KR100221231B1 - Model-based predictive control system and method - Google Patents

Abstract

A model-based predictive control system and a predictive control method suitable for a batch process or an iterative operation process, the predictive control system comprising: an estimator for estimating an output variable by measuring an output value from an algebraically modeled target process, and estimated by the estimating means. A predictor for predicting future control errors based on output variables, storage means for storing input / output variables of past batches of I / O variables and current time of current batch, prediction and control sections, constraints, reference trajectory values, Input means for inputting an objective function, values predicted by the predictor, input / output variables of past and current ash stored in the storage means, prediction and control intervals, constraints, and reference trajectories inputted by the input means; Input of the current time of the current batch by minimizing the objective function using quadratic programming (QP) based on the value By providing the calculation means for calculating the number, it is possible to effectively control the batch or repeat operation process and to completely track the reference trajectory even in case of model error or disturbance.

Description

Model-based Predictive Control System and Method

1 is a schematic view showing an example of a batch process to which the present invention is applied.

2 is a schematic showing changes in output variables of a batch process controlled in accordance with the present invention.

3 is a schematic diagram of a model-based predictive control system according to the present invention.

4 is a general flowchart of a model-based predictive control method according to the present invention.

5 is a flowchart of an algorithm constituting an objective function in the model-based predictive control method according to the present invention.

6 is a schematic flowchart of secondary programming used to minimize the value of the objective function given in the model-based predictive control method according to the present invention.

8 (a) and 8 (b) are schematic diagrams of target processes to which the RTP technique is applied.

9 is a schematic diagram showing a structure in which the control system of the present invention controls the target process to which the RTP technique is applied.

10 (a) and 10 (b) are graphs showing step test inputs and step test outputs for modeling a batch reactor.

11 is a graph for comparing the step response coefficient of the model of the batch reactor with the step response coefficient of the target process.

12 is a graph showing changes in input and output variables when the present invention is applied to a batch reactor.

* Explanation of symbols for main parts of the drawings

30: model predictive control system 42: estimator

44 predictor 46 calculation means

48: variable input means 50: target process

52: product

The present invention relates to model-based predictive control. More specifically, it is a combination of iterative learning control and feedback control. A model control system and a model control system suitable for controlling a batch process or an iterative operation process. It is about a method.

Model Predictive Control (MPC) is a basic control structure used in the field of industrial process control that has many control variables. It is an operation variable that models the target process by formula and predicts the control error in the future and minimizes it. Use an algorithm to calculate This model predictive control comprehensively expresses various contradictory requirements of the actual industrial field in the optimal criterion, and has the advantage of simultaneously satisfying multivariate systems and constraint handling.

However, current model prediction control is suitable for control of continuous process, but not for batch process or repetitive operation process. Firstly, in case of existing model prediction control, control error can be eliminated when setting value is constant. This is because the control error cannot be avoided for the time-varying reference trajectory, and as the model uncertainty increases, this phenomenon becomes more severe. Second, the same disturbance due to the nature of the feedback control ( This is because the control error of the type is repeated even if the disturbance continues.

A batch process refers to a process of producing a desired product by supplying raw materials and energy at a time. Unlike control of a continuous process, the control of a batch process requires tracking a time-varying reference trajectory defined over a predetermined time range. As the process characteristics generally change over time and the process variables change significantly during the batch process, the batch process loses its linearity, making it difficult to obtain a reliable process model. The problem of batch process control also appears in the control of the repetitive operation process, such as the operation control of a robot that repeatedly performs some of the same operations. In the ash analysis process or the repetitive operation process, there is a common point that a certain operation or operation is repeatedly repeated. The control using this repeatability is Arimoto et al. By Arimoto, S., Kawamura, S. and Miyazaki, "Bettering Operation of Robots by Learning", J. Robotics. Syst. 1 (1), pp 123-140, 1984.

In repeated wet control, the input trajectory for the currently running ash is calculated in an open loop using the values measured in the previous ash. Iterative learning control has the advantage that complete tracking is possible if the batch process is repeated even when there is a model error. However, iterative learning control is too sensitive to the high frequency components included in the output error, and has a disadvantage in that the processing capacity for constraints is poor. In order to overcome these shortcomings and to apply the concept of repetitive learning control to a wider range of industries, secondary repetitive learning control (Quadratic Criterion-based ILC, hereinafter referred to as 'Q-ILC') is described by Lee, KS and Lee, JH, "Model-based Refinement of Input Trajectories for Batch and Other Transient Processes", AlChE Annual Meeting, Chicago, paper 149i, 1996. Q-ILC is an input trajectory refinement algorithm for batch processes or other iterative processes. It can solve the problem of iterative learning control and can be configured in a more general form as an observer-based algorithm.

However, since Q-ILC provides only an open loop input signal and cannot be modified in real time, it is necessary to add feedback control to apply Q-ILC to the actual process.

