CN103345160B - The method for optimally controlling humidity of residual heat drying system - Google Patents

Abstract

The invention discloses a kind of method for optimally controlling humidity of residual heat drying system.First the present invention adopts the exiting flue gas humidity value of model predictive control method to residual heat drying system to control, make smoke moisture value excessively arrive set-point stably according to given reference locus, avoid because control inputs amount is excessive and cause drying article spontaneous combustion and cause security of system hidden danger; Consider the impact of system input control amount disturbance, add Front feedback control and form feed-forward and feedback complex controll, forecast model is corrected, while accelerating system disturbance input response, reduce the predicated error of system; After humidity value reaches set-point, adopt LQ method for optimally controlling to carry out optimized control to system, while strengthening system rejection to disturbance ability, make system gas consumption minimum.Present invention decreases the impact of input disturbance on system, improve control accuracy, make system consume energy minimum simultaneously, meet industrial power conservation requirement.

Description

The method for optimally controlling humidity of residual heat drying system

Technical field

The invention belongs to areas of information technology, relate to the model predictive control method (MAC in automatic technology, Model Algorithmic contral), Feedforward-feedback control method and LQ method for optimally controlling, be optimized control based on the humidity of above several method to residual heat drying system.

Background technology

Waste plastic oil-refining is the new technology of the waste plastics produced in life and industrial processes being carried out cracking oil refining.For ensureing efficiency and the safety of cracking process, drying and processing must be carried out to waste plastics before cracking is carried out to waste plastics.Be combustible due to waste plastics and be wherein also mingled with the flammable object such as waste paper, avoiding drying article spontaneous combustion for improving drying efficiency as far as possible, adopting when drying hot-air to mix the mode of drying with waste plastics.The efficiency that this mixing is dried and to the utilization factor of combustion gas depend on dry after the humidity value of exiting flue gas, in this drying system, when exiting flue gas humidity value reaches 50%, drying efficiency and combustion gas utilization factor reach the highest.But similar drying system in the past control in control algolithm reckon without the impact of smoke moisture, thus often make the drying effect of system bad, cracking waste plastics efficiency is not high, and causes combustion gas to waste, and does not meet energy-saving and cost-reducing requirement.

Summary of the invention

Object of the present invention is exactly the impact for not considering drying system middle outlet smoke moisture value in drying system in the past, makes drying efficiency not high, cause combustion gas waste and propose a kind of drying system in method for optimally controlling humidity.

The inventive method is the mixture model method for handover control that a kind of model predictive control method (MAC, Model Algorithmic contral), Feedforward-feedback control method and LQ method for optimally controlling combine.For the characteristic that drying article is inflammable, first model predictive control method (MAC is adopted, Model Algorithmic contral) the exiting flue gas humidity value of residual heat drying system is controlled, make humidity value reach 50% stably according to given reference locus, avoid because control inputs amount is excessive and cause drying article spontaneous combustion and cause security of system hidden danger; Consider the impact of system input control amount disturbance, add the complex controll that feedforward compensation forms feed-forward and feedback, forecast model is corrected, while accelerating system disturbance input response, reduce the predicated error of system; After humidity value reaches 50%, adopt LQ method for optimally controlling to carry out optimized control to system, while strengthening system rejection to disturbance ability, make system gas consumption minimum.

The concrete steps of the inventive method comprise:

Step one: the forecast model setting up system, by model predictive control method (MAC, Model Algorithmic contral) and Feedforward-feedback control method, controls the exiting flue gas humidity of residual heat drying system, makes humidity value reach 50% stably.

A. forecast model is set up

Concrete grammar is: with charging aperture flow, gas valve opening angle value, and cold air distribution valve opening value is input quantity, and the drying system exiting flue gas humidity value collected with humidity sensor is output quantity, sets up the discrete differential model based on least square method;

Wherein represent drying system gas outlet air humidity value, represent control inputs vector, the input disturbance vector of expression system; Control inputs vector sum disturbance input vector is

，

Wherein represent combustion gas two-port valve valve opening value, represent cold air distribution two-port valve valve opening value, represent charging aperture flow, by regulating in drying course , , three control inputs amounts control the air humidity in drying system. , , be respectively the disturbance input of three input quantities. , with represent the systematic parameter matrix obtained by linear least squares method

， ，

Wherein for scalar parameter to be identified, , for to be identified dimension matrix, nfor sampling number.

