CN105223812A - A kind of method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint - Google Patents

Abstract

The invention discloses a kind of method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint, comprise: step 1, for double-deck rare acetone rectifying industrial model predictive control system, obtain the gain model of the steady-state optimization layer of model predictive controller; Step 2, finds in gain model, the uncertain element in process gain matrix; Step 3, according to uncertain element and system interference variable, tries to achieve the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set; Step 4, according to the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set, obtains optimal control in dynamic layer output constraint.The method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint provided by the invention, is applicable to non-side's uncertain system, ensure that and enterprise profit is maximized the feasibility that optimal control in dynamic layer model predictive controller solves.

Description

A kind of method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint

Technical field

The present invention relates to industrial control field, be specifically related to a kind of method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint.

Background technology

Acetone is one of a kind of important basic organic, mainly for the manufacture of cellulose acetate film film, plastics and paint solvent.Under different application scenarios, require that acetone has different purity, sometimes require that purity is very high, or even anhydrous propanone, but this is very inconvenient, because acetone has volatility, also dissolubility is had, so, want to obtain highly purified acetone often very difficult.

Want the aqueous acetone solution of low-purity to rise to high-purity, the general method using continuous rectification.In chemical plant, distillation operation carries out in upright circular rectification column, and tower is built with the filler of some layers of column plate or filling certain altitude.

Usual rare ketone fractionator system is by tower body, tower reactor reboiler, tower top refrigeratory, the equipment such as return tank of top of the tower are formed, rare acetone enters tower body from middle part, middle pressure steam passes into the thermal source of tower reactor reboiler as rectification column, tower top chilled water enters tower top refrigeratory and provides low-temperature receiver to rectification column, condensation gasification is to the heavy constituent (water) of tower top, in tower, material is after gasification repeatedly and condensation, highly purified acetone gas from tower body top out, enter tower top refrigeratory and chilled water heat exchange, the gas be not condensed enters exhausting pipeline system, the acetone liquid part being condensed to uniform temperature is refluxed pump and returns to tower top as cold reflux, another part is as product acetone discharger, tower bottoms is the water with trace acetone, tower bottoms directly uses pump discharger as sewage.

In acetone rectifying industry, utilize double-layer structure model PREDICTIVE CONTROL to carry out production control in conjunction with enterprise's Production requirement can make enterprise profit maximize; the control system of rare acetone rectifying industry is often that non-side is uncertain; as double-deck model predictive controller; when running into non-side's uncertain system, the output constraint of its optimal control in dynamic layer is difficult to determine.At present, study widely the output constraint design of non-side's certainty annuity is existing in the world, but little for the output constraint design of non-side's uncertain system this kind of in rare acetone rectifying industry.

Summary of the invention

The invention provides a kind of method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint, be applicable to non-side's uncertain system, ensure that and enterprise profit is maximized the feasibility that optimal control in dynamic layer model predictive controller solves.

A method for designing for rare acetone rectifying industrial dynamics optimal control layer output constraint, comprising:

Step 1, for double-deck rare acetone rectifying industrial model predictive control system, obtains the gain model of the steady-state optimization layer of model predictive controller;

Step 2, finds in gain model, the uncertain element in process gain matrix;

Step 3, according to uncertain element and system interference variable, tries to achieve the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set;

Step 4, according to the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set, obtains optimal control in dynamic layer output constraint.

In double-decker rare acetone rectifying industrial model predictive control system, the output constraint of optimal control in dynamic layer needs to be provided by the steady-state optimization layer on upper strata, traditional predictive controller output constraint method for designing can only provide the output constraint of certainty annuity, do not have to consider the output constraint method for designing when system occurs uncertain, and rare acetone rectifying industrial control system is usually with uncertain and be non-side's (system input variable number is less than output variable number), utilize the method for designing of optimal control in dynamic layer output constraint provided by the invention, the output constraint providing lower one deck in steady-state optimization layer in double-decker rare acetone rectifying model predictive control system can be given, ensure the feasibility that optimal control in dynamic layer model predictive controller solves.

