CN101887239A - Adaptive industrial process optimal control system and method - Google Patents

Abstract

The invention relates to an adaptive industrial process optimal control system, which comprises an intelligent detecting instrument, a DCS system and a host computer, wherein the intelligent detecting instrument is connected with an industrial process object; the industrial process object, the intelligent detecting instrument, the DCS system and the host computer are connected with one another in turn; and the host computer comprises an information acquisition module, an initialization module, a constraint conversion module, an adaptive solution module, an iterative optimization module, a convergence judgment module and a result output module. The invention also provides an adaptive industrial process optimal control method. The system and the method can accurately and stably find the optimal solution for a non-linear industrial process optimal control problem, have high optimization solution efficiency, and are the optimal control system and method having extensive applicability.

Description

A kind of adaptive industrial process optimal control system and method

Technical field

The present invention relates to industrial process optimum control field, especially a kind of adaptive industrial process optimal control system.

Background technology

Any one industrial process is said from the strict sense, all is dynamic processes, promptly describes status of processes variable (as flow, temperature, pressure, liquid level etc.) evolution in time, the transfer in space and changes.Dynamic process is described by the differential equation or difference equation, is called dynamic model.Optimum control is exactly that the performance variable in the dynamic model is implemented control, makes the performance index of process reach optimum.

Some present optimal control problem method for solving, though can find separating of industrial process optimal control problem, but the slow and instability problem of convergence often appears, also may be absorbed in local optimum, be difficult to both guarantee global optimum's property that gained is separated, make finding the solution of optimal control problem stable, quick again.

Summary of the invention

Be difficult to not only accurately but also find apace optimum solution, deficiency poor for applicability in order to overcome existing industrial process optimal control system and method, the invention provides and a kind ofly can accurately find globally optimal solution and find the solution efficient, that applicability is wide adaptive industrial process optimal control system and method.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of adaptive industrial process optimal control system, comprise the field intelligent instrument, DCS system and the host computer that are connected with industrial process object, described industrial process object, intelligent detecting instrument, DCS system link to each other successively with host computer, and described host computer comprises:

Initialization module is used for the setting of initial parameter, discretize and the initial assignment of optimization variable z (t), and concrete steps are as follows:

(3.1) with time domain [t ₀, t _f] be divided into the n segment: [t ₀, t ₁], [t ₁, t ₂] ..., [t _N-1, t _n],

T wherein _n=t _fThe length of each time period is h=(t _f-t ₀)/n, wherein t ₀Represent the initial moment, t _fExpression stops constantly;

(3.2) optimization variable z (t) is carried out discretize on (3.1) described time slice, z (t) is replaced with by n segmentation often be worth the variable z that forms, and choose the initial value z of arbitrary constant as decision variable ⁰

(3.3) the convergence precision value ζ that judges whether iteration optimization stops is set,, stops iteration when optimization target values iteration error during less than ζ; Getting iterations k initial value is 0;

(3.4) the initial step length α 0 of iterative search is set;

The constraint modular converter is used for handling by intermediate variable the control variable boundary constraint of optimizing process, adopts following transfer equation:

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

To have boundary constraint u _Min≤ u (t) u _MaxControl variable u (t) trigonometric function that replaces with the intermediate variable z (t) that is not subjected to boundary constraint express formula, wherein subscript m in, max represent minimum value and maximal value, u respectively _Min, u _MaxDistinguish the lower bound and the upper bound of corresponding control variable, and z (t) is found the solution as optimization variable;

Self-adaptation is found the solution module, be used to find the solution the ordinary differential equation group of industrial process optimal control problem, for the gradient calculation of iteration optimizing module provides state variable and association's state variable information, also judging for the condition of convergence of convergence judge module provides objective function information, takes following steps to finish:

(4.1) find the solution the state equation group:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x _i(t ₀)＝x _i0(i＝1，2，...，m) (2)

Wherein f represents the differentiation function variable, and x (t) is the variable that m state variable formed, x _i(t) i state variable of expression, x _I0Be state variable x _iAt initial time t ₀Value;

(4.2) find the solution the co-state equation group:

$\frac{d{\mathrm{\λ}}_i\left(t\right)}{\mathrm{dt}}=-\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{{\∂x}_i}-{\mathrm{\λ}}_i\left(t\right)\·\frac{\∂f[x\left(t\right),\left(z\right)t,t]}{{\∂x}_i},$

i＝1，2，...，m

(3)

Wherein, ψ is respectively given objective function Non-integral and constant volume subitem, λ _i(t) be i association's state variable, λ (t) is m the variable that association's state variable is formed, λ _i(t _f) for assisting state variable λ _iAt terminal juncture t _fValue;

(4.3) state variable and the decision variable by gained calculates target function value:

Iteration optimizing module makes the decision variable z of objective function J optimum in order to search ^*, take following steps to finish, subscript k all represents iterations, initial assignment is zero:

(5.1) call self-adaptation and find the solution module, preserve state variable, association's state variable and the target function value of gained, described target function value is current target value J ^k

(5.2) calculate current gradient g ^k, subscript T represents variable or transpose of a matrix, i.e. the direction of search of iteration optimization:

$g^k=\{\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}+\mathrm{\λ}{\left(t\right)}^T\·{\frac{\∂f[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}\left\}\right|}_{z\left(t\right)=z^k,t=t_j},$ j＝0，1，2，...，n (5)