It is an object of the present invention to provide a model prediction system and a model predictive control method that can effectively control a batch process or an iterative operation process by combining Q-ILC and feedback control.

Still another object of the present invention is to provide a control system and a control method that actively cope with disturbances occurring in real time, and do not cause tracking control errors even when there is a model error.

In the present invention, the calculation of the control input is used together with the information about the past ash as well as the measured value in the current ash. Therefore, as the ash continues, repetitive disturbance can be completely eliminated, and when there is a model error, the time-varying reference trajectory can be perfectly tracked as the ash count increases.

The model predictive control system according to the present invention includes modeling means for modeling a plant in which a process is performed, an estimator for estimating an output variable by measuring a value from the plant in which the process is performed, an output variable estimated by the estimating means and a desired output. A predictor for predicting a deviation from the variable, storage means for storing the input / output variable of the past batch and the input / output variable before the current time of the current batch, input means for inputting a constraint, reference trajectory value, and an objective function section; A calculation means for calculating an input variable of a current time of a current batch using input values calculated by the estimator, input / output variables of a past ash and a current ash stored in the storage means, and an input variable calculated by the calculating means And a plant operating means for driving the plant.

The input variable calculator, which calculates the input variables of the current time of the current batch, calculates the optimized control input variable values using quadratic programming.

The model predictive control method according to the present invention comprises the steps of inputting an input / output variable of a previous batch and an input / output variable, a prediction and control section, a constraint, a reference trajectory value, and an objective function before the current point in time of the currently running batch, Estimating an output variable by measuring an output value, a predictor predicting a control error to be generated in the future based on the estimated output variable, configuring a second objective function, checking the input constraints, On the basis of the predicted value, the input and output variables of the past ash and the current ash, the input prediction and the control interval, the reference trajectory value of the input variables of the current ash and the input ash of the past ash to minimize the value Calculating a difference Δu _k (t), calculating a current time input variable Δu _k (t) of the current batch using the calculated Δu _k (t), and the system It includes applying the calculated input variables to the target process.

1 is a schematic of a batch process suitable for applying the present invention. The reactor 10 supplies heat supplied through the heating unit 16 and the temperature control valve 18 when the raw material 12 is introduced into the reactor 12 through the raw material supply control valve 14. Temperature Comtroller) to control the temperature in the reactor 10 to the required level to obtain the desired product (20). In the reactor 10, the same temperature raising and lowering operations are repeated every time the raw material 12 is injected. If the first raw material is introduced and the product is discharged, the model predictive control system 30 In the second batch, the information obtained from the first batch and the information generated during the current second batch are used together to determine the control variable and to adjust the temperature of the reactor 10.

For example, as shown in FIG. 2, if the ideal temperature change in the reactor follows the path indicated by the solid line 35 in the charts 32, 34, 36, and the actual temperature in the reactor varies along the dashed line 37, The model predictive control system 30 calculates the deviation from the ideal temperature change using the output variable y ₁ (t), which is the actual temperature of the reactor for each hour in the first batch, and determines the control variable u _l (t) to determine the actual temperature. Control the temperature regulating valve 18, for example, to follow the ideal temperature change.

In the second batch, the output variables y ₂ (t ₁ ), y ₂ (t ₂ ) and the input variables u ₂ (t ₁ ), u ₂ (t ₂ ), and the input / output variables of the first batch until the present time t ₃ The input variable u ₂ (t ₃ ) at the present time is calculated using quadratic programming (QP) consisting of y ₁ (t) and u ₁ (t).

Even in the third batch, when calculating the input variable u ₃ (t ₃ ) at the present time, the output variables y ₃ (t ₁ ), y ₃ (t ₂ ) and the input variable u ₃ (t ₁ ) before the current time t ₃ , u ₃ (t ₂ ) and the input and output variables y ₂ (t) and u ₂ (t) immediately before the current batch, that is, the second batch. However, since the input variable u ₂ (t) of the second batch includes information of the first batch, the calculation of the input variable u ₃ (t) of the _third batch includes all the governments of the past batch. That is, U _n (t) = I _n (t) is a set of all information measured from the first batch to the time point t of the nth batch.

_{k d k k-1 k k} 3 is a schematic diagram of a model-based predictive control system according to the present invention. The model-based predictive control system 30 includes an estimator 42 and an estimated output variable for estimating the output variable yk (t) from the target process 50 represented by G _p .

_{k d k k-1 k k}

Since the estimator 42 and the predictor 44 use the modeling G _m (56) that represents the target process 50 algebraically, even if there is a model error equal to the difference between G _p and G _m , the desired reference is obtained. It is possible to fully trace the trajectory value y _d . The estimator 42 estimating the actual output variable from the measured output value and the predictor 44 predicting the future output error are the reference trajectory values and the total input / output variable values (u _k-1 , y) before the prediction and control intervals. _k-1 ) 54 is also used.