Gain model in step 1 is as follows:

y＝Gu+G _dd

In formula: y is that the system that n × 1 is tieed up exports, y ∈ SOC;

G is the process gain matrix of n × m dimension;

U is the system input variable that m × 1 is tieed up, u ∈ SIC;

G _dfor the obstacle gain matrix of n × p dimension;

D is the system interference variable that p × 1 is tieed up, d ∈ DWC;

$SIC=\left\{u\right|u_i^{\min }\≤u_i\≤u_i^{\max };1\≤i\≤m\};$

$SOC=\left\{y\right|y_i^{\min }\≤y_i\≤y_i^{\max };1\≤i\≤n\};$

$DWC=\left\{d\right|d_i^{\min }\≤d_i\≤d_i^{\max };1\≤i\≤p\}.$

As preferably, output constraint reachable set LOKD is defined as follows:

LOKD (G, d)={ y|y=Gu+G _dd; U ∈ SIC, g _hk∈ Δ, G _dfor fixed value }

$LOKD=\underset{g_{hk}\∈\mathrm{\Δ}}{\∪}\underset{d\∈DWC}{\∪}LOKD(G,d)$

In formula, g _hkfor the uncertain element in process gain matrix G, be expressed as $g_{hk}^{\min }\≤g_{hk}\≤g_{hk}^{\max }$ Form, $\mathrm{\Δ}=\left\{g\right|g_{hk}^{\min }\≤g\≤g_{nk}^{\max }\};$

The coboundary LOKDSJ of output constraint reachable set is defined as follows:

$\begin{array}{c}LOKDSJ=C_{LOKD(\∀g_{hk}\∈\mathrm{\Δ},d=d^{\max })}\left(LOKD\right(\∀g_{hk}\∈\mathrm{\Δ},d\\ d^{\max })\∩LOKD(\∀g_{hk}\∈\mathrm{\Δ},d\≠d^{\max }))\end{array}$

The lower boundary LOKDXJ of output constraint reachable set is defined as follows:

$\begin{array}{c}LOKDXJ=C_{LOKD(\∀g_{hk}\∈\mathrm{\Δ},d=d^{\min })}\left(LOKD\right(\∀g_{hk}\∈\mathrm{\Δ},d\\ =d^{\min })\∩LOKD(\∀g_{hk}\∈\mathrm{\Δ},d\≠d^{\min }))\end{array}$

In step 3, the step calculating the coboundary of output constraint reachable set is as follows:

Step 3-a-1, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{\max })$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{max}),$ Be designated as L respectively _{s, max}and L _{s, min}, obtain L _{s, max}and L _{s, min}common factor I _s;

Step 3-a-2, by L _{s, max}and L _{s, min}summit be divided into two groups, be respectively with with the polyhedron formed and I _sthere is no intersection point;

Step 3-a-3, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{\max }-e)$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{max}-e),$ Be designated as L respectively _{s, maxe}and L _{s, mine}, e is arithmetic number;

Step 3-a-4, from with middlely select one group of summit and I respectively _sform polyhedron, and by form polyhedron respectively with L _{s, maxe}and L _{s, mine}carry out Intersection inspection, with L _{s, maxe}and L _{s, mine}the combination of all disjoint a kind of summit, is the summit of the coboundary LOKDSJ of output constraint reachable set, and the polyhedron that the summit of LOKDSJ is formed is the coboundary of output constraint reachable set.

