CN108710299A - A kind of continuous stirred tank reactor catalyst feed supplement optimal control system and method - Google Patents

Abstract

The invention discloses a kind of continuous stirred tank reactor catalyst feed supplement optimal control system and method, which is made of continuous stirred tank reactor, reactant concentration sensor, catalyst concn sensor, analog-digital converter, fieldbus networks, scattered control system, master control room state display module, digital analog converter, catalyst control valve door, coolant control valve end, temperature sensor.Reactant concentration sensor and catalyst concn sensor acquire material component concentration in reactor in real time, DCS obtains the optimum controling strategy of catalyst input quantity, coolant input quantity within the scope of the regulation production time by executing internal control variable parameter optimal control algorithm, and be converted to catalyst control valve door, coolant control valve opening degree instruction, so that catalyst control valve door and coolant control valve is made corresponding actions.While the present invention can ensure catalyst concn, reactant concentration and temperature deviation minimum, the usage amount of catalyst and coolant is minimized.

Description

A continuous stirred tank reactor catalyst feeding optimal control system and method

technical field

The invention relates to the production control field of a continuous stirred tank reactor, and mainly relates to an optimal control system for catalyst feeding in a continuous stirred tank reactor, which can automatically control the concentration of reactants, catalyst concentration and reactor temperature in the continuous stirred tank reactor, Minimize catalyst and coolant usage while keeping catalyst concentration, reactant concentration, and temperature from setpoint deviations.

Background technique

Continuous stirred tank reactors are widely used in industrial fields such as chemical production, fine chemical industry, biomedicine, and food production. For continuous stirred tank reactors, in the stable production process, the key factors affecting the product quality of reactants are the catalyst concentration and the internal temperature of the reactor. Due to the different production process requirements of different products, optimal control of the catalyst concentration, reactant concentration and temperature in the continuous stirred tank reactor according to the production process requirements is the key to tap the potential and increase efficiency of the continuous stirred tank reactor control system.

At present, optimal control theory and corresponding methods are rarely used in the control system of domestic continuous stirred tank reactor, and the parameters in the controller are often set by experience. After adopting the optimal control method, the concentration deviation of reactants and catalysts in the continuous stirred tank reactor can be controlled to be lower, and at the same time, the usage of catalysts and coolants can be further reduced, so as to tap potential and increase efficiency.

Contents of the invention

In order to improve the quality of the products produced by the continuous stirred tank reactor, ensure the minimum deviation between the catalyst concentration, the reactant concentration and the temperature and the set value, and minimize the usage of catalyst and coolant, the invention provides a continuous stirred tank reactor Catalyst feeding optimal control system.

The production process of this continuous stirred tank reactor can be described as:

x(t)=φ(t),t∈[-r,0]

x(t ₀ )=x ₀

g(u(t))≥0

Where t represents time; x(t) is the state vector composed of reactant concentration, catalyst concentration and reactor temperature, is its first derivative; x(tr) is the state vector with r time delay; u(t) represents the control vector composed of catalyst valve opening input and coolant valve opening input; u(ts) represents the control vector with s The control vector of time delay; f[x(tr), x(t), u(ts), u(t), t] is a set of time delay differential equations established according to the relationship of concentration conservation and energy conservation; φ(t) Indicates the value function of the state vector when t∈[-r,0]; Represents the value function of the control vector when t∈[-s,0]; x ₀ represents the initial node state value of the time-delay differential equation function; g(u(t)) is the constraint function of catalyst and coolant valve control.

In order to minimize the deviation of catalyst concentration, reactant concentration and temperature from the set value, and at the same time minimize the usage of catalyst and coolant, the optimal control mathematical model expression of this problem is:

min J＝J[x(t),u(t),t]

x(t)=φ(t),t∈[-r,0]

x(t ₀ )=x ₀

g(u(t))≥0

Where J[x(t), u(t), t] represents the production objective function of the continuous stirred tank reactor; t _f represents the production termination time.

In view of this, the technical solution adopted by the present invention is an optimal control system for catalyst feeding in a continuous stirred tank reactor, including a reactant concentration sensor and a catalyst concentration sensor arranged in the continuous stirred tank reactor, which collect the reactant concentration respectively and catalyst concentration; and a temperature sensor for collecting reactor temperature; reactant concentration, catalyst concentration and reactor temperature are converted into digital signals by an analog-to-digital converter, and the digital signal is input into the distributed control system through the field bus network, and the distributed control system controls the The variable parameterized optimal control method obtains the optimal control strategy of the catalyst input amount and coolant input amount that minimizes the deviation between the catalyst concentration, the reactant concentration, and the temperature and the set value, and the catalyst and coolant usage are the least. The optimal control strategy is converted into the opening instructions of the catalyst control valve and the coolant control valve, and then sent to the digital-analog converter through the fieldbus network, and the digital-analog converter converts the opening instructions into analog signals to control the catalyst control valve and coolant Control the action of the valve; the status display module in the main control room displays the catalyst concentration, reactant concentration, temperature and optimal control strategy obtained by the distributed control system.