(5.3) preserve current iteration point z ^kAnd gradient information g ^k

(5.4) if k=0, then step-size in search α ^kBe taken as initial value, i.e. α ^k=α 0, changes step (5.6);

Otherwise, determine step factor l with current point of iteration and more preceding information ^k:

$l^k=\frac{{\left(s^{k-1}\right)}^T\·y^{k-1}}{{\left|\right|y^{k-1}\left|\right|}^2}---\left(6\right)$

Wherein, s ^K-1The error of expression current iteration point and last iteration point, calculating formula is:

s ^k-1＝z ^k-z ^k-1 (7)

y ^K-1The gradient error of expression current iteration point and last iteration point, calculating formula is:

y ^k-1＝g ^k-g ^k-1 (8)

(5.5) get optimum stepsize ${\mathrm{\α}}^k=\min (\frac{\mathrm{\π}}{D\·\max \left(g^k\right)},l^k)---\left(9\right)$

Wherein, D is that coefficient rounds numerical value;

(5.6) calculate next iteration point:

z ^k+1＝z ^k-α ^k·g ^k (10)

(5.7) new iteration point z ^K+1Pass to self-adaptation and find the solution module to calculate new target function value J ^K+1, enter the convergence judge module then;

Convergence judge module: be used to judge whether the objective result of iteration optimizing module gained satisfies the condition of convergence:

|J ^k-J ^k+1|≤ζ (11)

Wherein, J ^kAnd J ^K+1Represent respectively the k time and target function value that the k+1 time iterative computation obtains, if following formula (11) is set up, show that the Error Absolute Value of a desired value that current iteration obtains and a preceding iteration gained desired value is no more than the convergence precision ζ of setting, then stop iteration optimization and calculate z ^K+1Be exactly optimizing decision variable z ^*(=z ^K+1), J ^K+1Be exactly optimal objective value J ^*(=J ^K+1), with z ^*, J ^*And corresponding iterations (k+1) is saved in output module as a result; If following formula (11) is false, then preserve desired value J ^K+1, get k=k+1, return the iterative that iteration optimizing module is carried out a new round then.

As preferred a kind of scheme: described host computer also comprises information acquisition module, is used to set the sampling time, gathers the multidate information of the industrial process object of being uploaded by field intelligent instrument.

Further, described host computer also comprises output module as a result, is used for the optimizing decision path z that iteration optimizing module is obtained ^*(t) through type (1) is converted into optimum control path u ^*(t), optimizing decision path z ^*(t) by variable z ^*Expression at times is then with u ^*(t) be transferred to the DCS system, and in the DCS system, show resulting optimization object information.

A kind of adaptive industrial process method for optimally controlling, described method for optimally controlling may further comprise the steps:

1) in the DCS system, specifies state variable and control variable, according to the up-and-down boundary u of the condition enactment control variable of the condition of actual production environment and performance constraint _Max, u _MinWith the sampling period of DCS, and with the historical data of corresponding each variable in the DCS database, control variable up-and-down boundary value u _Max, u _MinSend host computer to;

2) by the control variable boundary constraint in the intermediate variable processing optimizing process, adopt following transfer equation:

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

To have boundary constraint u _Min≤ u (t)≤u _MaxControl variable u (t) trigonometric function that replaces with the intermediate variable z (t) that is not subjected to boundary constraint express formula, wherein subscript m in, max represent minimum value and maximal value, u respectively _Min, u _MaxDistinguish the lower bound and the upper bound of corresponding control variable, and z (t) is found the solution as optimization variable;

3) the module initial parameter is provided with, and the data of DCS system input is carried out initialization process, finish according to following steps:

(3.1) with time domain [t ₀, t _f] be divided into the n segment: [t ₀, t ₁], [t ₁, t ₂] ..., [t _N-1, t _n], t wherein _n=t _fThe length of each time period is h=(t _f-t ₀)/n, wherein t ₀Represent the initial moment, t _fExpression stops constantly;

(3.2) optimization variable z (t) is carried out discretize on (3.1) described time slice, z (t) is replaced with by n segmentation often be worth the variable z that forms, and choose the initial value z of arbitrary constant as decision variable ⁰

(3.3) the convergence precision value ζ that judges whether iteration optimization stops is set,, stops iteration when optimization target values iteration error during less than ζ; Getting iterations k initial value is 0;

(3.4) the initial step length α 0＞0 of iterative search is set;

4) with the optimization variable z=z of current iteration step ^kThe substitution self-adaptation is found the solution module, and iterations k is 0 o'clock, z=z ⁰, obtain current state variable, association's state variable, and draw corresponding current target value J ^k, performing step is as follows:

(4.1) find the solution the state equation group:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x _i(t ₀)＝x _i0(i＝1，2，...，m) (2)

Wherein f represents the differentiation function variable, and x (t) is the variable that m state variable formed, x _i(t) i state variable of expression, x _I0Be state variable x _iAt initial time t ₀Value;

(4.2) find the solution the co-state equation group:

$\frac{d{\mathrm{\λ}}_i\left(t\right)}{\mathrm{dt}}=-\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{{\∂x}_i}-{\mathrm{\λ}}_i\left(t\right)\·\frac{\∂f[x\left(t\right),\left(z\right)t,t]}{{\∂x}_i},$

i＝1，2，...，m

(3)