4 is a general flowchart of a model-based predictive control method according to the present invention. First, an input / output variable value of a previous batch and an input / output variable value before a current time point of the current batch are input (60). The output variable from the target process is estimated (62), and the future output error is estimated using the estimated output variable, the input / output variable of the previous batch, and the input / output variable value before the current time of the current batch (64). Using the predicted values, construct a secondary objective function (66), check the constraints (68), and then optimize the control input parameter value Δu _k (t) (= calculate u _k -u _k-1 ) (70). Thus calculates the calculated u _k (t) using a _{Δu k (t) = u k} -1 (t) + Δu k (t) (72). Applying the first variable of u _k (t) to the target process (74), and when the sampling time has elapsed (76), inputting the I / O variable of the previous batch and the I / O variable value before the current time of the current batch ( Returning to 60), repeat the above steps.

를 이용하여

+ Δu_k ^T(t)RΔu_k(t) 형태로 표현되는 목적함수를 구성한다(80). 여기서 Q와 R은 양의 정부호 행렬이다. 대상공정을 모델링한 Gm과, 추정기, 예측기로부터

를 Δu_k(t)의 일차 함수형태로 변환하고(82), 다시 목적함수를 Δu_k(t)만의 이차함수 형태로 변환한다(84).The composition of the objective function follows the flow chart shown in Figure 5, which is the future output error predicted by the predictor.

Using

Construct an objective function expressed in the form Δu _k ^T (t) RΔu _k (t) (80). Where Q and R are positive definite matrices. From Gm modeling the target process, estimator and predictor

Is converted into a linear function form of Δu _k (t) (82), and the objective function is converted into a quadratic function form of Δu _k (t) alone (84).

Secondary programming used to minimize the value of a given objective function follows the flow shown in FIG. The constraints given for the size of the input variable, the rate of change of the input variable, or the output are reconstructed in equation form and then reconstructed into a determinant (90). We find Δu _k (t) where the value of the objective function is minimized while satisfying the given constraint (92). Determine if the found Δu _k value is Δu _k (t) that minimizes the objective function (94), determine the identified Δu _k (t) if it is minimum (96), and if it is not the minimum (92) Return to) and find Δu _k (t) where the value of the objective function is minimized while satisfying the given constraint.

Hereinafter, a method for implementing a model predictive control algorithm of the present invention in which iterative learning control and feedback control are combined will be described.

[Method 1]

end. Basic composition

In the description below, the symbol ' ^- ' represents a value that is under estimation that has not yet been corrected after the first state estimation, the symbol '＾' represents a fully estimated value, and the symbol '△' represents a deviation from the reference value. . Subscript 'k' means batch index and subscript 't' means time index.

Consider a discrete time nonlinear batch or iterative process consisting of n _u inputs and n _y outputs and with N sampling points. These target processes are operated within a limited time, and thus can be configured only within an input / output relation or a limited time interval. If x, y, d and x ₀ are correlated with each input, output and operation, and defined as an incoming disturbance and initial condition, a nonlinear batch or iterative process can be represented by the following algebraic expression.

Here, G denotes a logarithmic model of the dynamic system in which the process is performed, w denotes a disturbance having a correlation between different batches, and v denotes a random disturbance having no correlation between the different batches.

도 식(2)와 같이 정의된다. 행렬 G는 인과성을 부여하기 위해 하부 삼각 행렬이 되며, 시변 펄스 응답계수를 행렬의 원소로 가진다. 위의 식(1)로부터 출력오차에 대한 두 가지의 서로 다른 모델 표현을 유도할 수 있는데, 하나는 되먹임제어를 설계하기 위한 것이고 다른 하나는 반복학습과 되먹임 제어의 결합을 설계하기 위한 것이다.And,

It is defined as in Equation (2). The matrix G becomes a lower triangular matrix to give causality, and has a time-varying pulse response coefficient as an element of the matrix. We can derive two different model representations of the output error from Eq. (1) above, one to design feedback control and the other to design combination of iterative learning and feedback control.

If y _d and u _d are desired reference output trajectories and reference input trajectories, respectively, the following relations are obtained.

Reference values for d and x _o are similarly obtained. Assuming that v = 0 and Δu, e, n are defined as

The linearization model expressed by Equation (5) below can be obtained.

Δ represents a deviation from the mood value. The model represented by Eq. (5) is not related to the previous batch operation and can be used as a base model when developing feedback control designs.

On the other hand, when the subscripts k-1 and k represent the previous batch operation and the next batch operation data, respectively, and G, G _d , and G _x are constant regardless of the batch, the following equation ( The relational expression of two continuous process operation I / O variables represented by 6) and (7) can be obtained.

와 e사이의 관계식은 다음과 같이 얻어진다.Δdk and Δxo, k are also obtained in the same way, and the output error in two consecutive batches

The relation between and e is obtained as follows.