The distributed control system includes the following modules: an information collection module, which is used to obtain the differential equation of the reaction process of the continuous stirred tank reactor, the concentration of the reactant, the concentration of the catalyst, the temperature of the continuous stirred tank reactor, the limit of the opening of the catalyst valve, the opening of the coolant valve speed limit, production time frame.

The initialization module is used to set the number of time segments in the production process as N, and the corresponding control grid as T ^(k) , set the initial guess value u ^(k) (t ₀ ) of the valve opening of the catalyst and coolant, and set the calculated Accuracy tol, set the number of iterations k to zero.

TDDE (Time delay differential equations, time delay differential algebraic equations, TDDE for short) solution module, used to obtain the status information x ^(k) ( t) and the objective function value J ^(k) .

The sensitivity trajectory gradient solving module is used to obtain the objective function gradient information dJ ^(k) of this iteration.

NLP (Nonlinear programming, NLP for short) problem solving module is used to judge the convergence, if the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the value difference is less than the precision tol, then it is judged that the convergence is satisfied, and the input quantity of the catalyst and coolant in this iteration is converted into a control command of the valve opening of the catalyst and coolant, which is output by the control command output module.

The present invention also provides a method for optimal control of catalyst feeding in a continuous stirred tank reactor, comprising the following steps:

Step 1: Input the differential equation of the reaction process of the continuous stirred tank reactor, set the production time range, the opening limit of the catalyst control valve, and the opening limit of the coolant control valve.

Step 2: The reactant concentration sensor, catalyst concentration sensor and temperature sensor respectively collect the reactant concentration, catalyst concentration and reactor temperature through the analog-to-digital converter and send them back to the distributed control system through the field bus network, and display the status in the main control room. The above display enables the engineers in the control room to keep abreast of the production process.

Step 3: The distributed control system parameterizes the optimal control algorithm according to the control variables, and obtains the catalyst input amount and coolant input amount that minimize the deviation between the catalyst concentration, the reactant concentration, and the temperature and the set value, and at the same time use the least amount of catalyst and coolant. optimal control strategy.

Step 4: The distributed control system converts the optimal control strategy into opening instructions for catalyst control valves and coolant control valves, and sends them to digital-to-analog converters through the fieldbus network, so that catalyst control valves and coolant control valves The opening command executes the corresponding action.

The distributed control system (DCS) generates an optimal control solution algorithm for catalyst and coolant control valve opening instructions, and the operation steps are as follows:

Step 1): The information collection module obtains the differential equation of the reaction process of the continuous stirred tank reactor, the concentration of the reactant, the concentration of the catalyst, the temperature of the continuous stirred tank reactor, the opening limit of the catalyst valve, the limit of the opening of the coolant valve, and the production time range;

Step 2): The initialization module starts to run, calculates the current reactant concentration, catalyst concentration and the deviation between the temperature of the continuous stirred tank reactor and the set value under the stable production requirements according to the data collected by the information collection module, and sets the opening of the catalyst valve and the coolant valve The opening and production time interval parameters are parameterized by segmental constants. Set the number of time segments in the production process as N, and the corresponding control grid as T ^(k) , and set the initial guess value u of the catalyst and coolant valve openings. ^(k) (t ₀ ), set the calculation accuracy tol of the NLP problem, and set the number of iterations k to zero;

Step 3): Obtain the state information x ^(k) (t) and objective function value J ^(k) of catalyst concentration, reactant concentration and reactor temperature in band delay time system under this iteration by TDDE solution module;

Step 4): Obtain the iterative objective function gradient information dJ ^(k) by the sensitivity trajectory gradient solution module; skip step 5) and step 6) when k=0, and directly execute step 7);

Step 5): The NLP problem solving module is running, and the convergence judgment is performed through the NLP convergence judgment module. If the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the difference is less than the accuracy tol, it is judged that the convergence is satisfied, and the input of the catalyst and coolant in this iteration is converted into the control command output of the valve opening of the catalyst and coolant; if the convergence is not satisfied, continue to step 6 );

Step 6): Overwrite u ( ^{k -1)} (t), J ^{( k-1)} , dJ ^{( k-1 )} and add 1 to the number of iterations k;

Step 7): The NLP problem solving module 36 uses the objective function value and gradient information obtained in step 3) and step 4) to solve the optimization direction and the optimization step size, and perform optimization correction to obtain the ratio u ^{(k- 1)} (t) A better new catalyst and coolant valve opening control strategy u ^(k) (t). After this step is executed, jump to step 3) again until the NLP convergence judgment module is satisfied.