Pass through inverse transformation, becomes the non-parametric model based on impulse response transport function above-mentioned model conversation, i.e. drying system exiting flue gas humidity value forecast model:

Wherein represent the the humidity value of individual sampling instant exiting flue gas, for modeling time domain, represent the the control inputs variable in moment, represent the the input disturbance in moment.Wherein with computing formula as follows

，

,

represent and the formula in bracket is done inverse transformation.

B. Feedforward Controller Design

By forecast model

Have after arrangement

Wherein for transport function when controlled device does not have a disturbance, for the transport function of controlled device disturbance passage, and have

，

Add the output of system after feedforward control link become

Wherein for the transport function of feedforward controller.When shi You

Order , the transport function that can obtain feedforward controller is .Thus, the output of feedforward controller is

C. adopt feedforward-feedback control method to correct system, realize closed low predictions

Concrete grammar is as follows: with walk out of the actual value of mouthful smoke moisture with the humidity value in this moment do difference, can the error amount in this moment .Utilize this error to the prediction of individual sampling instant exports carry out feedback modifiers, after obtaining correcting the the prediction of output value of individual sampling instant for

，

Wherein for Ratio for error modification, for prediction time domain.

Setting value is reached, by the appointment reference locus in model predictive control method (MAC, Model Algorithmic contral) in order to what make humidity value safety and steady ? the value of individual sampling instant is taken as

，

Wherein for exporting setting value; for reference time given constant; for the sampling period.The time constant of reference locus be worth larger, then the flexibility of system is stronger, and robustness is stronger, but the rapidity controlled is deteriorated.

D. the optimal control law of model predictive control method (MAC, Model Algorithmic contral) calculates

Select the quadratic performance index of output error and controlled quentity controlled variable weighting, it is expressed as follows:

Wherein , be respectively the weighting coefficient of prediction output error and controlled quentity controlled variable, for the control inputs that moment is total, for moment feedforward controller exports, for prediction time domain, for controlling time domain, and have .

Write quadratic performance index as vector form to have

Wherein with for Weighting Matrices, generally diagonal matrix form can be chosen , , the element on diagonal line , suitable value can be chosen according to the system of reality. for total control inputs vector; for reference input vector; for prediction of output value vector.

Vector is controlled to the unknown differentiate, even , just can draw optimal control law

Wherein for error correction vector, value generally desirable 1.

,

Wherein , for dimension matrix, can once calculate simultaneously from arrive all controlled quentity controlled variables in moment, calculating provide in step a.

In actual applications, in order to reduce error as far as possible, the present invention adopts closed loop control algorithm, namely only performs the control action of current time , and subsequent time controlled quentity controlled variable press again calculating formula recursion one step rerun.Now, the instant controlled quentity controlled variable of optimum control can be written as

Wherein .

Step 2: after drying system exiting flue gas humidity value reaches 50%, adopts LQ method for optimally controlling to carry out optimized control to system.

Concrete grammar is as follows:

Initial time, with charging aperture flow, gas valve opening angle value, cold air distribution valve opening value for control inputs amount, utilizes the forecast Control Algorithm of step one, controls the smoke moisture in residual heat drying system.In order to make amount of consumed gas minimum, after exiting flue gas humidity value reaching 50%, with burnt gas valve aperture for single control input quantity, being realized the optimum control of system by regulating gas valve opening value, reaching energy-conservation object.

The state-space expression that can be obtained system above by the forecast model set up after model conversion is:

，

Wherein , for exiting flue gas humidity, for charging aperture flow, for cold air distribution valve opening value, for burnt gas valve opening value, for the state value of initial time, with for the constant matrices obtained by identification, represent theorem in Euclid space.

