CN102540897A - Method for carrying out composite predictive control on coagulant dosage of water treatment - Google Patents

Abstract

The invention provides a method for carrying out composite predictive control on coagulant dosage of water treatment and relates to a method for controlling coagulant dosage of water treatment, and the method can be used for solving the problem of complex control over nonlinear uncertain objects during a coagulation process. The method comprises the following specific steps of: establishing a composite predictive control model; through detecting the turbidity of untreated water and the turbidity of effluent during the coagulation process of water treatment and combining an effluent quality set value, inputting the turbidity of untreated water, the turbidity of effluent and the effluent quality set value into the composite predictive control model so as to solve the real-time control quantity of coagulant dosage of water treatment, wherein in the establishment of the composite predictive control model, the coagulant dosage of water treatment in a water plant is controlled by utilizing composite predictive control method of simplified DMC (Dynamic Matrix Control) and untreated water quality disturbance feed-forward predictive control, and the turbidity of untreated water during feed-forward control can be predicted by utilizing a time sequence predication method based on AR (Auto Regression) predication. According to the invention, the control accuracy is improved by utilizing the combination of simplified DMC and feed-forward predictive control, and the problem that sampling usually has a certain time interval is solved by utilizing the time sequence predication method based on AR predication; and the method provided by the invention can be used for controlling the coagulant dosage of water treatment in the water plant.

Description

The compound forecast Control Algorithm of a kind of water treatment coagulation administration

Technical field

The compound forecast Control Algorithm of a kind of water treatment coagulation administration relates to water treatment coagulation administration control method field.

Background technology

Coagulation is the gordian technique in water factory's technology, directly influences water factory system quality, and the key factor that influences coagulation effect is the dosage of coagulant dose.Accurate control dispensing not only can guarantee effluent characteristics, and significant for reducing water producing cost.Dispensing control at present remains in following problem:

1,, domesticly mainly delivery turbidity is carried out indirect detection, though can reflect the variation of water turbidity fast based on instruments such as electric current apparatuss in the coagulation context of detection; But this instrument exists various water quality parameters and intersects; So poor anti jamming capability, process conditions require high, the adjustment trouble; Difficult in maintenance, this technical application is limited.

2, domestic employing closed loop PID control on control method because that the coagulation administration process has is non-linear, the time become, large time delay, the effect that PID control is difficult to obtain.

3, many research departments propose various Intelligent Control Strategy, and like fuzzy control, ANN Control etc., these control algolithms are in experimental study and emulation aspect, as yet through engineering approaches not.

For overcoming the above problems, be necessary to design a kind of water treatment coagulation administration forecast Control Algorithm, reach following purpose:

1, provides a kind of coagulation administration control engineering method of practicality.This method is used Prediction and Control Technology, solves the complicated problem of non-linear, the uncertain object of coagulation process, with feeding back the raising control accuracy that combines with feedforward.

Can forecast in the method that 2, its forecast is the result promptly use in the feedforward control in compound control to source quality, the scientific management that can be water factory again provides foundation.

3, this method can realize saving the medicine function under the prerequisite that guarantees stable effluent characteristics, thereby reduces the water producing cost of water factory.

Summary of the invention

The purpose of this invention is to provide the compound forecast Control Algorithm of a kind of water treatment coagulation administration, with the complicated problem of non-linear, the uncertain object that solves coagulation process; Because the source water quality sampling has certain time interval usually, cause occurring the problem that physically irrealizable advance item need be done forecast to source quality.

The present invention realizes through following step: utilize compound predictive control model; Through detecting the source water turbidity and the delivery turbidity of water treatment coagulation process; In conjunction with the effluent quality setting value; Import compound predictive control model and try to achieve the instant controlled quentity controlled variable of water treatment coagulation administration amount, the foundation of said compound predictive control model may further comprise the steps:

One, the coagulation process modeling utilizes the principle that the type signal response combines with least square; Set up coagulation process in disturb model and disturb model outward, in to disturb model be to be input quantity with the dosage, be output quantity with water treatment coagulation delivery turbidity; Disturbing model outward and be with the source water turbidity is input quantity; With water treatment coagulation delivery turbidity is output quantity, in to disturb model be that the design of feedback PREDICTIVE CONTROL is used, it is used for the control of design feed forward prediction to disturb model outward.The model of being set up is two inertia objects that hysteresis is arranged, and it is described in order to drag:

Formula one: $G\left(s\right)=\frac{{\mathrm{Ke}}^{-\mathrm{\τ\; s}}}{(T_{1}s+1)(T_{2}s+1)}$

Wherein K is a scale-up factor, and τ is the pure delay time, T ₁And T ₂Time constant for two inertia.K, τ, T ₁, T ₂Relation below available is tried to achieve:

Formula two: V=U θ+Ω

In the formula, $V=\left[\begin{array}{c}C\left(1\right)\\ C\left(2\right)\\ ...\\ C\left(m\right)\end{array}\right],$ $U=\left[\begin{array}{cccc}1& -1& -A\left(1\right)& -B\left(1\right)\\ 2& -1& -A\left(2\right)& -B\left(2\right)\\ ...& ...& ...& ...\\ m& -1& -A\left(m\right)& -B\left(m\right)\end{array}\right],$ $\mathrm{\&theta;}=\left[\begin{array}{c}K\\ \mathrm{K\&tau;}\\ T_1{T}_2\\ {\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA0000143427890000021.png,HDA0000143427890000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000143427890000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{c}{\mathrm{\&Omega;}}_1\\ {\mathrm{\&Omega;}}_2\\ ...\\ {\mathrm{\&Omega;}}_m\end{array}\right].$

