CN105223812A

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

Info

Publication number: CN105223812A
Application number: CN201510593554.1A
Authority: CN
Inventors: 谢磊; 谢澜涛
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2015-09-17
Filing date: 2015-09-17
Publication date: 2016-01-06

Abstract

The invention discloses a design method for the output constraint of the dynamic optimization control layer of the distilling industry of diacetone, comprising: Step 1, aiming at the distilling industry model predictive control system of the double-layer structure, obtaining the steady state of the model predictive controller The gain model of the optimization layer; step 2, find the uncertain elements in the process gain matrix in the gain model; step 3, obtain the upper boundary of the output constrained reachable set and the output constrained reachable set based on the uncertain elements and system disturbance variables The lower boundary of the set; step 4, according to the upper boundary of the output constraint reachable set and the lower boundary of the output constraint reachable set, the output constraints of the dynamic optimization control layer are obtained. The design method for the output constraint of the dynamic optimization control layer of the rectification industry of diacetone provided by the invention is suitable for non-square uncertain systems, ensures the feasibility of solving the model predictive controller of the dynamic optimization control layer, and maximizes the profit of the enterprise.

Description

A Design Method of Output Constraints of Control Layer for Dynamic Optimization of Distillation Industry of Diacetone

技术领域technical field

本发明涉及工业控制领域，具体涉及一种稀丙酮精馏工业动态优化控制层输出约束的设计方法。The invention relates to the field of industrial control, in particular to a design method for dynamically optimizing the output constraints of a control layer in the rectification industry of propylene glycol.

背景技术Background technique

丙酮是一种重要的基本有机原料之一，主要用于制造醋酸纤维素胶片薄膜、塑料以及涂料溶剂。在不同的应用场合下，要求丙酮具有不同的纯度，有时要求纯度很高，甚至是无水丙酮，但这是很有困难的，因为丙酮极具挥发性，也极具溶解性，所以，想要得到高纯度的丙酮往往十分困难。Acetone is one of the important basic organic raw materials, mainly used in the manufacture of cellulose acetate films, plastics and paint solvents. In different applications, acetone is required to have different purity, sometimes it is required to be of high purity, even anhydrous acetone, but this is very difficult, because acetone is extremely volatile and soluble, so, I want to It is often very difficult to obtain high-purity acetone.

要想把低纯度的丙酮水溶液提升到高纯度，一般使用连续精馏的方法。化工厂中精馏操作是在直立圆形的精馏塔内进行的，塔内装有若干层塔板或充填一定高度的填料。In order to raise the low-purity acetone aqueous solution to high-purity, continuous distillation is generally used. The rectification operation in the chemical plant is carried out in a vertical circular rectification column, which is equipped with several layers of trays or filled with a certain height of packing.

通常稀丙酮精馏塔系统由塔体、塔釜再沸器、塔顶冷却器、塔顶回流罐等设备构成，稀丙酮从中部进入塔体，中压蒸汽通入塔釜再沸器作为精馏塔的热源，塔顶冷却水进入塔顶冷却器给精馏塔提供冷源，冷凝气化至塔顶的重组分(水)，塔内物料经多次的气化和冷凝后，高纯度的丙酮气从塔体顶部出来，进入塔顶冷却器与冷却水换热，未被冷凝的气体进入放空管道系统，被冷凝至一定温度的丙酮液体一部分被回流泵打回至塔顶作为冷回流，另一部分作为丙酮产品排出装置，塔釜液为带有微量丙酮的水，塔釜液作为污水直接用泵排出装置。Usually diacetone rectification column system is composed of tower body, tower reboiler, tower top cooler, tower top reflux tank and other equipment. The heat source of the distillation tower, the cooling water at the top of the tower enters the top cooler to provide a cold source for the rectification tower, and condenses and vaporizes the heavy components (water) at the top of the tower. After repeated gasification and condensation, the materials in the tower have high purity The acetone gas comes out from the top of the tower and enters the top cooler to exchange heat with the cooling water. The uncondensed gas enters the vent pipe system, and part of the acetone liquid condensed to a certain temperature is pumped back to the top of the tower by the reflux pump as cold reflux. , the other part is used as acetone product discharge device, the tower bottom liquid is water with a small amount of acetone, and the tower bottom liquid is used as sewage to directly discharge the device with a pump.

在丙酮精馏工业中结合企业生产需求利用双层结构模型预测控制进行生产控制能使得企业利润最大化，稀丙酮精馏工业的控制系统往往是非方不确定的，作为双层结构的模型预测控制器，当遇到非方不确定系统时，其动态优化控制层的输出约束很难确定。目前，国际上对非方确定系统的输出约束设计已有广泛的研究，但对于稀丙酮精馏工业中这类非方不确定系统的输出约束设计却很少。In the acetone distillation industry, combined with the production needs of enterprises, the use of double-layer structure model predictive control for production control can maximize the profit of enterprises. The control system of diacetone distillation industry is often non-square and uncertain. When encountering a non-square uncertain system, the output constraints of its dynamic optimization control layer are difficult to determine. At present, there have been extensive researches on the output constraint design of non-square deterministic systems in the world, but there are few studies on the output constraint design of such non-square uncertain systems in the distilling industry of allycetone.