Choose quadratic performance index

Wherein for prediction time domain, s, q _d , r _d for the real symmetrical weighting matrix of positive definite of dimension, generally chooses diagonal matrix , , , the element on diagonal line , , suitably can choose according to running characteristic.

According to matrix in state equation awith bvalue, solve the Riccati matrix equation of discrete-time system

Wherein irepresent the unit matrix of dimension, can solve positive definite symmetric matrices w( k).Can design discrete time LQ optimal controller thus, the optimum humid control rule of corresponding feedback of status is .This method for optimally controlling will make moisture control system have gain margin and phase margin.

The present invention be directed to drying article in this mixing drying system and do not consider drying system smoke moisture containing fire goods and traditional oven dry control algolithm, and make system drying efficiency and fuel availability not high, and the drying system method for optimally controlling humidity proposed.The present invention adopts Feedforward-feedback control and Model Predictive Control (MAC, Model Algorithmic contral) closed loop control method that combines, can according to control overflow, constantly carry out feedback compensation, finally obtain optimum valve opening value, feedforward compensation link can be accelerated system and reduce error to the response of input disturbance.Model predictive control method (MAC is adopted when drying and starting, Model Algorithmic contral), the output of system can be made to reach designated value gradually according to intended trajectory, eliminate the potential safety hazard causing drying article spontaneous combustion because valve opening is excessive, make system transitional processes steady simultaneously.After system humidity reaches designated value, adopt LQ method for optimally controlling to control, amount of consumed gas can be made minimum while guarantee system stability.Adopt feed-forward and feedback composite control method, model predictive control method (MAC, Model Algorithmic contral) and LQ method for optimally controlling combine mixing control method, can eliminate because valve opening crosses the potential safety hazard of ambassador's drying article spontaneous combustion, reduce the impact of input disturbance on system, improve control accuracy, make system consume energy minimum simultaneously, meet industrial energy-saving safe requirement.

Embodiment

Residual heat drying system humidity optimal control method, adopt Feedforward-feedback control method and model predictive control method (MAC, Model Algorithmic contral) to combine at the initial stage of oven dry to control the valve opening of combustion gas two-port valve, cold air distribution two-port valve and feed rate.Specific implementation method is as follows:

1) forecast model is determined in the value of each parameter matrix

Adopt the linear least squares method method of multi input-multiple output system to carry out identification to systematic parameter, systematic parameter is

， ，

Wherein , , for sampling number, , , estimated value can by formula unbiased esti-mator obtain, the parameter matrix wherein measured with the output valve matrix measured be specifically calculated as follows

Wherein for sample time domain one group of sampled value of interior control input quantity, for sample time domain one group of sampled value of interior input disturbance amount, for the sampled value that a group system of corresponding control inputs amount and disturbance input amount exports, such sampled value has group. in a ₁... a _n , b ₀₁ b ₀₂ b ₀₃... b _n1 b _n2 b _n3 , c ₀₁ c ₀₂ c ₀₃... c _n1 c _n2 c _n3 three groups of data are respectively in corresponding forecast model , , the coefficient of every fraction.

2) determination of feedforward controller parameter and the calculating of correction rear prediction output valve.Owing to there is model mismatch and error when the modeling of reality and parameter estimation, the output valve of forecast model may depart from actual value, so need to revise output.Consider the impact of input quantity disturbance, simultaneously for enhancing system is to the response speed of disturbance input, the present invention adopts feedforward-feedback control to correct prediction output.

In aforesaid Feedforward Controller Design, obtain the transport function of feedforward controller

The wherein transport function of controlled device with the transport function of disturbance passage be respectively

，

Substituted into controller transfer function, the transport function of feedforward controller can be obtained

Wherein , obtain by during System Discrimination.

Prediction output valve after each time correction is

Wherein for error prediction model, for moment humidity sensor to the sampled value of exiting flue gas, represent the predicted value of moment exiting flue gas humidity, for error correction vector, generally desirable value be 1.