Wherein,

ψ is respectively given objective function Non-integral and constant volume subitem, λ _i(t) be i association's state variable, λ (t) is m the variable that association's state variable is formed, λ _i(t _f) for assisting state variable λ _iAt terminal juncture t _fValue;

(4.3) state variable and the decision variable by gained calculates target function value:

5) find the solution state variable and the association's state variable information that module draws by self-adaptation, calculate the direction of search and the step-length of iteration optimization, find the solution the decision variable z that makes the more approaching optimum of objective function J, the step of implementing the iteration optimizing is as follows, subscript k all represents iterations, and initial assignment is zero:

(5.1) invocation step 4) result of calculation, preserve state variable, association's state variable and the target function value of gained, described target function value is current target value J ^k

(5.2) calculate current gradient g ^k, subscript T represents variable or transpose of a matrix, i.e. the direction of search of iteration optimization:

$g^k=\{\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}+\mathrm{\λ}{\left(t\right)}^T\·{\frac{\∂f[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}\left\}\right|}_{z\left(t\right)=z^k,t=t_j},$ j＝0，1，2，...，n (5)

(5.3) preserve current iteration point z ^kAnd gradient information g ^k

(5.4) if k=0, then step-size in search α ^kBe taken as initial value, i.e. α ^k=α 0, changes step (5.6);

Otherwise, determine step factor l with current point of iteration and more preceding information ^k:

$l^k=\frac{{\left(s^{k-1}\right)}^T\·y^{k-1}}{{\left|\right|y^{k-1}\left|\right|}^2}---\left(6\right)$

Wherein, s ^K-1The error of expression current iteration point and last iteration point, calculating formula is:

s ^k-1＝z ^k-z ^k-1 (7)

y ^K-1The gradient error of expression current iteration point and last iteration point, calculating formula is:

y ^k-1＝g ^k-g ^k-1 (8)

(5.5) get optimum stepsize ${\mathrm{\α}}^k=\min (\frac{\mathrm{\π}}{D\·\max \left(g^k\right)},l^k)---\left(9\right)$

Wherein, D is that coefficient rounds numerical value;

(5.6) calculate next iteration point:

z ^k+1＝z ^k-α ^k·g ^k (10)

(5.7) new iteration point z ^K+1Pass to step (5.4) to calculate new target function value J ^K+1, enter the convergence judge module then;

6) judge the condition of convergence | J ^k-J ^K+1| whether≤ζ satisfies middle J ^kAnd J ^K+1Represent respectively the k time and target function value that the k+1 time iterative computation obtains,, then preserve desired value J if do not satisfy ^K+1, get k=k+1, change step 4) again over to, carry out the iteration optimizing of a new round; If satisfy, then termination of iterations calculates, z ^K+1Be exactly the optimizing decision variable, J ^K+1Be exactly the optimal objective value, preserve z ^*, J ^*And iterations (k+1) arrives output module as a result.

Further, in the described step 1), the data of the industrial process object that field intelligent instrument is gathered are sent in the real-time data base of DCS system, output to host computer in each sampling period from the latest data that the database of DCS system obtains, and carry out initialization process at the initialization module of host computer.

Further again, in the described step 6), the optimizing decision variable z that obtains ^*To be converted to optimum control curve u by output module as a result ^*(t), and on the man-machine interface of host computer show u ^*(t) and optimal objective value J ^*Simultaneously, optimum control curve u ^*(t) will pass to the DCS system by communication interface, and in the DCS system, show resulting optimization object information.

Beneficial effect of the present invention mainly shows: can search out separating of industrial process nonlinear system optimal control problem, and has the very high efficient of finding the solution, the convergence good stability, therefore the every field in industrial process dynamic simulation and optimum control all is with a wide range of applications.

Description of drawings

Fig. 1 is the hardware structure diagram of industrial process optimal control system provided by the present invention;

Fig. 2 is the principle assumption diagram that host computer of the present invention is realized method for optimally controlling.

Embodiment

Specify the present invention below with reference to the accompanying drawings.

Embodiment 1

With reference to Fig. 1, Fig. 2, a kind of adaptive industrial process optimal control system comprises the field intelligent instrument 2, DCS system and the host computer 6 that are connected with industrial process object 1, and described DCS system is made of bus interface 3, active station 4, database 5; Field intelligent instrument 2, DCS system, host computer 6 link to each other successively by fieldbus, and described host computer comprises:

Initialization module 9 is used for the setting of initial parameter, discretize and the initial assignment of optimization variable z (t), and concrete steps are as follows:

(3.1) with time domain [t ₀, t _f] be divided into the n segment: [t ₀, t ₁], [t ₁, t ₂] ..., [t _N-1, t _n], t wherein _n=t _fThe length of each time period is h=(t _f-t ₀)/n;

(3.2) optimization variable z (t) is carried out discretize on (3.1) described time slice, z (t) is replaced with by n segmentation often be worth the variable z (being decision variable) that forms, and choose the initial value z of arbitrary constant as decision variable ⁰

(3.3) the convergence precision value ζ that judges iteration optimization and whether stop (when optimization target values iteration error during less than ζ, stopping iteration) is set; Getting iterations k initial value is 0;

(3.4) the initial step length α 0 of iterative search is set;

Constraint modular converter 8:, adopt following transfer equation by the control variable boundary constraint in the intermediate variable processing optimizing process:

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

To have boundary constraint u _Min≤ u (t)≤u _MaxControl variable u (t) trigonometric function that replaces with the intermediate variable z (t) that is not subjected to boundary constraint express formula, wherein subscript m in, max represent minimum value and maximal value, u respectively _Min, u _MaxDistinguish the lower bound and the upper bound of corresponding control variable, and z (t) is found the solution as optimization variable.