와 e는 식(8)에 의해 다음과 같은 관계식을 갖는다.Output error

And e have the following relation by Equation (8).

Equations (8) and (9) above can also be employed in Q-ILC, and Equation (8) can be used to derive a more general form of the algorithm combining feedback control and iterative learning control. . According to this model representation, the time correlation in vk is directly reflected in the predictor design.

I. Model-based Iterative Learning Control (Q-ILC)

In the batch process or the half-run operation process, the input trajectory for the currently running ash is corrected by using the information of the past ash as well as the information measured in the current ash. Iterative learning control refers to an input correction algorithm that modifies the input trajectory using measurements of past batch operations. Among the many iterative learning control algorithms, the present invention uses Q-ILC. Q-ILC uses a static model representation represented by Equation (8) above, inverse model-based ILC, constraints. It can be widely applied to observer-based or minimum-maximum algorithms with or without conditions.

The model for Q-ILC is constructed by the first equation of equation (8) and equation (9) as follows.

The purpose of the Q-ILC is to design a learning algorithm for constructing ΔU _k = f (I _k-1 ) that satisfies the following properties (11) when Δw _k = v _k = 0 . Where I _k-1 represents information available after the k-1 th batch has ended.

Now, model-based learning control constructs the following objective function to calculate the value of the input variable for the next process operation.

Where Q and R are PD (Positive Definite) matrices. The cost function has a penalty term for the input change between two consecutive batch operations, which can reduce the sensitivity to high frequency components in the input variable calculations. 11) It is possible to construct non-square and / or row-rank deficient multivariate systems with the same iterative learning control while achieving the objective expressed by 11).

In the absence of constraints, the objective function in equation (12) is linear and quadratic. Therefore, the steady-equivalence principle is applied, and the solution can be obtained using the objective function shown in equation (13). have.

Here, e _{k | k-1} is obtained from the state estimator, and the state estimator is configured as follows.

Here, the observer gain Kk can be generally used as a tuning factor, and Kalman gain can be used when statistical information of noise such as disturbance is given.

In the absence of constraints, the solution to minimize the value of the above objective function is found as follows.

here,

Q-ILC has the following properties. As for convergence, Q-ILC satisfies the objective function given by Eq. (11) for all G, regardless of how Q and R are selected, as shown in Eq. (15). Under reasonable assumptions about constraints, this convergence also appears if there are constraints. Next, for robustness, the objective function of Eq. (11) can be found even when there is a model error limited within a certain range. As can be seen from equation (15), in the Q-ILC control, the normal position deviation can be eliminated when k increases by performing an integral operation on the batch index. On the other hand, in the conventional iterative learning control was too sensitive to the high frequency components included in the output error when calculating the input variable, Q-ILC can reduce the sensitivity to these high frequency components while maintaining the asymptotic convergence property.

All. Model-based feedback control

Here, how the predictive control algorithm for the batch process composed of the model G represented by equation (5) is constructed will be described.

C-1. State space model construction

If we first reconstruct G, we can write

u(t)-u_d(t))에 관계된 (n_y·N)×n_u블록 행렬이다. 따라서 앞의 모델식(5)는 다음과 같이 쓸 수 있다.Where G (t) is Δu (t) (

(n _y N) x n _u block matrices associated with u (t) -u _d (t)). Therefore, the previous model equation (5) can be written as

Where n is the sum of all disturbances. If we define e (t) as

Since e (N) = e, Equation (5) can be reconstructed as the following state space model.

Where e (t) is the measurement of the output error at time t,

to be.

C-2. Predictor design

It can be estimated through the e (t) state estimator. Assuming that e (t | t1) represents an estimate of e (t) based on a value measured up to t1? t in a batch, the state estimator can be constructed as follows.

Here, K (t) may be used as a tuning variable, and given statistical information on disturbance and noise, K (t) may be substituted for Kalman gain. For example, if you define

Assuming that E {w} = 0 and E {nn ^T } = Rn, K (t) is obtained by the following dynamic Riccatti equation.

In this case, the state estimator and Riccati equation are initialized as follows each time the batch operation starts.

Now, considering m control inputs, the future control inputs can be predicted as e (t + m | t), so that the following predictor can be constructed.

here,

to be.

e (t + m | t) is defined for all batches, but the t · n _y component is not affected by Δu ^m (t) because of the causality of G. The observer gain K (t) should be designed to change over time to match the time varying structure of H (t).

C-3. Calculation of Input Variables

The movement of the variable of the control input is calculated from the following secondary programming (QP).

Where ε is the surplus variable introduced for the term given to the output variable. If no constraints are given, the least-squares solution can be found:

la. Combining Model-based Iterative Learning Control with Model-based Feedback Control

Q-ILC and model-based feedback control described earlier have their advantages and disadvantages, respectively. Q-ILC can minimize tracking errors despite model errors, but lacks the ability to cope with disturbances occurring in real time. On the contrary, model-based feedback control copes well with real-time disturbances, but there is a fear of causing severe tracking offset when there is model error.

