CN101901006A

CN101901006A - A two-layer optimized industrial process optimal control system and method

Info

Publication number: CN101901006A
Application number: CN2010102137960A
Authority: CN
Inventors: 刘兴高; 陈珑
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2010-06-30
Filing date: 2010-06-30
Publication date: 2010-12-01

Abstract

A double-layer optimized industrial process optimal control system, including on-site intelligent instruments connected to industrial process objects, a DCS system and a host computer, the industrial process objects, on-site intelligent detection instruments, DCS systems and an upper computer are connected in sequence, the The host computer described above includes a signal acquisition module, an initialization module, a constraint transformation module and a double-layer optimization module. The present invention also provides a double-layer optimized industrial process optimal control method, which converts the optimal control problem with fixed boundary value constraints into a double-layer optimization problem through a double-layer programming strategy, and performs iterative optimization. The invention can accurately solve the optimal control problem of the industrial process with the characteristic of fixed boundary value, and the solution is stable, efficient and accurate, and is an optimal control system and method with wide applicability.

Description

A two-layer optimized industrial process optimal control system and method

技术领域technical field

本发明涉及工业过程控制领域，尤其是一种双层优化的工业过程最优控制系统。The invention relates to the field of industrial process control, in particular to a double-layer optimized industrial process optimal control system.

背景技术Background technique

随着工业过程对在线最优控制的需求的不断增加，改进最优控制算法的求解性能，提高其在线应用的计算效率和准确性，已经变得越来越重要。With the increasing demand for online optimal control in industrial processes, it has become more and more important to improve the solution performance of optimal control algorithms and improve the computational efficiency and accuracy of their online applications.

工业过程最优控制问题往往具有状态变量边值固定约束，如阀门、反应器容量、压力、摩尔分率等的限制。因此，边值固定问题是工业过程最优控制研究的一个前沿和热点。The optimal control problems of industrial processes often have fixed constraints on the boundary values of state variables, such as constraints on valves, reactor capacity, pressure, and mole fraction. Therefore, the fixed boundary value problem is a frontier and hot spot in the research of optimal control of industrial processes.

罚函数法是处理边值固定问题的常用策略，它在原目标函数的基础上增加罚函数项构成新的目标函数，从而消除了动态模型中的边值固定约束，但是罚函数法的有效性与惩罚因子的取值密切相关，选值不当将导致病态，严重影响计算效果，而如何选取合适的惩罚因子并无成规可循，往往需要逐步试算，效率较低。Penalty function method is a common strategy to deal with the problem of fixed boundary value. It adds penalty function items on the basis of the original objective function to form a new objective function, thereby eliminating the boundary value fixed constraints in the dynamic model. However, the effectiveness of the penalty function method is different from The value of the penalty factor is closely related. Improper selection of the value will lead to pathological conditions and seriously affect the calculation effect. However, there is no rule to follow on how to select the appropriate penalty factor, and it often needs to be calculated step by step, which is inefficient.

发明内容Contents of the invention

为了克服现有的罚函数法在处理边值固定最优控制问题时会出现病态现象、以及计算不准确、求解效率低的不足，本发明提供了一种能够准确、快速地找到边值固定问题的最优解、且稳定性高、适用性广的双层优化的工业过程最优控制系统及方法。In order to overcome the shortcomings of the existing penalty function method in dealing with the optimal control problem with fixed boundary value, such as ill-conditioned phenomenon, inaccurate calculation and low solution efficiency, the present invention provides a method that can accurately and quickly find the problem with fixed boundary value An optimal control system and method for a double-layer optimized industrial process with high stability and wide applicability.

本发明解决其技术问题所采用的技术方案是：The technical solution adopted by the present invention to solve its technical problems is:

一种双层优化的工业过程最优控制系统，包括与工业过程对象连接的现场智能检测仪表、DCS系统和上位机，所述工业过程对象、现场智能检测仪表、DCS系统和上位机依次相连，所述的上位机包括：A double-layer optimized industrial process optimal control system, including on-site intelligent detection instruments connected with industrial process objects, a DCS system and a host computer, the industrial process objects, on-site intelligent detection instruments, DCS systems and an upper computer are connected in sequence, The host computer includes:

信号采集模块，用于设定采样时间，采集由现场智能仪表上传的工业过程对象的动态信息；The signal acquisition module is used to set the sampling time and collect the dynamic information of the industrial process object uploaded by the on-site smart instrument;

初始化模块，用于初始参数的设置，决策变量z(t)的离散化和初始赋值，具体步骤如下：The initialization module is used for the setting of initial parameters, the discretization and initial assignment of the decision variable z(t), and the specific steps are as follows:

(3.1)将时间域[0，t_f]平均分成N小段：[0，t₁]，[t₁，t₂]，…，[t_N-1，t_N]，其中，t_N＝t_f；每个时间段的长度为t_f/N，t_f表示终止时刻；(3.1) Divide the time domain [0, t _f ] into N segments on average: [0, t ₁ ], [t ₁ , t ₂ ], ..., [t _N-1 , t _N ], where t _N =t _f ; the length of each time period is t _f /N, and t _f represents the termination moment;

(3.2)对n维决策变量z(t)在步骤(3.1)所述时间分段上进行离散化，即每个决策变量用N个分段常值表示，并取初始决策变量z⁰为任意常数；(3.2) Discretize the n-dimensional decision variable z(t) in the time segment described in step (3.1), that is, each decision variable is represented by N piecewise constant values, and the initial decision variable z ⁰ is taken as any constant;

(3.3)设内外层优化的收敛精度分别为ζ₁、ζ₂，当优化目标值迭代误差小于收敛精度时，停止迭代，迭代次数分别为k、l；设内层优化的初始搜索步长为α0、γ0，迭代搜索的初始决策变量为z1⁰；(3.3) Let the convergence precision of the inner and outer layer optimization be ζ ₁ and ζ ₂ respectively, when the iteration error of the optimization target value is less than the convergence precision, stop the iteration, and the iteration times are k and l respectively; let the initial search step of the inner layer optimization be α0, γ0, the initial decision variable of iterative search is z1 ⁰ ;

约束转化模块，用于转化边值固定最优控制问题中的控制变量边界约束和状态变量终值约束，采取以下步骤来完成：The constraint conversion module is used to convert the control variable boundary constraints and state variable final value constraints in the boundary value fixed optimal control problem, and the following steps are taken to complete:

(3.1)通过中间变量处理控制变量边界约束，即对于具有式(1)所示边界约束的(3.1) Process control variable boundary constraints through intermediate variables, that is, for the boundary constraints shown in formula (1)

u_min≤u(t)≤u_max (1)u _min ≤ u(t) ≤ u _max (1)

m维控制变量u(t)，u_min、u_max均为常量，分别对应控制变量的下界和上界，下标min、max分别表示最小值和最大值，采取以下变换：The m-dimensional control variable u(t), u _min and u _max are constants, corresponding to the lower bound and upper bound of the control variable respectively, and the subscripts min and max represent the minimum and maximum values respectively, and the following transformations are adopted:

u(t)＝0.5(u_max-u_min)×{sin[z(t)]+1}+u_min (2)u(t)＝0.5(u _max -u _min )×{sin[z(t)]+1}+u _min (2)

将u(t)转化为不受边界约束的中间变量z(t)的三角函数表达式，并把z(t)作为最优控制问题的决策变量进行求解；Transform u(t) into the trigonometric function expression of the intermediate variable z(t) which is not bound by the boundary, and solve z(t) as the decision variable of the optimal control problem;

(3.2)将状态变量终值约束转化为新的目标函数，即对于具有终值约束式(3)：(3.2) Transform the final value constraint of the state variable into a new objective function, that is, for the final value constraint (3):

x_j(t_f)＝x_jf j＝1，2，..，c (3)x _j (t _f ) = x j _f j = 1, 2, . . . , c (3)

的状态变量x_j(t)，其中，c表示受终值约束的状态变量个数，x_jf为给定的常量，x_j(t_f)表示状态变量x_j(t)在终端时刻t_f的取值，构造如下目标函数式(4)：state variable x _j (t), where c represents the number of state variables subject to final value constraints, x _jf is a given constant, and x _j (t _f ) represents state variable x _j (t) at terminal time t _f The value of , construct the following objective function formula (4):

${J J}_{11} = = {Σ Σ}_{j j = = 11}^{c c} {[[{x x}_{j j} (({t t}_{f f})) - - {x x}_{jf jf}]]}^{22} - - - - - - ((44))$

J₁为双层优化模块求解的内层目标函数；J ₁ is the inner layer objective function solved by the double-layer optimization module;

双层优化模块，用于寻找不仅能使最优控制问题的目标函数J₂最优，The double-layer optimization module is used to find the objective function _J2 that can not only make the optimal control problem optimal,

而且能够满足终值约束式(3)和状态方程式(6)：And it can satisfy the final value constraint (3) and the state equation (6):

$\frac{dx dx ((t t))}{dt dt} = = f f [[x x ((t t)),, z z ((t t)),, t t]],, x x ((00)) = = {x x}_{00} - - - - - - ((66))$