Self-adaptation is found the solution module 10, be used to find the solution the ordinary differential equation group of industrial process optimal control problem, for the gradient calculation of iteration optimizing module 11 provides state variable and association's state variable information, also judging for the condition of convergence of convergence judge module 12 provides objective function information, takes following steps to finish:

(4.1) find the solution the state equation group:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x _i(t ₀)＝x _i0?i＝1，2，...，m (2)

Wherein, f represents the differentiation function variable, and x (t) is the variable that m state variable formed, x _i(t) i state variable of expression, x _I0Be state variable x _iAt initial time t ₀Value, by state variable initial value x _I0Obtain state variable at each discrete value x constantly by the forward integration _i(t), i=1,2 ..., m;

(4.2) find the solution the co-state equation group:

$\frac{d{\mathrm{\λ}}_i\left(t\right)}{\mathrm{dt}}=-\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{{\∂x}_i}-{\mathrm{\λ}}_i\left(t\right)\·\frac{\∂f[x\left(t\right),\left(z\right)t,t]}{{\∂x}_i},$ i＝1，2，...，m

(3)

Wherein,

ψ is respectively given objective function

Non-integral and constant volume subitem, λ _i(t) be i association's state variable, λ (t) is m the variable that association's state variable is formed, λ _i(t _f) for assisting state variable λ _iAt terminal juncture t _fValue, by the state variable terminal value λ of association _i(t _f) obtain association's state variable at each discrete value λ constantly by reverse integral _i(t), i=1,2 ..., m;

(4.3) state variable and the decision variable by gained calculates target function value:

Iteration optimizing module 11 is used to search the decision variable z that makes objective function J optimum ^*, take following steps to finish, subscript k all represents iterations, initial assignment is zero:

(5.1) call self-adaptation and find the solution module 10, state variable, association's state variable and the target function value of preserving gained (are current target value J ^k)

(5.2) calculate current gradient g ^k(subscript T represents variable or transpose of a matrix), the i.e. direction of search of iteration optimization:

$g^k=\{\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}+\mathrm{\λ}{\left(t\right)}^T\·{\frac{\∂f[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}\left\}\right|}_{z\left(t\right)=z^k,t=t_j},$ j＝0，1，2，...，n (5)

(5.3) preserve current iteration point z ^kAnd gradient information g ^k

(5.4) if k=0, then step-size in search α ^kBe taken as initial value, i.e. α ^k=α 0, changes step (5.6);

Otherwise, utilize current point of iteration and more preceding information to determine step factor l ^k:

$l^k=\frac{{\left(s^{k-1}\right)}^T\·y^{k-1}}{{\left|\right|y^{k-1}\left|\right|}^2}---\left(6\right)$

Wherein, s ^K-1The error of expression current iteration point and last iteration point, calculating formula is:

s ^k-1＝z ^k-z ^k-1 (7)

y ^K-1The gradient error of expression current iteration point and last iteration point, calculating formula is:

y ^k-1＝g ^k-g ^k-1 (8)

(5.5) get optimum stepsize ${\mathrm{\α}}^k=\min (\frac{\mathrm{\π}}{D\·\max \left(g^k\right)},l^k)---\left(9\right)$

Wherein D is that coefficient rounds numerical value;

(5.6) calculate next iteration point:

z ^k+1＝z ^k-α ^k·g ^k (10)

(5.7) new iteration point z ^K+1Pass to self-adaptation and find the solution module to calculate new target function value J ^K+1, enter convergence judge module 12 then;

Convergence judge module 12: be used to judge whether the objective result of iteration optimizing module 11 gained satisfies the condition of convergence:

|J ^k-J ^k+1|≤ζ (11)

J wherein ^kAnd J ^K+1Represent respectively the k time and target function value that the k+1 time iterative computation obtains.If following formula (11) is set up, show that the desired value that current iteration obtains and the Error Absolute Value of a preceding iteration gained desired value are no more than the convergence precision ζ of setting, then stop iteration optimization calculating, zk+1 is exactly optimizing decision variable z ^*(=z ^K+1), J ^K+1Be exactly optimal objective value J ^*(=J ^K+1), with z ^*, J ^*And corresponding iterations (k+1) is saved in output module 13 as a result; If following formula (11) is false, then preserve desired value J ^K+1, get k=k+1, return the iterative that iteration optimizing module 11 is carried out a new round then.

Described host computer also comprises information acquisition module 7, is used to set the sampling time, gathers the multidate information of the industrial process object of being uploaded by field intelligent instrument; And output module 13 as a result, be used for the optimizing decision path z that iteration optimizing module is obtained ^*(t) (by variable z ^*Expression at times) through type (1) is converted into optimum control path u ^*(t), then with u ^*(t) be transferred to the DCS system, and in the DCS system, show resulting optimization object information.