The advantages of the two control concepts are complementary, so a proper combination of the two control techniques can result in a new control technique that is well suited for batch process or repetitive process control.

One way to combine Q-ILC with model-based feedback control is to consider predictive control in which the learning control signal is combined as a feedforward open-loop bias signal, which is based on a simple combined model-based prediction. Sex can lead to instability. If u ^LC is the learning control signal for the current batch obtained by the iterative learning control algorithm, and Δu ^LC ≒ u ^LC -u _d , the following relation can be obtained.

If the predictive control is designed from such a model, the control signal will be determined to minimize the previously described objective function with Δu + Δu ^LC . This means that Δu ^LC has virtually no influence on the control input result. When the model for the process has an error, the control input will be calculated to remove the incorrectly predicted output error. The result from this consideration is that the learning function of repetitive learning control loses its meaning in the simple combined type, and therefore a new coupling technique is needed to preserve the learning ability.

As already explained, the learning in the iterative learning control is possible by the integral operation of the controller acting as the operation is repeated. When the controller is in the form of output error, the output error converges to zero as the operation is repeated. From the fact that model predictive control generally has a different form in a continuous process, the following two approaches are possible. One is to have a predictive control function that maintains the secondary figure of merit based model learning control structure proposed by the inventor, and the other is to have an integral action as the operation is repeated.

D-1. Algorithm without Constraints

La-1-1. State space model composition

(t)와 e_k(t)를 다음과 같이 정의한다.First, to construct a state space model

(t) and e _k (t) are defined as

E _k (t) is also defined in the same way. Thus e _k (N) = e _k and e _k (N) = e _k . Then, we get the following state-space model:

이다.here,

to be.

R-1-2. Predictor design

와 t

는 다음과 같은 상태 추정기를 통해 추정될 수 있다.In equation (32) above

And t

Can be estimated by the following state estimator.

The state estimator is initialized as follows when a new process run begins.

Given a statistical government, Kalman gain is used as K _k (t), for which we first introduce the following definition:

k(t)={e₁,…,e_k-1,e_k(1),…,e_k(t)}는 현재 운전중인 공정의 초기부터 시간 t까지의 정보이다. Kalman 이득은 다음과 같은 동적 리카티 방정식으로부터 구해진다.here

k (t) = {e ₁ ,... , e _k-1 , e _k (1),... , e _k (t)} is information from the beginning of the current running process to time t. The Kalman gain is obtained from the following dynamic Ricardi equation.

if,

If not, the state estimator and Riccati equation are initialized as follows.

If ek (t + m) is an estimated value of an output error for a future control input from t to t + m-1, ek (t + m) is expressed as follows.

here,

R-1-3. Calculation of Input Variables

The calculation of the control input variables is obtained through the following secondary programming.

The control input variables for the case of no constraint are as follows.

Every hour, only the first value, Δu _k (t), of Δu _k ^m (t) obtained through this secondary programming is applied to the process.

D-2. Algorithm with Constraints

The algorithm with constraints is identical to the algorithm without constraints, except that constraint equations must be included in secondary programming for reasons of physical constraints or stability.

La-2-1. Constraint Equation

In most industrial sites, process variables are often limited within a certain range. Constraints are given, for example, on the size of the input variable, the rate of change of the input variable, and the output. The constraint on the size of the input variable can be expressed by the following equation (43).

The rate of change of the input for the time index is expressed by the following equation (44).

Here, δ represents a difference according to a discrete time index.

Meanwhile, the change rate of the input variable with respect to the batch index can be written as follows.

It is useful to adjust the above constraints only by limiting the input variable to a range that can be represented by the linear model of the nonlinear batch process near u _k-1 .

Constraints on the output are defined for all batches. Considering soft constraints to avoid potential infeasibility, it can be expressed as:

The upper and lower bounds of all constraints depend on ash, and the constraint equation above is Δu_k It can be reconstructed into a more general form of m (t). First, the constraint expression of the input variable represented by equation (43) is reconstructed as follows.

Assuming δu _k (0) = u _k (0), δu _k ^m (t) can be written as

here,

Therefore, we obtain the following constraint equation.

here,

The constraints on the output can be reconstructed as follows:

Equation (45) and equation (47) are combined into one equation when the intersection of the weak areas is taken. If Δu _k ^{m, low ”*} t) and Δu _k ^{m, hi” *} t) are the lower and upper limits of the weak area, respectively, the constraint equation above can be combined in the following general form.

here,

D-2-2. Calculation of Input Variables

By adding a penalty term for the slack variable resulting from soft constraints, the secondary programming is modified as follows under the conditions of equations (39) and (54):

Substituting equation (39) into equation (56), the secondary programming is reconstructed as follows under the condition of equation (54).