As preferably, in step 3, the step calculating the lower boundary of output constraint reachable set is as follows:

Step 3-b-1, obtains $LOKD(g_{nk}=g_{hk}^{\max },d=d^{\min })$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{\min }),$ Be designated as L ' respectively _{s, max}and L ' _{s, min}, obtain L ' _{s, max}and L ' _{s, min}common factor I ' _s;

Step 3-b-2, by L ' _{s, max}and L ' _{s, min}summit be divided into two groups, be respectively with with the polyhedron formed and I ' _sthere is no intersection point;

Step 3-b-3, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{min}+e)$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{min}+e),$ Be designated as L ' respectively _{s, maxe}and L ' _{s, mine}, e is arithmetic number;

Step 3-b-4, from with middlely select one group of summit and I ' respectively _sform polyhedron, and by form polyhedron respectively with L ' _{s, maxe}and L ' _{s, mine}carry out Intersection inspection, with L ' _{s, maxe}and L ' _{s, mine}the combination of all disjoint a kind of summit, is the summit of the lower boundary LOKDSJ of output constraint reachable set, and the polyhedron that the summit of LOKDSJ is formed is the lower boundary of output constraint reachable set.

As preferably, in step 3-a-2, by L _{s, max}and L _{s, min}summit be divided into the method for two groups as follows:

Select L arbitrarily _{s, max}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I _sseek common ground, if occur simultaneously for empty, namely obtain and I _sdisjoint with

Select L arbitrarily _{s, min}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I _sseek common ground, if occur simultaneously for empty, namely obtain and I _sdisjoint

As preferably, in step 3-b-2, by L ' _{s, max}and L ' _{s, min}summit be divided into the method for two groups as follows:

Select L ' arbitrarily _{s, max}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I ' _sseek common ground, if occur simultaneously for empty, namely obtain and I ' _sdisjoint with

Select L ' arbitrarily _{s, min}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I ' _sseek common ground, if occur simultaneously for empty, namely obtain and I ' _sdisjoint

As preferably, optimal control in dynamic layer output constraint LOJX is defined as follows:

LOJX(α)＝{y|b ₁≤y-y ₀≤b ₂}

$b_1={\[\frac{-\mathrm{\α}}{w_1}\frac{-\mathrm{\α}}{w_2}...\frac{-\mathrm{\α}}{w_n}\]}^T,b_2={\[\frac{\mathrm{\α}}{w_1}\frac{\mathrm{\α}}{w_2}...\frac{\mathrm{\α}}{w_n}\]}^T$

y ₀＝[y ₀₁y ₀₂...y _0n] ^T，y＝[y ₁y ₂...y _n] ^T

In formula: w ₁w ₂... w _nfor weight; y ₀be the nominal steady-state values of process, y is that system exports.

In step 4, the step calculating optimal control in dynamic layer output constraint is as follows:

Step 4-1, utilizes iterative algorithm to try to achieve α _{+ 1}and α _-1, make LOJX (α _{+ 1}) tangent with LOKDSJ, point of contact is v _{+ 1}; LOJX (α _-1) tangent with LOKDXJ, point of contact is v _-1;

Step 4-2, note v _{+ 1}=[y ₁₊y ₂₊... y _n+], v _-1=[y _1-y _2-... y _n-], then optimal control in dynamic layer output constraint LOJX is:

LOJX＝{y|min(v ₊₁,v _-1)≤y-y ₀≤max(v ₊₁,v _-1)}。

The method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint provided by the invention, is applicable to non-side's uncertain system, ensure that and enterprise profit is maximized the feasibility that optimal control in dynamic layer model predictive controller solves.

Accompanying drawing explanation

Fig. 1 is the L of two-dimentional system _{s, max}, L _{s, min}and I _s;

Fig. 2 is the L of three dimension system _{s, max}and I _ssummit;

Fig. 3 is the solving of LOKDSJ in two-dimentional system;

Fig. 4 is r=1:1:1, y ₀lOJX and SOC of=(0,0,0);

Fig. 5 is r=1:1:1, y ₀lOKD and SOC of=(0,0,0);

Fig. 6 is r=1:1:1, y ₀lOJX and LOKD of=(0,0,0);

Fig. 7 is r=1:1:1, y ₀lOJX and LOKD that during=(0,0,0), different angles are observed;

Fig. 8 is LOJX, LOKDSJ and LOKDXJ;

Fig. 9 is the LOJX changing view, LOKDSJ and LOKDXJ.