发明内容Contents of the invention

本发明提供了一种稀丙酮精馏工业动态优化控制层输出约束的设计方法，适用于非方不确定系统，确保了动态优化控制层模型预测控制器求解的可行性，使企业利润能够最大化。The invention provides a design method for the output constraint of the dynamic optimization control layer in the rectification industry of diacetone, which is suitable for non-square uncertain systems, ensures the feasibility of solving the dynamic optimization control layer model predictive controller, and maximizes the profit of the enterprise .

一种稀丙酮精馏工业动态优化控制层输出约束的设计方法，包括：A design method for the dynamic optimization control layer output constraints of the distilling industry of propylene glycol, including:

步骤1，针对双层结构的稀丙酮精馏工业模型预测控制系统，求出模型预测控制器的稳态优化层的增益模型；Step 1, aiming at the industrial model predictive control system for the rectification of diacetone with two-layer structure, obtain the gain model of the steady-state optimization layer of the model predictive controller;

步骤2，找到增益模型中，过程增益矩阵中的不确定元素；Step 2, find the uncertain elements in the process gain matrix in the gain model;

步骤3，依据不确定元素和系统干扰变量，求得输出约束可达集的上边界和输出约束可达集的下边界；Step 3. Obtain the upper boundary of the output constrained reachable set and the lower bound of the output constrained reachable set according to the uncertain elements and system disturbance variables;

步骤4，依据输出约束可达集的上边界和输出约束可达集的下边界，得到动态优化控制层输出约束。Step 4, according to the upper boundary of the output constraint reachable set and the lower boundary of the output constraint reachable set, the output constraints of the dynamic optimization control layer are obtained.

在双层结构稀丙酮精馏工业模型预测控制系统中，动态优化控制层的输出约束需要由上层的稳态优化层给出，传统的预测控制器输出约束设计方法只能给出确定系统的输出约束，没有考虑当系统出现不确定性时的输出约束设计方法，而稀丙酮精馏工业控制系统通常带有不确定性且是非方(系统输入变量数目小于输出变量数目)的，利用本发明提供的动态优化控制层输出约束的设计方法，能够给在双层结构稀丙酮精馏模型预测控制系统中的稳态优化层中给出下一层的输出约束，保证动态优化控制层模型预测控制器求解的可行性。In the industrial model predictive control system for the distillation of propylene glycol with a double-layer structure, the output constraints of the dynamic optimization control layer need to be given by the upper steady-state optimization layer, and the traditional output constraint design method of the predictive controller can only give the output of the definite system Constraints, without considering the output constraint design method when the uncertainty occurs in the system, and the industrial control system of propylene glycol distillation usually has uncertainty and is non-square (the number of system input variables is less than the number of output variables), and the present invention provides The design method of the output constraints of the dynamic optimization control layer can give the output constraints of the next layer in the steady-state optimization layer in the model predictive control system of the two-layer structure propylene glycol distillation, and ensure the dynamic optimization control layer model predictive controller solution feasibility.

步骤1中的增益模型如下：The gain model in step 1 is as follows:

y＝Gu+G_ddy=Gu+G _d d

式中：y为n×1维的系统输出，y∈SOC；In the formula: y is the n×1-dimensional system output, y∈SOC;

G为n×m维的过程增益矩阵；G is an n×m dimensional process gain matrix;

u为m×1维的系统输入变量，u∈SIC；u is an m×1-dimensional system input variable, u∈SIC;

G_d为n×p维的干扰增益矩阵；G _d is an interference gain matrix of n×p dimension;

d为p×1维的系统干扰变量，d∈DWC；d is the system disturbance variable of p×1 dimension, d∈DWC;

$S S I I C C = = {{u u | | {u u}_{i i}^{min min} \leq \leq {u u}_{i i} \leq \leq {u u}_{i i}^{max max};; 11 \leq \leq i i \leq \leq m m}};;$

$S S O o C C = = {{y the y | | {y the y}_{i i}^{min min} \leq \leq {y the y}_{i i} \leq \leq {y the y}_{i i}^{max max};; 11 \leq \leq i i \leq \leq n no}};;$

$D D. W W C C = = {{d d | | {d d}_{i i}^{min min} \leq \leq {d d}_{i i} \leq \leq {d d}_{i i}^{max max};; 11 \leq \leq i i \leq \leq p p}} . .$

作为优选，输出约束可达集LOKD定义如下：As a preference, the output constraint reachable set LOKD is defined as follows:

LOKD(G,d)＝{y|y＝Gu+G_dd；u∈SIC,g_hk∈Δ，G_d为固定值}LOKD(G,d)＝{y|y＝Gu+G _d d; u∈SIC, g _hk ∈Δ, G _d is a fixed value}