Described TDDE solving module adopts the extended second-order third-order Runge-Kutta method, and the solution formula is:

K ₁ ＝f[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i ),S ^(k) (t _i -r),t _i ]

K ₂ ＝f[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i )+K ₁ h/2,S ^(k) (t _i -r) ,t _i +h/2]

K ₃ ＝f[u ^(k) ,u ^(k) (t _i -s),x ^(k) (t _i )-hK ₁ +2K ₂ h,S ^(k) (t _i -r),t _i +h]

x ^(k) (t _i +h)＝x ^(k) (t _i )+h(K ₁ +4K ₂ +K ₃ )/6

Among them, f(·) is the function describing the differential equation of the continuous stirred tank reactor reaction process, t _i represents the integration node selected by the Runge-Kutta method, u ^(k) (t _i ) represents the catalyst and coolant at the kth The valve opening control amount of the t _i -th integration node in the iteration, u ^(k) (t _i -s) represents the valve opening control amount of the catalyst and coolant at the t _i -th integration node with a time delay of s in the k-th iteration , x ^(k) (t _i ) represents the status information of the stirred tank reactor catalyst, reactants, and reactor temperature at the t _i integration node in the k iteration, and S ^(k) (t _i -r) represents the stirred tank reactor Reactor catalyst, reactant, and reactor temperature state information at the t _i integration node with r time delay in the k iteration of the reactor temperature, h represents the integration step size, K ₁ , K ₂ , and K ₃ respectively represent the Runge-Kutta method The function value of the differential equation of the continuous stirred tank reactor reaction process at the three integration nodes t _i , t _i +h/2, t _i +h in the integration process.

The described sensitivity trajectory gradient solving module adopts the extended sensitivity trajectory equation method:

Step 1): Define the extended trajectory sensitivity equation of the kth iteration as follows:

The solution formula of Γ ^(k) (t) is:

where t represents time, Indicates the derivative of the extended sensitivity trajectory equation with respect to t in the k-th iteration, f( ) is the state differential equation function describing the reaction of the stirred tank reactor, Γ ^(k) (t ₀ ) represents the extended sensitivity trajectory equation in the k-th iteration The initial node state value at , x ₀ represents the initial node state value of the state differential equation function, and F(·) is the function describing the sensitivity equation.

Step 2): Using the extended second-order third-order Runge-Kutta method to solve the value of the extended sensitivity trajectory equation Γ ^(k) (t) at each integration time, the solution formula is:

Q ₁ ＝F[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i ),S ^(k) (t _i -r),t _i ]

Q ₂ ＝F[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i )+Q ₁ h/2,S ^(k) (t _i -r) ,t _i +h/2]

Q ₃ ＝F[u ^(k) ,u ^(k) (t _i -s),x ^(k) (t _i )-hQ ₁ +2Q ₂ h,S ^(k) (t _i -r),t _i +h]

Γ ^(k) (t _i +h)=Γ ^(k) (t _i )+h(Q ₁ +4Q ₂ +Q ₃ )/6

Among them, t _i represents the integration node selected by the Runge-Kutta method, u( ^k) (t _i ) represents the valve opening control amount of the catalyst and coolant at the t _i integration node in the k iteration, u ^(k) (t _i -s) represents the valve opening control amount of the catalyst and coolant at the t _i integration node with a time delay of s in the k-th iteration, and x ^(k) (t _i ) represents the catalyst and reactants of the stirred tank reactor , the status information of the t _i integration node of the reactor temperature in the k iteration, S ^(k) (t _i -r) represents the stirred tank reactor catalyst, reactants, and reactor temperature in the k iteration of the t _i The state information of the integration node with a time delay of r, F(·) is the function describing the sensitivity equation, h represents the integration step size, K ₁ , K ₂ , and K ₃ respectively represent the three integrals in the integration process of the Runge-Kutta method The function value of the sensitivity equation at nodes t _i , t _i +h/2, t _i +h.

Step 3): According to the obtained state information x ^(k) (t) and the extended sensitivity trajectory equation Γ ^(k) (t), solve the gradient information dJ ^(k) of the objective function:

Among them, Φ(u ^(k) (t),x ^(k) (t),t _f ) represents the objective function at the end of the continuous stirred tank reactor production process, L(u ^(k) (t),u ^(k) (ts), x ^(k) (t), S ^(k) (tr), t) represent the integral objective function of the continuous stirred tank reactor production process, and N represents the time segment number of the continuous stirred tank reactor production process.

Described NLP problem solving module adopts the following steps to realize:

Step 1): If the absolute value difference between the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration is less than the accuracy tol, it is judged that the convergence is satisfied, and this iteration The catalyst and coolant input amount control strategy is converted to the catalyst and coolant valve opening instruction output; if the convergence is not satisfied, continue to step 2);

Step 2): Overwrite the value of u ( ^{k -1)} (t), J ^{( k-1)} , dJ ^{( k-1 )} and increase the number of iterations k by 1;

Step 3): Take the catalyst and coolant input amount control strategy u ^(k-1) (t) as a point in the vector space, denoted as P ₁ , and the value of the objective function corresponding to P ₁ is J ^(k-1) ;

Step 4): Starting from point P ₁ , according to the selected NLP algorithm and the objective function gradient information dJ ^(k-1) at point P ₁ , construct an optimization direction d ^(k-1) and step size in the vector space α ^(k-1) ;

Step 5): Construct the other corresponding u ^(k) (t) in the vector space through the formula u ^(k) (t)=u ^(k-1) (t)+α ^(k-1) d ^(k-1) a point P ₂ ;

Step 6): use optimization correction to obtain another point P ₃ corresponding to u ^(k) (t) in the vector space, so that the objective function value J ^(k) corresponding to P ₃ is better than J ^(k-1) ; enter Step 1) Carry out convergence judgment.

