&theta;}\left(k\right)=\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g\&lsqb;w2(i,1)u(k-d-1)+w2(i,2)y(k-1)\&rsqb;---\left(7\right)$

In order to predict the result of future course, can g (θ (k)) and respectively at central point θ ₀with carry out linearization process and can obtain following equation:

$\begin{array}{c}g\left(\mathrm{\&theta;}\right(k\left)\right)=g\left({\mathrm{\&theta;}}_0\right)+g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)\&lsqb;\mathrm{\&theta;}\left(k\right)-{\mathrm{\&theta;}}_0\&rsqb;+\mathrm{\&epsiv;}\left(\mathrm{\&phi;}\right(k\left)\right)\\ =g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)\mathrm{\&theta;}\left(k\right)+g\left({\mathrm{\&theta;}}_0\right)-g^{\&prime;}\left({\mathrm{\&theta;}}_0\right){\mathrm{\&theta;}}_0+\mathrm{\&epsiv;}\left(\mathrm{\&phi;}\right(k\left)\right)\end{array}---\left(9\right)$

Wherein φ (k)=[u (k-d-1), y _m(k-1)] ^t, ε and it is nonlinear function.

Can be obtained further by above-mentioned expression formula:

Can be found by above formula relevant to future anticipation moieties into close, that therefore a higher-order function can be ignored.Thus following form can be obtained:

$\begin{array}{c}{y}_m\left(k\right)={\mathrm{\&alpha;}}_1{y}_m(k-1)+{\mathrm{\&beta;}}_{0}u(k-d-1)\\ +\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right)\&lsqb;w2(i,1)u(k-d-1)+w2(i,2)y(k-1)\&rsqb;+C\end{array}---\left(12\right)$

Wherein $C=\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)\&lsqb;g\left({\mathrm{\&theta;}}_{i0}\right)-g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right){\mathrm{\&theta;}}_{i0}\&rsqb;+g\left({\mathrm{\&theta;}}_0\right)-g^{\&prime;}\left({\mathrm{\&theta;}}_0\right){\mathrm{\&theta;}}_0$ Be a constant term, following equation can be obtained:

y(k)＝a ₁y(k-1)+b ₀u(k-d-1)+C(13)

Wherein $\begin{array}{c}{a}_1={\mathrm{\&alpha;}}_1+\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right)w2(i,2)\\ b_1={\mathrm{\&beta;}}_1+\underset{i=1}{\overset{I}{\&Sigma;}}w3\left(i\right)g^{\&prime;}\left({\mathrm{\&theta;}}_0\right)g^{\&prime;}\left({\mathrm{\&theta;}}_{i0}\right)w2(i,1)\end{array}---\left(14\right)$

2-2. carries out difference operator Δ=1-z by above formula (13) two ends ^-1conversion, after difference, the output of model is y _m(k), the following result of its form:

y _m(k)＝A ₁y _m(k-1)+A ₂y _m(k-2)+B _1,0Δu(k-d-1)(15)

Wherein A ₁=1+a ₁, A ₂=-a ₁, B _1,0=b ₀.

2-3. utilizes the modelling pfc controller of above formula (15), and it can be divided into three parts by us.Part I is y _past(k+d+p) it is determined by the input and output in past in coking furnace, and Part II is G _pu _pdecided by the input quantity present and following in coking furnace, Part III be predicated error it be decided by feedback error wherein in the tangible k moment, the spatial choice of anticipation function is N _y:

$\begin{array}{c}\hat{y}(k+d+p/k)=y_{past}(k+d+p)+G_p{U}_p+\&lsqb;y\left(k\right)-\hat{y}\left(k\right)\&rsqb;\\ p=1,2,\mathrm{...},N_y\end{array}---\left(16\right)$

Wherein U _p=(Δ u (k), Δ u (k+1) ..., Δ u (k+p-1)) ^t

$\begin{array}{c}{G}_p=\left[\begin{array}{cccc}{B}_{1,0}& & & \\ B_{2,0}& B_{1,0}& 0& \\ \mathrm{...}& \mathrm{...}& & \\ B_{p,0}& B_{p-1,0}& \mathrm{...}& B_{1,0}\end{array}\right]\\ B_{k,0}=b_{k-1}+\underset{j=1}{\overset{k-1}{\&Sigma;}}{A}_j{B}_{k-j,0},k=2,\mathrm{3...},p\end{array}---\left(17\right)$

In the PREDICTIVE CONTROL of coking furnace oxygen content, controlled quentity controlled variable is the connection that is closely related with the characteristic of systematic procedure and initial set value.