的最优决策变量z^*(t)，其中，

、ψ分别表示在终点条件下和在一段时间内目标函数的组成部分，x表示给定的n维状态变量，x₀表示初始时刻(t＝0)的状态变量值，f表示函数变量，采取内外两层优化的结构进行求解：The optimal decision variable z ^* (t), where,

, ψ represent the components of the objective function under the terminal condition and within a period of time respectively, x represents the given n-dimensional state variable, x ₀ represents the value of the state variable at the initial moment (t=0), f represents the function variable, take The optimized structure of the inner and outer layers is solved:

(4.1)内层优化，即寻找使目标函数J₁最优的决策变量z1(t)，且z1(t)须满足状态方程式(6)和内层优化的协态方程式(7)：(4.1) Inner layer optimization, that is, to find the decision variable z1(t) that makes the objective function J ₁ optimal, and z1(t) must satisfy the state equation (6) and the co-state equation (7) of the inner layer optimization:

$\frac{dλ dλ ((t t))}{dt dt} = = - - λ λ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z ((t t)),, t t]]}{&PartialD; &PartialD; x x},,$ $λ λ (({t t}_{f f})) = = \frac{{&PartialD; &PartialD; J J}_{11}}{&PartialD; &PartialD; x x (({t t}_{f f}))} - - - - - - ((77))$

其中，λ(t)表示m维协态变量，上标T表示变量转置，式(6)与式(7)构成内层常微分方程系统；内层优化所得的最优决策变量z1(t)传给外层作为外层优化的初始解；Among them, λ(t) represents the m-dimensional co-state variable, superscript T represents variable transposition, formula (6) and formula (7) constitute the inner ordinary differential equation system; the optimal decision variable z1(t ) is passed to the outer layer as the initial solution for outer layer optimization;

(4.2)外层优化，即在内层优化基础上搜寻使目标函数J₂最优的决策变量z2(t)，且z2(t)须满足状态方程式(6)和外层优化的协态方程式(8)：(4.2) Outer layer optimization, that is, to search for the decision variable z2(t) that optimizes the objective function J ₂ on the basis of inner layer optimization, and z2(t) must satisfy the state equation (6) and the co-state equation of outer layer optimization (8):

$\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - θ {(t)}^{T} \cdot \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},$ $\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - θ {(t)}^{T} \cdot \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},$

其中，θ(t)表示m维协态变量，

、ψ分别表示在终点条件下和在一段时间内目标函数J₂的组成部分，式(6)与式(8)构成外层常微分方程系统；外层优化所得的最优决策变量z2(t)就是双层优化的最优解z^*(t)，相应的J₂值就是双层优化的最优目标值J^*；Among them, θ(t) represents the m-dimensional costate variable,

, ψ respectively denote the components of the objective function J ₂ under the terminal condition and within a period of time, formula (6) and formula (8) constitute the outer ordinary differential equation system; the optimal decision variable z2(t ) is the optimal solution z ^* (t) of double-layer optimization, and the corresponding _J2 value is the optimal target value J ^* of double-layer optimization;

然后，保存双层优化得到的最优结果z^*(t)和J^*。Then, save the optimal results z ^* (t) and J ^* obtained by the double-layer optimization.

作为优选的一种方案：所述双层优化模块中，采用如下步骤进行内外层优化：As a preferred solution: in the double-layer optimization module, the following steps are used to optimize the inner and outer layers:

所述步骤(4.1)的内层优化按照以下算法步骤来实现，上标k表示迭代次数：The inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the number of iterations:

4.1.1)选取迭代初始点z1⁰，若k＝l＝0，则z1⁰＝z⁰，否则z1⁰取值为外层输入的z2^l；4.1.1) Select the iteration initial point z1 ⁰ , if k=l=0, then z1 ⁰ =z ⁰ , otherwise z1 ⁰ takes the value of z2 ^l input by the outer layer;

4.1.2)将第k次的迭代点z1^k代入内层常微分方程系统，k＝0时，z1^k＝z1⁰，对式(6)和(7)分别进行前向积分和后向积分，求解出状态变量x和协态变量λ，并由式(4)计算出第k次迭代的目标值J₁ ^k；4.1.2) Substitute the k-th iteration point z1 ^k into the inner ordinary differential equation system, when k=0, z1 ^k =z1 ⁰ , perform forward integration and backward integration on formulas (6) and (7) respectively , solve the state variable x and the co-state variable λ, and calculate the target value J ₁ ^k of the kth iteration by formula (4);

4.1.3)判断收敛条件式(9)是否成立，若成立，则内层的最优解z1^*＝z1^k，将z1^*传给外层，作为外层迭代的初始解；否则转步骤(4.1.4)，式(9)表达如下：；4.1.3) Judging whether the convergence condition (9) is valid, if it is valid, then the optimal solution z1 ^* = z1 ^k of the inner layer, and transfer z1 ^* to the outer layer as the initial solution of the outer layer iteration; otherwise, go to the step ( 4.1.4), formula (9) is expressed as follows:;

|J₁ ^k-J₁ ^j+1|≤ζ₁ (9)|J ₁ ^k -J ₁ ^j+1 |≤ζ ₁ (9)

4.1.4)将状态变量x和迭代点z1^k代入式(10)计算梯度g^k：4.1.4) Substituting state variable x and iteration point z1 ^k into formula (10) to calculate gradient g ^k :

${g g}^{k k} ((t t)) = = λ λ {((t t))}^{T T} \cdot &Center Dot; \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 11 ((t t)),, t t]]}{&PartialD; &PartialD; z z 11 ((t t))} - - - - - - ((1010))$

保存z1^k和g^k，然后计算搜索方向d^k，d^k-1表示前一次迭代的搜索方向，β^k是中间参数：Save z1 ^k and g ^k , and then calculate the search direction d ^k , where d ^k-1 represents the search direction of the previous iteration, and β ^k is an intermediate parameter:

$d^{k} = \{\begin{matrix} - g^{k}, & k = 1; \\ - g^{k} + β^{k} d^{k - 1}, & k &GreaterEqual; 2 . \end{matrix}$ 其中， $β^{k} = \frac{{(g^{k})}^{T} (g^{k} - g^{k - 1})}{{| | g^{k - 1} | |}^{2}} - - - (11)$ $d^{k} = \{\begin{matrix} - g^{k}, & k = 1; \\ - g^{k} + β^{k} d^{k - 1}, & k &Greater Equal; 2 . \end{matrix}$ in, $β^{k} = \frac{{(g^{k})}^{T} (g^{k} - g^{k - 1})}{{| | g^{k - 1} | |}^{2}} - - - (11)$

4.1.5)确定最佳搜索步长α^k：若k＝0，则取α^k＝α0，转步骤4.1.6)；4.1.5) Determine the optimal search step size α ^k : if k=0, then take α ^k =α0, go to step 4.1.6);

否则，从当前的迭代点z1^k出发，沿方向d^k作一维搜索，寻找最佳步长因子α^*，满足：Otherwise, starting from the current iteration point z1 ^k , do a one-dimensional search along the direction d ^k to find the optimal step factor α ^* , satisfying:

$H h 11 (({z z 11}^{k k} + + {α α}^{* *} \cdot &Center Dot; {d d}^{k k})) = = \underset{α α &GreaterEqual; &Greater Equal; 00}{min min} H h 11 (({z z 11}^{k k} + + α α \cdot &Center Dot; {d d}^{k k})) - - - - - - ((1212))$

其中，H1表示内层优化问题的哈密顿函数，由式(13)计算出，

表示在α∈[0，+∞)中寻找使H1达到最小值的步长α^*，式(13)表达如下：Among them, H1 represents the Hamiltonian function of the inner layer optimization problem, which is calculated by formula (13),

Indicates that in α∈[0, +∞), find the step size α ^* that makes H1 reach the minimum value, and the formula (13) is expressed as follows:

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)H1=λ(t) ^T f[x(t), z1(t), t] (13)

取

D为系数取整数值；Pick

D is an integer value for the coefficient;

4.1.6)计算下一个迭代点4.1.6) Calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)z1 ^k+1 ＝z1 ^k +α ^k d ^k (14)

4.1.7)将迭代次数加1，即k＝k+1，将步骤4.1.6)中的z1^k+1保存为当前点z1^k继续迭代，转步骤4.1.2)；4.1.7) Add 1 to the number of iterations, i.e. k=k+1, save z1 ^k+1 in step 4.1.6) as the current point z1 ^k to continue iteration, turn to step 4.1.2);

所述步骤(4.2)的外层优化依照以下算法步骤来实现，上标l表示当前迭代次数：The outer layer optimization of the step (4.2) is realized according to the following algorithm steps, and the superscript 1 represents the current iteration number:

4.2.1)取外层优化的当前迭代点为z2^l＝z1^*，l初值为0；4.2.1) Take the current iteration point of outer layer optimization as z2 ^l = z1 ^* , and the initial value of l is 0;