Given constraints, Δu obtained after determining the control input variable that minimizes the value of the objective function while satisfying all given constraints through quadratic programming._k Δu, the first of m (t)_kOnly (t) is applied to the process.

[Method 2]

The model-based predictive control algorithm according to the present invention can be simplified as follows. This is to more easily apply the present invention to the actual process control and to increase the control speed.

end. If there are no constraints

The state estimator equation (14) described in 'implementation method 1' is

[Equation 14]

It can be decomposed as follows.

In general, observer gain or estimator gain K can be used as a tuning variable, and given statistical information, it can be substituted for Kalman gain. The control input variable can be calculated by finding the input variable that minimizes the given objective function value in the form

The solution of this objective function is

Each MA is applied between the top and second programming only △ U _{k + 1} (t) The first value △ u _k (t) obtained by the blind in the same process.

I. If there is a constraint

Given a constraint, the second programming can determine the control input variable that satisfies all the given constraints while minimizing the value of the objective function, and then the first value of Δu _k ^m (t) is Δu _k (t). Applied to the process.

The objective function when there is a constraint is

Where ε is the surplus introduced for the term given to the output variable.

Hereinafter, an example in which model-based prediction control according to the present invention is applied to an actual process will be described.

Application Example 1. Simulation

In order to confirm the performance of the model predictive control system according to the present invention, the following multiple input / output systems were simulated. For a process where the transfer function is expressed as Gp (s) and the output of the plant has an average of 0 and a variance of 0.01, the modeling Gm (s) is known as the process and the control system is designed with a sampling interval of 1.

The results of the simulations are shown in Figures 7 (a) and 7 (b). Where the subscript indicates the batch index. In FIG. 7 (a), the output 1 shows an excellent tracking performance for the input 1 despite the model error and the measurement error, and the change in the process input side is not significant. In addition, it can be seen that there is a model error in combination with the model prediction controller, so that the tracking performance of the first batch operation is excellent.

In addition, as shown in FIG. 7 (b), despite the stepwise disturbance flowing into the output side y ₂ during the second process operation with respect to the output 2, the value of the input / output variable converges to the reference trajectory regardless. It can be seen that the convergence is excellent.

Application Example 2. RTP

Among the wafer processing processes currently used in the production of semiconductor products, oxidation process, annealing process, and chemical vapor deposition process (CVD) are designed as separate large processes to process a large number of silicon wafers in large quantities. Has been. However, as the trend of semiconductor products has recently changed to a variety of products, there is an increasing demand for custom-made and functional semiconductor products suitable for special applications and interest in wafer processing processes suitable for them.

The current method of processing wafers in large quantities is not suitable for the technical orientation of producing a small amount of semiconductor devices without defects because many defects can come out if the operating conditions are not properly controlled. In addition, the batch processing of several wafers may cause the temperature distribution on each wafer to vary, resulting in inconsistent silicon surface conditions during oxidation and doping.

There was a study on RTP (Rapid Thermal Processing) developed as a new process that can solve the problems of the existing process. RTP is described, for example, in “J. Nulman, "Rapid Thermal Processing of High Quality Silicon Dioxide Films", Solid State Technol., June, 1986 or J. S. Mercier, I. D. Calder, R. P. Beerkens, and H. M. NAguib, "Rapid Isothermal Fusion of PSG films", J. Electrochem. Soc., 132, 2432, 1986, by using a laser source or a halogen lamp arranged in a concentric manner, the wafer inserted in the process of independently processing the wafers one by one is raised to the required temperature within a very high time. After CVD, heat treatment, thermal oxidation, etc., the process is designed to be performed in one device. RTP is emerging as a highly economical process due to its relatively small device and reduced defect rate. The key to RTP operation is to control the temperature on the entire surface of the silicon wafer to be raised and maintained uniformly at high times. However, the current RTP has a lot of problems in temperature control, the spread is not spread.

Although many control methods have been studied to solve these problems of RTP, most of the studies have been made to improve the existing process control method and show a limitation in improving control performance. One important system feature that is often overlooked in RTP process control studies is that the RTP operation has a repetitive nature. In such a process, it is possible to feed back the results of the past batch operation to improve the operation results in the next batch.

For example, consider the process shown in FIG. In this process, the semiconductor wafer 110 is placed in the reaction chamber 100, and a heater, for example, an infrared heater 104, 106, 108 is used to raise the temperature of the wafer to apply a desired material to the wafer surface or to perform heat treatment. It is one of the batch process. The infrared heater is configured concentrically as shown in FIG. 8 (a). As mentioned earlier, in this process it is important to raise the temperature of the wafer uniformly to the desired temperature in a short time.