$L L O o K K D D. = = \underset{{g g}_{h h k k} &Element; &Element; Δ Δ}{\cup \cup} \underset{d d &Element; &Element; D D. W W C C}{\cup \cup} L L O o K K D D. ((G G,, d d))$

式中，g_hk为过程增益矩阵G中的不确定元素，将其表示为 $g_{h k}^{\min} \leq g_{h k} \leq g_{h k}^{\max}$ 的形式， $Δ = {g | g_{h k}^{\min} \leq g \leq g_{n k}^{\max}};$ where g _hk is the uncertain element in the process gain matrix G, expressed as $g_{h k}^{\min} \leq g_{h k} \leq g_{h k}^{\max}$ form, $Δ = {g | g_{h k}^{\min} \leq g \leq g_{no k}^{\max}};$

输出约束可达集的上边界LOKDSJ定义如下：The upper bound LOKDSJ of the output constrained reachable set is defined as follows:

$\begin{matrix} L L O o K K D D. S S J J = = {C C}_{L L O o K K D D. ((&ForAll; &ForAll; {g g}_{h h k k} &Element; &Element; Δ Δ,, d d = = {d d}^{max max}))} ((L L O o K K D D. ((&ForAll; &ForAll; {g g}_{h h k k} &Element; &Element; Δ Δ,, d d \\ {d d}^{max max})) \cap \cap L L O o K K D D. ((&ForAll; &ForAll; {g g}_{h h k k} &Element; &Element; Δ Δ,, d d &NotEqual; &NotEqual; {d d}^{max max})))) \end{matrix}$

输出约束可达集的下边界LOKDXJ定义如下：The lower bound LOKDXJ of the output constrained reachable set is defined as follows:

$\begin{matrix} L L O o K K D D. X x J J = = {C C}_{L L O o K K D D. ((&ForAll; &ForAll; {g g}_{h h k k} &Element; &Element; Δ Δ,, d d = = {d d}^{min min}))} ((L L O o K K D D. ((&ForAll; &ForAll; {g g}_{h h k k} &Element; &Element; Δ Δ,, d d \\ = = {d d}^{min min})) \cap \cap L L O o K K D D. ((&ForAll; &ForAll; {g g}_{h h k k} &Element; &Element; Δ Δ,, d d &NotEqual; &NotEqual; {d d}^{min min})))) \end{matrix}$

步骤3中，计算输出约束可达集的上边界的步骤如下：In step 3, the steps to calculate the upper boundary of the output constraint reachable set are as follows:

步骤3-a-1，求出 $L O K D (g_{h k} = g_{h k}^{\max}, d = d^{\max})$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x}),$ 分别记为L_s,max和L_s,min，求出L_s,max和L_s,min的交集I_s；Step 3-a-1, find $L o K D. (g_{h k} = g_{h k}^{\max}, d = d^{\max})$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x}),$ Record them as L _s,max and L _s,min respectively, and find the intersection I _s of L _s,max and L _s,min ;

步骤3-a-2，将L_s，max和L_s，min的顶点分为两组，分别为和和所组成的多面体与I_s没有交点；Step 3-a-2, divide the vertices of L _{s, max} and L _{s, min} into two groups, respectively and and The formed polyhedron has no intersection with I _s ;

步骤3-a-3，求出 $L O K D (g_{h k} = g_{h k}^{\max}, d = d^{\max} - e)$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x} - e),$ 分别记为L_s,maxe和L_s,mine，e为正实数；Step 3-a-3, find $L o K D. (g_{h k} = g_{h k}^{\max}, d = d^{\max} - e)$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x} - e),$ Recorded as L _{s, maxe} and L _{s, mine} respectively, e is a positive real number;

步骤3-a-4，从和中分别选出一组顶点与I_s构成多面体，并将构成的多面体分别与L_s,maxe和L_s,mine进行相交性检验，与L_s,maxe和L_s,mine都不相交的一种顶点组合，即为输出约束可达集的上边界LOKDSJ的顶点，LOKDSJ的顶点所构成的多面体即为输出约束可达集的上边界。Step 3-a-4, from and Select a group of vertices and I _s to form a polyhedron respectively, and conduct the intersection test on the formed polyhedron with L _{s, maxe} and L _{s, mine} respectively, and a kind that does not intersect with L _{s, maxe} and L _{s, mine} The combination of vertices is the vertices of the upper boundary LOKDSJ of the output constraint reachable set, and the polyhedron formed by the vertices of LOKDSJ is the upper boundary of the output constraint reachable set.