The beneficial effects of the present invention are mainly manifested in: while ensuring the minimum catalyst concentration, reactant concentration and temperature deviation, the consumption of catalyst and coolant is minimized, the cost of raw materials in the production process is realized to be economical, and the potential is tapped to increase efficiency.

Description of drawings

Fig. 1 is a functional schematic diagram of the present invention;

Fig. 2 is a structural representation of the present invention;

Fig. 3 is a DCS internal module structure diagram of the present invention;

Fig. 4 is to the catalyzer that embodiment 1 obtains, coolant input amount control strategy diagram;

Fig. 5 is a graph showing the state change of reactant concentration, catalyst concentration and reactor temperature deviation in Example 1 under the control strategy shown in Fig. 4 .

Detailed ways

Referring to Fig. 1 and Fig. 2, control system of the present invention, comprises the sensor 22 (comprising reactant concentration sensor 22-1 and catalyst concentration sensor 22-2 that is arranged in continuous stirred tank reactor 21, collects reactant concentration and catalyst concentration respectively Concentration; And the temperature sensor 22-3 of gathering reactor temperature); Reactant concentration, catalyst concentration and reactor temperature are converted into digital signal by analog-to-digital converter 23, and this digital signal is input distributed control system 25 through Fieldbus network 24, The distributed control system 25 obtains the optimal catalyst input amount and coolant input amount that minimizes the catalyst concentration, reactant concentration, and temperature deviations from the set values, and at the same time minimizes catalyst and coolant usage, according to the control variable parameterization optimal control method. control strategy, and convert the optimal control strategy into the opening instructions of the catalyst control valve and the coolant control valve, and then send them to the digital-to-analog converter 27 through the fieldbus network 24, and the digital-to-analog converter 27 converts the opening instructions into analog After the signal, the control valve 28 (including the catalyst control valve 28-1 and the coolant control valve 28-2) acts; the state display module 26 of the main control room displays the catalyst concentration, reactant concentration, temperature and optimal control system obtained by the distributed control system 25. Strategy.

Example 1

The continuous stirred tank reactor uses raw material A and catalyst B to produce chemical product C. The reaction is carried out during the stirring process of the motor. The concentration x ₁ (t) of reactant C and the concentration x ₂ (t) of catalyst B in the reaction process are mainly controlled by the reaction The reactor coolant valve opening u ₁ (t) and the catalyst feed valve opening u ₂ (t) are realized, wherein the ratio controller composed of coolant and reactant outlet temperature controls the internal temperature of the reactor, and the catalyst feed is controlled by Divided into two parts: direct input 0.1u ₂ (t) and delayed mixed input 0.9u ₂ (ts), the duration of the production process is 0.2 hours, the opening range of the catalyst control valve is -1 to 1, and the opening of the coolant control valve is degree is -2 to 2, the optimal control requirement of this production process is to obtain catalyst and coolant valves that minimize the deviation of catalyst concentration, reactant concentration and temperature values from the set values, and minimize the amount of catalyst and coolant usage Control strategy, the mathematical model of the optimal control problem is:

R(t)＝(1+x ₁ (t))(1+x ₂ (t))exp(25x ₃ (t)/(1+x ₃ (t)))

x ₃ (t)=-0.02,-r≤t≤0

u ₂ (t)=1,-s≤t≤0

r=0.015, s=0.02

x(0)=[0.49-0.0002-0.02]

|u ₁ (t)|≤2,|u ₂ (t)|≤1

Among them, J represents the production control objective function, t represents the production time (h), s represents the delay time of catalyst input (h), r represents the delay time of reactant temperature (h), x ₁ (t) is the Concentration (mol/L), x ₂ (t) is the concentration of catalyst B (mol/L), x ₃ (t) represents the reactant outlet temperature (°C), u ₁ (t) represents the opening of the reactor coolant valve , u ₂ (t) represents the opening of the catalyst feed valve of the reactor, and the values in x(0) represent the initial concentration of reactant A, the initial concentration of catalyst B and the initial temperature of the reactant outlet respectively.

DCS runs the internal optimal control algorithm, and its operation process is shown in Figure 3, and the execution steps are as follows:

Step 1): The engineer in the control room inputs the differential equation of the reaction process of the continuous stirred tank reactor, sets the production time range as [0,0.2](h), the opening of the catalyst control valve is limited to [-1,1], the coolant control The valve opening is limited to [-2, 2], and the above information is input into the information collection module 31;

Step 2): the initialization module 32 starts to run, and the information collection module collects the initial concentration of the reactant, the initial concentration of the catalyst, and the initial temperature, and calculates that the current concentration of the reactant and the set value deviation under the stable production requirements are 0.49mol/L, and the concentration of the catalyst is different from the set value. The deviation of the fixed value is -0.0002mol/L, and the deviation between the temperature of the continuous stirred tank reactor and the set value is -0.02°C. The information acquisition module collects the catalyst valve opening, coolant valve opening, and production time range input by the engineer. Segment constant parameterization, set the number of time segments in the production process as N=40, set the initial guess value u ^(k) (t ₀ )=0.2 of the valve opening of the catalyst and coolant, and set the calculation accuracy tol of the NLP problem as 10 ^-4 , set the number of iterations k to zero;