When the radius r of the semiconductor wafer 110 is R and the thickness z is Z, the material, radius r, thickness z, etc. of the semiconductor wafer are used as variables, and a mathematical model is constructed through thermal analysis of RTP. It is simplified to the order reduction model that can be tuned to utilize the system. This order reduction model is tuned through parameter estimation using model recognition technique, and then a linearization model for control system design is derived. The temperature of the wafer surface at which the desired reaction will occur T ₀ , T ₁ ,. , T _n will be the output variable of the control system controlling the target process, and the currents u ₁ , u ₂ , u _3, etc., supplied to the heater will be the control input variables. The heaters 104, 106 and 108 are all arranged concentrically and the semiconductor wafer 110 is symmetrical about the center so that the temperatures T ₀ , T ₁ ,... , And measure T _n as output variable.

9 is a schematic diagram showing a state in which the model-based predictive control system according to the present invention is combined with the process of FIG. 8. The temperature measured at the surface of the wafer enters the interface 12 through the analog input unit 122, which converts the analog temperature signal into a data form suitable for the control system 130. The control system 130 estimates the wafer temperature value of the current batch, the wafer temperature variable for the batch before the current batch, the current variable supplied to the heater and the wafer temperature variable before the current point in time for the current batch, Current variables are used to predict future output errors. As mentioned earlier, after checking the constraints, use quadratic programming to calculate Δu _k (t), which minimizes the value of a given objective function, and calculate u _k (t) using Δu _k (t). Send interface 120 the first value of u _k (t). The interface 120 converts the control input variable provided from the control system 130 into a signal suitable for the analog output unit 124, and the converted signal is respectively transmitted through an infrared heater (thyristor 126, 127, 128; thyristor). 104, 106, 108.

Application Example 3 Batch Reactor

In general, a batch reactor (Batch reactor) after the reaction material is introduced into the reactor, the temperature is raised to the first reaction and then the temperature is further raised to further induce the same reaction and then lowered the product from the reactor The process of discharging the gas is repeated. For the simulation of such a batch reactor, the following reactor and the reaction formula is represented by the formula.

Where T is the temperature in the reactor, U is the overall heat transfer coefficient, A is the heat transfer area, M is the total mass of the reactant, Tj is the temperature of the reactor jacket, Cp is the heat capacity coefficient of the reactor internals, and Ca is the reactant in the reactor. The concentration is shown, and ΔHR means heat of reaction.

The reaction heat ΔHR is proportional to e ^{−1 / T} , k is proportional to e ^{1 / T} , and the step test results and step response obtained by first modeling for the control of a batch reactor, which is a nonlinear system, are shown in FIGS. (b) is obtained as shown in FIG.

The model of the target process obtained as a result of the step test is the same as the solid line of FIG. 11. As a result of performing the model-based predictive control according to the present invention using this model, the control input signal u ₁ , as shown in FIG. If you enter u ₂ , u ₃ , u ₅ , u ₇ , you get output like y ₁ , y ₂ , y ₃ , y ₅ , y ₇ . From the fifth batch, you can see that the output tracks the reference trajectory almost accurately. On the other hand, the inputs u ₁ , u ₂ , and u ₃ are in a state in which the range of Δu is limited by constraints.

Re-modeling the target process using input / output variables that accurately track the reference trajectory is indicated by the * line in FIG. 11. Although there are many errors with the initial modeling, using the model predictive control of the present invention, As shown in the figure, robust tracking and model error can be achieved.

Application Example 4. Batch Type

In some small plants, volatile products are recovered from the liquid solution via batch distillation. The mixture is placed in a distiller or reboiler and heat is supplied through a coil or through the vessel wall to vaporize some of the liquid to reach the boiling point. However, since it is not possible to control the purity, it is controlled through a batch process with reflux to increase the purity and to achieve the desired purity at the desired time. In this case, the model-based predictive control method of the present invention for the batch process is used.

Application Example 5. Heating Process

The industry requires heating in advance before the flow or material entering the majority of processes, which can be classified as heating, batch operation, or batch processes before heating. . Therefore, after the flow or material is precisely heated to the desired temperature in the main process, and then transferred to the main process, an accurate solution is obtained using the control method of the present invention and applied to the control variable, and then heated to the desired temperature.

Application Example 6. Chemical Vapor Deposition

The silicon epitaxy process, which is one of the semiconductor processes, grows a single crystal film on a silicon wafer and is an important process for fabricating microelectronic circuits. At this time, the main method to be used is to vapor-phase deposition by injecting a silicon wafer into a heating furnace, such as a chemical vapor deposition furnace induction heating horizontal reactor or induction heating vertical heating furnace to form a single crystal film. The properties of the single crystal film produced by this process depend on the thickness of the crystal film, the crystal structure bonding, the resistance, and the like. The integrity of the substrate crystals; Until now, the size of the silicon wafer was small so that it could be overcome by the device construction method. However, in the situation where the size of the silicon wafer is increased due to the development of technology, the temperature uniformity on the silicon wafer related to the defective rate of wafer processing becomes a problem. . So control is needed, and this epitaxy process is a typical batch process that follows the reference temperature trajectory and controls the temperature of the entire surface to be uniform.