4.2.2)将z2^l代入外层常微分方程系统，对式(6)和(8)分别进行前向积分和后向积分，求解出状态变量x和协态变量θ，并由式(5)计算出第1次迭代的目标值J₂ ^l；4.2.2) Substituting z2 ^l into the outer ordinary differential equation system, performing forward integration and backward integration on equations (6) and (8) respectively, to solve the state variable x and co-state variable θ, and formula (5 ) to calculate the target value J ₂ ^l of the first iteration;

4.2.3)判断收敛条件式(15)是否成立，若成立，则双层优化的最优解z^*＝z2^l，最优目标函数值J^*＝J₂ ^l，保存并传递z^*和J^*到输出显示模块；否则转下一步；式(15)表达如下：4.2.3) Judging whether the convergence condition (15) is valid, if it is valid, then the optimal solution z ^* = z2 ^l of the double-layer optimization, the optimal objective function value J ^* = J ₂ ^l , save and transfer z ^* and J ^* to the output display module; otherwise turn to the next step; formula (15) is expressed as follows:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)|J ₂ ^l -J ₂ ^l+1 |≤ζ ₂ (15)

4.2.4)将状态变量x和迭代点z2^l代入式(16)计算梯度h^l：4.2.4) Substitute state variable x and iteration point z2 ^l into formula (16) to calculate gradient h ^l :

${h h}^{l l} ((t t)) = = \frac{&PartialD; &PartialD; ψ ψ [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} + + θ θ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} - - - - - - ((1616))$

保存z2^l和h^l，然后计算搜索方向e^l，e^l-1表示前一次迭代的搜索方向，η^l是中间参数：Save z2 ^l and h ^l , and then calculate the search direction e ^l , e ^l-1 represents the search direction of the previous iteration, and η ^l is an intermediate parameter:

$e^{l} = \{\begin{matrix} - h^{l}, & l = 1; \\ - h^{l} + η^{l} e^{l - 1}, & l &GreaterEqual; 2 . \end{matrix}$ 其中， $η^{l} = \frac{{(h^{l})}^{T} (h^{l} - h^{l - 1})}{{| | h^{l - 1} | |}^{2}} - - - (17)$ $e^{l} = \{\begin{matrix} - h^{l}, & l = 1; \\ - h^{l} + η^{l} e^{l - 1}, & l &Greater Equal; 2 . \end{matrix}$ in, $η^{l} = \frac{{(h^{l})}^{T} (h^{l} - h^{l - 1})}{{| | h^{l - 1} | |}^{2}} - - - (17)$

4.2.5)确定最佳搜索步长γ^l：若l＝0，则取γ^l＝γ0，转步骤4.2.6)；4.2.5) Determine the optimal search step size γ ^l : if l=0, then take γ ^l =γ0, go to step 4.2.6);

否则，从当前的迭代点z2^l出发，沿方向h^l作一维搜索，寻找最佳步长因子γ^*，满足：Otherwise, starting from the current iteration point z2 ^l , do a one-dimensional search along the direction h ^l to find the optimal step factor γ ^* , satisfying:

$H h 22 (({z z 22}^{l l} + + {γ γ}^{* *} \cdot &Center Dot; {e e}^{l l})) = = \underset{γ γ &GreaterEqual; &Greater Equal; 00}{min min} H h 22 (({z z 22}^{l l} + + {γ γ \cdot &Center Dot; e e}^{l l})) - - - - - - ((1818))$

其中，H2表示外层优化问题的哈密顿函数，由式(19)计算出，

表示在γ∈[0，+∞)中寻找使H2达到最小值的步长γ^*；Among them, H2 represents the Hamiltonian function of the outer layer optimization problem, which is calculated by formula (19),

Represents looking for the step size γ ^* that makes H2 reach the minimum value in γ∈[0, +∞);

H2＝ψ[x(t)，z2(t)，t]+θ(t)^T·f[x(t)，z2(t)，t] (19)H2=ψ[x(t), z2(t), t]+θ(t) ^T f[x(t), z2(t), t] (19)

取

B为系数取整数值；Pick

B is an integer value for the coefficient;

4.2.6)计算下一个迭代点：4.2.6) Calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)z2 ^l+1 ＝z2 ^l +γ ^l d ^l (20)

4.2.7)将迭代次数加1，即l＝l+1，将步骤4.2.6)中的z2^l+1保存为当前点z2^l继续迭代，转步骤4.2.2)。4.2.7) Add 1 to the number of iterations, that is, l=l+1, save z2 ^l+1 in step 4.2.6) as the current point z2 ^l to continue iteration, and turn to step 4.2.2).

进一步，所述上位机还包括：输出显示模块，用于将双层优化模块计算出的最优决策结果z^*(t)通过式(2)转化为最优控制轨线u^*(t)，然后将u^*(t)和最优目标值J^*传输给DCS系统，并在DCS系统中显示所得到的优化结果信息。Further, the host computer also includes: an output display module, which is used to convert the optimal decision result z ^* (t) calculated by the double-layer optimization module into the optimal control trajectory u ^* (t) through formula (2), Then transmit u ^* (t) and the optimal target value J ^* to the DCS system, and display the obtained optimization result information in the DCS system.

一种双层优化的工业过程最优控制方法，所述的最优控制方法包括以下步骤：A kind of double-layer optimized industrial process optimal control method, described optimal control method comprises the following steps:

1)在DCS系统中指定最优控制的状态变量和控制变量，根据实际生产环境的条件和操作限制的条件设定控制变量的上下边界u_max、u_min和DCS的采样周期，并将DCS数据库中相应各变量的历史数据，控制变量上下边界值u_max、u_min传送给上位机；1) Designate the state variables and control variables for optimal control in the DCS system, set the upper and lower boundaries of the control variables u _max , u _min and the sampling period of DCS according to the conditions of the actual production environment and operating restrictions, and save the DCS database The historical data of the corresponding variables in the control variable u _max and u _min are transmitted to the host computer;

2)转化最优控制问题中的边值固定约束：2) Transform the boundary value fixed constraints in the optimal control problem:

(2.1)利用中间变量z(t)对具有边界约束(2.1) Use the intermediate variable z(t) to have boundary constraints

u_min≤u(t)≤u_max (1)u _min ≤ u(t) ≤ u _max (1)

的m维控制变量u(t)进行转换：The m-dimensional control variable u(t) is transformed:

(2.2)将状态变量终值约束式(3)转化为新的目标函数J₁式(4)：(2.2) Transform the state variable final value constraint formula (3) into a new objective function J ₁ formula (4):

x_j(t_f)＝x_jf(j＝1，2，..，c) (3)x _j (t _f )=x _jf (j=1, 2, .., c) (3)

其中，c表示受终值约束的状态变量个数，x_jf为给定的常量，x_j(t_f)表示状态变量x_j(t)在终端时刻t_f的取值，J₁也是双层优化模块求解的内层目标函数；Among them, c represents the number of state variables constrained by the final value, x _jf is a given constant, x _j (t _f ) represents the value of the state variable x _j (t) at the terminal time t _f , and J ₁ is also a double-layer The inner objective function solved by the optimization module;

3)对初始参数进行设置，并对DCS系统输入的数据进行初始化处理，按照以下步骤完成：3) Set the initial parameters, and initialize the data input by the DCS system, and complete according to the following steps:

(3.1)将时间域[0，t_f]平均分成N小段：[0，t₁]，[t₁，t₂]，…，[t_N-1，t_N]，其中t_N＝t_f；每个时间段的长度为t_f/N；(3.1) Divide the time domain [0, t _f ] into N segments on average: [0, t ₁ ], [t ₁ , t ₂ ], ..., [t _N-1 , t _N ], where t _N =t _f ;The length of each time segment is t _f /N;

(3.2)对n维决策变量z(t)在(3.1)所述时间分段上进行离散化，即每个决策变量用N个分段常值表示，并取初始决策变量z⁰为任意常数；(3.2) Discretize the n-dimensional decision variable z(t) in the time segment described in (3.1), that is, each decision variable is represented by N piecewise constant values, and the initial decision variable z ⁰ is taken as an arbitrary constant ;

(3.3)设内外层优化的收敛精度分别为ζ₁、ζ₂，迭代次数分别为k、l；设内层优化的初始搜索步长为α0、γ0，迭代搜索的初始决策变量为z1⁰；(3.3) Set the convergence accuracy of the inner and outer layer optimization as ζ ₁ and ζ ₂ , and the iteration times as k and l respectively; set the initial search step size of the inner layer optimization as α0 and γ0, and the initial decision variable of iterative search as z1 ⁰ ;

4)寻找不仅能使最优控制问题的目标函数式(5)最优，而且能够满足终值约束式(3)和状态方程式(6)的最优决策变量z^*(t)，并将z^*(t)和相应的最优目标值J^*传给输出显示模块，通过采取内外两层优化的结构来进行求解：4) Find the optimal decision variable z ^* (t) that can not only optimize the objective function (5) of the optimal control problem, but also satisfy the final value constraint (3) and the state equation (6), and set z ^* (t) and the corresponding optimal target value J ^* are passed to the output display module, and are solved by adopting an internal and external two-layer optimized structure:

$\frac{dx (t)}{dt} = f [x (t), z (t), t],$ x(0)＝x₀ (6) $\frac{dx (t)}{dt} = f [x (t), z (t), t],$ x(0)=x ₀ (6)

$\frac{dλ dλ ((t t))}{dt dt} = = - - λ λ {((t t))}^{T T} \cdot &Center Dot; \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z ((t t)),, t t]]}{&PartialD; &PartialD; x x},,$ $λ λ (({t t}_{f f})) = = \frac{{&PartialD; &PartialD; J J}_{11}}{&PartialD; &PartialD; x x (({t t}_{f f}))} - - - - - - ((77))$

$\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - {θ (t)}^{T} \cdot \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},$

\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - {θ (t)}^{T} &Center Dot; \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},

其中，θ(t)表示m维协态变量，

作为优选的一种方案：所述步骤(4.1)的内层优化按照以下算法步骤来实现，上标k表示迭代次数：As a preferred solution: the inner layer optimization of the step (4.1) is implemented according to the following algorithm steps, and the superscript k represents the number of iterations:

|J₁ ^k-J₁ ^j+1|≤ζ₁ (9)|J ₁ ^k -J ₁ ^j+1 |≤ζ ₁ (9)

${g g}^{k k} ((t t)) = = λ λ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 11 ((t t)),, t t]]}{&PartialD; &PartialD; z z 11 ((t t))} - - - - - - ((1010))$

$H h 11 (({z z 11}^{k k} + + {α α}^{* *} \cdot \cdot {d d}^{k k})) = = \underset{α α &GreaterEqual; &Greater Equal; 00}{min min} H h 11 (({z z 11}^{k k} + + α α \cdot &Center Dot; {d d}^{k k})) - - - - - - ((1212))$

其中，H1表示内层优化问题的哈密顿函数，由式(13)计算出，

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)H1=λ(t) ^T f[x(t), z1(t), t] (13)

取

D为系数取整数值；Pick

D is an integer value for the coefficient;

4.1.6)计算下一个迭代点4.1.6) Calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)z1 ^k+1 ＝z1 ^k +α ^k d ^k (14)

所述步骤(4.2)的外层优化依照以下算法步骤来实现，上标l表示当前迭代次数：The outer layer optimization of the step (4.2) is realized according to the following algorithm steps, and the superscript 1 represents the current number of iterations:

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)|J ₂ ^l -J ₂ ^l+1 |≤ζ ₂ (15)

${h h}^{l l} ((t t)) = = \frac{&PartialD; &PartialD; ψ ψ [[x x ((t t)),, z z 22 ((t t)) . . t t]]}{&PartialD; &PartialD; z z 22 ((t t))} + + θ θ {((t t))}^{T T} \cdot &Center Dot; \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} - - - - - - ((1616))$

$H h 22 (({z z 22}^{l l} + + {γ γ}^{* *} \cdot &Center Dot; {e e}^{l l})) = = \underset{γ γ &GreaterEqual; &Greater Equal; 00}{min min} H h 22 (({z z 22}^{l l} + + γ γ \cdot &Center Dot; {e e}^{l l})) - - - - - - ((1818))$

其中，H2表示外层优化问题的哈密顿函数，由式(19)计算出，

取

B为系数取整数值；Pick

B is an integer value for the coefficient;

4.2.6)计算下一个迭代点：4.2.6) Calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)z2 ^l+1 ＝z2 ^l +γ ^l d ^l (20)

进一步，所述步骤1)中，将现场智能仪表所采集的工业过程对象的数据传送到DCS系统的实时数据库中，在每个采样周期从DCS系统的数据库得到的最新数据输出到上位机，并在上位机的初始化模块进行初始化处理。Further, in the step 1), the data of the industrial process object collected by the field smart instrument is transmitted to the real-time database of the DCS system, and the latest data obtained from the database of the DCS system is output to the host computer at each sampling period, and Perform initialization processing in the initialization module of the upper computer.

再进一步，所述步骤(4.2.3)中，得到的最优决策变量z^*将通过结果输出模块转换为最优控制曲线u^*(t)，并在上位机的人机界面上显示u^*(t)和最优目标值J^*；同时，最优控制曲线u^*(t)将通过总线接口传给DCS系统的控制站，并在DCS系统中显示所得到的优化结果信息。Further, in the step (4.2.3), the obtained optimal decision variable z ^* will be converted into the optimal control curve u ^* (t) through the result output module, and u ^* will be displayed on the man-machine interface of the host computer (t) and the optimal target value J ^* ; at the same time, the optimal control curve u ^* (t) will be transmitted to the control station of the DCS system through the bus interface, and the obtained optimization result information will be displayed in the DCS system.

本发明的有益效果主要表现在：能够准确地找到具有边值固定特性的工业过程最优控制问题的最优解，而且优化求解效率高、稳定性好，因此在工业过程最优控制的各领域都具有广泛的应用前景。The beneficial effects of the present invention are mainly manifested in: the optimal solution of the optimal control problem of industrial process with fixed boundary value can be accurately found, and the optimal solution has high efficiency and good stability, so it is widely used in various fields of optimal control of industrial process All have broad application prospects.

附图说明Description of drawings

图1是本发明所提供的工业过程最优控制系统的硬件结构图；Fig. 1 is the hardware structural diagram of the industrial process optimal control system provided by the present invention;

图2是本发明上位机实现最优控制方法的原理结构图。Fig. 2 is a schematic structure diagram of the upper computer realizing the optimal control method of the present invention.

具体实施方式Detailed ways

下面根据附图具体说明本发明。The present invention will be described in detail below according to the accompanying drawings.

实施例1Example 1

参照图1、图2，一种双层优化的工业过程最优控制系统，包括与工业过程对象1连接的现场智能仪表2、DCS系统以及上位机6，所述的DCS系统由总线接口3、控制站4和数据库5构成；现场智能仪表2、DCS系统、上位机6通过现场总线依次相连，所述的上位机包括：With reference to Fig. 1, Fig. 2, a kind of industrial process optimal control system of double-layer optimization, comprises the scene intelligent instrument 2, DCS system and upper computer 6 that are connected with industrial process object 1, described DCS system is composed of bus interface 3, The control station 4 and the database 5 are formed; the on-site intelligent instrument 2, the DCS system, and the host computer 6 are sequentially connected through the field bus, and the host computer includes:

(2.1)通过中间变量处理控制变量边界约束，即对于具有式(1)所示边界约束的(2.1) Process control variable boundary constraints through intermediate variables, that is, for the boundary constraints shown in formula (1)

u_min≤u(t)≤u_max (1)u _min ≤ u(t) ≤ u _max (1)

m维控制变量u(t)，下标min、max分别表示最小值和最大值，u_min、u_max均为常量，分别对应控制变量的下界和上界，采取以下变换：For the m-dimensional control variable u(t), the subscripts min and max represent the minimum and maximum values respectively, u _min and u _max are constants, corresponding to the lower and upper bounds of the control variable, and the following transformations are adopted:

(2.2)将状态变量终值约束转化为新的目标函数，即对于具有终值约束式(3)：(2.2) Transform the final value constraint of the state variable into a new objective function, that is, for the final value constraint (3):

x_j(t_f)＝x_jf(j＝1，2，...，c) (3)x _j (t _f )=x _jf (j=1, 2, . . . , c) (3)

的状态变量x_f(t)，其中c表示受终值约束的状态变量个数，x_jf为给定的常量，x_j(t_f)表示状态变量x_j(t)在终端时刻t_f的取值，构造如下目标函数式(4)：The state variable x _f (t) of the state variable x f (t), where c represents the number of state variables subject to the final value constraints, x _jf is a given constant, x _j (t _f ) represents the state variable x _j (t) at the terminal time t _f value, construct the following objective function formula (4):

$\frac{dx (t)}{dt} = f [x (t), z (t), t],$ x(0)＝x⁰ (6) $\frac{dx (t)}{dt} = f [x (t), z (t), t],$ x(0)=x ⁰ (6)

的最优决策变量z^*(t)式(5)(6)中

、ψ分别表示在终点条件下和在一段时间内目标函数的组成部分，x表示给定的n维状态变量，x₀表示初始时刻(t＝0)的状态变量值，f表示函数变量，采取内外两层优化的结构进行求解：The optimal decision variable z ^* (t) in formula (5) (6)

(4.1)内层优化，目的是寻找使目标函数J₁最优的决策变量z1(t)，且z1(t)须满足状态方程(式(6))和内层优化的协态方程式(7)：(4.1) Inner layer optimization, the purpose is to find the decision variable z1(t) that makes the objective function J ₁ optimal, and z1(t) must satisfy the state equation (formula (6)) and the co-state equation of the inner layer optimization (7 ):

其中λ(t)表示m维协态变量，上标T表示变量转置，式(6)与式(7)构成内层常微分方程系统；内层优化所得的最优决策变量z1(t)传给外层作为外层优化的初始解；Among them, λ(t) represents the m-dimensional co-state variable, and the superscript T represents the variable transposition. Equation (6) and Equation (7) constitute the inner ordinary differential equation system; the optimal decision variable z1(t) obtained by the inner optimization Pass to the outer layer as the initial solution for outer layer optimization;