Step 3): obtain the state information x ^(k) (t) and objective function value J ^(k) of catalyst concentration, reactant concentration and reactor temperature in band delay time system under this iteration by TDDE solving module 34;

Step 4): Obtain this iterative objective function gradient information dJ ^(k) by the sensitivity track gradient solution module 35; when k=0, skip step 5) and step 6) and directly execute step 7);

Step 5): The NLP problem solving module 36 runs, and the convergence judgment is carried out by the NLP convergence judgment module. If the absolute value of the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration If the value difference is less than the accuracy of 10 ^-4 , it is judged that the convergence is satisfied, and the input of the catalyst and coolant in this iteration is converted into the control command output of the valve opening of the catalyst and coolant; if the convergence is not satisfied, continue Execute step 6);

Step 6): Overwrite u ( ^{k -1)} (t), J ^{( k-1)} , dJ ^{( k-1 )} and add 1 to the number of iterations k;

Step 7): The NLP problem solving module 36 uses the objective function value and gradient information obtained in step 3) and step 4) to solve the optimization direction and the optimization step size, and perform optimization correction to obtain the ratio u ^{(k-1 )} (t) A better new catalyst and coolant valve opening control strategy u ^(k) (t). After this step is executed, jump to step 3) again until the NLP convergence judgment module is satisfied.

Described TDDE solving module adopts the extended second-order third-order Runge-Kutta method, and the solution formula is:

K ₁ ＝f[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i ),S ^(k) (t _i -r),t _i ]

K ₂ ＝f[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i )+K ₁ h/2,S ^(k) (t _i -r) ,t _i +h/2]

K ₃ ＝f[u ^(k) ,u ^(k) (t _i -s),x ^(k) (t _i )-hK ₁ +2K ₂ h,S ^(k) (t _i -r),t _i +h]

x ^(k) (t _i +h)＝x ^(k) (t _i )+h(K ₁ +4K ₂ +K ₃ )/6

Among them, f(·) is the function describing the differential equation of the reaction process of the continuous stirred tank reactor, t _i represents the integration node selected by the Runge-Kutta method, u ^(k )(t _i ) represents the catalyst and coolant at the kth The valve opening control amount of the t _i -th integration node in the iteration, u ^(k) (t _i -s) represents the valve opening control amount of the catalyst and coolant at the t _i -th integration node with a time delay of s in the k-th iteration , x ^(k) (t _i ) represents the status information of the stirred tank reactor catalyst, reactants, and reactor temperature at the t _i integration node in the k iteration, and S ^(k) (t _i -r) represents the stirred tank reactor Reactor catalyst, reactant, and reactor temperature state information at the t _i integration node with r time delay in the k iteration of the reactor temperature, h represents the integration step size, K ₁ , K ₂ , and K ₃ respectively represent the Runge-Kutta method The differential equation function values of the three nodes in the continuous stirred tank reactor reaction process during the integration process.

The described sensitivity trajectory gradient solving module adopts the extended sensitivity trajectory equation method:

Step 1): Define the extended trajectory sensitivity equation of the kth iteration as follows:

The solution formula of Γ ^(k) (t) is:

where t represents time, Indicates the derivative of the extended sensitivity trajectory equation with respect to t in the k-th iteration, f(·) is the differential equation describing the reaction process of the continuous stirred tank reactor, Γ ^(k) (t ₀ ) represents the extended sensitivity trajectory equation at the k-th iteration The initial node state value of , x ₀ represents the initial node state value of the state differential equation function.

Step 2): Using the extended second-order third-order Runge-Kutta method to solve the value of the extended sensitivity trajectory equation Γ ^(k) (t) at each integration time, the solution formula is:

Q ₁ ＝F[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i ),S ^(k) (t _i -r),t _i ]

Q ₂ ＝F[u ^(k) (t _i ),u ^(k) (t _i -s),x ^(k) (t _i )+Q ₁ h/2,S ^(k) (t _i -r) ,t _i +h/2]

Q ₃ ＝F[u ^(k) ,u ^(k) (t _i -s),x ^(k) (t _i )-hQ ₁ +2Q ₂ h,S ^(k) (t _i -r),t _i +h]

Γ ^(k) (t _i +h)=Γ ^(k) (t _i )+h(Q ₁ +4Q ₂ +Q ₃ )/6

Among them, t _i represents the integral node selected by the Runge-Kutta method, u ^(k) (t _i ) represents the valve opening control amount of the catalyst and coolant at the node t _i in the k iteration, u ^(k) ( t _i -s) represents the valve opening control amount of the catalyst and coolant at the t _i node with a time delay of s in the k-th iteration, and x ^(k) (t _i ) represents the catalyst, reactant, and reaction of the stirred tank reactor The status information of the t _i node in the kth iteration of the reactor temperature, S ^(k) (t _i -r) represents the stirred tank reactor catalyst, reactants, and reactor temperature in the kth iteration of the t _i node with r State information under time delay, F(·) is the function describing the sensitivity equation, h is the integration step size, K ₁ , K ₂ , K ₃ are the function values of the three nodes in the integration process of Runge-Kutta method respectively.