作为优选，步骤3中，计算输出约束可达集的下边界的步骤如下：Preferably, in step 3, the steps of calculating the lower bound of the output constrained reachable set are as follows:

步骤3-b-1，求出 $L O K D (g_{n k} = g_{h k}^{\max}, d = d^{\min})$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{\min}),$ 分别记为L’_s,max和L’_s,min，求出L’_s,max和L’_s,min的交集I’_s；Step 3-b-1, find $L o K D. (g_{no k} = g_{h k}^{\max}, d = d^{\min})$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{\min}),$ Recorded as L' _{s, max} and L' _{s, min} respectively, and find the intersection I' _s of L' _{s, max} and L' _{s, min} ;

步骤3-b-2，将L’_s,max和L’_s,min的顶点分为两组，分别为和和所组成的多面体与I’_s没有交点；Step 3-b-2, divide the vertices of L' _s,max and L' _s,min into two groups, respectively and and The formed polyhedron has no intersection with I _'s ;

步骤3-b-3，求出 $L O K D (g_{h k} = g_{h k}^{\max}, d = d^{m i n} + e)$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{m i n} + e),$ 分别记为L’_s,maxe和L’_s,mine，e为正实数；Step 3-b-3, find $L o K D. (g_{h k} = g_{h k}^{\max}, d = d^{m i no} + e)$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{m i no} + e),$ Recorded as L' _{s, maxe} and L' _{s, mine} respectively, e is a positive real number;

步骤3-b-4，从和中分别选出一组顶点与I’_s构成多面体，并将构成的多面体分别与L’_s,maxe和L’_s,mine进行相交性检验，与L’_s,maxe和L’_s,mine都不相交的一种顶点组合，即为输出约束可达集的下边界LOKDSJ的顶点，LOKDSJ的顶点所构成的多面体即为输出约束可达集的下边界。Step 3-b-4, from and Select a group of vertices and I' _s to form a polyhedron respectively, and conduct intersection test with L' s, _maxe and L' s, _mine respectively, and L' _{s, maxe} and L' _{s, mine} are all A disjoint combination of vertices is the vertices of the lower boundary LOKDSJ of the output constrained reachable set, and the polyhedron formed by the vertices of LOKDSJ is the lower bound of the output constrained reachable set.

作为优选，步骤3-a-2中，将L_s,max和L_s,min的顶点分为两组的方法如下：As a preference, in step 3-a-2, the method of dividing the vertices of L _{s, max} and L _{s, min} into two groups is as follows:

任意选出L_s,max的一半顶点作为一个组合，将每种组合的顶点所构成的多面体与I_s求交集，若交集为空，即得到与I_s不相交的和 Randomly select half of the vertices of L _{s and max} as a combination, and intersect the polyhedron formed by the vertices of each combination with I _s , if the intersection is empty, then get the disjoint I _s and

任意选出L_s,min的一半顶点作为一个组合，将每种组合的顶点所构成的多面体与I_s求交集，若交集为空，即得到与I_s不相交的 Randomly select half of the vertices of L _{s and min} as a combination, and intersect the polyhedron formed by the vertices of each combination with I _s , if the intersection is empty, then get the disjoint I _s

作为优选，步骤3-b-2中，将L’_s,max和L’_s,min的顶点分为两组的方法如下：As a preference, in step 3-b-2, the method of dividing the vertices of L' _{s, max} and L' _{s, min} into two groups is as follows:

任意选出L’_s,max的一半顶点作为一个组合，将每种组合的顶点所构成的多面体与I’_s求交集，若交集为空，即得到与I’_s不相交的和 Randomly select half of the vertices of L' _{s and max} as a combination, and intersect the polyhedron formed by the vertices of each combination with I' _s , if the intersection is empty, you can get a disjoint with I' _s and

任意选出L’_s,min的一半顶点作为一个组合，将每种组合的顶点所构成的多面体与I’_s求交集，若交集为空，即得到与I’_s不相交的 Randomly select half of the vertices of L' _{s and min} as a combination, and intersect the polyhedron formed by the vertices of each combination with I' _s , if the intersection is empty, you can get a non-intersecting polyhedron with I' _s

作为优选，动态优化控制层输出约束LOJX定义如下：As a preference, the dynamic optimization control layer output constraint LOJX is defined as follows:

LOJX(α)＝{y|b₁≤y-y₀≤b₂}LOJX(α)＝{y|b ₁ ≤yy ₀ ≤b ₂ }

${b b}_{11} = = {[[\frac{- - α α}{{w w}_{11}} \frac{- - α α}{{w w}_{22}} ... ... \frac{- - α α}{{w w}_{n no}}]]}^{T T},, {b b}_{22} = = {[[\frac{α α}{{w w}_{11}} \frac{α α}{{w w}_{22}} ... ... \frac{α α}{{w w}_{n no}}]]}^{T T}$

y₀＝[y₀₁y₀₂...y_0n]^T，y＝[y₁y₂...y_n]^T y ₀ =[y ₀₁ y ₀₂ ...y _0n ] ^T , y=[y ₁ y ₂ ...y _n ] ^T

式中：w₁w₂...w_n为权重；y₀是过程的标称稳态值，y为系统输出。In the formula: w ₁ w ₂ ... w _n is the weight; y ₀ is the nominal steady-state value of the process, and y is the system output.