(4.2)外层优化，目的是在内层优化基础上搜寻使目标函数J₂最优的决策变量z2(t)，且z2(t)须满足状态方程式(6)和外层优化的协态方程式(8)：(4.2) Outer layer optimization, the purpose is to search for the decision variable z2(t) that makes the objective function _J2 optimal on the basis of inner layer optimization, and z2(t) must satisfy the state equation (6) and the co-state of outer layer optimization Equation (8):

\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - {θ (t)}^{T} &Center Dot; \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},

其中，θ(t)表示m维协态变量，

, ψ respectively denote the components of the objective function J ₂ under the terminal condition and within a period of time, formula (6) and formula (8) constitute the outer ordinary differential equation system; the optimal decision variable z2(t ) is exactly the optimal solution z ^* (t) of double-layer optimization, and _the corresponding J value is exactly the optimal target value J ^* of double-layer optimization;

并将最优结果z^*(t)和J^*传给输出显示模块；And pass the optimal result z ^* (t) and J ^* to the output display module;

输出显示模块，用于将双层优化模块计算出的最优决策结果z^*(t)通过式(2)转化为最优控制轨线u^*(t)，然后将u^*(t)和最优目标值J^*传输给DCS系统，并在DCS系统中显示所得到的优化结果信息。The output display module is used to transform the optimal decision result z ^* (t) calculated by the double-layer optimization module into the optimal control trajectory u ^* (t) through formula (2), and then u ^* (t) and the most The optimal target value J ^* is transmitted to the DCS system, and the obtained optimization result information is displayed in the DCS system.

所述上位机的双层优化模块采用如下步骤进行内外层优化。所述步骤(4.1)的内层优化按照以下算法步骤来实现，上标k表示迭代次数：The double-layer optimization module of the upper computer adopts the following steps to optimize the inner and outer layers. The inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the number of iterations:

4.1.3)判断收敛条件式(9)是否成立，若成立，则内层的最优解z1^*＝z1^k，将z1^*传给外层，作为外层迭代的初始解；否则转步骤(4.1.4)；4.1.3) Judging whether the convergence condition (9) is valid, if it is valid, then the optimal solution z1 ^* = z1 ^k of the inner layer, and transfer z1 ^* to the outer layer as the initial solution of the outer layer iteration; otherwise, go to the step ( 4.1.4);

|J₁ ^k-J₁ ^k+1|≤ζ₁ (9)|J ₁ ^k -J ₁ ^k+1 |≤ζ ₁ (9)

其中H1表示内层优化问题的哈密顿函数，由式(13)计算出，

表示在α∈[0，+∞)中寻找使H1达到最小值的步长α^*；where H1 represents the Hamiltonian function of the inner optimization problem, which is calculated by formula (13),

Indicates that in α∈[0, +∞), the step size α ^* that makes H1 reach the minimum value is sought;

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)H1=λ(t) ^T f[x(t), z1(t), t] (13)

取D为系数取整数值；Pick D is an integer value for the coefficient;

4.1.6)计算下一个迭代点4.1.6) Calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)z1 ^k+1 ＝z1 ^k +α ^k d ^k (14)

将迭代次数加1，即k＝k+1，将步骤4.1.6)中的z1^k+1保存为当前点z1^k继续迭代，转步骤4.1.2)；Add 1 to the number of iterations, i.e. k=k+1, save z1 ^k+1 in step 4.1.6) as current point z1 ^k to continue iteration, turn to step 4.1.2);

所述步骤(4.2)的外层优化依照以下算法步骤来实现(上标l表示当前迭代次数)：The outer layer optimization of the step (4.2) is realized according to the following algorithm steps (superscript 1 represents the current number of iterations):

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)|J ₂ ^l -J ₂ ^l+1 |≤ζ ₂ (15)

${h h}^{l l} ((t t)) = = \frac{&PartialD; &PartialD; ψ ψ [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} + + θ θ {((t t))}^{T T} \cdot &Center Dot; \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} - - - - - - ((1616))$

其中H2表示外层优化问题的哈密顿函数，由式(19)计算出，

表示在γ∈[0，+∞)中寻找使H2达到最小值的步长γ^*；where H2 represents the Hamiltonian function of the outer layer optimization problem, which is calculated by formula (19),

取B为系数取整数值；Pick B is an integer value for the coefficient;

4.2.6)计算下一个迭代点：4.2.6) Calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)z2 ^l+1 ＝z2 ^l +γ ^l d ^l (20)

本实施案例的系统硬件结构图如附图1所示，所述最优控制系统的核心包括带人机界面的上位机6中的约束转换模块8、初始化模块9和双层优化模块10三大功能模块，此外还包括：现场智能仪表2、DCS系统和现场总线。所述的DCS系统由总线接口3、控制站4、数据库5组成；工业过程对象1、现场智能仪表2、DCS系统、上位机6通过现场总线依次相连，实现信息流的上传和下达，上位机与底层系统及时进行信息交换，实现系统的在线优化。The system hardware structure diagram of this implementation case is shown in accompanying drawing 1, and the core of described optimal control system includes the constraint conversion module 8 in the upper computer 6 with man-machine interface, initialization module 9 and double-layer optimization module 10 three major Functional modules, in addition, include: field intelligent instrument 2, DCS system and field bus. The DCS system is composed of a bus interface 3, a control station 4, and a database 5; the industrial process object 1, the on-site intelligent instrument 2, the DCS system, and the upper computer 6 are connected in sequence through the field bus to realize the upload and release of information flow, and the upper computer Exchange information with the underlying system in a timely manner to achieve online optimization of the system.

实施例2Example 2

参照图1和图2，一种双层优化的工业过程最优控制方法，所述最优控制方法按照以下步骤实施：Referring to Fig. 1 and Fig. 2, a kind of optimal control method of industrial process of double-layer optimization, described optimal control method is implemented according to the following steps:

1)、在DCS系统中指定状态变量和控制变量，根据实际生产环境的条件和操作限制的条件设定控制变量的上下边界u_max、u_min和DCS的采样周期，并将DCS数据库5中相应各变量的历史数据，控制变量上下边界值u_max、u_min传送给上位机6；在上位机的信息采集模块7中，设定采样时间，采集现场智能仪表输入的工业过程对象的数据，保存到DCS系统的实时数据库5中，并在每个采样周期将DCS系统的数据库5所得的最新数据输出到上位机的约束转化模块8和初始化模块9进行处理；1), specify the state variables and control variables in the DCS system, set the upper and lower boundaries u _max , u _min of the control variables and the sampling period of DCS according to the conditions of the actual production environment and the conditions of the operation limit, and set the corresponding values in the DCS database 5 The historical data of each variable, the upper and lower boundary values u _max and u _min of the control variables are transmitted to the host computer 6; in the information collection module 7 of the host computer, the sampling time is set, the data of the industrial process object input by the on-site smart instrument is collected, and saved In the real-time database 5 of the DCS system, and output the latest data obtained by the database 5 of the DCS system to the constraint transformation module 8 and the initialization module 9 of the upper computer in each sampling period for processing;

2)在上位机的约束转化模块8中，首先，利用中间变量z(t)对具有式(1)所示边界约束的m维控制变量u(t)进行转换式(2)，将u(t)转化为不受边界约束的中2) In the constraint conversion module 8 of the upper computer, first, use the intermediate variable z(t) to convert the m-dimensional control variable u(t) with the boundary constraints shown in formula (1) into formula (2), and u( t) is transformed into a medium that is not bound by the boundary

u_min≤u(t)≤u_max (1)u _min ≤ u(t) ≤ u _max (1)

间变量z(t)的三角函数表达式，并把z(t)作为最优控制问题的决策变量进行求解；然后，将状态变量终值约束式(3)转化为新的目标函数J₁：The trigonometric function expression of the intermediate variable z(t), and solve z(t) as the decision variable of the optimal control problem; then, transform the state variable final value constraint formula (3) into a new objective function J ₁ :

其中，c表示受终值约束的状态变量个数，x_jf为给定的常量，x_j(t_f)表示状态变量x_j(t)在终端时刻t_f的取值，J₁也是双层优化模块10求解的内层目标函数。Among them, c represents the number of state variables constrained by the final value, x _jf is a given constant, x _j (t _f ) represents the value of the state variable x _j (t) at the terminal time t _f , and J ₁ is also a double-layer The inner objective function to be solved by the optimization module 10.