Step 3): According to the obtained state information x ^(k) (t) and the extended sensitivity trajectory equation Γ ^(k) (t), solve the gradient information dJ ^(k) of the objective function:

Among them, Φ(u ^(k) (t),x ^(k) (t),t _f ) represents the objective function at the end of the continuous stirred tank reactor production process, L(u ^(k) (t),u ^(k) (ts), x ^(k) (t), S ^(k) (tr), t) represent the integral objective function of the continuous stirred tank reactor production process, and N represents the time segment number of the continuous stirred tank reactor production process.

Described NLP problem solving module adopts the following steps to realize:

Step 1): If the absolute value difference between the objective function value J ^(k) of this iteration and the objective function value J ^(k-1) of the previous iteration is less than the accuracy tol, it is judged that the convergence is satisfied, and this iteration The catalyst and coolant input amount control strategy is converted to the catalyst and coolant valve opening instruction output; if the convergence is not satisfied, continue to step 2);

Step 2): Overwrite the value of u ( ^{k -1)} (t), J ^{( k-1)} , dJ ^{( k-1 )} and increase the number of iterations k by 1;

Step 3): Take the catalyst and coolant input amount control strategy u ^(k-1) (t) as a point in the vector space, denoted as P ₁ , and the value of the objective function corresponding to P ₁ is J ^(k-1) ;

Step 4): Starting from point P ₁ , according to the selected NLP algorithm and the objective function gradient information dJ ^(k-1) at point P ₁ , construct an optimization direction d ^(k-1) and step size in the vector space α ^(k-1) ;

Step 5): Construct the other corresponding u ^(k) (t) in the vector space through the formula u ^(k) (t)=u ^(k-1) (t)+α ^(k-1) d ^(k-1) a point P ₂ ;

Step 6): use optimization correction to obtain another point P ₃ corresponding to u ^(k) (t) in the vector space, so that the objective function value J ^(k) corresponding to P ₃ is better than J ^(k-1) ; enter Step 1) Carry out convergence judgment.

The results of the catalyst and coolant valve opening control strategy are shown in Figure 4, and Figure 5 is the state change diagram of the reactant concentration, catalyst concentration, and reactant outlet temperature deviation corresponding to the catalyst and coolant valve opening control strategy in Figure 4 . Finally, the DCS uses the obtained catalyst and coolant valve opening control strategy as the catalyst and coolant control valve opening command to output to the digital-to-analog converter at the catalyst and coolant control valve end through the field bus network, so that the control valve is controlled according to the received At the same time, the reactant concentration sensor and catalyst concentration sensor collect the reactant concentration and catalyst concentration of the reactor in real time, and the temperature sensor collects the reactor temperature in real time, and sends it back to the DCS through the analog-to-digital converter and the field bus network. displayed in the main control room.

The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be assumed that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field of the present invention, without departing from the concept of the invention, some simple deduction or replacement can also be made, which should be regarded as belonging to the protection scope of the present invention.

Claims (7)

1. a kind of continuous stirred tank reactor catalyst feed supplement optimal control system, it is characterised in that：It is continuously stirred including being set to The reactant concentration sensor (22-1) and catalyst concn sensor (22-2) in kettle reactor (21) are mixed, respectively acquisition reaction Object concentration and catalyst concn；And the temperature sensor (22-3) of acquisition temperature of reactor；Reactant concentration, catalyst concn Digital signal is converted to by analog-digital converter (23) with temperature of reactor, the digital signal is through fieldbus networks (24) input point Control system (25) is dissipated, scattered control system (25) keeps catalyst dense according to control variable parameter method for optimally controlling acquisition Degree, reactant concentration and temperature catalyst and the minimum catalyst of coolant usage amount respectively and while setting value deviation minimum Input quantity, coolant input quantity optimum controling strategy, and optimum controling strategy is converted into catalyst control valve door, coolant control Then the opening degree instruction of valve processed is sent to digital analog converter (27), digital analog converter (27) by fieldbus networks (24) Catalyst control valve door (28-1) and coolant control valve (28-2) action are controlled after opening degree instruction is converted to analog signal； Master control room state display module (26) show scattered control system (25) obtain catalyst concn, reactant concentration, temperature with And optimum controling strategy.

2. a kind of continuous stirred tank reactor catalyst feed supplement optimal control system according to claim 1, it is characterised in that： The scattered control system (25) includes：Information acquisition module (31), it is micro- for obtaining continuous stirred tank reactor reaction process Divide equation, reactant concentration, catalyst concn, continuous stirred tank reactor temperature, the limitation of catalyst valve opening, coolant valve The limitation of door aperture, production time range；

Initialization module (32) is N for production process time slice number to be arranged, and corresponding control grid is T^(k), setting urges The initial guess u of agent, coolant valve aperture^(k)(t₀), setup algorithm precision tol, by iterations k zero setting；

TDDE solves module (34), for obtaining catalyst concn, reactant concentration in current iteration lower band delayed time system With the status information x of temperature of reactor^(k)(t) and target function value J^(k)；

Sensitivity track gradient solves module (35), for obtaining current iteration target function gradient information dJ^(k)；

NLP problem solver modules (36) are for carrying out convergence judgement, if the target function value J of current iteration^(k)With the last time The target function value J of iteration^(k-1)The difference of absolute value be less than precision tol, then judge that convergence meets, and urging current iteration Agent and the input quantity of coolant are converted to the control instruction of catalyst and coolant valve aperture by control instruction output module (37) it exports.