Given reference locus , , wherein for exporting setting value; for reference time given constant; for the sampling period.Prediction output valve after feedback compensation and reference locus are compared, draws predicated error scope.If predicated error is comparatively large, then readjust combustion gas two-port valve, cold air distribution two-port valve valve opening value and charging aperture flow, until predicated error controlled in certain scope.

3) given weighting matrix , , the element on diagonal line ... , ... suitable value can be chosen according to actual requirement, work as predicated error when being controlled within a certain range, more easy during for making by-pass valve control aperture, the present invention adopts the mode exporting controlling increment to control valve opening.

Set up the quadratic performance index of prediction of output error and controlled quentity controlled variable weighting, be described below: wherein , for control inputs increment, and

Wherein .

Order , have after abbreviation

By above formula launch can try to achieve from arrive moment carry out order opened loop control increment , ..., , namely

in formula .

Above computation process all can be realized by computer program, and computing machine is by AD conversion module to input, output data sampling, and sampled data is kept in built database.Calculate optimum control increment by computing machine, by D/A conversion module, working control input quantity is regulated, thus control the humidity of residual heat drying system.

Set up performance index and solve optimal control law, the error of forecast model can be made minimum, calculated by optimal control law, the minimal valve aperture in minimum control inputs amount and native system can be obtained, thus reach energy-conservation object.

4) after the exiting flue gas humidity value of drying system reaches 50%, systematic evaluation is carried out optimum control to LQ method for optimally controlling to system.

Initial time, with charging aperture flow, gas valve opening angle value, cold air distribution valve opening value for control inputs amount, utilizes the forecast Control Algorithm of step one, controls the smoke moisture in residual heat drying system.In order to make amount of consumed gas minimum, after exiting flue gas humidity value reaching 50%, with burnt gas valve aperture for single control input quantity, being realized the optimum control of system by regulating gas valve opening value, realizing energy-conservation object.The state-space expression that can be obtained system above by the forecast model set up after model conversion is:

，

Wherein , for exiting flue gas humidity, for charging aperture flow, for cold air distribution valve opening value, for burnt gas valve opening value, for the state value of initial time, with for the constant matrices obtained by identification.

Choose quadratic performance index

Wherein for prediction time domain, s, q _d , r _d for the real symmetrical weighting matrix of positive definite of dimension, generally chooses diagonal matrix , , , the element on diagonal line ... , ... , ... suitably can choose according to running characteristic.

According to matrix in state equation awith bvalue, solve following discrete-time system Riccati matrix equation

Wherein irepresent the unit matrix of dimension, can solve positive definite symmetric matrices w( k).Thus can discrete time LQ optimal controller, corresponding state feeds back optimum humid control rule and is .Sampled to the input and output value of system by each A/D module, sampled value gives LQ optimal controller, solves through LQ controller, exports the optimal state feed-back control of residual heat drying system humidity value

The control inputs value of die change block just adjustable real system is filled again by DA.Utilize LQ optimum control can strengthen the robustness of system, optimized control is carried out to the combustion gas input of residual heat drying system simultaneously, make gas consumption minimum, meet industrial power conservation requirement.

The present invention adopts model predictive control method (MAC, Model Algorithmic contral), and the mixture model method for handover control that Feedforward-feedback control method and LQ method for optimally controlling combine is optimized control to the humidity of residual heat drying system.This method eliminates the potential safety hazard that may cause drying article spontaneous combustion because valve opening is excessive, realizes the control of humidity in residual heat drying system fast and accurately.By designated model performance index, calculate optimal control law and the control energy resource consumption of system and firing rate can be made all to reach minimum, realize the optimum control of the humidity in residual heat drying system, reach the energy-saving and cost-reducing of enterprise.