步骤4中，计算动态优化控制层输出约束的步骤如下：In step 4, the steps for calculating the output constraints of the dynamic optimization control layer are as follows:

步骤4-1，利用迭代算法求得α₊₁和α_-1，使LOJX(α₊₁)与LOKDSJ相切，切点为v₊₁；LOJX(α_-1)与LOKDXJ相切，切点为v_-1；Step 4-1, using iterative algorithm to obtain α ₊₁ and α _-1 , so that LOJX(α ₊₁ ) is tangent to LOKDSJ, and the tangent point is v ₊₁ ; LOJX(α _-1 ) is tangent to LOKDXJ, and the tangent point is for v _-1 ;

步骤4-2，记v₊₁＝[y₁₊y₂₊...y_n+],v_-1＝[y_1-y_2-...y_n-]，则动态优化控制层输出约束LOJX为：Step 4-2, record v ₊₁ ＝[y ₁₊ y ₂₊ ... y _n+ ], v _-1 ＝[y _1- y _2- ... y _n- ], then dynamically optimize the output constraints of the control layer LOJX is:

LOJX＝{y|min(v₊₁,v_-1)≤y-y₀≤max(v₊₁,v_-1)}。LOJX={y|min(v ₊₁ ,v _-1 ) _≤yy0≤max (v ₊₁ ,v _-1 )}.

本发明提供的稀丙酮精馏工业动态优化控制层输出约束的设计方法，适用于非方不确定系统，确保了动态优化控制层模型预测控制器求解的可行性，使企业利润能够最大化。The design method for the output constraint of the dynamic optimization control layer of the rectification industry of diacetone provided by the invention is suitable for non-square uncertain systems, ensures the feasibility of solving the model predictive controller of the dynamic optimization control layer, and maximizes the profit of the enterprise.

附图说明Description of drawings

图1为二维系统的L_s,max、L_s,min和I_s；Figure 1 shows L _s,max , L _s,min and I _s of the two-dimensional system;

图2为三维系统的L_s,max和I_s的顶点；Fig. 2 is the vertex of L _{s, max} and I _s of the three-dimensional system;

图3为二维系统中LOKDSJ的求解；Fig. 3 is the solution of LOKDSJ in the two-dimensional system;

图4为r＝1:1:1，y₀＝(0,0,0)的LOJX和SOC；Fig. 4 is r=1:1:1, y ₀ =(0,0,0) LOJX and SOC;

图5为r＝1:1:1，y₀＝(0,0,0)的LOKD和SOC；Figure 5 shows the LOKD and SOC of r=1:1:1, y ₀ =(0,0,0);

图6为r＝1:1:1，y₀＝(0,0,0)的LOJX和LOKD；Fig. 6 is r=1:1:1, y ₀ =(0,0,0) LOJX and LOKD;

图7为r＝1:1:1，y₀＝(0,0,0)时不同角度观察的LOJX和LOKD；Figure 7 shows LOJX and LOKD observed from different angles when r=1:1:1, y ₀ =(0,0,0);

图8为LOJX，LOKDSJ和LOKDXJ；Figure 8 shows LOJX, LOKDSJ and LOKDXJ;

图9为换视角观察的LOJX，LOKDSJ和LOKDXJ。Figure 9 shows LOJX, LOKDSJ and LOKDXJ viewed from different angles of view.

具体实施方式detailed description

下面结合附图，对本发明稀丙酮精馏工业动态优化控制层输出约束的设计方法做详细描述。The following is a detailed description of the design method of the industry dynamic optimization control layer output constraints of the propylene ketone distillation industry in conjunction with the accompanying drawings.

步骤1，针对双层结构的稀丙酮精馏工业模型预测控制系统，求出模型预测控制器的稳态优化层的增益模型。Step 1, aiming at the industrial model predictive control system for distilling propylene glycol with double-layer structure, obtain the gain model of the steady-state optimization layer of the model predictive controller.

增益模型为：y＝Gu+G_ddThe gain model is: y=Gu+G _d d

步骤2，找到增益模型中，过程增益矩阵中的不确定元素，不确定元素记为g_hk，本发明提供的方法适用于过程增益矩阵中仅存在一个不确定元素的情况。Step 2, find the uncertain element in the process gain matrix in the gain model, the uncertain element is denoted as g _hk , the method provided by the present invention is applicable to the case where there is only one uncertain element in the process gain matrix.

步骤3，依据不确定元素和系统干扰变量，求得输出约束可达集的上边界和输出约束可达集的下边界。Step 3. According to the uncertain elements and system disturbance variables, the upper boundary of the output constrained reachable set and the lower bound of the output constrained reachable set are obtained.