B, A, C are respectively step response; Step response difference and integration, θ are measured parameter, and Ω is a noise; Change the data of surveying the variation of water treatment coagulation delivery turbidity according to the dosage step; Change the data of surveying the variation of water treatment coagulation delivery turbidity according to source water turbidity step, according to the typical response and the aforesaid modeling method that record two groups of data

Ask model parameter with the least square formula:

Formula three: $\widehat{\mathrm{\&theta;}}={\left(U^{T}U\right)}^{-1}{U}^{T}V$

Two, the model simplification of DMC is convenient to Project Realization in order to improve real-time, and basic DMC algorithm is simplified.Because coagulation process is the overdamping object, can use single order inferred-zero object approximate.

The model of uniting of setting up departments is G (z ^-1),

Formula four: G (z ^-1)=g ₁z ^-1+ g ₂z ^-2L+g _nz ^-nL+g _Nz ^-N

In the formula, g ₁, g ₂..., g _n..., g _NBe impulse response coefficient, for a stable process, the g in the formula four _Nz ^-nLater on each item can be by exponential representation, so formula four can be reduced to formula five:

$G\left(z^{-1}\right)=g_1{z}^{-1}+g_2{z}^{-2}L{g}_{n-1}{z}^{-(n-1)}+\frac{g_n{z}^{-n}}{1-{\mathrm{qz}}^{-1}}$

In the formula five,

A wherein _N-1, a _n, a _NBe the step response parameter.

Basic DMC model is Y _m(k+1)=A Δ U (k)+A ₀U (k-1), wherein:

Formula six:

$A_{0}U(k-1)=\left[\begin{array}{c}{g}_N{z}^{-(N-1)}+g_{N-1}{z}^{-(N-2)}+...+g_3{z}^{-2}+a_2{z}^{-1}\\ g_N{z}^{-(N-2)}+g_{N-1}{z}^{-(N-3)}+...+g_4{z}^{-3}+a_3{z}^{-1}\\ ...\\ g_N{z}^{-(N-P)}+g_{N-1}{z}^{-(N-P+1)}+...+g_{P+2}{z}^{-(P+1)}+a_{P+1}{z}^{-1}\end{array}\right]$

Reduce to the n rank from the forecast model of formula five visible DMC by the N rank, control algolithm is simplified, real-time improves.So A in the basic DMC model ₀U (k-1) is reduced to,

$A_{0}U(k-1)\&ap;\left[\begin{array}{c}{a}_2{z}^{-1}+g_3{z}^{-2}+...+g_{n-1}{z}^{-(n-2)}+\frac{g_n{z}^{-(n-1)}}{1-{\mathrm{qz}}^{-1}}\\ a_3{z}^{-1}+g_4{z}^{-2}+...+g_{n-1}{z}^{-(n-3)}+\frac{g_n{z}^{-(n-2)}}{1-{\mathrm{qz}}^{-1}}\\ ...\\ a_{p+1}{z}^{-1}+g_{p+2}{z}^{-2}+...+g_{n-1}{z}^{-(n-p-1)}+\frac{g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}\end{array}\right]u\left(k\right)---\left(7\right)$

Three, DMC simplifies control A ₀After U (k-1) simplified, the instant controlled quentity controlled variable u (k) of water treatment coagulation administration amount was a formula eight:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+p)-\frac{d\left(k\right)g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]$

In the formula, $F\left(z^{-1}\right)==\frac{1}{d\left(k\right)}[1+f_1{z}^{-1}+...+f_{n-P-1}{z}^{-(n-p-1)}+f_{n-p}{z}^{-(n-p)}+...+f_{n-2}{z}^{-(n-2)}];$

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000143427890000021.png,HDA0000143427890000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{d}_{1i}{a}_{i+1}-1;$

$f_k=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=\mathrm{2,3},...,n-p-1);$

$f_k=\underset{i=1}{\overset{n-k-1}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=n-p,...,n-2);$

G _m(z ^-1)=g ₁z ^-1+ g ₂z ^-2L g _N-1z ^-(n-1), D _r(z ^-1) be that parameter can be asked F (z in the control law ^-1) can ask for controller, d (k) is the source water turbidity, y _r(k+p) set for water quality, y (k) is a water treatment coagulation delivery turbidity, and e (k) is the margin of error, h _fBe the error weighting coefficient

Four, water quality disturbance feedforward PREDICTIVE CONTROL d (k) is source water turbidity disturbance, G ₁(s) and G ₂(s) be the inside and outside model of disturbing, feedforward controller G _qControl is G as a result _q(s) by principle of invariance,

Five, the compound PREDICTIVE CONTROL of dispensing process

The source water quality disturbance feedforward PREDICTIVE CONTROL that the DMC of step 3 is simplified control and step 4 combines and carries out compound control; Utilize source water quality disturbance feedforward PREDICTIVE CONTROL result that DMC is simplified control and carry out the source water quality disturbance compensation; Make the instant controlled quentity controlled variable u (k) of water treatment coagulation administration amount more accurate

U this moment (k) is a formula nine:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}[D_r\left(z^{-1}\right)(y_r(k+P)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)]+G_q\left(s\right)$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe error weighting coefficient, G _q(s) be feedforward controller control result, y _r(k+p) be the effluent quality setting value.