Embodiment

Below in conjunction with accompanying drawing, the method for designing of the present invention's rare acetone rectifying industrial dynamics optimal control layer output constraint is described in detail.

A method for designing for rare acetone rectifying industrial dynamics optimal control layer output constraint, comprising:

Step 1, for double-deck rare acetone rectifying industrial model predictive control system, obtains the gain model of the steady-state optimization layer of model predictive controller.

Gain model is: y=Gu+G _dd

In formula: y is that the system that n × 1 is tieed up exports, y ∈ SOC;

G is the process gain matrix of n × m dimension;

U is the system input variable that m × 1 is tieed up, u ∈ SIC;

G _dfor the obstacle gain matrix of n × p dimension;

D is the system interference variable that p × 1 is tieed up, d ∈ DWC;

$SIC=\left\{u\right|u_i^{\min }\≤u_i\≤u_i^{\max };1\≤i\≤m\};$

$SOC=\left\{y\right|y_i^{\min }\≤y_i\≤y_i^{\max };1\≤i\≤n\};$

$DWC=\left\{d\right|d_i^{\min }\≤d_i\≤d_i^{\max };1\≤i\≤p\}.$

Step 2, finds in gain model, and the uncertain element in process gain matrix, uncertain element is designated as g _hk, method provided by the invention is applicable to the situation that only there is a uncertain element in process gain matrix.

Step 3, according to uncertain element and system interference variable, tries to achieve the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set.

Output constraint reachable set LOKD is defined as follows:

LOKD (G, d)={ y|y=Gu+G _dd; U ∈ SIC, g _hk∈ Δ, G _dfor fixed value }

$LOKD=\underset{g_{hk}\∈\mathrm{\Δ}}{\∪}\underset{d\∈DWC}{\∪}LOKD(G,d)$

In formula, g _hkfor the uncertain element in process gain matrix G, be expressed as $g_{hk}^{\min }\≤g_{hk}\≤g_{hk}^{\max }$ Form, $\mathrm{\Δ}=\left\{g\right|g_{hk}^{\min }\≤g\≤g_{hk}^{\max }\};$

The coboundary LOKDSJ of output constraint reachable set is defined as follows:

$\begin{array}{c}LOKDSJ=C_{LOKD(\∀g_{hk}\∈\mathrm{\Δ},d=d^{\max })}\left(LOKD\right(\∀g_{hk}\∈\mathrm{\Δ},d\\ d^{\max })\∩LOKD(\∀g_{hk}\∈\mathrm{\Δ},d\≠d^{\max }))\end{array}$

The lower boundary LOKDXJ of output constraint reachable set is defined as follows:

$\begin{array}{c}LOKDXJ=C_{LOKD(\∀g_{hk}\∈\mathrm{\Δ},d=d^{\min })}\left(LOKD\right(\∀g_{hk}\∈\mathrm{\Δ},d\\ =d^{\min })\∩LOKD(\∀g_{hk}\∈\mathrm{\Δ},d\≠d^{\min }))\end{array}$

In step 3, the step calculating the coboundary of output constraint reachable set is as follows:

Step 3-a-1, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{\max })$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{max}),$ Be designated as L respectively _{s, max}and L _{s, min}, obtain L _{s, max}and L _{s, min}common factor I _s.

Common factor I _ssolve and utilize MPT (Multi-ParametricToolbox) to carry out, Fig. 1 is the L that two dimension exports _{s, max}, L _{s, min}and I _s, in two-dimentional system, L _{s, max}and L _{s, min}corresponding one section of straight line respectively, common factor I _sit is the intersection point of two straight lines.

As shown in Figure 2, the three-dimensional L exported _{s, max}and L _{s, min}a corresponding rectangle plane respectively, common factor I _sit is the intersection of two rectangle planes.

Step 3-a-2, by L _{s, max}and L _{s, min}summit be divided into two groups, be respectively with with the polyhedron formed and I _sthere is no intersection point.