输出约束可达集LOKD定义如下：The output constraint reachable set LOKD is defined as follows:

式中，g_hk为过程增益矩阵G中的不确定元素，将其表示为 $g_{h k}^{\min} \leq g_{h k} \leq g_{h k}^{\max}$ 的形式， $Δ = {g | g_{h k}^{\min} \leq g \leq g_{h k}^{\max}};$ where g _hk is the uncertain element in the process gain matrix G, expressed as $g_{h k}^{\min} \leq g_{h k} \leq g_{h k}^{\max}$ form, $Δ = {g | g_{h k}^{\min} \leq g \leq g_{h k}^{\max}};$

步骤3-a-1，求出 $L O K D (g_{h k} = g_{h k}^{\max}, d = d^{\max})$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x}),$ 分别记为L_s,max和L_s,min，求出L_s,max和L_s,min的交集I_s。Step 3-a-1, find $L o K D. (g_{h k} = g_{h k}^{\max}, d = d^{\max})$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x}),$ Record them as L _s,max and L _s,min respectively, and find the intersection I _s of L _s,max and L _s,min .

交集I_s的求解利用MPT(Multi-ParametricToolbox)进行，图1为二维输出的L_s,max、L_s,min和I_s，二维系统中，L_s,max和L_s,min分别对应一段直线，交集I_s为两直线的交点。The solution of the intersection I _s is carried out using MPT (Multi-ParametricToolbox). Figure 1 shows the two-dimensional output of L _s,max , L _s,min and I _s . In the two-dimensional system, L _s,max and L _s,min correspond to A straight line, the intersection I _s is the intersection point of two straight lines.

如图2所示，三维输出的L_s,max和L_s,min分别对应一矩形平面，交集I_s为两矩形平面的交线。As shown in Figure 2, L _{s, max} and L _{s, min} of the three-dimensional output correspond to a rectangular plane respectively, and the intersection I _s is the intersection line of the two rectangular planes.

步骤3-a-2，将L_s，max和L_s，min的顶点分为两组，分别为和和所组成的多面体与I_s没有交点。Step 3-a-2, divide the vertices of L _{s, max} and L _{s, min} into two groups, respectively and and The formed polyhedron has no intersection with I _s .

针对二维系统而言，L_s,max为一段直线，L_s,max的顶点即为直线的两端点，针对三维系统而言，L_s,max为一矩形平面，L_s,max的顶点即为矩形的四个顶点。For a two-dimensional system, L _s,max is a straight line, and the vertex of L _s,max is the two ends of the line. For a three-dimensional system, L _s,max is a rectangular plane, and the apex of L _s,max is are the four vertices of the rectangle.

该步骤中，将L_s,max和L_s,min的顶点分为两组的原则是，使获得的和所组成的多面体与I_s没有交点，为了达到这一效果，分组的方法如下：In this step, the principle of dividing the vertices of L _s,max and L _s,min into two groups is to make the obtained and The formed polyhedron has no intersection with I _s , in order to achieve this effect, the method of grouping is as follows:

由于L_s,max的特殊性，L_s,max的顶点数都为偶数，若顶点数为k，则任意选出一半顶点构成的组合的个数为种，利用MPT工具箱，对每种组合的顶点所构成的多面体与I_s求交集，若交集为空，则说明不相交，进行完次求交集后，可以得到与I_s不相交的和 Due to the particularity of L _{s, max} _, the number of vertices of L s, max is even, if the number of vertices is k, then the number of combinations composed of randomly selected half vertices is First, use the MPT toolbox to find the intersection of the polyhedron and I _s formed by the vertices of each combination. If the intersection is empty, it means that they do not intersect. After seeking the intersection for the second time, we can get the disjoint with I _s and

同理计算如下：Simultaneous computing as follows:

步骤3-a-3，求出 $L O K D (g_{h k} = g_{h k}^{\max}, d = d^{\max} - e)$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x} - e),$ 分别记为L_s,maxe和L_s,mine，e为正实数；在能够接受的精度范围内，e为一个趋近于0的正实数，通常e取10^-4。Step 3-a-3, find $L o K D. (g_{h k} = g_{h k}^{\max}, d = d^{\max} - e)$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{m a x} - e),$ They are recorded as L _s,maxe and L _s,mine respectively, and e is a positive real number; within the acceptable precision range, e is a positive real number close to 0, and usually e takes 10 ^-4 .

如图3所示，针对二维系统，L_s,maxe相对L_s,max有一微小位移，L_s,mine相对L_s,min有一微小位移，求解得到的LOKDSJ(粗实线所示部分)与L_s,maxe和L_s,mine均不相交。As shown in Figure 3, for a two-dimensional system, L _s,maxe has a small displacement relative to L _s,max , and L _s,mine has a small displacement relative to L _s,min . The obtained LOKDSJ (the part shown by the thick solid line) and Neither L _s,maxe nor L _s,mine intersect.