3)在上位机的初始化模块9中，对初始参数进行设置，并对DCS系统输入的数据进行初始化处理，按照以下步骤完成：3) In the initialization module 9 of the upper computer, the initial parameters are set, and the data input by the DCS system is initialized, and the process is completed according to the following steps:

(3.3)设内外层优化的收敛精度分别为ζ₁、ζ₂，迭代次数分别为k、l(初值均取为0)；设内层优化的初始搜索步长为α0、γ0，迭代搜索的初始决策变量为z1⁰；(3.3) Set the convergence accuracy of inner and outer layer optimization to be ζ ₁ and ζ ₂ respectively, and the number of iterations to be k and l respectively (both initial values are taken as 0); let the initial search step of inner layer optimization be α0 and γ0, and iterative search The initial decision variable of is z1 ⁰ ;

4)在上位机的双层优化模块10中，寻找不仅能使最优控制问题的目标函数J₂式(5)最优，而且能够满足终值约束式(3)和状态方程式(6)的最优决策变量z^*(t)，并将z^*(t)和相应的最优目标值J^*传给输出显示模块。通过采取内外两层优化的结构来进行求解：4) In the double-layer optimization module 10 of the upper computer, search for the objective function _J2 (5) that can not only optimize the optimal control problem, but also satisfy the final value constraint (3) and the state equation (6) The optimal decision variable z ^* (t), and z ^* (t) and the corresponding optimal target value J ^* are transmitted to the output display module. Solve by adopting an internal and external two-layer optimized structure:

(4.1)内层优化，目的是寻找使目标函数J₁最优的决策变量z1(t)，且z1(t)须满足状态方程式(6)和内层优化的协态方程式(7)：(4.1) Inner layer optimization, the purpose is to find the decision variable z1(t) that makes the objective function J ₁ optimal, and z1(t) must satisfy the state equation (6) and the co-state equation (7) of the inner layer optimization:

其中，λ(t)表示m维协态变量，上标T表示变量转置，式(6)Among them, λ(t) represents the m-dimensional costate variable, superscript T represents variable transposition, formula (6)

与式(7)构成内层常微分方程系统；内层优化所得的最优决策变量z1(t)传给外层作为外层优化的初始解；and formula (7) constitute the inner layer ordinary differential equation system; the optimal decision variable z1(t) obtained from the inner layer optimization is passed to the outer layer as the initial solution of the outer layer optimization;

(4.2)外层优化，目的是在内层优化基础上搜寻使目标函数J₂最优的决策变量z2(t)，且z2(t)须满足状态方程(式(6))和外层优化的协态方程式(8)：(4.2) Outer layer optimization, the purpose is to search for the decision variable z2(t) that makes the objective function J ₂ optimal on the basis of inner layer optimization, and z2(t) must satisfy the state equation (Formula (6)) and outer layer optimization The costate equation (8):

\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - {θ (t)}^{T} &Center Dot; \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},

其中，θ(t)表示m维协态变量，

4.1.1)选取迭代初始点z1⁰，若k＝k＝0，则z1⁰＝z⁰，否则z1⁰取值为外层输入的z2^l；4.1.1) Select the iteration initial point z1 ⁰ , if k=k=0, then z1 ⁰ =z ⁰ , otherwise z1 ⁰ takes the value of z2 ^l input by the outer layer;

|J₁ ^k-J₁ ^k+1|≤ζ₁ (9)|J ₁ ^k -J ₁ ^k+1 |≤ζ ₁ (9)

其中，H1表示内层优化问题的哈密顿函数，由式(13)计算出，

H1＝λ(t)^T·f[x(t)，z1(t)，t] (13)H1=λ(t) ^T f[x(t), z1(t), t] (13)

取

D为系数取整数值；Pick

D is an integer value for the coefficient;

4.1.6)计算下一个迭代点4.1.6) Calculate the next iteration point

z1^k+1＝z1^k+α^k·d^k (14)z1 ^k+1 ＝z1 ^k +α ^k d ^k (14)

|J₂ ^l-J₂ ^l+1|≤ζ₂ (15)|J ₂ ^l -J ₂ ^l+1 |≤ζ ₂ (15)

4.2.5)确定最佳搜索步长γ^l：若l＝0，则取γ^l＝γ0，转步骤4.2.6)；否则，从当前的迭代点z2^l出发，沿方向h^l作一维搜索，寻找最佳步长因子γ^*，满足：4.2.5) Determine the optimal search step size γ ^l : if l=0, then take γ ^l = γ0, go to step 4.2.6); otherwise, starting from the current iteration point z2 ^l , make a one-dimensional search along the direction h ^l Search to find the optimal step factor γ ^* that satisfies:

其中，H2表示外层优化问题的哈密顿函数，由式(19)计算出，表示在γ∈[0，+∞)中寻找使H2达到最小值的步长γ^*；Among them, H2 represents the Hamiltonian function of the outer layer optimization problem, which is calculated by formula (19), Represents looking for the step size γ ^* that makes H2 reach the minimum value in γ∈[0, +∞);

取

B为系数取整数值；Pick

B is an integer value for the coefficient;

4.2.6)计算下一个迭代点：4.2.6) Calculate the next iteration point:

z2^l+1＝z2^l+γ^l·d^l (20)z2 ^l+1 ＝z2 ^l +γ ^l d ^l (20)

5)在上位机的输出显示模块11中，所述步骤(4.2.3)中所得的最优决策变量z^*将通过式(2)转换为最优控制曲线u^*(t)，并和最优目标值J^*一起显示在上位机的人机界面上；同时，最优控制曲线u^*(t)将通过总线接口传给DCS系统的控制站，并在DCS系统中显示所得到的优化结果信息。5) In the output display module 11 of the host computer, the optimal decision variable z ^* obtained in the step (4.2.3) will be converted into the optimal control curve u ^* (t) by the formula (2), and the optimal The optimal target value J ^* is displayed on the man-machine interface of the upper computer; at the same time, the optimal control curve u ^* (t) will be transmitted to the control station of the DCS system through the bus interface, and the obtained optimization results will be displayed in the DCS system information.

系统投运：System commissioning:

A.利用定时器，设置好每次数据检测和采集的时间间隔；A. Use the timer to set the time interval for each data detection and collection;

B.现场智能仪表2检测工业过程对象1的数据并传送至DCS系统的实时数据库5中，得到最新的变量数据；B. The on-site smart instrument 2 detects the data of the industrial process object 1 and transmits it to the real-time database 5 of the DCS system to obtain the latest variable data;

C.在上位机6的约束转化模块8中，对控制变量边界约束进行处理，将处理的结果作为初始化模块9和双层优化模块10的输入；C. In the constraint conversion module 8 of the upper computer 6, the control variable boundary constraints are processed, and the result of the processing is used as the input of the initialization module 9 and the double-layer optimization module 10;

D.在上位机6的初始化模块9中，根据实际生产需求和操作限制条件对各模块相关参数和变量进行初始化处理，将处理的结果作为双层优化模块10的输入；D. In the initialization module 9 of the upper computer 6, according to actual production requirements and operating constraints, the relevant parameters and variables of each module are initialized, and the results of the processing are used as the input of the double-layer optimization module 10;

E.上位机6的双层优化模块10，依据约束转化模块8的变量代换关系和新的目标函数信息进行双层迭代优化，优化的结果传送到输出显示模块11；E. The double-layer optimization module 10 of the host computer 6 carries out double-layer iterative optimization according to the variable substitution relationship of the constraint conversion module 8 and the new objective function information, and the optimized result is sent to the output display module 11;

F.上位机6的输出显示模块11，依据约束转化模块8的变量代换关系对双层优化模块10计算出的最优决策曲线进行转换，然后将所得的最优控制结果信息传输给DCS系统，并显示于上位机6的人机界面和DCS系统的控制站4，同时通过DCS系统和现场总线将所得到的优化结果信息传输到现场工作站进行显示，并由现场工作站来执行最优操作。F. The output display module 11 of the upper computer 6 converts the optimal decision curve calculated by the double-layer optimization module 10 according to the variable substitution relationship of the constraint conversion module 8, and then transmits the obtained optimal control result information to the DCS system , and displayed on the man-machine interface of the upper computer 6 and the control station 4 of the DCS system, and at the same time, the obtained optimization result information is transmitted to the field workstation for display through the DCS system and the field bus, and the field workstation performs the optimal operation.

上述实施例用来解释说明本发明，而不是对本发明进行限制，在本发明的精神和权利要求的保护范围内，对本发明作出的任何修改和改变，都落入本发明的保护范围。The above-mentioned embodiments are used to illustrate the present invention, rather than to limit the present invention. Within the spirit of the present invention and the protection scope of the claims, any modification and change made to the present invention will fall into the protection scope of the present invention.