For two-dimentional system, L _{s, max}be one section of straight line, L _{s, max}summit be the two-end-point of straight line, for three dimension system, L _{s, max}be a rectangle plane, L _{s, max}summit be four summits of rectangle.

In this step, by L _{s, max}and L _{s, min}summit be divided into the principle of two groups to be, make acquisition with the polyhedron formed and I _sdo not have intersection point, in order to reach this effect, the method for grouping is as follows:

Select L arbitrarily _{s, max}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I _sseek common ground, if occur simultaneously for empty, namely obtain and I _sdisjoint with

Due to L _{s, max}singularity, L _{s, max}number of vertex be all even number, if number of vertex is k, then selecting arbitrarily the number of combination that half summit forms is kind, utilize MPT tool box, the polyhedron that the summit of often kind of combination is formed and I _sseek common ground, if occur simultaneously for empty, then illustrate non-intersect, carried out secondary seek common ground after, can obtain and I _sdisjoint with

In like manner calculate as follows:

Select L arbitrarily _{s, min}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I _sseek common ground, if occur simultaneously for empty, namely obtain and I _sdisjoint

Step 3-a-3, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{\max }-e)$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{max}-e),$ Be designated as L respectively _{s, maxe}and L _{s, mine}, e is arithmetic number; In the accuracy rating that can accept, e be one level off to 0 arithmetic number, usual e gets 10 ^-4.

Step 3-a-4, from with middlely select one group of summit and I respectively _sform polyhedron, and by form polyhedron respectively with L _{s, maxe}and L _{s, mine}carry out Intersection inspection, with L _{s, maxe}and L _{s, mine}the combination of all disjoint a kind of summit, is the summit of the coboundary LOKDSJ of output constraint reachable set, and the polyhedron that the summit of LOKDSJ is formed is the coboundary of output constraint reachable set.

As shown in Figure 3, for two-dimentional system, L _{s, maxe}relative L _{s, max}there is a micro-displacement, L _{s, mine}relative L _{s, min}there is a micro-displacement, solve the LOKDSJ (shown in heavy line part) and L that obtain _{s, maxe}and L _{s, mine}all non-intersect.

By in select one group of summit, select one group of summit, this two groups of summits and I _sform polyhedron, one has kind of situation, by the polyhedron that forms in these four kinds of situations respectively with L _{s, maxe}and L _{s, mine}carry out Intersection inspection, with L _{s, maxe}and L _{s, mine}the combination of all disjoint a kind of summit, is the summit of required LOKDSJ, and the polyhedron that the summit of LOKDSJ is formed is the coboundary LOKDSJ of output constraint reachable set.

In like manner, the step calculating the lower boundary of output constraint reachable set is as follows:

Step 3-b-1, obtains $LOKD(g_{nk}=g_{hk}^{\max },d=d^{\min })$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{\min }),$ Be designated as L ' respectively _{s, max}and L ' _{s, min}, obtain L ' _{s, max}and L ' _{s, min}common factor I ' _s.

Step 3-b-2, by L ' _{s, max}and L ' _{s, min}summit be divided into two groups, be respectively with with the polyhedron formed and I ' _sthere is no intersection point.

In this step, by L ' _{s, max}and L ' _{s, min}summit be divided into the method for two groups as follows:

Select L ' arbitrarily _{s, max}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I ' _sseek common ground, if occur simultaneously for empty, namely obtain and I ' _sdisjoint with

Select L ' arbitrarily _{s, min}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I ' _sseek common ground, if occur simultaneously for empty, namely obtain and I ' _sdisjoint

Step 3-b-3, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{min}+e)$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{min}+e),$ Be designated as L ' respectively _{s, maxe}and L ' _{s, mine}, e is arithmetic number, and e gets 10 ^-4.

Step 3-b-4, from with middlely select one group of summit and I ' respectively _sform polyhedron, and by form polyhedron respectively with L ' _{s, maxe}and L ' _{s, mine}carry out Intersection inspection, with L ' _{s, maxe}and L ' _{s, mine}the combination of all disjoint a kind of summit, is the summit of the lower boundary LOKDSJ of output constraint reachable set, and the polyhedron that the summit of LOKDSJ is formed is the lower boundary of output constraint reachable set.