The present invention also provides another kind of technical scheme: in practice; Because the source water quality sampling has certain time interval usually; Cause occurring physically irrealizable advance item; Therefore need forecast that source water quality is mainly considered the variation of turbidity to the source water turbidity, the turbidity forecast is to utilize the past of source water turbidity parameter and real information to making prediction future.Consider that Project Realization adopts the time series method of prediction based on the AR model:

x _n＝φ ₁x _n-1+...+φ _px _n-p+ε _n

X in the formula _nBe the turbidity sequence, φ is the AR model coefficient, and p is a model order, ε _nBe noise.

P rank φ ₁... φ _pIndividual parameter can be used the recursive least-squares identification, can forecast so use the AR model

Sequence, k=1,2 ...

Step 4 can not realize that so can consider with this method d (k+m) to be predicted, with d^ (k+m), m>=1 replaces d (k+m), and d^ (k+m) is inputed to feedforward controller G if advance item physics occurs among the source water turbidity d (k) when concrete the realization _q, obtain feedforward controller G _qControl is G ' as a result _q(s), utilize based on the time series of AR model and forecast that the source water quality disturbance feedforward PREDICTIVE CONTROL result who obtains simplifies control to DMC and carries out the source water quality disturbance compensation, obtain the instant controlled quentity controlled variable u (k) of more accurate water treatment coagulation administration amount:

Formula ten:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+P)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{{1-\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]+{G^{\&prime;}}_q\left(s\right)$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe error weighting coefficient, G ' _q(s) forecast the source water quality disturbance feedforward PREDICTIVE CONTROL result who obtains for feedforward controller based on the time series of AR model.

The beneficial effect of the invention:

1, conventional relatively dosage control method, this compound PREDICTIVE CONTROL precision improve since will feedover with feedback comprehensively, adopt PREDICTIVE CONTROL again; Adapt to dispensing process features of the object; Simultaneously main disturbance is compensated, make coagulation water delivering orifice water stabilization, dosage is also stable.

2, advanced relatively control method; This method real-time has improved owing to adopted the DMC algorithm of simplifying, and the order of controller reduces greatly, and the calculated amount in the control law reduces; Employing is based on the feedforward compensation control of AR; Realized because source water quality sampling has certain time interval usually, cause occurring physically can not realizing and produce the compensation of advance item, be easy to Project Realization and popularization.

3, reduce the dependence of checkout gear more thornyly to the detection of system water coagulation at present, some means all have shortcoming in various degree, use this control method and mainly detect turbidity, apply compound PREDICTIVE CONTROL based on the variation of turbidity.Therefore the pick-up unit that does not rely on some complicacies, is difficult to safeguard.

4, water stabilization reduces dosage this method and relies on compound PREDICTIVE CONTROL, guarantees that delivery turbidity is stable, and precision satisfies technological requirement.Because delivery turbidity is stable, the control corresponding amount is that dosage is stable, and its effect is both can save dose, can increase the life-span of chemicals feed pump again.

Description of drawings

Fig. 1 is the compound forecast Control Algorithm schematic diagram of this water treatment coagulation administration, and Fig. 2 is an IMC structural drawing of simplifying the DMC algorithm, and Fig. 3 is the feedforward control schematic diagram, and Fig. 4 is the IMC structural drawing of compound PREDICTIVE CONTROL

Fig. 5 is that the Simulation Control of embodiment is exported figure as a result

Fig. 6 is the Simulation Control input results figure of embodiment

Embodiment

Specify embodiment of the present invention below in conjunction with Fig. 1 to Fig. 4.

Embodiment one:

As shown in Figure 1; Utilize compound predictive control model; Through detecting the source water turbidity and the delivery turbidity of water treatment coagulation process; In conjunction with the effluent quality setting value, import the instant controlled quentity controlled variable that compound predictive control model is tried to achieve water treatment coagulation administration amount, the foundation of said compound predictive control model may further comprise the steps:

One, the coagulation process modeling utilizes the principle that the type signal response combines with least square; Set up coagulation process in disturb model and disturb model outward, in to disturb model be to be input quantity with the dosage, be output quantity with water treatment coagulation delivery turbidity; Disturbing model outward and be with the source water turbidity is input quantity; With water treatment coagulation delivery turbidity is output quantity, in to disturb model be that the design of feedback PREDICTIVE CONTROL is used, it is used for the control of design feed forward prediction to disturb model outward.The model of being set up is two inertia objects that hysteresis is arranged, and it is described in order to drag:

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

Wherein K is a scale-up factor, and τ is the pure delay time, T ₁And T ₂Time constant for two inertia.K, τ, T ₁, T ₂Relation below available is tried to achieve:

Formula two: V=U θ+Ω

In the formula, $V=\left[\begin{array}{c}C\left(1\right)\\ C\left(2\right)\\ ...\\ C\left(m\right)\end{array}\right],$ $U=\left[\begin{array}{cccc}1& -1& -A\left(1\right)& -B\left(1\right)\\ 2& -1& -A\left(2\right)& -B\left(2\right)\\ ...& ...& ...& ...\\ m& -1& -A\left(m\right)& -B\left(m\right)\end{array}\right],$ $\mathrm{\&theta;}=\left[\begin{array}{c}K\\ \mathrm{K\&tau;}\\ T_1{T}_2\\ {\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA0000143427890000021.png,HDA0000143427890000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000143427890000031.png"\; state="\{\{state\}\}">T</figure-callout>}}_2\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{c}{\mathrm{\&Omega;}}_1\\ {\mathrm{\&Omega;}}_2\\ ...\\ {\mathrm{\&Omega;}}_m\end{array}\right].$