The system hardware structure figure of the implementation case as shown in Figure 1, described optimal control system core comprises that constraint modular converter 8, initialization module 9, the self-adaptation in the host computer 6 of being with man-machine interface find the solution 5 big functional modules such as module 10, iteration optimizing module 11, convergence judge module 12, comprises in addition: field intelligent instrument 2, DCS system and fieldbus.Described DCS system is made up of bus interface 3, active station 4, database 5; Industrial process object 1, field intelligent instrument 2, DCS system, host computer 6 link to each other successively by fieldbus, realize uploading and assigning of information flow, and host computer and first floor system are in time carried out message exchange, realize the on-line optimization of system.

Embodiment 2

See figures.1.and.2, a kind of adaptive industrial process method for optimally controlling, described method for optimally controlling is implemented according to following steps:

1) in the DCS system, specifies state variable and control variable, according to the up-and-down boundary u of the condition enactment control variable of the condition of actual production environment and performance constraint _Max, u _MinWith the sampling period of DCS, and with the historical data of corresponding each variable in the DCS database 5, control variable up-and-down boundary value u _Max, u _MinSend host computer 6 to.

2) in the constraint modular converter 8 of host computer,, control variable u (t) ∈ [u of boundary constraint will be subjected to by the trigonometric function replacement _Min, u _Max] be converted into the function expression of another unrestricted variable z (t), that is:

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

Then, z (t) is optimized as optimization variable finds the solution, the z that finally tries to achieve (t) substitution (1) formula promptly obtains corresponding u (t).

3) in the initialization module 9 of host computer, each module initial parameter of host computer is provided with, and the data of DCS system input are carried out initialization process, finish according to following steps:

(3.1) time domain [t of optimum control is set ₀, t _f], and time slice counts n, time domain is divided into the n segment: [t ₀, t ₁], [t ₁, t ₂] ..., [t _N-1, t _n], the length of each time period is h=(t _f-t ₀)/n;

(3.2) optimization variable z (t) is carried out discretize on (3.1) described time slice, use often is worth the variable z (being decision variable) that forms by n segmentation and represents z (t), and chooses the initial value z of decision variable ⁰, can be taken as simple constant;

(3.3) at the convergence judge module 12 of host computer, require convergence precision ζ value is set according to the solving precision of reality, generally be taken as 10 ^-6Can meet the demands.It is 0 that optimization iterations k initial count is set;

(3.4) the initial step length α 0＞0 of iterative search is set;

4) with the optimization variable z=z of current iteration step ^k(iterations k is 0 o'clock, z=z ⁰) the substitution self-adaptation finds the solution module, obtain current state variable, association's state variable, and draw corresponding current target value J ^kPerforming step is as follows:

(4.1) numerical solution state equation group:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x _i(t ₀)＝x _i0?i＝1，2，...，m (2)

Wherein, f represents the differentiation function variable, and x (t) is m dimension state variable, x _i(t) i state variable of expression, x _I0Be state variable x _iAt initial time t ₀Value;

(4.2) find the solution the co-state equation group:

$\frac{d{\mathrm{\λ}}_i\left(t\right)}{\mathrm{dt}}=-\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{{\∂x}_i}-{\mathrm{\λ}}_i\left(t\right)\·\frac{\∂f[x\left(t\right),\left(z\right)t,t]}{{\∂x}_i},$

i＝1，2，...，m (3)

Wherein,

ψ is respectively given objective function

Non-integral and constant volume subitem, λ _i(t) be i association's state variable, λ (t) is m the variable that association's state variable is formed, λ _i(t _f) be i the state variable λ of association _iAt terminal juncture t _fValue;

(4.3) state variable and the decision variable by gained calculates target function value:

5) find the solution state variable and the association's state variable information that module 10 draws by self-adaptation, calculate the direction of search and the step-length of iteration optimization, make the decision variable z of objective function J optimum in order to search ^*, take following steps to finish, subscript k all represents iterations, initial assignment is zero:

(5.1) invocation step 4) result of calculation, preserve state variable, association's state variable and the target function value of gained, described target function value is current target value J ^k

(5.2) calculate current gradient g ^k, promptly the direction of search of iteration optimization (wherein, x (t) and λ (t) are respectively and find the solution the current state variable that draws and association's state variable, and subscript T represents variable or transpose of a matrix:

$g^k=\{\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}+\mathrm{\λ}{\left(t\right)}^T\·{\frac{\∂f[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}\left\}\right|}_{z\left(t\right)=z^k,t=t_j},$ j＝0，1，2，...，n (5)

(5.3) preserve current iteration point z ^kAnd gradient information g ^k

(5.4) if k=0, then step-size in search α ^kBe taken as initial value, i.e. α ^k=α 0, changes step (5.6);

Otherwise, utilize current point of iteration and more preceding information to determine step factor l ^k:

$l^k=\frac{{\left(s^{k-1}\right)}^T\·y^{k-1}}{{\left|\right|y^{k-1}\left|\right|}^2}---\left(6\right)$

Wherein, s ^K-1The error of expression current iteration point and last iteration point, calculating formula is:

s ^k-1＝z ^k-z ^k-1 (7)

y ^K-1The gradient error of expression current iteration point and last iteration point, calculating formula is:

y ^k-1＝g ^k-g ^k-1 (8)