由中选出一组顶点，选出一组顶点，这两组顶点与I_s构成多面体，一共有种情况，将这四种情况下构成的多面体分别与L_s,maxe和L_s,mine进行相交性检验，与L_s,maxe和L_s,mine都不相交的一种顶点组合，即为所求的LOKDSJ的顶点，LOKDSJ的顶点所构成的多面体即为输出约束可达集的上边界LOKDSJ。Depend on Select a set of vertices from the Select a group of vertices, these two groups of vertices and I _s form a polyhedron, a total of In this case, the polyhedron formed in these four cases is tested for intersection with L _s,maxe _and L _s _,mine respectively, and a combination of vertices that do not intersect with L s,maxe and L s,mine is the all The vertices of the obtained LOKDSJ, the polyhedron formed by the vertices of LOKDSJ is the upper boundary LOKDSJ of the output constrained reachable set.

同理，计算输出约束可达集的下边界的步骤如下：Similarly, the steps to calculate the lower bound of the output constraint reachable set are as follows:

步骤3-b-1，求出 $L O K D (g_{n k} = g_{h k}^{\max}, d = d^{\min})$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{\min}),$ 分别记为L’_s,max和L’_s,min，求出L’_s,max和L’_s,min的交集I’_s。Step 3-b-1, find $L o K D. (g_{no k} = g_{h k}^{\max}, d = d^{\min})$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{\min}),$ Denote as L' _s,max and L' _s,min respectively, and find the intersection I' _s of L' _s,max and L' _s,min .

步骤3-b-2，将L’_s，max和L’_s，min的顶点分为两组，分别为和和所组成的多面体与I’_s没有交点。Step 3-b-2, divide the vertices of L' _{s, max} and L' _{s, min} into two groups, respectively and and The formed polyhedron has no intersection with I _'s .

该步骤中，将L’_s,max和L’_s,min的顶点分为两组的方法如下：In this step, the method of dividing the vertices of L' _{s, max} and L' _{s, min} into two groups is as follows:

步骤3-b-3，求出 $L O K D (g_{h k} = g_{h k}^{\max}, d = d^{m i n} + e)$ 和 $L O K D (g_{h k} =$ $g_{h k}^{\min}, d = d^{m i n} + e),$ 分别记为L’_s,maxe和L’_s,mine，e为正实数，e取10^-4。Step 3-b-3, find $L o K D. (g_{h k} = g_{h k}^{\max}, d = d^{m i no} + e)$ and $L o K D. (g_{h k} =$ $g_{h k}^{\min}, d = d^{m i no} + e),$ They are recorded as L' _s,maxe and L' _s,mine respectively, e is a positive real number, and e takes 10 ^-4 .

步骤4，依据输出约束可达集的上边界和输出约束可达集的下边界，Step 4, according to the upper boundary of the output constraint reachable set and the lower boundary of the output constraint reachable set,

得到动态优化控制层输出约束。The output constraints of the dynamic optimization control layer are obtained.

动态优化控制层输出约束LOJX定义如下：The dynamic optimization control layer output constraint LOJX is defined as follows:

LOJX(α)＝{y|b₁≤y-y₀≤b₂}LOJX(α)＝{y|b ₁ ≤yy ₀ ≤b ₂ }

式中：w₁w₂...w_n为用户自己决定的权重，默认情况下都为1，并记r＝w_n:w_n-1:…：w₂:w₁，用于设置权重，y₀是过程的标称稳态值，y为系统输出。In the formula: w ₁ w ₂ ...w _n is the weight decided by the user himself, and it is 1 by default, and r=w _n :w _n-1 :...:w ₂ :w ₁ is used to set the weight , y ₀ is the nominal steady-state value of the process, and y is the system output.

计算动态优化控制层输出约束的步骤如下：The steps to calculate the output constraints of the dynamic optimization control layer are as follows:

步骤4-1，利用迭代算法(参见文献FernandoV.Lima,ChristosGeorgakis,Designofoutputconstraintsformodel-basednon-squarecontrollersusingintervaloperability.JournalofProcessControl18(2008)610–620)求得α₊₁和α_-1，使LOJX(α₊₁)与LOKDSJ相切，切点为v₊₁；LOJX(α_-1)与LOKDXJ相切，切点为v_-1；Step 4-1, use iterative algorithm (see literature FernandoV.Lima, ChristosGeorgakis, Design of output constraints for model-based non-square controllers using intervaloperability. Journal of Process Control18 (2008) 610–620) to obtain α ₊₁ and α _-1 , so that LOJX(α ₊₁ ) and LOKDSJ Tangent, the tangent point is v ₊₁ ; LOJX(α _-1 ) is tangent to LOKDXJ, the tangent point is v _-1 ;

仿真实施例Simulation example

为了更直观地展示本发明的设计方法，考虑一个在稀丙酮精馏工业的稳态优化层具有低维度的系统，它们的原点在标称稳态点y₀。稳态优化层系统描述如下：In order to demonstrate the design method of the present invention more intuitively, consider a system with low-dimensionality in the steady-state optimization layer of the propylene glycol distillation industry, and their origins are at the nominal steady-state point y ₀ . The steady-state optimization layer system is described as follows:

$(\begin{matrix} {y the y}_{11} \\ {y the y}_{22} \\ {y the y}_{33} \end{matrix}) = = (\begin{matrix} {g g}_{1111} & 0.3 0.3 \\ - - 0.42 0.42 & - - 0.23 0.23 \\ 0.65 0.65 & 0.53 0.53 \end{matrix}) (\begin{matrix} {u u}_{11} \\ {u u}_{22} \end{matrix}) + + (\begin{matrix} 0.3 0.3 \\ 0.5 0.5 \\ 0.5 0.5 \end{matrix}) {d d}_{11}$

SIC＝{u∈R²|||u||_∞≤1}，SOC＝{y∈R³|||y||_∞≤1}，DWC＝{-1≤d₁≤1}，求得的输出约束为LOJX＝{(y₁,y₂,y₃)|-0.49≤y₁≤0.49,-0.49≤y₁≤0.49,-0.49≤y₁≤0.49}。SIC={u∈R ² |||u|| _∞ ≤1}, SOC={y∈R ³ |||y|| _∞ ≤1}, DWC={-1≤d ₁ ≤1}, The obtained output constraint 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}.

权重r＝1:1:1,y₀＝(0,0,0)时，LOJX和SOC的关系见图4，LOKD和SOC的关系见图5，LOJX和LOKD的关系见图6和图7，LOJX，LOKDSJ和LOKDXJ关系见图8和图9。When the weight r=1:1:1, y ₀ =(0,0,0), the relationship between LOJX and SOC is shown in Figure 4, the relationship between LOKD and SOC is shown in Figure 5, and the relationship between LOJX and LOKD is shown in Figure 6 and Figure 7 , LOJX, LOKDSJ and LOKDXJ are shown in Figure 8 and Figure 9.

如图8和图9所示，LOJX为一个恰好与LOKDSJ和LOKDXJ都相切的多面体，本发明中的相切是指LOJX与LOKDSJ和LOKDXJ都分别有且仅有一个交点。As shown in Fig. 8 and Fig. 9, LOJX is a polyhedron that is exactly tangent to both LOKDSJ and LOKDXJ. The tangent in the present invention means that LOJX has only one intersection point with LOKDSJ and LOKDXJ respectively.

由于选例的特殊性与r和y₀设置的简单性，使得求得的输出约束为一个规范的多面体。当情况复杂时，输出约束会随选取的r有不同的形状。Due to the particularity of the selected example and the simplicity of setting r and y ₀ , the obtained output is constrained to be a canonical polyhedron. When the situation is complex, the output constraints will have different shapes depending on the choice of r.

Claims

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;

S I C = {u | u_{i}^{\min} \leq u_{i} \leq u_{i}^{\max}; 1 \leq i \leq m};

S O C = {y | y_{i}^{\min} \leq y_{i} \leq y_{i}^{\max}; 1 \leq i \leq n};

D W C = {d | d_{i}^{\min} \leq d_{i} \leq d_{i}^{\max}; 1 \leq i \leq 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 }

L O K D = \underset{g_{h k} &Element; Δ}{\cup} \underset{d &Element; D W C}{\cup} L O K D (G, d)

In formula, g _hkfor the uncertain element in process gain matrix G, be expressed as

g_{h k}^{\min} \leq g_{h k} \leq g_{h k}^{\max}

Form,

Δ = {g | g_{h k}^{\min} \leq g \leq g_{h k}^{\max}};

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

\begin{matrix} L O K D S J = C_{L O K D (&ForAll; g_{h k} &Element; Δ, d = d^{\max})} (L O K D (&ForAll; g_{h k} &Element; Δ, d \\ = d^{\max}) \cap L O K D (&ForAll; g_{h k} &Element; Δ, d &NotEqual; d^{\max})) \end{matrix}

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

\begin{matrix} L O K D X J = C_{L O K D (&ForAll; g_{h k} &Element; Δ, d = d^{\min})} (L O K D (&ForAll; g_{h k} &Element; Δ, d \\ = d^{\min}) \cap L O K D (&ForAll; g_{h k} &Element; Δ, d &NotEqual; d^{\min})) \end{matrix}

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

Step 3-a-1, obtains

L O K D (g_{h k} = g_{h k}^{\max}, d = d^{m a x})

With

L O K D (g_{h k} =

g_{h k}^{\min}, d = d^{m a x}),

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

L O K D (g_{h k} = g_{h k}^{\max}, d = d^{m a x} - e)

With

L O K D (g_{h k} =

g_{h k}^{\min}, d = d^{m a x} - 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

L O K D (g_{h k} = g_{h k}^{\max}, d = d^{m i n})

With

L O K D (g_{h k} =

g_{h k}^{\min}, d = d^{m i n}),

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

L O K D (g_{h k} = g_{h k}^{\max}, d = d^{m i n} + e)

With

L O K D (g_{h k} =

g_{h k}^{\min}, d = d^{m i n} + 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{- α}{w_{1}} \frac{- α}{w_{2}} ... \frac{- α}{w_{n}}]}^{T},

b_{2} = {[\frac{α}{w_{1}} \frac{α}{w_{2}} ... \frac{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)}。