B, A, C are respectively step response; Step response difference and integration, θ are measured parameter, and Ω is a noise; Change the data of surveying the variation of water treatment coagulation delivery turbidity according to the dosage step; Change the data of surveying the variation of water treatment coagulation delivery turbidity according to source water turbidity step, according to the typical response and the aforesaid modeling method that record two groups of data

Ask model parameter with the least square formula:

Formula three: $\widehat{\mathrm{\&theta;}}={\left(U^{T}U\right)}^{-1}{U}^{T}V$

Two, the model simplification of DMC is convenient to Project Realization in order to improve real-time, and basic DMC algorithm is simplified.Because coagulation process is the overdamping object, can use single order inferred-zero object approximate.

The model of uniting of setting up departments is G (z ^-1),

Formula four: G (z ^-1)=g ₁z ^-1+ g ₂z ^-2L+g _nz ^-nL+g _Nz ^-N

In the formula, g ₁, g ₂..., g _n..., g _NBe impulse response coefficient, for a stable process, the g in the formula four _Nz ^-nLater on each item can be by exponential representation, so formula four can be reduced to formula five:

$G\left(z^{-1}\right)=g_1{z}^{-1}+g_2{z}^{-2}L{g}_{n-1}{z}^{-(n-1)}+\frac{g_n{z}^{-n}}{1-{\mathrm{qz}}^{-1}}$

In the formula five,

A wherein _N-1, a _n, a _NBe the step response parameter.

Basic DMC model is Y _m(k+1)=A Δ U (k)+A ₀U (k-1), wherein:

Formula six:

$A_{0}U(k-1)=\left[\begin{array}{c}{g}_N{z}^{-(N-1)}+g_{N-1}{z}^{-(N-2)}+...+g_3{z}^{-2}+a_2{z}^{-1}\\ g_N{z}^{-(N-2)}+g_{N-1}{z}^{-(N-3)}+...+g_4{z}^{-3}+a_3{z}^{-1}\\ ...\\ g_N{z}^{-(N-P)}+g_{N-1}{z}^{-(N-P+1)}+...+g_{P+2}{z}^{-(P+1)}+a_{P+1}{z}^{-1}\end{array}\right]$

Reduce to the n rank from the forecast model of formula five visible DMC by the N rank, control algolithm is simplified, real-time improves.So A in the basic DMC model ₀U (k-1) is reduced to,

$A_{0}U(k-1)\&ap;\left[\begin{array}{c}{a}_2{z}^{-1}+g_3{z}^{-2}+...+g_{n-1}{z}^{-(n-2)}+\frac{g_n{z}^{-(n-1)}}{1-{\mathrm{qz}}^{-1}}\\ a_3{z}^{-1}+g_4{z}^{-2}+...+g_{n-1}{z}^{-(n-3)}+\frac{g_n{z}^{-(n-2)}}{1-{\mathrm{qz}}^{-1}}\\ ...\\ a_{p+1}{z}^{-1}+g_{p+2}{z}^{-2}+...+g_{n-1}{z}^{-(n-p-1)}+\frac{g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}\end{array}\right]u\left(k\right)---\left(7\right)$

Three, DMC simplifies control A ₀After U (k-1) simplified, the simplification of DMC control was as shown in Figure 2:

Among the figure, G _m(z ^-1)=g ₁z ^-1+ g ₂z ^-2L g _N-1z ^-(n-1), D _r(z ^-1) be that parameter can be asked F (z in the control law ^-1) can ask for controller, d (k) is the source water turbidity, y _r(k+p) set for water quality, y (k) is a water treatment coagulation delivery turbidity, and e (k) is the margin of error, h _fBe the error weighting coefficient, the water treatment coagulation administration amount among the figure the time controlled quentity controlled variable u (k) be formula eight:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+p)-\frac{d\left(k\right)g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]$

In the formula, $F\left(z^{-1}\right)==\frac{1}{d\left(k\right)}[1+f_1{z}^{-1}+...+f_{n-P-1}{z}^{-(n-p-1)}+f_{n-p}{z}^{-(n-p)}+...+f_{n-2}{z}^{-(n-2)}];$

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA0000143427890000021.png,HDA0000143427890000031.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{d}_{1i}{a}_{i+1}-1;$

$f_k=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=\mathrm{2,3},...,n-p-1);$

$f_k=\underset{i=1}{\overset{n-k-1}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=n-p,...,n-2).$

Four, water quality disturbance feedforward PREDICTIVE CONTROL is as shown in Figure 3:

Source d (k) is source water turbidity disturbance among the figure, G ₁(s) and G ₂(s) be the inside and outside model of disturbing, as previously mentioned.Feedforward controller G _qControl is G as a result _q(s) by principle of invariance,

Five, the compound PREDICTIVE CONTROL of dispensing process

As shown in Figure 4; The source water quality disturbance feedforward PREDICTIVE CONTROL that the DMC of step 3 is simplified control and step 4 combines and carries out compound control; Utilize source water quality disturbance feedforward PREDICTIVE CONTROL result that DMC is simplified control and carry out the source water quality disturbance compensation; Make the instant controlled quentity controlled variable u (k) of water treatment coagulation administration amount more accurate

U this moment (k) is a formula nine:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}[D_r\left(z^{-1}\right)(y_r(k+P)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)]+G_q\left(s\right)$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe error weighting coefficient, G _qBe feedforward controller control result.