(5.5) get optimum stepsize ${\mathrm{\α}}^k=\min (\frac{\mathrm{\π}}{D\·\max \left(g^k\right)},l^k)---\left(9\right)$

Wherein, D is that coefficient rounds numerical value;

(5.6) calculate next iteration point:

z ^k+1＝z ^k-α ^k·g ^k (10)

(5.7) new iteration point z ^K+1Pass to self-adaptation and find the solution module 10, by step (5.4) to calculate new target function value J ^K+1, enter convergence judge module 12 then;

6) convergence judge module 12 is judged the condition of convergence | J ^k-J ^K+1|≤whether satisfied (J wherein ^kAnd J ^K+1Represent respectively the k time and target function value that the k+1 time iterative computation obtains), if do not satisfy, then preserve desired value J ^K+1, get k=k+1, change step 4) again over to, carry out the iteration optimizing of a new round; If satisfy, then termination of iterations calculates, z ^K+1Be exactly that the optimizing decision variable (is expressed as z ^*=z ^K+1), J ^K+1Be exactly that the optimal objective value (is expressed as J ^*=J ^K+1), preserve z ^*, J ^*And iterations (k+1) arrives output module 13 as a result.

System puts into operation

A. utilize timer, set the time interval of each Data Detection and collection;

B. field intelligent instrument 2 detects the data of industrial process object 1 and is sent in the real-time data base 5 of DCS system, obtains up-to-date variable data;

C. in the constraint modular converter 8 of host computer 6, boundary constraint is handled to control variable, with the result that the handles input as initialization module 9;

D. in the initialization module 9 of host computer 6, each module correlation parameter and variable are carried out initialization process, with the result that handles input as iteration optimizing module 11 according to actual production demand and performance constraint condition;

E. the self-adaptation of host computer 6 is found the solution module 10, finds the solution according to the initial decision variable or the iteration decision variable of 11 inputs of iteration optimizing module, and the state variable of gained, association's state variable and desired value are passed iteration optimizing module 11 again back;

F. the iteration optimizing module 11 of host computer 6, find the solution the variable information that module 10 draws according to the substitution of variable relation of constraint modular converter 8 and self-adaptation and carry out gradient calculation, and according to the result of determination enforcement iteration optimization that restrains judge module 12, the result of optimization passes to output module 13 as a result;

G. the convergence judge module 12 of host computer 6 is judged whether termination of iterations optimization according to the condition of convergence, and the result of gained passes to iteration optimizing module 11 and output module 13 as a result.

The object information of display industry process optimum control on the man-machine interface of host computer 6, host computer 6 is passed to the DCS system with resulting optimum control curve, and show resulting optimization object information at the active station 4 of DCS system, by DCS system and fieldbus resulting optimization object information is transferred to the work on the spot station simultaneously and shows, and carry out optimum operation by the work on the spot station.

The foregoing description is used for the present invention that explains, rather than limits the invention, and in the protection domain of spirit of the present invention and claim, any modification and change to the present invention makes all fall into protection scope of the present invention.

Claims (6)

1. adaptive industrial process optimal control system, comprise the field intelligent instrument, DCS system and the host computer that are connected with industrial process object, described industrial process object, intelligent detecting instrument, DCS system link to each other successively with host computer, it is characterized in that: described host computer comprises:

Initialization module is used for the setting of initial parameter, discretize and the initial assignment of optimization variable z (t), and concrete steps are as follows:

(3.1) with time domain [t ₀, t _f] be divided into the n segment: [t ₀, t ₁], [t ₁, t ₂] ..., [t _N-1, t _n], t wherein _n=t _fThe length of each time period is h=(t _f-t ₀)/n, wherein t ₀Represent the initial moment, t _fExpression stops constantly;

(3.2) optimization variable z (t) is carried out discretize on (3.1) described time slice, z (t) is replaced with by n segmentation often be worth the variable z that forms, and choose the initial value z of arbitrary constant as decision variable ⁰

(3.3) the convergence precision value ζ that judges whether iteration optimization stops is set,, stops iteration when optimization target values iteration error during less than ζ; Getting iterations k initial value is 0;

(3.4) the initial step length α 0 of iterative search is set;

The constraint modular converter is used for handling by intermediate variable the control variable boundary constraint of optimizing process, adopts following transfer equation:

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

To have boundary constraint u _Min≤ u (t)≤u _MaxControl variable u (t) trigonometric function that replaces with the intermediate variable z (t) that is not subjected to boundary constraint express formula, wherein subscript m in, max represent minimum value and maximal value, u respectively _Min, u _MaxDistinguish the lower bound and the upper bound of corresponding control variable, and z (t) is found the solution as optimization variable;

Self-adaptation is found the solution module, be used to find the solution the ordinary differential equation group of industrial process optimal control problem, for the gradient calculation of iteration optimizing module provides state variable and association's state variable information, also judging for the condition of convergence of convergence judge module provides objective function information, takes following steps to finish:

(4.1) find the solution the state equation group:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x _i(t ₀)＝x _i0(i＝1，2，，m) (2)

Wherein f represents the differentiation function variable, and x (t) is the variable that m state variable formed, x _i(t) i state variable of expression, x _I0Be state variable x _iAt initial time t ₀Value;

(4.2) find the solution the co-state equation group:

$\frac{{\mathrm{d\λ}}_i\left(t\right)}{\mathrm{dt}}=-\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{{\∂x}_i}-{\mathrm{\λ}}_i\left(t\right)\·\frac{\∂f[x\left(t\right),z\left(t\right),t]}{{\∂x}_i},$

i＝1，2，...，m

(3)

Wherein,

ψ is respectively given objective function

Non-integral and constant volume subitem, λ _i(t) be i association's state variable, λ (t) is m the variable that association's state variable is formed, λ _i(t _f) for assisting state variable λ _iAt terminal juncture t _fValue;

(4.3) state variable and the decision variable by gained calculates target function value:

Iteration optimizing module makes the decision variable z of objective function J optimum in order to search ^*, take following steps to finish, subscript k all represents iterations, initial assignment is zero:

(5.1) call self-adaptation and find the solution module, preserve state variable, association's state variable and the target function value of gained, described target function value is current target value J ^k

(5.2) calculate current gradient g ^k, subscript T represents variable or transpose of a matrix, i.e. the direction of search of iteration optimization:

$g^k={\{\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}+\mathrm{\λ}{\left(t\right)}^T\·\frac{\∂f[x\left(t\right),z\left(t\right),t}{\∂z\left(t\right)}\}|}_{z\left(t\right)=z^k,t=t_j},$ j＝0，1，2，...，n (5)

(5.3) preserve current iteration point z ^kAnd gradient information g ^k

(5.4) if k=0, then step-size in search α ^kBe taken as initial value, i.e. α ^k=α 0, changes step (5.6);

Otherwise, determine step factor l with current point of iteration and more preceding information ^k:

$l^k=\frac{{\left(s^{k-1}\right)}^T\·y^{k-1}}{{\left|\right|y^{k-1}\left|\right|}^2}---\left(6\right)$

Wherein, s ^K-1The error of expression current iteration point and last iteration point, calculating formula is:

s ^k-1＝z ^k-z ^k-1 (7)

y ^K-1The gradient error of expression current iteration point and last iteration point, calculating formula is:

y ^k-1＝g ^k-g ^k-1 (8)

(5.5) get optimum stepsize ${\mathrm{\α}}^k=\min (\frac{\mathrm{\π}}{D\·\max \left(g^k\right)},l^k)---\left(9\right)$

Wherein, D is that coefficient rounds numerical value;

(5.6) calculate next iteration point:

z ^k+1＝z ^k-α ^k·g ^k (10)

(5.7) new iteration point z ^K+1Pass to self-adaptation and find the solution module to calculate new target letter

Numerical value J ^K+1, enter the convergence judge module then;

Convergence judge module: be used to judge whether the objective result of iteration optimizing module gained satisfies the condition of convergence:

|J ^k-J ^k+1|≤ζ (11)

Wherein, J ^kAnd J ^K+1Represent respectively the k time and target function value that the k+1 time iterative computation obtains, if following formula (11) is set up, show that the Error Absolute Value of a desired value that current iteration obtains and a preceding iteration gained desired value is no more than the convergence precision ζ of setting, then stop iteration optimization and calculate z ^K+1Be exactly optimizing decision variable z ^*(=z ^K+1), J ^K+1Be exactly optimal objective value J ^*(=J ^K+1), with z ^*, J ^*And corresponding iterations (k+1) is saved in output module as a result; If following formula (11) is false, then preserve desired value J ^K+1, get k=k+1, return the iterative that iteration optimizing module is carried out a new round then.

2. a kind of adaptive industrial process optimal control system according to claim 1, it is characterized in that: described host computer also comprises information acquisition module, be used to set the sampling time, gather the multidate information of the industrial process object of uploading by field intelligent instrument.

3. a kind of adaptive industrial process optimal control system according to claim 1 and 2, it is characterized in that: described host computer also comprises output module as a result, is used for the optimizing decision path z that iteration optimizing module is obtained ^*(t) through type (1) is converted into optimum control path u ^*(t), optimizing decision path z ^*(t) by variable z ^*Expression at times is then with u ^*(t) be transferred to the DCS system, and in the DCS system, show resulting optimization object information.

4. method for optimally controlling that a kind of adaptive industrial process optimal control system as claimed in claim 1 is realized, it is characterized in that: described method for optimally controlling may further comprise the steps:

1) in the DCS system, specifies state variable and control variable, according to the up-and-down boundary u of the condition enactment control variable of the condition of actual production environment and performance constraint _Max, u _MinWith the sampling period of DCS, and with the historical data of corresponding each variable in the DCS database, control variable up-and-down boundary value u _Max, u _MinSend host computer to;

2) by the control variable boundary constraint in the intermediate variable processing optimizing process, adopt following transfer equation:

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

To have boundary constraint u _Min≤ u (t)≤u _MaxControl variable u (t) trigonometric function that replaces with the intermediate variable z (t) that is not subjected to boundary constraint express formula, wherein subscript m in, max represent minimum value and maximal value, u respectively _Min, u _MaxDistinguish the lower bound and the upper bound of corresponding control variable, and z (t) is found the solution as optimization variable;

3) the module initial parameter is provided with, and the data of DCS system input is carried out initialization process, finish according to following steps:

(3.1) with time domain [t ₀, t _f] be divided into the n segment: [t ₀, t ₁], [t ₁, t ₂] ..., [t _N-1, t _n], t wherein _n=t _fThe length of each time period is h=(t _f-t ₀)/n, wherein t ₀Represent the initial moment, t _fExpression stops constantly;