Application Example 7. Robot Motion Control

Currently used in automobile manufacturing plants and electronics production processes, robots are still used only for one task such as screwing, picking and moving objects, and used only for repetitive tasks in various assembly lines. . The model-based predictive control of the present invention can be applied as an example of an industrial robot or an iterative process that always performs the same reference trajectory in accordance with the moving time of the assembly line.

Application Example 8. Semiconductor Single Crystal Growth Process

This process grows silicon crystals, which are mainly used in the semiconductor process, and the importance is being emphasized as the semiconductor industry is in the spotlight.

This process dissolves the silicon into a liquid state and then grows the silicon as pure crystals that are not only uniform in size but also free of impurities by controlling the temperature of the silicon liquid and the strength of the magnetic field that is artificially walked around. Therefore, the relationship between the temperature of the silicon liquid, the magnetic field, and the rotational speed of the disc becomes the control input variable, and the diameter and purity at each point of the grown silicon crystal become the output variable. As the same operation is repeated, the control input variable value can be obtained to grow crystals with a constant desired diameter.

Claims (14)

A model-based predictive control system suitable for control of a batch process or an iterative operation process that can be algebraically modeled, comprising: an estimator for estimating an output variable by measuring an output value from a target process, and an output variable estimated by the estimating means; A predictor that predicts the control error in the future, a storage means for storing the input / output variables of the past batch and the input / output variables before the time of the current batch, and inputting the prediction and control section, the constraint, the reference trajectory value, and the objective function. An objective based on an input means, a value predicted by the predictor, input / output variables of past and current ash stored in the storage means, prediction and control intervals, constraints, and reference trajectory values inputted by the input means; Model-based predictive control system with calculation means for calculating the current time input variable of the current batch with a minimum of functions . The model-based prediction control system according to claim 1, wherein the model Gk of the target process is a lower triangular matrix consisting of time-varying pulse response coefficients obtained through a model recognition process. The model-based predictive control system according to claim 1, wherein the input variable calculating means uses quadratic programming. 2. The model-based predictive control system of claim 1, wherein the calculation means is calculated to apply the first term of the input variable to the metabolic process. The model-based prediction control system of claim 1, wherein the input / output variable has a convergence in which the trajectory of the input / output variable enters a reference input / output trajectory value as the number of batch operations increases. 2. The model-based predictive control system of claim 1, wherein the objective function comprises an input variable of a current time of a current running batch and a second type of output variable to be obtained as the input variable is applied to a target process. Model-based predictive control method suitable for control of batch process or iterative operation process that can be algebraically modeled, I / O variables of previous batch and I / O variables before current point of current running batch, prediction and control section, constraints, criteria Inputting a trajectory value and an objective function, estimating an output variable by measuring an output value from a target process, a predictor for predicting a control error to be generated based on the estimated output variable, and a secondary objective function. Constructing, checking the input constraints, and calculating the value of the secondary objective function based on the predicted value, the input / output variables of the past ash and the current ash, the input prediction and control interval, and the reference trajectory value. Calculating a difference Δu _k (t) between the input variable of the current pollen that is minimized and the input variable of the past ash, and using the calculated Δu _k (t) Calculating a current time input variable u _k (t) of the current batch, and applying the calculated input variable to a target process. 8. The method of claim 7, wherein the estimating step includes a first estimation step of removing a noise component from an output value output from a target process, and a step of correcting the first estimated value. 8. The method of claim 7, wherein the calculating of the input variable at the current point in time of the current batch uses secondary programming. 8. The method of claim 7, wherein the target process is a lower triangular matrix as follows.

h (t ₁ , t ₂ ): Pulse response coefficient of time t ₂ obtained through model recognition at time t ₁ . 8. The method of claim 7, wherein applying the input variable to the target process applies only the first term of the calculated u _k (t) to the target process. 8. The method of claim 7, wherein the objective function comprises an input variable of a current time of a current running batch and a secondary form of an output variable to be obtained as the input variable is applied to a target process. 8. The method of claim 7, wherein constructing the quadratic objective function comprises output errors from the modeling and predicted output variables.

To convert to the first function form of the difference Δu _k (t) between the input variable of the current batch and the input variable of the previous batch, and convert to the quadratic function form of Δu _k (t). Model-based predictive control method. 10. The method of claim 9, wherein the secondary programming comprises: reconstructing the determinant after reconstructing the constraint into a mathematical form, finding a Δu _k (t) in which the value of the objective function is minimized while satisfying the given constraint; Checking whether or not the found? U _k value is the minimum of the objective function, and if the value found in the verification step is not minimum, u _k (t) which minimizes the value of the objective function while satisfying the given constraint. Model-based predictive control method comprising the step of returning to the step of finding.

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