As shown in Figure 4: G among the figure _cBe feedback forecasting controller, G _gBe the feed forward prediction controller, f (k) is the turbidity disturbance, y _r(k+p) be the effluent quality setting value, G ₁Be the interior model of disturbing, the forecast model of G for simplifying, G ₂For disturbing model outward.

Embodiment two: this embodiment is the improved procedure on embodiment one basis; In practice; Because the source water quality sampling has certain time interval usually, cause occurring physically irrealizable advance item, therefore need forecast the source water turbidity; Source water quality is mainly considered the variation of turbidity, and the turbidity forecast is to utilize the past of source water turbidity parameter and real information to making prediction future.Consider that Project Realization adopts the time series method of prediction based on the AR model:

x _n＝φ ₁x _n-1+...+φ _px _n-p+ε _n

X in the formula _nBe the turbidity sequence, φ is the AR model coefficient, and p is a model order, ε _nBe noise.

P rank φ ₁... φ _pIndividual parameter can be used the recursive least-squares identification, can forecast so use the AR model

Sequence, k=1,2 ...

Step 4 can not realize that so can consider with this method d (k+m) to be predicted, with d^ (k+m), m>=1 replaces d (k+m), and d^ (k+m) is inputed to feedforward controller G if advance item physics occurs among the source water turbidity d (k) in the embodiment one when concrete the realization _q, obtain feedforward controller G _qControl is G ' as a result _q(s), utilize based on the time series of AR model and forecast that the source water quality disturbance feedforward PREDICTIVE CONTROL result who obtains simplifies control to DMC and carries out the source water quality disturbance compensation, obtain the instant controlled quentity controlled variable u (k) of more accurate water treatment coagulation administration amount:

Formula ten:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+P)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{{1-\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]+{G^{\&prime;}}_q\left(s\right)$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe error weighting coefficient, G ' _q(s) forecast the source water quality disturbance feedforward PREDICTIVE CONTROL result who obtains for feedforward controller based on the time series of AR model.

Embodiment three:

On certain water factory's simulation coagulation administration device, to use compound PREDICTIVE CONTROL is example, provides implementation.

1, surveys the step response curve modeling

With the dosage step change measure that water turbidity changes like table 1:

The table 1 dose experiment measured value of ascending to heaven

With source water turbidity step change measure that water turbidity changes like table 2:

The table 2 turbidity experiment measured value of ascending to heaven

According to table 1 and table 2 typical response and aforesaid modeling method, disturb model in obtaining: $G_1\left(s\right)=\frac{-1.04}{(11.44s+1)(1.08s+1)}{e}^{-4s},$ Disturb model outward: $G_2\left(s\right)=\frac{1.05}{(9.03s+1)(0.50s+1)}{e}^{-2s},$ From G ₁(s) and G ₂(s) the visible overdamping object that is.

2, source quality forecast

Use the AR model description to do to the source quality sequence

x(k)＝φ ₁x(k-1)+φ ₂x(k-2)+φ ₃x(k-3)+ε(k)

P=3 in the model wherein, i.e. three rank, φ ₁=0.71, φ ₂=0.15, φ ₃=-0.13, ignore noise ε _nSo forecasting model does

3, DMC model simplification

To a in the formula four ₁, a ₂A _P+1, g ₃, g ₄G _N-1, g _nUtilize table 1, can provide corresponding value.And n=8, p=6 is with in the concrete outcome substitution control corresponding framework.

4, DMC simplifies control

Will

With

In the block diagram that substitution realizes, calculate F (z ^-1), D _r(z ^-1), h _fThereby can provide the instant control u (k) that simplifies DMC

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}[D_r\left(z^{-1}\right)(y_r(k+p)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right))-h_{f}e\left(k\right)]$

5, source water quality disturbance feedforward PREDICTIVE CONTROL

Because

With G ₁(s) and G ₂(s) after the substitution,

$G_q\left(s\right)=\frac{13.01{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000143427890000031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+13.16s+1.05}{{4.696\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000143427890000031.png"\; state="\{\{state\}\}">s</figure-callout>}}^2+9.911s+1.04}{e}^{2s}$

With G _q(s) after the discretize, the sampling time is 2min, and then outer to have disturbed a step leading in feedforward, and m gets 1, substitution AR forecasting model then, and d^ (k+1)=0.71d^ (k)+0.15d^ (k-1)-0.13d^ (k-2) inputs to feedforward controller with d^ (k+m) replacement d (k+m).