Step 4, according to the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set,

Obtain optimal control in dynamic layer output constraint.

Optimal control in dynamic layer output constraint LOJX is defined as follows:

LOJX(α)＝{y|b ₁≤y-y ₀≤b ₂}

$b_1={\[\frac{-\mathrm{\α}}{w_1}\frac{-\mathrm{\α}}{w_2}\mathrm{...}\frac{-\mathrm{\α}}{w_n}\]}^T,b_2={\[\frac{\mathrm{\α}}{w_1}\frac{\mathrm{\α}}{w_2}\mathrm{...}\frac{\mathrm{\α}}{w_n}\]}^T$

y ₀＝[y ₀₁y ₀₂...y _0n] ^T，y＝[y ₁y ₂...y _n] ^T

In formula: w ₁w ₂... w _nfor the self-determining weight of user, be all 1 under default situations, and remember r=w _n: w _n-1: ...: w ₂: w ₁, for arranging weight, y ₀be the nominal steady-state values of process, y is that system exports.

The step calculating optimal control in dynamic layer output constraint is as follows:

Step 4-1, utilize iterative algorithm (see document FernandoV.Lima, ChristosGeorgakis, Designofoutputconstraintsformodel-basednon-squarecontrol lersusingintervaloperability.JournalofProcessControl18 (2008) 610 – 620) try to achieve α _{+ 1}and α _-1, make LOJX (α _{+ 1}) tangent with LOKDSJ, point of contact is v _{+ 1}; LOJX (α _-1) tangent with LOKDXJ, point of contact is v _-1;

Step 4-2, note v _{+ 1}=[y ₁₊y ₂₊... y _n+], v _-1=[y _1-y _2-... y _n-], then optimal control in dynamic layer output constraint LOJX is:

LOJX＝{y|min(v ₊₁,v _-1)≤y-y ₀≤max(v ₊₁,v _-1)}。

Emulation embodiment

In order to show method for designing of the present invention more intuitively, consider that one has the system of low dimension at the steady-state optimization layer of rare acetone rectifying industry, their initial point is at nominal steady state point y ₀.Steady-state optimization layer system is described below:

$\left(\begin{array}{c}{y}_1\\ y_2\\ y_3\end{array}\right)=\left(\begin{array}{cc}{g}_{11}& 0.3\\ -0.42& -0.23\\ 0.65& 0.53\end{array}\right)\left(\begin{array}{c}{u}_1\\ u_2\end{array}\right)+\left(\begin{array}{c}0.3\\ 0.5\\ 0.5\end{array}\right)d_1$

SIC={u ∈ R ²|| | u|| _∞≤ 1}, SOC={y ∈ R ³|| | y|| _∞≤ 1}, DWC={-1≤d ₁≤ 1}, the output constraint of trying to achieve is LOJX={ (y ₁, y ₂, y ₃) |-0.49≤y ₁≤ 0.49 ,-0.49≤y ₁≤ 0.49 ,-0.49≤y ₁≤ 0.49}.

Weight r=1:1:1, y ₀during=(0,0,0), the relation of LOJX and SOC is shown in Fig. 4, and the relation of LOKD and SOC is shown in Fig. 5, and the relation of LOJX and LOKD is shown in Fig. 6 and Fig. 7, and LOJX, LOKDSJ and LOKDXJ relation is shown in Fig. 8 and Fig. 9.

As shown in Figure 8 and Figure 9, LOJX is a polyhedron lucky and LOKDSJ and LOKDXJ is tangent, and tangent LOJX and the LOKDSJ of referring in the present invention and LOKDXJ has respectively and only has an intersection point.

Owing to selecting singularity and r and y of example ₀the simplicity arranged, makes the output constraint of trying to achieve be the polyhedron of a specification.When situation is complicated, output constraint can have different shapes with the r chosen.