3. carrying out the side of continuous stirred tank reactor catalyst feed supplement optimum control using control system described in claims 1 or 22 Method includes the following steps：

Step 1：Input the continuous stirred tank reactor reaction process differential equation, setting production time range, catalyst control valve The limitation of door aperture, the limitation of coolant control valve aperture；

Step 2：Reactant concentration sensor (22-1), catalyst concn sensor (22-2) and temperature sensor (22-3) point Not Cai Ji reactant concentration, catalyst concn and temperature of reactor after analog-digital converter (23) use fieldbus networks (24) It is passed back to scattered control system (25), and is shown in master control room state display module (26)；

Step 3：For scattered control system (25) according to control variable parameter optimal control algorithm, acquisition makes catalyst concn, anti- It is catalyst and coolant usage amount minimum catalyst input quantity while answering object concentration and temperature and setting value deviation minimum, cold But agent input quantity optimum controling strategy；

Step 4：Optimum controling strategy is converted to catalyst control valve door, coolant control valve by scattered control system (25) Opening degree instruction, be sent to digital analog converter (27) by fieldbus networks (24), make catalyst control valve door (28-1) and Coolant control valve (28-2) executes corresponding actions according to the opening degree instruction received.

4. the method for continuous stirred tank reactor catalyst feed supplement optimum control according to claim 3, it is characterised in that：Step The rapid three control variable parameter optimal control algorithm specifically includes following steps：

Step 1)：Information acquisition module (31) obtains the continuous stirred tank reactor reaction process differential equation, and reactant concentration is urged Agent concentration, continuous stirred tank reactor temperature, the limitation of catalyst valve opening, the limitation of coolant valve aperture, production time Range；

Step 2)：Initialization module (32) calculates current under steady production requires according to the data that information acquisition module (31) acquires Reactant concentration, catalyst concn and continuous stirred tank reactor temperature and setting value deviation, it is setting catalyst valve opening, cold But agent valve opening, production time interval parameter, are parameterized using piece-wise constant, and setting production process time slice number is N, Corresponding control grid is T^(k), setting catalyst, coolant valve aperture initial guess u^(k)(t₀), set NLP problems Computational accuracy tol, by iterations k zero setting；

Step 3)：It is dense that TDDE solves catalyst concn, reactant in module (34) acquisition current iteration lower band delayed time system The status information x of degree and temperature of reactor^(k)(t) and target function value J^(k)；

Step 4)：Module (35), which is solved, by sensitivity track gradient obtains current iteration target function gradient information dJ^(k)；Work as k Step 5) and step 6) are skipped when=0, directly execute step 7)；

Step 5)：NLP problem solver modules (36) carry out convergence judgement, if the target function value J of current iteration^(k)With it is upper The target function value J of an iteration^(k-1)The difference of absolute value be less than precision tol, then judge that convergence meets, and by current iteration Catalyst and the input quantity of coolant be converted to the control instruction output of catalyst and coolant valve aperture；If convergence It is unsatisfactory for, then continues to execute step 6)；

Step 6)：Use u^(k)(t),J^(k),dJ^(k)The last iteration u of value covering^(k-1)(t),J^(k-1),dJ^(k-1)Value, and will repeatedly Generation number k adds 1；

Step 7)：NLP problem solver modules (36) are believed using the target function value and gradient obtained in step 3) and step 4) Breath solves search direction and optimizing step-length, and carries out optimizing amendment, and u is compared in acquisition^(k-1)(t) more preferably new catalyst and cooling Agent valve opening control strategy u^(k)(t)；3) step gos to step again after the completion of executing, until NLP convergences judge mould Until block meets.

5. the method for continuous stirred tank reactor catalyst feed supplement optimum control according to claim 4, it is characterised in that：Institute It states specifically using extension two level three rank Runge Kutta method in step 3), solution formula is：

K₁=f[u^(k)(t_i),u^(k)(t_i-s),x^(k)(t_i),S^(k)(t_i-r),t_i]

K₂=f[u^(k)(t_i),u^(k)(t_i-s),x^(k)(t_i)+K₁h/2,S^(k)(t_i-r),t_i+h/2]

K₃=f[u^(k),u^(k)(t_i-s),x^(k)(t_i)-hK₁+2K₂h,S^(k)(t_i-r),t_i+h]

x^(k)(t_i+ h)=x^(k)(t_i)+h(K₁+4K₂+K₃)/6

Wherein, f () is the function for describing the continuous stirred tank reactor reaction process differential equation, t_iIndicate Runge Kutta method The integral node of selection, u^(k)(t_i) indicate catalyst, the coolant t in kth time iteration_iThe valve opening of integral node controls Amount, u^(k)(t_i- s) indicate t in kth time iteration_iValve opening control of the integral node with catalyst, coolant under s time delays Amount processed, x^(k)(t_i) indicate stirred tank reactor catalyst, reactant, the temperature of reactor t in kth time iteration_iIntegral node Status information, S^(k)(t_i- r) indicate t in stirred tank reactor catalyst, reactant, temperature of reactor kth time iteration_iProduct Partial node indicates integration step, K with the status information under r time delays, h₁、K₂、K₃Runge kutta method integral process is indicated respectively In 3 integral node t_i、t_i+h/2、t_iThe functional value of the continuous stirred tank reactor reaction process differential equation under+h.