6, compound PREDICTIVE CONTROL realizes

Through the source water turbidity and the delivery turbidity of actual detected water treatment coagulation process, in conjunction with the effluent quality setting value, the input controlling models is tried to achieve the instant controlled quentity controlled variable of water treatment coagulation administration amount; Realize compound PREDICTIVE CONTROL and do corresponding emulation, its simulation result such as Fig. 5, Fig. 6, PID represents the closed loop PID method of prior art among Fig. 5, Fig. 6; Simplify DMC and represent compound forecast Control Algorithm of the present invention; Can find out that by Fig. 5 under the environment that the turbidity disturbance is arranged, compound Predictive Control System output has certain fluctuation in the starting stage. compare with PID; Simplify DMC and can reach balance at short notice; Overshoot is very little, and robustness is good, and system has good performance for tracking.Prove that this compound forecast Control Algorithm is suitable for the coagulation administration process.Can find out by Fig. 6, when coagulation process arrives identical delivery turbidity, adopt the dosage of simplifying the DMC method, than adopting the PID method that tangible minimizing is arranged.

Claims (2)

1. compound forecast Control Algorithm of water treatment coagulation administration; It is characterized in that the compound forecast Control Algorithm of said water treatment coagulation administration is to utilize compound predictive control model; Through detecting the source water turbidity and the delivery turbidity of water treatment coagulation process; In conjunction with the effluent quality setting value, import the instant controlled quentity controlled variable that compound predictive control model is tried to achieve water treatment coagulation administration amount, said compound predictive control model is set up through following steps:

One, the coagulation process modeling utilizes the principle that the type signal response combines with least square; Set up coagulation process in disturb model and disturb model outward, in to disturb model be to be input quantity with the dosage, be output quantity with water treatment coagulation delivery turbidity; Disturbing model outward and be with the source water turbidity is input quantity; With water treatment coagulation delivery turbidity is output quantity, in to disturb model be that the design of feedback PREDICTIVE CONTROL is used, it is used for the control of design feed forward prediction to disturb model outward.The model of being set up is two inertia objects that hysteresis is arranged, and it is described in order to drag:

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

Wherein K is a scale-up factor, and τ is the pure delay time, T ₁And T ₂Be the time constant of two inertia, K, τ, T ₁, T ₂Relation below available is tried to achieve:

Formula two: V=U θ+Ω

In the formula, $V=\left[\begin{array}{c}C\left(1\right)\\ C\left(2\right)\\ ...\\ C\left(m\right)\end{array}\right],$ $U=\left[\begin{array}{cccc}1& -1& -A\left(1\right)& -B\left(1\right)\\ 2& -1& -A\left(2\right)& -B\left(2\right)\\ ...& ...& ...& ...\\ m& -1& -A\left(m\right)& -B\left(m\right)\end{array}\right],$ $\mathrm{\&theta;}=\left[\begin{array}{c}K\\ \mathrm{K\&tau;}\\ T_1{T}_2\\ T_1+T_2\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{c}{\mathrm{\&Omega;}}_1\\ {\mathrm{\&Omega;}}_2\\ ...\\ {\mathrm{\&Omega;}}_m\end{array}\right]$

B, A and C are respectively step response, step response difference and step response integration in the formula; θ is a measured parameter, and Ω is a noise, through the experiment of ascending to heaven; Change the data of surveying the variation of water treatment coagulation delivery turbidity according to the dosage step; Change the data of surveying the variation of water treatment coagulation delivery turbidity according to source water turbidity step, according to the typical response and the aforesaid modeling method that record two groups of data

Ask model parameter with the least square formula:

Formula three: $\widehat{\mathrm{\&theta;}}={\left(U^{T}U\right)}^{-1}{U}^{T}V$

Two, the DMC model simplification can use single order inferred-zero object approximate because coagulation process is the overdamping object,

The model of uniting of setting up departments is G (z ^-1),

Formula four: G (z ^-1)=g ₁z ^-1+ g ₂z ^-2L+g _nz ^-nL+g _Nz ^-N

Wherein, g ₁, g ₂..., g _n..., g _NBe impulse response coefficient, for a stable process, the g in the formula four _Nz ^-nLater on each item can be by exponential representation, so formula four can be reduced to formula five:

$G\left(z^{-1}\right)=g_1{z}^{-1}+g_2{z}^{-2}L{g}_{n-1}{z}^{-(n-1)}+\frac{g_n{z}^{-n}}{1-{\mathrm{qz}}^{-1}}$

Wherein,

A wherein _N-1, a _n, a _NBe the step response parameter.

Basic DMC model is Y _m(k+1)=A Δ U (k)+A ₀U (k-1), wherein:

Formula six:

$A_{0}U(k-1)=\left[\begin{array}{c}{g}_N{z}^{-(N-1)}+g_{N-1}{z}^{-(N-2)}+...+g_3{z}^{-2}+a_2{z}^{-1}\\ g_N{z}^{-(N-2)}+g_{N-1}{z}^{-(N-3)}+...+g_4{z}^{-3}+a_3{z}^{-1}\\ ...\\ g_N{z}^{-(N-P)}+g_{N-1}{z}^{-(N-P+1)}+...+g_{P+2}{z}^{-(P+1)}+a_{P+1}{z}^{-1}\end{array}\right]$

Forecast model by formula five visible DMC is reduced to the n rank by the N rank, and basic DMC model is simplified, and formula six is reduced to formula seven:

$A_{0}U(k-1)\&ap;\left[\begin{array}{c}{a}_2{z}^{-1}+g_3{z}^{-2}+...+g_{n-1}{z}^{-(n-2)}+\frac{g_n{z}^{-(n-1)}}{1-{\mathrm{qz}}^{-1}}\\ a_3{z}^{-1}+g_4{z}^{-2}+...+g_{n-1}{z}^{-(n-3)}+\frac{g_n{z}^{-(n-2)}}{1-{\mathrm{qz}}^{-1}}\\ ...\\ a_{p+1}{z}^{-1}+g_{p+2}{z}^{-2}+...+g_{n-1}{z}^{-(n-p-1)}+\frac{g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}\end{array}\right]u\left(k\right)$