(3.2) optimization variable z (t) is carried out discretize on (3.1) described time slice, z (t) is replaced with by n segmentation often be worth the variable z that forms, and choose the initial value z of arbitrary constant as decision variable ⁰

(3.3) the convergence precision value ζ that judges whether iteration optimization stops is set,, stops iteration when optimization target values iteration error during less than ζ; Getting iterations k initial value is 0;

(3.4) the initial step length α 0＞0 of iterative search is set;

4) with the optimization variable z=z of current iteration step ^kThe substitution self-adaptation is found the solution module, and iterations k is 0 o'clock, z=z ⁰, obtain current state variable, association's state variable, and draw corresponding current target value J ^k, performing step is as follows:

(4.1) find the solution the state equation group:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x _i(t ₀)＝x _i0(i＝1，2，...，m) (2)

Wherein f represents the differentiation function variable, and x (t) is the variable that m state variable formed, x _i(t) i state variable of expression, x _I0Be state variable x _iAt initial time t ₀Value;

(4.2) find the solution the co-state equation group:

$\frac{{\mathrm{d\λ}}_i\left(t\right)}{\mathrm{dt}}=-\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{{\∂x}_i}-{\mathrm{\λ}}_i\left(t\right)\·\frac{\∂f[x\left(t\right),z\left(t\right),t]}{{\∂x}_i},$ i＝1，2，...，m

(3)

Wherein,

ψ is respectively given objective function

Non-integral and constant volume subitem, λ _i(t) be i association's state variable, λ (t) is m the variable that association's state variable is formed, λ _i(t _f) for assisting state variable λ _iAt terminal juncture t _fValue;

(4.3) state variable and the decision variable by gained calculates target function value:

5) find the solution state variable and the association's state variable information that module draws by self-adaptation, calculate the direction of search and the step-length of iteration optimization, find the solution the decision variable z that makes the more approaching optimum of objective function J, the step of implementing the iteration optimizing is as follows, subscript k all represents iterations, and initial assignment is zero:

(5.1) invocation step 4) result of calculation, preserve state variable, association's state variable and the target function value of gained, described target function value is current target value J ^k

(5.2) calculate current gradient g ^k, subscript T represents variable or transpose of a matrix, i.e. the direction of search of iteration optimization:

$g^k={\{\frac{\∂\mathrm{\ψ}[x\left(t\right),z\left(t\right),t]}{\∂z\left(t\right)}+\mathrm{\λ}{\left(t\right)}^T\·\frac{\∂f[x\left(t\right),z\left(t\right),t}{\∂z\left(t\right)}\}|}_{z\left(t\right)=z^k,t=t_j},$ j＝0，1，2，...，n (5)

(5.3) preserve current iteration point z ^kAnd gradient information g ^k

(5.4) if k=0, then step-size in search α ^kBe taken as initial value, i.e. α ^k=α 0, changes step (5.6);

Otherwise, determine step factor lk with current point of iteration and more preceding information:

$l^k=\frac{{\left(s^{k-1}\right)}^T\·y^{k-1}}{{\left|\right|y^{k-1}\left|\right|}^2}---\left(6\right)$

Wherein, s ^K-1The error of expression current iteration point and last iteration point, calculating formula is:

s ^k-1＝z ^k-z ^k-1 (7)

y ^K-1The gradient error of expression current iteration point and last iteration point, calculating formula is:

y ^k-1＝g ^k-g ^k-1 (8)

(5.5) get optimum stepsize ${\mathrm{\α}}^k\min (\frac{\mathrm{\π}}{D\·\max \left(g^k\right)},l^k)---\left(9\right)$

Wherein, D is that coefficient rounds numerical value;

(5.6) calculate next iteration point:

z ^k+1＝z ^k-α ^k·g ^k (10)

(5.7) new iteration point z ^K+1Pass to step (5.4) to calculate new target function value J ^K+1, enter the convergence judge module then;

6) judge the condition of convergence | J ^k-J ^K+1| whether≤ζ satisfies middle J ^kAnd J ^K+1Represent respectively the k time and target function value that the k+1 time iterative computation obtains,, then preserve desired value J if do not satisfy ^K+1, get k=k+1, change step 4) again over to, carry out the iteration optimizing of a new round; If satisfy, then termination of iterations calculates, z ^K+1Be exactly the optimizing decision variable, J ^K+1Be exactly the optimal objective value, preserve z ^*, J ^*And iterations (k+1) arrives output module as a result.

5. method for optimally controlling as claimed in claim 4, it is characterized in that: in the described step 1), the data of the industrial process object that field intelligent instrument is gathered are sent in the real-time data base of DCS system, output to host computer in each sampling period from the latest data that the database of DCS system obtains, and carry out initialization process at the initialization module of host computer.

6. as claim 4 or 5 described method for optimally controlling, it is characterized in that: in the described step 6), the optimizing decision variable z that obtains ^*To be converted to optimum control curve u by output module as a result ^*(t), and on the man-machine interface of host computer show u ^*(t) and optimal objective value J ^*Simultaneously, optimum control curve u ^*(t) will pass to the DCS system by communication interface, and in the DCS system, show resulting optimization object information.

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