Claims (1)

1. the method for optimally controlling humidity of residual heat drying system, is characterized in that the concrete steps of the method are:

Step one: the forecast model setting up system, by model predictive control method and Feedforward-feedback control method, controls the exiting flue gas humidity of residual heat drying system, makes humidity value reach 50% stably;

A. forecast model is set up

Concrete grammar is: with charging aperture flow, gas valve opening angle value, and cold air distribution valve opening value is input quantity, and the drying system exiting flue gas humidity value collected with humidity sensor is output quantity, sets up the discrete differential model based on least square method;

A(z ^-1)y(k)＝B(z ^-1)u(k)+C(z ^-1)ξ(k)

Wherein y (k) represents drying system gas outlet air humidity value, and u (k) represents control inputs vector, and ξ (k) represents the input disturbance vector of system; Control inputs vector sum disturbance input vector is

u(k)＝[u ₁(k),u ₂(k),u ₃(k)] ^T，ξ(k)＝[ξ ₁(k),ξ ₂(k),ξ ₃(k)] ^T

Wherein u ₁k () represents combustion gas two-port valve valve opening value, u ₂k () represents cold air distribution two-port valve valve opening value, u ₃k () represents discrete differential model charging aperture flow, by regulating u in drying course ₁(k), u ₂(k), u ₃k () three control inputs amounts control the air humidity in drying system; ξ ₁(k), ξ ₂(k), ξ ₃k () is respectively the disturbance input of three input quantities; A (z ^-1), B (z ^-1) and C (z ^-1) represent the systematic parameter matrix obtained by linear least squares method

$A\left(z^{-1}\right)=1+\underset{i=1}{\overset{n}{\Σ}}{a}_i{z}^{-i},B\left(z^{-1}\right)=\underset{i=0}{\overset{n}{\Σ}}{B}_i{z}^{-i},C\left(z^{-1}\right)=\underset{i=0}{\overset{n}{\Σ}}{C}_i{z}^{-i}$

Wherein a _ifor scalar parameter to be identified, B _i, C _ifor to be identified 1 × 3 dimension matrix, n is sampling number;

By Z inverse transformation, above-mentioned model conversation is become the non-parametric model based on impulse response transport function, i.e. drying system exiting flue gas humidity value forecast model:

$\begin{array}{c}\hat{y}\left(k+j\right)=g_{1}u\left(k+j-1\right)+g_{2}u\left(k+j-2\right)+g_{3}u\left(k+j-3\right)+...+g_{N}u\left(k+j-N\right)\\ +s_1\mathrm{\ξ}\left(k+j-1\right)+s_2\mathrm{\ξ}\left(k+j-2\right)+s_3\mathrm{\ξ}\left(k+j-3\right)+...s_N\mathrm{\ξ}\left(k+j-N\right)\\ =\underset{i=1}{\overset{N}{\Σ}}{g}_{i}u\left(k+j-i\right)+\underset{i=1}{\overset{N}{\Σ}}{s}_i\mathrm{\ξ}\left(k+j-i\right)\end{array}$

Wherein represent the humidity value of a kth+j sampling instant exiting flue gas, N is modeling time domain, and u (k+j-i) represents the control inputs variable in kth+j-i moment, and ξ (k+j-i) represents the input disturbance in kth+j-i moment; Wherein g _iand s _icomputing formula as follows

$g_i={\mathrm{ZT}}^{-1}\[\frac{B\left(z^{-1}\right)}{A\left(z^{-1}\right)}\],i=(1,2,3,...,N)$

$s_i={\mathrm{ZT}}^{-1}\[\frac{C\left(z^{-1}\right)}{A\left(z^{-1}\right)}\],i=(1,2,3,...,N)$

ZT ^-1represent and Z inverse transformation is done to the formula in bracket;

B. Feedforward Controller Design

By forecast model

A(z ^-1)y(k)＝B(z ^-1)u(k)+C(z ^-1)ξ(k)

Have after arrangement

y(k)＝G(z ^-1)u(k)+G _ξ(z ^-1)ξ(k)

Wherein G (z ^-1) be transport function when controlled device does not have a disturbance, G _ξ(z ^-1) be the transport function of controlled device disturbance passage, and have

$G\left(z^{-1}\right)=\frac{B\left(z^{-1}\right)}{A\left(z^{-1}\right)},G_{\mathrm{\ξ}}\left(z^{-1}\right)=\frac{C\left(z^{-1}\right)}{A\left(z^{-1}\right)}$