Claims (7)

1. a method for designing for rare acetone rectifying industrial dynamics optimal control layer output constraint, is characterized in that, comprising:

Step 1, for double-deck rare acetone rectifying industrial model predictive control system, obtains the gain model of the steady-state optimization layer of model predictive controller;

Step 2, finds in gain model, the uncertain element in process gain matrix;

Step 3, according to uncertain element and system interference variable, tries to achieve the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set;

Step 4, according to the coboundary of output constraint reachable set and the lower boundary of output constraint reachable set, obtains optimal control in dynamic layer output constraint.

2. the method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint as claimed in claim 1, it is characterized in that, the gain model in step 1 is as follows:

Y＝Ｇu+G _dd

In formula: y is that the system that n × 1 is tieed up exports, y ∈ SOC;

G is the process gain matrix of n × m dimension;

U is the system input variable that m × 1 is tieed up, u ∈ SIC;

G _dfor the obstacle gain matrix of n × p dimension;

D is the system interference variable that p × 1 is tieed up, d ∈ DWC;

$SIC=\left\{u\right|u_i^{\min }\≤u_i\≤u_i^{\max };1\≤i\≤m\};$

$SOC=\left\{y\right|y_i^{\min }\≤y_i\≤y_i^{\max };1\≤i\≤n\};$

$DWC=\left\{d\right|d_i^{\min }\≤d_i\≤d_i^{\max };1\≤i\≤p\}.$

3. the method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint as claimed in claim 2, it is characterized in that, output constraint reachable set LOKD is defined as follows:

LOKD (G, d)={ y|y=Gu+G _dd; U ∈ SIC, g _hk∈ Δ, G _dfor fixed value }

$LOKD=\underset{g_{hk}\∈\mathrm{\Δ}}{\∪}\underset{d\∈DWC}{\∪}LOKD(G,d)$

In formula, g _hkfor the uncertain element in process gain matrix G, be expressed as $g_{hk}^{\min }\≤g_{hk}\≤g_{hk}^{\max }$ Form, $\mathrm{\Δ}=\left\{g\right|g_{hk}^{\min }\≤g\≤g_{hk}^{\max }\};$

The coboundary LOKDSJ of output constraint reachable set is defined as follows:

$\begin{array}{c}LOKDSJ=C_{LOKD(\∀g_{hk}\∈\mathrm{\Δ},d=d^{\max })}\left(LOKD\right(\∀g_{hk}\∈\mathrm{\Δ},d\\ =d^{\max })\∩LOKD(\∀g_{hk}\∈\mathrm{\Δ},d\≠d^{\max }))\end{array}$

The lower boundary LOKDXJ of output constraint reachable set is defined as follows:

$\begin{array}{c}LOKDXJ=C_{LOKD(\∀g_{hk}\∈\mathrm{\Δ},d=d^{\min })}\left(LOKD\right(\∀g_{hk}\∈\mathrm{\Δ},d\\ =d^{\min })\∩LOKD(\∀g_{hk}\∈\mathrm{\Δ},d\≠d^{\min }))\end{array}$

In step 3, the step calculating the coboundary of output constraint reachable set is as follows:

Step 3-a-1, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{max})$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{max}),$ Be designated as L respectively _{s, max}and L _{s, min}, obtain L _{s, max}and L _{s, min}common factor I _s;

Step 3-a-2, by L _{s, max}and L _{s, min}summit be divided into two groups, be respectively with with the polyhedron formed and I _sthere is no intersection point;

Step 3-a-3, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{max}-e)$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{max}-e),$ Be designated as L respectively _{s, maxe}and L _{s, mine}, e is arithmetic number;

Step 3-a-4, from with middlely select one group of summit and I respectively _sform polyhedron, and by form polyhedron respectively with L _{s, maxe}and L _{s, mine}carry out Intersection inspection, with L _{s, maxe}and L _{s, mine}the combination of all disjoint a kind of summit, is the summit of the coboundary LOKDSJ of output constraint reachable set, and the polyhedron that the summit of LOKDSJ is formed is the coboundary of output constraint reachable set.