Three, DMC simplifies the A after the simplification that control obtains with step 2 ₀U (k-1) realizes the simplification control of DMC, and the instant controlled quentity controlled variable u (k) of water treatment coagulation administration amount is a formula eight:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+p)-\frac{d\left(k\right)g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]$

In the formula, $F\left(z^{-1}\right)==\frac{1}{d\left(k\right)}[1+f_1{z}^{-1}+...+f_{n-p-1}{z}^{-(n-p-1)}+f_{n-p}{z}^{-(n-p)}+...+f_{n-2}{z}^{-(n-2)}];$

$f_1=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{d}_{1i}{a}_{i+1}-1;$

$f_k=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=\mathrm{2,3},...,n-p-1);$

$f_k=\underset{i=1}{\overset{n-k-1}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=n-p,...,n-2);$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe the error weighting coefficient, f (k) is the disturbance of turbidity sequence, and p is a model order;

Four, source water quality disturbance feedforward PREDICTIVE CONTROL is for source water turbidity d (k) disturbance, feedforward controller G _qControl is G as a result _q(s) by principle of invariance, relation below existing:

G in the formula ₁(s), G ₂(s) disturb model in described, disturb model outward for step 1;

Five, the compound predictive control model of dispensing process is set up source water quality disturbance feedforward PREDICTIVE CONTROL that DMC with step 3 simplifies control and step 4 and is combined and carry out compound control; Utilize source water quality disturbance feedforward PREDICTIVE CONTROL result that DMC is simplified control and carry out the source water quality disturbance compensation, obtain the instant controlled quentity controlled variable u (k) of more accurate water treatment coagulation administration amount:

Formula nine:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}[D_r\left(z^{-1}\right)(y_r(k+P)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)]+G_q\left(s\right)$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe error weighting coefficient, G _q(s) be feedforward controller control result.

2. compound forecast Control Algorithm of water treatment coagulation administration; It is characterized in that the compound forecast Control Algorithm of said water treatment coagulation administration is to utilize compound predictive control model; Through detecting the source water turbidity and the delivery turbidity of water treatment coagulation process; In conjunction with the effluent quality setting value, import the instant controlled quentity controlled variable that compound predictive control model is tried to achieve water treatment coagulation administration amount, said compound predictive control model is set up through following steps:

One, the coagulation process modeling utilizes the principle that the type signal response combines with least square; Set up coagulation process in disturb model and disturb model outward, in to disturb model be to be input quantity with the dosage, be output quantity with water treatment coagulation delivery turbidity; Disturbing model outward and be with the source water turbidity is input quantity; With water treatment coagulation delivery turbidity is output quantity, in to disturb model be that the design of feedback PREDICTIVE CONTROL is used, it is used for the control of design feed forward prediction to disturb model outward.The model of being set up is two inertia objects that hysteresis is arranged, and it is described in order to drag:

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

Wherein K is a scale-up factor, and τ is the pure delay time, T ₁And T ₂Be the time constant of two inertia, K, τ, T ₁, T ₂Relation below available is tried to achieve:

Formula two: V=U θ+Ω

In the formula, $V=\left[\begin{array}{c}C\left(1\right)\\ C\left(2\right)\\ ...\\ C\left(m\right)\end{array}\right],$ $U=\left[\begin{array}{cccc}1& -1& -A\left(1\right)& -B\left(1\right)\\ 2& -1& -A\left(2\right)& -B\left(2\right)\\ ...& ...& ...& ...\\ m& -1& -A\left(m\right)& -B\left(m\right)\end{array}\right],$ $\mathrm{\&theta;}=\left[\begin{array}{c}K\\ \mathrm{K\&tau;}\\ T_1{T}_2\\ T_1+T_2\end{array}\right],$ $\mathrm{\&Omega;}=\left[\begin{array}{c}{\mathrm{\&Omega;}}_1\\ {\mathrm{\&Omega;}}_2\\ ...\\ {\mathrm{\&Omega;}}_m\end{array}\right]$

B, A, C are respectively step response in the formula, and step response difference and integration, θ are measured parameter; Ω is a noise; Through the experiment of ascending to heaven, change the data of surveying the variation of water treatment coagulation delivery turbidity according to the dosage step, change according to source water turbidity step and survey the data that water treatment coagulation delivery turbidity changes; According to the typical response and the aforesaid modeling method that record two groups of data

Ask model parameter with the least square formula:

Formula three: $\widehat{\mathrm{\&theta;}}={\left(U^{T}U\right)}^{-1}{U}^{T}V$

Two, the DMC model simplification can use single order inferred-zero object approximate because coagulation process is the overdamping object,

The model of uniting of setting up departments is G (z ^-1),

Formula four: G (z ^-1)=g ₁z ^-1+ g ₂z ^-2L+g _nz ^-nL+g _Nz ^-N

Wherein, g ₁, g ₂..., g _n..., g _NBe impulse response coefficient, for a stable process, the g in the formula four _Nz ^-nLater on each item can be by exponential representation, so formula four can be reduced to formula five:

$G\left(z^{-1}\right)=g_1{z}^{-1}+g_2{z}^{-2}L{g}_{n-1}{z}^{-(n-1)}+\frac{g_n{z}^{-n}}{1-{\mathrm{qz}}^{-1}}$

Wherein,

A wherein _N-1, a _n, a _NBe the step response parameter.