$u(k+i)=\underset{j=1}{\overset{M}{\&Sigma;}}{\mathrm{\&lambda;}}_j{f}_j\left(i\right)---\left(18\right)$

Wherein λ _jweight coefficient, f _ji () is the value of basis function at sampling instant i, M is basis function

y _ref(k+d)＝y(k)

(19)

y _ref(k+d+p)＝μ ^py(k)+(1-μ ^p)y _s

p＝1,2,…,N _y

Wherein μ is smoothing factor, y _sit is setting value

2-4.. optimality criterion is as follows:

$J=min{\left(y_{ref}\right(k+d+N_y)-\hat{y}(k+d+N_y/k\left)\right)}^2---\left(20\right)$

Thus obtain the controlling increment of oxygen content, calculate k moment Oxygen control amount:

$\begin{array}{c}\mathrm{\&Delta;}u\left(k\right)=\left(y_{ref}\right(k+d+N_y)-y_{past}(k+d+N_y)-y(k)+\hat{y}(k\left)\right)/B_{N_y,0}\\ u\left(k\right)={\mathrm{\&lambda;}}_1=u(k-1)+\mathrm{\&Delta;}u\left(k\right)\end{array}---\left(21\right)$

The controlled quentity controlled variable obtained is acted on controlled device by 2-5., by the time repeats step 2-2 to step 2-4 during subsequent time and continues controlled quentity controlled variable u (k+1) cycling successively solving controlled device.

Claims (1)

1. a predictive functional control algorithm for coking heater oxygen content, is characterized in that the concrete steps of the method are:

1). set up the model of controlled device

1-1. is enough become by linear processes two parts due to the model of controlled device, describes it as following form:

y(k)＝y _L(k)+y _NL(k)(1)

Wherein y _lk () is the output of linear model under step response, y _nLk () passes through y _l(k) and y (k) | _i, (i=1,2 ..., N) between the nonlinear model determined of deviation, y (k) | _i, (i=1,2 ..., N) and be the output of controlled device y (k) in i moment real process, N is the sampled point number exported;

The linear segment of 1-2. model is obtained by step response, and y (t) is the actual output of model, and y (∞) is that the stable state of model exports, U ₀it is the enlargement factor of input signal; The y (t) exported uses form state, the gain of model is expressed as

According to the feature of model process, the linear segment of model is described as following form:

Y ^*t () is described by mode below;

Wherein get y ^*(t ₁)=0.39, y ^*(t ₂)=0.63, t ₂>t ₁> τ, delay time T and response time T can obtain:

T＝2(t ₂-t ₁)(4)

τ＝2t ₁-t ₂

Non-linear partial in 1-3. model is by following acquisition:

If wherein y _lik () is y _lk () is in the value of corresponding time point; The y of non-linear partial in model _nLk (), is made by BPNN value minimum value, model is as follows:

Wherein w ₂(i, j) (j=1,2), w ₃i () is the connection weight of neural network power link layer, I is the number of output node, and g (x) activation function is chosen as g (x)=1/ (1+e ^-x), the delay link in model is equivalent to d=τ/T _s; By sampling time T _s, be expressed as following form by after the model discretize of controlled device:

y(k)＝α ₁y(k-1)+β ₀u(k-d-1)+y _NL(k)(6)

Wherein α ₁, β ₀it is coefficient corresponding in equation;

2). PREDICTIVE CONTROL function controller designs:

2-1. the prediction of output

If:

In order to predict the result of future course, g (θ (k)) and respectively at central point θ ₀with carry out linearization process and obtain following equation:

Wherein φ (k)=[u (k-d-1), y _m(k-1)] ^t, ε and it is nonlinear function;

Can be obtained further by above-mentioned expression formula:

Found by above formula relevant to future anticipation moieties into close, be a higher-order function, can ignore; Thus obtain following form:

Wherein be a constant term, following equation can be obtained:

y(k)＝a ₁y(k-1)+b ₀u(k-d-1)+C(13)

Wherein

2-2. carries out difference operator Δ=1-z by above formula (13) two ends ^-1conversion, after difference, the output of model is y _m(k), the following result of its form:

y _m(k)＝A ₁y _m(k-1)+A ₂y _m(k-2)+B _1,0Δu(k-d-1)(15)

Wherein A ₁=1+a ₁, A ₂=-a ₁, B _1,0=b ₀;

2-3. utilizes the modelling pfc controller of above formula (15), it is divided into three parts; Part I is y _past(k+d+p) it is determined by the input and output in past, and Part II is G _pu _pbe decided by the present and following input quantity, Part III is predicated error, and it is decided by feedback error wherein in the tangible k moment, the spatial choice of anticipation function is N _y:

Wherein U _p=(Δ u (k), Δ u (k+1) ..., Δ u (k+p-1)) ^t

In the strategy of PREDICTIVE CONTROL, controlled quentity controlled variable is the connection that is closely related with the characteristic sum initial set value of systematic procedure;

Wherein λ _jweight coefficient, f _ji () is the value of basis function at sampling instant i, M is basis function

y _ref(k+d)＝y(k)(19)

y _ref(k+d+p)＝μ ^py(k)+(1-μ ^p)y _s

p＝1,2,…,N _y

Wherein μ is smoothing factor, y _sit is setting value

2-4. optimality criterion is as follows:

Thus obtain controlling increment, calculate the controlled quentity controlled variable in k moment:

u(k)＝λ ₁＝u(k-1)+Δu(k)

The controlled quentity controlled variable obtained is acted on controlled device by 2-5., by the time repeats step 2-2 to step 2-4 during subsequent time and continues controlled quentity controlled variable u (k+1) cycling successively solving controlled device.