Claims

1. A double-layer optimized industrial process optimal control system, including on-site intelligent detection instruments, DCS systems and host computers connected with industrial process objects, said industrial process objects, on-site intelligent detection instruments, DCS systems and upper computers in sequence Connected, it is characterized in that: described upper computer comprises:

The signal acquisition module is used to set the sampling time and collect the dynamic information of the industrial process object uploaded by the on-site smart instrument;

The initialization module is used for the setting of initial parameters, the discretization and initial assignment of the decision variable z(t), and the specific steps are as follows:

(3.1) Divide the time domain [0, t _f ] into N segments on average: [0, t ₁ ], [t ₁ , t ₂ ], ..., [t _N-1 , t _N ], where t _N =t _f ; the length of each time period is t _f /N, and tf represents the termination moment;

(3.2) Discretize the n-dimensional decision variable z(t) in the time segment described in step (3.1), that is, each decision variable is represented by N piecewise constant values, and the initial decision variable z ⁰ is taken as any constant;

(3.3) Let the convergence precision of the inner and outer layer optimization be ζ ₁ and ζ ₂ respectively, when the iteration error of the optimization target value is less than the convergence precision, stop the iteration, and the iteration times are k and l respectively; let the initial search step of the inner layer optimization be α0, γ0, the initial decision variable of iterative search is z1 ⁰ ;

The constraint conversion module is used to convert the control variable boundary constraints and state variable final value constraints in the boundary value fixed optimal control problem, and the following steps are taken to complete:

(2.1) Process control variable boundary constraints through intermediate variables, that is, for the boundary constraints shown in formula (1)

u _min ≤ u(t) ≤ u _max (1)

The m-dimensional control variable u(t), u _min and u _max are constants, corresponding to the lower bound and upper bound of the control variable respectively, and the subscripts min and max represent the minimum and maximum values respectively, and the following transformations are adopted:

u(t)＝0.5(u _max -u _min )×{sin[z(t)]+1}+u _min (2)

Transform u(t) into the trigonometric function expression of the intermediate variable z(t) which is not bound by the boundary, and solve z(t) as the decision variable of the optimal control problem;

(2.2) Transform the final value constraint of the state variable into a new objective function, that is, for the final value constraint (3):

x _j (t _f ) = x _{j f} j = 1, 2, . . . , c (3)

state variable x _j (t), where c represents the number of state variables subject to final value constraints, x _jf is a given constant, and x _j (t _f ) represents state variable x _j (t) at terminal time t _f The value of , construct the following objective function formula (4):

{J J}_{11} = = {Σ Σ}_{j j = = 11}^{c c} {[[{x x}_{j j} (({t t}_{f f})) - - {x x}_{jf jf}]]}^{22} - - - - - - ((44))

J ₁ is the inner layer objective function solved by the double-layer optimization module;

The double-layer optimization module is used to find the objective function _J2 that can not only make the optimal control problem optimal,

And it can satisfy the final value constraint (3) and the state equation (6):

\frac{dx (t)}{dt} = f [x (t), z (t), t],

x(0)=x ₀ (6)

The optimal decision variable z ^* (t), where,

(4.1) Inner layer optimization, that is, to find the decision variable z1(t) that makes the objective function J ₁ optimal, and z1(t) must satisfy the state equation (6) and the co-state equation (7) of the inner layer optimization:

\frac{dλ dλ ((t t))}{dt dt} = = - - λ λ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z ((t t)),, t t]]}{&PartialD; &PartialD; x x},,

λ λ (({t t}_{f f})) = = \frac{{&PartialD; &PartialD; J J}_{11}}{&PartialD; &PartialD; x x (({t t}_{f f}))} - - - - - - ((77))

Among them, λ(t) represents the m-dimensional co-state variable, superscript T represents variable transposition, formula (6) and formula (7) constitute the inner ordinary differential equation system; the optimal decision variable z1(t ) is passed to the outer layer as the initial solution for outer layer optimization;

(4.2) Outer layer optimization, that is, to search for the decision variable z2(t) that optimizes the objective function J ₂ on the basis of inner layer optimization, and z2(t) must satisfy the state equation (6) and the co-state equation of outer layer optimization (8):

\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - θ {(t)}^{T} &Center Dot; \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},

Among them, θ(t) represents the m-dimensional costate variable,

Then, save the optimal results z ^* (t) and J ^* obtained by the double-layer optimization.

2. the optimal control system of the industrial process of double-layer optimization as claimed in claim 1, is characterized in that: in described double-layer optimization module, adopt following steps to carry out inner and outer layer optimization:

The inner layer optimization of the step (4.1) is realized according to the following algorithm steps, and the superscript k represents the number of iterations:

4.1.1) Select the iteration initial point z1 ⁰ , if k=l=0, then z1 ⁰ =z ⁰ , otherwise z1 ⁰ takes the value of z2 ^l input by the outer layer;

4.1.2) Substitute the k-th iteration point z1 ^k into the inner ordinary differential equation system, when k=0, z1 ^k =z1 ⁰ , perform forward integration and backward integration on formulas (6) and (7) respectively , solve the state variable x and the co-state variable λ, and calculate the target value J ₁ ^k of the kth iteration by formula (4);

4.1.3) Judging whether the convergence condition (9) is valid, if it is valid, then the optimal solution z1 ^* = z1 ^k of the inner layer, and transfer z1 ^* to the outer layer as the initial solution of the outer layer iteration; otherwise, go to the step ( 4.1.4), formula (9) is expressed as follows:;

|J ₁ ^k -J ₁ ^k+1 |≤ζ ₁ (9)

4.1.4) Substituting state variable x and iteration point z1 ^k into formula (10) to calculate gradient g ^k :

{g g}^{k k} ((t t)) = = λ λ {((t t))}^{T T} \cdot &Center Dot; \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 11 ((t t)),, t t]]}{&PartialD; &PartialD; z z 11 ((t t))} - - - - - - ((1010))

Save z1 ^k and g ^k , and then calculate the search direction d ^k , where d ^k-1 represents the search direction of the previous iteration, and β ^k is an intermediate parameter:

d^{k} = \{\begin{matrix} - g^{k}, & k = 1; \\ - g^{k} + β^{k} d^{k - 1}, & k &Greater Equal; 2 . \end{matrix}

in,

β^{k} = \frac{{(g^{k})}^{T} (g^{k} - g^{k - 1})}{{| | g^{k - 1} | |}^{2}} - - - (11)

4.1.5) Determine the optimal search step size α ^k : if k=0, take α ^k = α0, and go to step 4.1.6); otherwise, start from the current iteration point z1 ^k and make a one-dimensional search along the direction d ^k Search to find the optimal step size factor α ^* that satisfies:

H h 11 (({z z 11}^{k k} + + {α α}^{* *} \cdot &Center Dot; {d d}^{k k})) = = \underset{α α &GreaterEqual; &Greater Equal; 00}{min min} H h 11 (({z z 11}^{k k} + + α α \cdot &Center Dot; {d d}^{k k})) - - - - - - ((1212))

Among them, H1 represents the Hamiltonian function of the inner layer optimization problem, which is calculated by formula (13),

H1=λ(t) ^T f[x(t), z1(t), t] (13)

Pick

D is an integer value for the coefficient;

4.1.6) Calculate the next iteration point

z1 ^k+1 ＝z1 ^k +α ^k d ^k (14)

4.1.7) Add 1 to the number of iterations, i.e. k=k+1, save z1 ^k+1 in step 4.1.6) as the current point z1 ^k to continue iteration, turn to step 4.1.2);

The outer layer optimization of the step (4.2) is realized according to the following algorithm steps, and the superscript 1 represents the current number of iterations:

4.2.1) Take the current iteration point of outer layer optimization as z2 ^l = z1 ^* , and the initial value of l is 0;

4.2.2) Substituting z2 ^l into the outer ordinary differential equation system, performing forward integration and backward integration on equations (6) and (8) respectively, to solve the state variable x and co-state variable θ, and formula (5 ) to calculate the target value J ₂ ^l of the lth iteration;

4.2.3) Judging whether the convergence condition (15) is valid, if it is valid, then the optimal solution z ^* = z2 ^l of the double-layer optimization, the optimal objective function value J ^* = J ₂ ^l , save and transfer z ^* and J ^* to the output display module; otherwise turn to the next step; formula (15) is expressed as follows:

|J ₂ ^l -J ₂ ^l+1 |≤ζ ₂ (15)

4.2.4) Substitute state variable x and iteration point z2 ^l into formula (16) to calculate gradient h ^l :

{h h}^{l l} ((t t)) = = \frac{&PartialD; &PartialD; ψ ψ [[x x ((t t)),, z z 22 ((t t)) . . t t]]}{&PartialD; &PartialD; z z 22 ((t t))} + + θ θ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} - - - - - - ((1616))

Save z2 ^l and h ^l , and then calculate the search direction e ^l , e ^l-1 represents the search direction of the previous iteration, and η ^l is an intermediate parameter:

e^{l} = \{\begin{matrix} - h^{l}, & l = 1; \\ - h^{l} + η^{l} e^{l - 1}, & l &Greater Equal; 2 . \end{matrix}

in,

η^{l} = \frac{{(h^{l})}^{T} (h^{l} - h^{l - 1})}{{| | h^{l - 1} | |}^{2}} - - - (17)

4.2.5) Determine the optimal search step size γ ^l : if l=0, then take γ ^l = γ0, go to step 4.2.6); otherwise, starting from the current iteration point z2 ^l , make a one-dimensional search along the direction h ^l Search to find the optimal step factor γ ^* that satisfies:

H h 22 (({z z 22}^{l l} + + {γ γ}^{* *} \cdot &Center Dot; {e e}^{l l})) = = \underset{γ γ &GreaterEqual; &Greater Equal; 00}{min min} H h 22 (({z z 22}^{l l} + + {γ γ \cdot &Center Dot; e e}^{l l})) - - - - - - ((1818))

Among them, H2 represents the Hamiltonian function of the outer layer optimization problem, which is calculated by formula (19),

H2=ψ[x(t), z2(t), t]+θ(t) ^T f[x(t), z2(t), t] (19)

B is an integer value for the coefficient;

4.2.6) Calculate the next iteration point:

z2 ^l+1 ＝z2 ^l +γ ^l d ^l (20)

4.2.7) Add 1 to the number of iterations, that is, l=l+1, save z2 ^l+1 in step 4.2.6) as the current point z2 ^l to continue iteration, and turn to step 4.2.2).