After adding feedforward control link, output y (k) of system becomes

y(k)＝G(z ^-1)(u(k)+D _ξ(z ^-1)ξ(k))+G _ξ(z ^-1)ξ(k)

＝G(z ^-1)u(k)+G(z ^-1)D _ξ(z ^-1)ξ(k)+G _ξ(z ^-1)ξ(k)

Wherein D _ξ(z ^-1) be the transport function of feedforward controller; Have when u (k)=0

$\frac{y\left(k\right)}{\mathrm{\ξ}\left(k\right)}=G\left(z^{-1}\right)D_{\mathrm{\ξ}}\left(z^{-1}\right)+G_{\mathrm{\ξ}}\left(z^{-1}\right)$

Make G (z ^-1) D _ξ(z ^-1)+G _ξ(z ^-1)=0, the transport function that can obtain feedforward controller is D _ξ(z ^-1)=-G (z ^-1) ^-1g _ξ(z ^-1); Thus, the output of feedforward controller is

u _ξ(k)＝D _ξ(z ^-1)ξ(k)＝-G(z ^-1) ^-1G _ξ(z ^-1)ξ(k)

C. adopt feedforward-feedback control method to correct system, realize closed low predictions

Concrete grammar is as follows: walk out of the actual value y (k) of mouthful smoke moisture and the humidity value in this moment by kth do difference, can the error amount in this moment this error is utilized to export the prediction of a jth sampling instant carry out feedback modifiers, obtain the prediction of output value y correcting the sampling instant of rear jth _c(k+j) be

$y_c(k+j)=\hat{y}(k+j)+he\left(k\right),j=1,2,...,P$

Wherein h is Ratio for error modification, and P is prediction time domain;

Setting value is reached, by the appointment reference locus y in model predictive control method in order to what make humidity value safety and steady _rbe taken as in the value of a jth sampling instant

$y_r(k+j)=y\left(k\right)+\[\mathrm{\ω}-y\left(k\right)\](1-e^{-{\mathrm{jT}}_s/\mathrm{\τ}}),j=0,1,2,...P$

Wherein ω is for exporting setting value; τ is reference time given constant; T _sfor the sampling period; The timeconstantτ value of reference locus is larger, then the flexibility of system is stronger, and robustness is stronger, but the rapidity controlled is deteriorated;

D. the optimal control law of model predictive control method calculates

Select the quadratic performance index of output error and controlled quentity controlled variable weighting, it is expressed as follows:

$J\left(k\right)=\underset{j=1}{\overset{P}{\Σ}}{q}_j{\[y_c(k+j)-y_r(k+j)\]}^2+\underset{i=1}{\overset{M}{\Σ}}{r}_i{\[u_0(k+i-1)\]}^2$

Wherein q _j, r _ibe respectively the weighting coefficient of prediction output error and controlled quentity controlled variable, u ₀(k+i-1)=u (k+i-1)+u _n(k+i-1) be the control inputs that the k+i-1 moment is total, u _n(k+i-1) for k+i-1 moment feedforward controller exports, P is prediction time domain, and M is control time domain, and has M≤P≤N;

Write quadratic performance index as vector form to have

$J\left(k\right)={\[Y_c(k+1)-Y_r(k+1)\]}^{T}Q\[Y_c(k+1)-Y_r(k+1)\]+U_0^T\left(k\right){\mathrm{RU}}_0\left(k\right)$

Wherein Q and R is Weighting Matrices, chooses diagonal matrix form Q=diag (q ₁q _p), R=diag (r ₁..., r _m), the element q on diagonal line ₁q _p, r ₁r _msuitable value can be chosen according to the system of reality; U ₀(k)=[u ₀(k+1) ... u ₀(k+M)] ^tfor total control inputs vector; Y _r(k+1)=[y _r(k+1) ... y _r(k+P)] ^tfor reference input vector; Y _c(k+1)=[y _c(k+1) ... y _c(k+P)] ^tfor prediction of output value vector;