6. the method for continuous stirred tank reactor catalyst feed supplement optimum control according to claim 4, it is characterised in that：Institute State sensitivity track gradient solve module (35) use extend sensitivity equation of locus method for：

(1) the Extended workflow-net sensitivity equation for defining kth time iteration is as follows：

Γ^(k)(t) solution formula is：

Wherein, t indicates the time,Indicating the derivative for extending sensitivity equation of locus for t in kth time iteration, f () is The state differential equation function of stirred tank reactor reaction, Γ are described^(k)(t₀) indicate extension sensitivity equation of locus in kth time Start node state value when iteration, x₀Indicate that the start node state value of state differential equation function, F () are that description is sensitive Spend the function of equation；

(2) extension sensitivity equation of locus Γ is solved using extension two level three rank Runge Kutta method^(k)(t) at each integral moment Value, solution formula is：

Q₁=F[u^(k)(t_i),u^(k)(t_i-s),x^(k)(t_i),S^(k)(t_i-r),t_i]

Q₂=F[u^(k)(t_i),u^(k)(t_i-s),x^(k)(t_i)+Q₁h/2,S^(k)(t_i-r),t_i+h/2]

Q₃=F[u^(k),u^(k)(t_i-s),x^(k)(t_i)-hQ₁+2Q₂h,S^(k)(t_i-r),t_i+h]

Γ^(k)(t_i+ h)=Γ^(k)(t_i)+h(Q₁+4Q₂+Q₃)/6

Wherein, t_iIndicate the integral node of Runge Kutta method choice, u^(k)(t_i) indicate catalyst, coolant in kth time iteration In t_iThe valve opening controlled quentity controlled variable of integral node, u^(k)(t_i- s) indicate t in kth time iteration_iIntegral node band s time delays The valve opening controlled quentity controlled variable of lower catalyst, coolant, x^(k)(t_i) indicate stirred tank reactor catalyst, reactant, reactor temperature Degree t in kth time iteration_iThe status information of integral node, S^(k)(t_i- r) indicate stirred tank reactor catalyst, reactant, T in temperature of reactor kth time iteration_iFor integral node with the status information under r time delays, F () is description sensitivity side The function of journey, h indicate integration step, K₁、K₂、K₃3 integral node t in runge kutta method integral process are indicated respectively_i、t_i+ h/2、t_iThe functional value of sensitivity equation under+h；

(3) according to obtained status information x^(k)(t) and extension sensitivity equation of locus Γ^(k)(t), the gradient of object function is solved Information dJ^(k)：

Wherein, Φ (u^(k)(t),x^(k)(t),t_f) indicate continuous stirred tank reactor production process end time object function, L (u^(k)(t),u^(k)(t-s),x^(k)(t),S^(k)(t-r), t) indicate continuous stirred tank reactor production process integral target function, N Indicate continuous stirred tank reactor production process time slice number.

7. the method for continuous stirred tank reactor catalyst feed supplement optimum control according to claim 4, it is characterised in that：Institute NLP problem solvings are stated to realize using following steps：

Step 1)：If the target function value J of current iteration^(k)With the target function value J of last iteration^(k-1)Absolute value it Difference is less than precision tol, then judges that convergence meets, and the catalyst of current iteration and coolant input control strategy are converted It is exported for the opening degree instruction of catalyst, coolant valve；If convergence is unsatisfactory for, step 2) is continued to execute；

Step 2)：Use u^(k)(t),J^(k),dJ^(k)The last iteration u of value covering^(k-1)(t),J^(k-1),dJ^(k-1)Value, and will repeatedly Generation number k increases by 1；

Step 3)：By catalyst and coolant input control strategy u^(k-1)(t) it as some point in vector space, is denoted as P₁, P₁Corresponding target function value is exactly J^(k-1)；

Step 4)：From point P₁It sets out, according to the NLP algorithms of selection and point P₁The target function gradient information dJ at place^(k-1), construct to A search direction d in quantity space^(k-1)With step-length α^(k-1)；

Step 5)：Pass through formula u^(k)(t)=u^(k-1)(t)+α^(k-1)d^(k-1)U is corresponded in construction vector space^(k)(t) another Point P₂；

Step 6)：It corrects to obtain using optimizing and corresponds to u in vector space^(k)(t) another point P₃So that P₃Corresponding target Functional value J^(k)Compare J^(k-1)It is more excellent；Enter step 1) progress convergence judgement.