Basic DMC model is Y _m(k+1)=A Δ U (k)+A ₀U (k-1), wherein:

Formula six:

$A_{0}U(k-1)=\left[\begin{array}{c}{g}_N{z}^{-(N-1)}+g_{N-1}{z}^{-(N-2)}+...+g_3{z}^{-2}+a_2{z}^{-1}\\ g_N{z}^{-(N-2)}+g_{N-1}{z}^{-(N-3)}+...+g_4{z}^{-3}+a_3{z}^{-1}\\ ...\\ g_N{z}^{-(N-P)}+g_{N-1}{z}^{-(N-P+1)}+...+g_{P+2}{z}^{-(P+1)}+a_{P+1}{z}^{-1}\end{array}\right]$

Forecast model by formula five visible DMC is reduced to the n rank by the N rank, and basic DMC model is simplified, and formula six is reduced to formula seven:

$A_{0}U(k-1)\&ap;\left[\begin{array}{c}{a}_2{z}^{-1}+g_3{z}^{-2}+...+g_{n-1}{z}^{-(n-2)}+\frac{g_n{z}^{-(n-1)}}{1-{\mathrm{qz}}^{-1}}\\ a_3{z}^{-1}+g_4{z}^{-2}+...+g_{n-1}{z}^{-(n-3)}+\frac{g_n{z}^{-(n-2)}}{1-{\mathrm{qz}}^{-1}}\\ ...\\ a_{p+1}{z}^{-1}+g_{p+2}{z}^{-2}+...+g_{n-1}{z}^{-(n-p-1)}+\frac{g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}\end{array}\right]u\left(k\right)$

Three, DMC simplifies the A after the simplification that control obtains with step 2 ₀U (k-1) realizes the simplification control of DMC, and the instant controlled quentity controlled variable u (k) of water treatment coagulation administration amount is a formula eight:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+p)-\frac{d\left(k\right)g_n{z}^{-(n-p)}}{1-{\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]$

In the formula, $F\left(z^{-1}\right)==\frac{1}{d\left(k\right)}[1+f_1{z}^{-1}+...+f_{n-p-1}{z}^{-(n-p-1)}+f_{n-p}{z}^{-(n-p)}+...+f_{n-2}{z}^{-(n-2)}];$

$f_1=\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{d}_{1i}{a}_{i+1}-1;$

$f_k=\underset{i=1}{\overset{P}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=\mathrm{2,3},...,n-p-1);$

$f_k=\underset{i=1}{\overset{n-k-1}{\mathrm{\&Sigma;}}}{d}_{1i}{g}_{i+k},(k=n-p,...,n-2);$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe the error weighting coefficient, f (k) is the disturbance of turbidity sequence, and p is a model order;

Four, source water quality disturbance feedforward PREDICTIVE CONTROL is for source water turbidity d (k) disturbance, feedforward controller G _qControl is G as a result _q(s) by principle of invariance, relation below existing:

G in the formula ₁(s), G ₂(s) disturb model in described, disturb model outward for step 1;

Use based on the time series method of prediction of AR model and source water turbidity d (k) advance item predicted with d^ (k+m), m >=1 replaces d (k+m), adopt time series method of prediction to be based on the AR model:

x _n＝φ ₁x _n-1+...+φ _px _n-p+ε _n

X in the formula _nBe source water turbidity sequence, φ is the AR model coefficient, and p is a model order, ε _nBe noise, p rank φ ₁... φ _pIndividual parameter can be used the recursive least-squares identification, can forecast in the time series method of prediction that is based on the AR model

Sequence, k=1,2,

Calculate d^ (k+m) according to described time series method of prediction, d^ (k+m) is inputed to feedforward controller G based on the AR model _q, obtain feedforward controller G _qControl is G ' as a result _q(s);

Five, the compound predictive control model of dispensing process is set up source water quality disturbance feedforward PREDICTIVE CONTROL that DMC with step 3 simplifies control and step 4 and is combined and carry out compound control; Utilization forecasts that based on the time series of AR model the source water quality disturbance feedforward PREDICTIVE CONTROL result who obtains simplifies control to DMC and carries out the source water quality disturbance compensation, obtains the instant controlled quentity controlled variable u (k) of more accurate water treatment coagulation administration amount:

Formula ten:

$u\left(k\right)=\frac{1}{F\left(z^{-1}\right)}\left[D_r\left(z^{-1}\right)(y_r(k+P)-\frac{d\left(k\right)g_n{z}^{-(n-P)}}{{1-\mathrm{qz}}^{-1}}u\left(k\right)-h_{f}e\left(k\right)\right]+{G^{\&prime;}}_q\left(s\right)$

F (z wherein ^-1), D _r(z ^-1) be the controller parameter, can calculate y by model and control weight matrices _r(k+p) be the effluent quality setting value, d (k) is the source water turbidity, and e (k) is the margin of error, h _fBe error weighting coefficient, G ' _q(s) forecast the source water quality disturbance feedforward PREDICTIVE CONTROL result who obtains for feedforward controller based on the time series of AR model.

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