4. the method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint as claimed in claim 3, is characterized in that, in step 3, the step calculating the lower boundary of output constraint reachable set is as follows:

Step 3-b-1, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{min})$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{min}),$ Be designated as L ' respectively _{s, max}and L ' _{s, min}, obtain L ' _{s, max}and L ' _{s, min}common factor I ' _s;

Step 3-b-2, by L ' _{s, max}and L ' _{s, min}summit be divided into two groups, be respectively with with the polyhedron formed and I ' _sthere is no intersection point;

Step 3-b-3, obtains $LOKD(g_{hk}=g_{hk}^{\max },d=d^{min}+e)$ With $LOKD(g_{hk}=$ $g_{hk}^{\min },d=d^{min}+e),$ Be designated as L ' respectively _{s, maxe}and L ' _{s, mine}, e is arithmetic number;

Step 3-b-4, from with middlely select one group of summit and I ' respectively _sform polyhedron, and by form polyhedron respectively with L ' _{s, maxe}and L ' _{s, mine}carry out Intersection inspection, with L ' _{s, maxe}and L ' _{s, mine}the combination of all disjoint a kind of summit, is the summit of the lower boundary LOKDSJ of output constraint reachable set, and the polyhedron that the summit of LOKDSJ is formed is the lower boundary of output constraint reachable set.

5. the method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint as claimed in claim 4, is characterized in that, in step 3-a-2, by L _{s, max}and L _{s, min}summit be divided into the method for two groups as follows:

Select L arbitrarily _{s, max}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I _sseek common ground, if occur simultaneously for empty, namely obtain and I _sdisjoint with

Select L arbitrarily _{s, min}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I _sseek common ground, if occur simultaneously for empty, namely obtain and I _sdisjoint

6. the method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint as claimed in claim 5, is characterized in that, in step 3-b-2, by L ' _{s, max}and L ' _{s, min}summit be divided into the method for two groups as follows:

Select L ' arbitrarily _{s, max}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I ' _sseek common ground, if occur simultaneously for empty, namely obtain and I ' _sdisjoint with

Select L ' arbitrarily _{s, min}half summit as a combination, the polyhedron that forms of summit that often kind is combined and I ' _sseek common ground, if occur simultaneously for empty, namely obtain and I ' _sdisjoint

7. the method for designing of rare acetone rectifying industrial dynamics optimal control layer output constraint as claimed in claim 6, it is characterized in that, optimal control in dynamic layer output constraint LOJX is defined as follows:

LOJX(α)＝{y|b ₁≤y-y ₀≤b ₂}

$b_1={\[\frac{-\mathrm{\α}}{w_1}\frac{-\mathrm{\α}}{w_2}\mathrm{...}\frac{-\mathrm{\α}}{w_n}\]}^T,$ $b_2={\[\frac{\mathrm{\α}}{w_1}\frac{\mathrm{\α}}{w_2}\mathrm{...}\frac{\mathrm{\α}}{w_n}\]}^T$

y ₀＝[y ₀₁y ₀₂…y _0n] ^T，y＝[y ₁y ₂…y _m] ^T

In formula: w ₁w ₂w _nfor weight; y ₀be the nominal steady-state values of process, y is that system exports;

In step 4, the step calculating optimal control in dynamic layer output constraint is as follows:

Step 4-1, utilizes iterative algorithm to try to achieve α _{+ 1}and α _-1, make LOJX (α _{+ 1}) tangent with LOKDSJ, point of contact is ν _{+ 1}; LOJX (α _-1) tangent with LOKDXJ, point of contact is ν _-1;

Step 4-2, note ν _{+ 1}=[y ₁₊y ₂₊y _n+], ν _-1=[y _1-y _2-y _n-], then optimal control in dynamic layer output constraint LOJX is:

LOJX＝{y|min(ν ₊₁,ν _-1)≤y-y ₀≤max(ν ₊₁,ν _-1)}。