3. the optimal control system of the industrial process of double-layer optimization as claimed in claim 1 or 2, is characterized in that: described upper computer also comprises: output display module, is used for the optimum decision-making that double-layer optimization module calculates The result z ^* (t) is converted into the optimal control trajectory u ^* (t) through formula (2), and then u ^* (t) and the optimal target value J ^* are transmitted to the DCS system, and the DCS system displays the The obtained optimization result information.

4. a kind of optimal control method that the industrial process optimal control system of double-layer optimization as claimed in claim 1 realizes, it is characterized in that: described optimal control method comprises the following steps:

1) Designate the state variables and control variables for optimal control in the DCS system, set the upper and lower boundaries of the control variables u _max , u _min and the sampling period of DCS according to the conditions of the actual production environment and operating restrictions, and save the DCS database The historical data of the corresponding variables in the control variable u _max and u _min are transmitted to the host computer;

2) Transform the boundary value fixed constraints in the optimal control problem:

(2.1) Use the intermediate variable z(t) to have boundary constraints

u _min ≤ u(t) ≤ u _max (1)

The m-dimensional control variable u(t) is transformed:

u(t)＝0.5(u _max -u _min )×{sin[z(t)]+1}+u _min (2)

(2.2) Transform the state variable final value constraint formula (3) into a new objective function J ₁ formula (4):

x _j (t _f )=x _jf (j=1, 2, . . . , c) (3)

{J J}_{11} = = {Σ Σ}_{j j = = 11}^{c c} {[[{x x}_{j j} (({t t}_{f f})) - - {x x}_{jf jf}]]}^{22} - - - - - - ((44))

Among them, c represents the number of state variables constrained by the final value, x _jf is a given constant, x _j (t _f ) represents the value of the state variable x _j (t) at the terminal time t _f , and J ₁ is also a double-layer The inner objective function solved by the optimization module;

3) Set the initial parameters, and initialize the data input by the DCS system, and complete according to the following steps:

(3.1) Divide the time domain [0, t _f ] into N segments on average: [0, t ₁ ], [t ₁ , t ₂ ], ..., [t _N-1 , t _N ], where t _N =t _f ;The length of each time segment is t _f /N;

(3.2) Discretize the n-dimensional decision variable z(t) in the time segment described in (3.1), that is, each decision variable is represented by N piecewise constant values, and the initial decision variable z ⁰ is taken as an arbitrary constant ;

(3.3) Set the convergence accuracy of the inner and outer layer optimization as ζ ₁ and ζ ₂ , and the iteration times as k and l respectively; set the initial search step size of the inner layer optimization as α0 and γ0, and the initial decision variable of iterative search as z1 ⁰ ;

4) Find the optimal decision variable z ^* (t) that can not only optimize the objective function (5) of the optimal control problem, but also satisfy the final value constraint (3) and the state equation (6), and set z ^* (t) and the corresponding optimal target value J ^* are passed to the output display module, and are solved by adopting an internal and external two-layer optimized structure:

\frac{dx (t)}{dt} = f [x (t), z (t), t],

x(0)=x ₀ (6)

(4.1) Inner layer optimization, that is, to find the decision variable z1(t) that makes the objective function J1 optimal, and z1(t) must satisfy the state equation (6) and the co-state equation (7) of the inner layer optimization:

\frac{dλ dλ ((t t))}{dt dt} = = - - λ λ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z ((t t)),, t t]]}{&PartialD; &PartialD; x x},,

λ λ (({t t}_{f f})) = = \frac{{&PartialD; &PartialD; J J}_{11}}{&PartialD; &PartialD; x x (({t t}_{f f}))} - - - - - - ((77))

\frac{dθ (t)}{dt} = - \frac{&PartialD; ψ [x (t), z (t), t]}{&PartialD; x} - θ {(t)}^{T} &Center Dot; \frac{&PartialD; f [x (t), z (t), t]}{&PartialD; x},

Among them, θ(t) represents the m-dimensional costate variable,

5. optimal control method as claimed in claim 4, is characterized in that: the internal optimization of described step (4.1) realizes according to following algorithm step, and superscript k represents number of iterations:

|J ₁ ^k -J ₁ ^j+1 |≤ζ ₁ (9)

{g g}^{k k} ((t t)) = = λ λ {((t t))}^{T T} \cdot \cdot \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 11 ((t t)),, t t]]}{&PartialD; &PartialD; z z 11 ((t t))} - - - - - - ((1010))

d^{k} = \{\begin{matrix} - g^{k}, & k = 1; \\ - g^{k} + β^{k} d^{k - 1}, & k &Greater Equal; 2 . \end{matrix}

in,

β^{k} = \frac{{(g^{k})}^{T} (g^{k} - g^{k - 1})}{{| | g^{k - 1} | |}^{2}} - - - (11)

H h 11 (({z z 11}^{k k} + + {α α}^{* *} \cdot &Center Dot; {d d}^{k k})) = = \underset{α α &GreaterEqual; &Greater Equal; 00}{min min} H h 11 (({z z 11}^{k k} + + α α \cdot &Center Dot; {d d}^{k k})) - - - - - - ((1212))

H1=λ(t) ^T f[x(t), z1(t), t] (13)

Pick

D is an integer value for the coefficient;

4.1.6) Calculate the next iteration point

z1 ^k+1 ＝z1 ^k +α ^k d ^k (14)

4.2.2) Substituting z2 ^l into the outer ordinary differential equation system, performing forward integration and backward integration on formulas (6) and (8) respectively, to solve the state variable x and co-state variable θ, and formula (5 ) to calculate the target value J ₂ ^l of the first iteration;

4.2.3) Judging whether the convergence condition (15) is valid, if it is valid, then the optimal solution of the double-layer optimization z ^* = z2 ^l , the optimal objective function value J ^* = J ₂ ^l , save and transfer z ^* and J ^* to the output display module; otherwise turn to the next step; formula (15) is expressed as follows:

|J ₂ ^l -J ₂ ^l+1 |≤ζ ₂ (15)

{h h}^{l l} ((t t)) = = \frac{&PartialD; &PartialD; ψ ψ [[x x ((t t)),, z z 22 ((t t)) . . t t]]}{&PartialD; &PartialD; z z 22 ((t t))} + + θ θ {((t t))}^{T T} \cdot &Center Dot; \frac{&PartialD; &PartialD; f f [[x x ((t t)),, z z 22 ((t t)),, t t]]}{&PartialD; &PartialD; z z 22 ((t t))} - - - - - - ((1616))

Save z2 ^l and h ^l , and then calculate the search direction e ¹ , where e ^1-1 represents the search direction of the previous iteration, and η ^l is an intermediate parameter:

e^{l} = \{\begin{matrix} - h^{l}, & l = 1; \\ - h^{l} + η^{l} e^{l - 1}, & l &Greater Equal; 2 . \end{matrix}

in,

η^{l} = \frac{{(h^{l})}^{T} (h^{l} - h^{l - 1})}{{| | h^{l - 1} | |}^{2}} - - - (17)

4.2.5) Determine the optimal search step size γ ^l : if l=0, then take γ ^l = γ0, and go to step 4.2.6); otherwise, start from the current iteration point z2 ^l and make a one-dimensional search along the direction h ^l Search to find the optimal step factor γ ^* that satisfies:

H h 22 (({z z 22}^{l l} + + {γ γ}^{* *} \cdot &Center Dot; {e e}^{l l})) = = \underset{γ γ &GreaterEqual; &Greater Equal; 00}{min min} H h 22 (({z z 22}^{l l} + + {γ γ \cdot &Center Dot; e e}^{l l})) - - - - - - ((1818))

H2=ψ[x(t), z2(t), t]+θ(t) ^T f[x(t), z2(t), t] (19)

Pick

B is an integer value for the coefficient;

4.2.6) Calculate the next iteration point:

z2 ^l+1 ＝z2 ^l +γ ^l d ^l (20)

6. The optimal control method as claimed in claim 4 or 5, characterized in that: in the step 1), the data of the industrial process object collected by the field smart instrument is transmitted to the real-time database of the DCS system, and every The latest data obtained from the database of the DCS system for a sampling period is output to the host computer, and the initialization module of the host computer performs initialization processing.

7. The optimal control method as claimed in claim 4 or 5, characterized in that: in the step (4.2.3), the optimal decision variable z ^* obtained will be converted into optimal control curve u by the result output module ^* (t), and display u ^* (t) and the optimal target value J ^* on the man-machine interface of the upper computer; at the same time, the optimal control curve u ^* (t) will be transmitted to the control station of the DCS system through the bus interface , and display the obtained optimization result information in the DCS system.