Vector U is controlled to the unknown ₀(k) differentiate, even just optimal control law can be drawn

$U_0\left(k\right)={(G_1^T{\mathrm{QG}}_1+R)}^{-1}{G}_1^{T}Q\[Y_r(k+1)-G_2{U}_0(k-1)-He\left(k\right)\]$

Wherein H=[h ₁h _p] ^tfor error correction vector, h ₁h _pvalue desirable 1;

Wherein 2≤ρ≤N-3, for M × M ties up matrix, once can calculate all controlled quentity controlled variables in the moment from k to k+M+1, g simultaneously _icalculating provide in step a;

In order to reduce error as far as possible, adopt closed loop control algorithm, namely only perform the control action u of current time ₀(k), and subsequent time controlled quentity controlled variable u ₀(k+1) u is pressed again ₀k calculating formula recursion one step of () is reruned; Now, the instant controlled quentity controlled variable of optimum control can be written as

$u_0\left(k\right)=d_1^T\[Y_r(k+1)-G_2{U}_0(k-1)-He\left(k\right)\]$

Wherein $d_1^T=(1,0,...0){(G_1^T{\mathrm{QG}}_1+R)}^{-1}{G}_1^{T}Q;$

Step 2: after drying system exiting flue gas humidity value reaches 50%, adopts LQ method for optimally controlling to carry out optimized control to system;

Concrete grammar is as follows:

Initial time, with charging aperture flow, gas valve opening angle value, cold air distribution valve opening value for control inputs amount, utilizes the forecast Control Algorithm of step one, controls the smoke moisture in residual heat drying system; In order to make amount of consumed gas minimum, after exiting flue gas humidity value reaches 50%, with combustion gas two-port valve valve opening value for single control input quantity, being realized the optimum control of system by regulating gas two-port valve valve opening value, reaching energy-conservation object;

The state-space expression that can be obtained system above by the forecast model set up after model conversion is:

x(k+1)＝Ax(k)+Bu ₁(k)，x(0)＝x ₀

Wherein x (k)=[x ₁(k), x ₂(k), x ₃(k)] ^t, x ₁k () is exiting flue gas humidity, x ₂k () is state-space expression charging aperture flow, x ₃k () is cold air distribution valve opening value, x ₀for the state value of initial time, u ₁k () represents combustion gas two-port valve valve opening value, with for the constant matrices obtained by identification, represent theorem in Euclid space;

Choose quadratic performance index

$J\left(k\right)=\frac{1}{2}{x}^T\left(P\right)Sx\left(P\right)+\frac{1}{2}\underset{k=1}{\overset{P}{\Σ}}\[x^T\left(k\right)Q_{d}x\left(k\right)+u^T\left(k\right)R_d{u}_1\left(k\right)\]$

Wherein P is prediction time domain, S, Q _d, R _dbe the real symmetrical weighting matrix of positive definite of 3 × 3 dimensions, choose diagonal matrix S=diag (s ₁, s ₂, s ₃), Q _d=diag (q _d1, q _d2, q _d3), R _d=diag (r _d1, r _d2, r _d3), the element s on diagonal line ₁s ₃, q _d1q _d3, r _d1r _d3suitably can choose according to running characteristic;

According to the value of matrix A in state equation and B, solve the Riccati matrix equation of discrete-time system

$W\left(k\right)=Q_d+A^{T}W(k+1){[I+{\mathrm{BR}}_d^{-1}{B}^{T}W(k+1)]}^{-1}A$

Wherein I represents 3 × 3 unit matrixs tieed up, and can solve positive definite symmetric matrices W (k); Can design discrete time LQ optimal controller thus, the optimum humid control rule of corresponding feedback of status is $u_1\left(k\right)=-R_d^{-1}{B}^T{A}^{-T}\[W\left(k\right)-Q_d\]x\left(k\right);$ This method for optimally controlling will make moisture control system have the gain margin of (1/2, ∞) and the phase margin of 60 °.