JP6088399B2 - Control method and control apparatus - Google Patents

Description

  The present invention relates to a control method and a control apparatus using a crystallization process model that models a batch cooling crystallization process.

  The crystallization process is characterized in that fine crystals can be obtained with less energy and is widely used. When a batch cooling crystallization process in which various types of crystals are produced in a stirred crystallizer is controlled, it is required to precisely control the crystallization temperature that defines the quality immediately after the first batch operation. For this reason, the inventor has proposed a B2B (Batch to Batch) control system based on a process model (see Non-Patent Document 1).

Morimasa Ogawa, “Model-based B2B Control of Batch Polymerization Process”, Transactions of the Society of Instrument and Control Engineers, Vol. 46, no. 3, p. 139-148, 2010

  In the B2B control system disclosed in Non-Patent Document 1, PID control is adopted for reaction temperature control which is the main body of batch reaction process control. The PID parameters will be adjusted empirically through batch operation. However, since the process nonlinearity is strong and the process dynamics change greatly with the batch elapsed time, it is difficult to appropriately adjust the PID parameters by empirical rules alone.

  In addition, the B2B control system disclosed in Non-Patent Document 1 targets the batch reaction process, does not support ramp-like target value changes unique to the batch cooling crystallization process, and is disclosed in Non-Patent Document 1. The applied B2B control system cannot be directly applied to the batch cooling crystallization process. As described above, the B2B control system that controls the batch cooling crystallization process has not been established as a practical and general control method.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a control method and a control device of a B2B control method that are more practical and general than conventional ones.

The control method of the present invention comprises a combination of a crystallization temperature T _c of a raw material in a crystallizer, a refrigerant inlet temperature T _wi used for cooling the raw material, a refrigerant outlet temperature T _wo, and a refrigerant circulation flow rate f _w. Using actual data as series data as input to the crystallization process model that models the batch cooling crystallization process, the model parameters of the crystallization process model are adjusted, and a transfer function model that linearly approximates the crystallization process model is created. A model adjustment step to be obtained, a control parameter of the first controller for calculating the first manipulated variable so that the crystallization temperature T _c matches the crystallization temperature target value, the transfer function model and a predetermined control parameter using a setting rule, Andashi the crystallization temperature T _c after the steady-state control deviation and crystallization temperature target value for the crystallization temperature target value which changes in a ramp shape is shifted to a constant value from the ramp-shaped change A control parameter adjustment step of adjusting the over preparative tolerance as adjustment measure, the feed-forward compensation rule predetermined crystallization temperature coolant inlet temperature set point as T _c is consistent with the desired crystallization temperature target value A target value change amount calculation step for obtaining a time pattern of the change amount of the crystallization temperature, and a crystallization temperature target value change rate gradually during a predetermined time before and after the switching point at which the crystallization temperature target value switches from a ramp-like change to a constant value. In accordance with the elapsed time of the batch based on the undershoot suppression step of giving the crystallization temperature target value to the first controller with a slow change speed and the change time pattern of the refrigerant inlet temperature target value. A change amount of the refrigerant inlet temperature target value is output, and a sum of the change amount of the refrigerant inlet temperature target value and the first manipulated variable is used as a refrigerant inlet temperature target value. And over-forward compensation step, that as the refrigerant inlet temperature T _wi coincides with the coolant inlet temperature set point second controller calculates the second manipulated variable and a control step of adjusting the injection amount of the refrigerant It is a feature.

Also, one configuration example of the control method of the present invention is characterized in that a PI-D algorithm is selected in advance as a control algorithm of the first controller.
Further, in one configuration example of the control method of the present invention, the control parameter setting rule is that the maximum undershoot value of the crystallization temperature T _{c is} a condition that keeps the steady control deviation with respect to the ramp-shaped target value change at a specified value. Either a PI setting rule for obtaining a PI parameter so as to be closest to the undershoot allowable value, or a PID setting rule for converting a PI parameter obtained by the PI setting rule into a PID parameter.

The control device of the present invention also includes a first controller that calculates a first manipulated variable so that the crystallization temperature T _c of the raw material in the crystallizer coincides with the target crystallization temperature in the batch cooling crystallization process. And a second controller for calculating the second manipulated variable so as to adjust the refrigerant injection amount so that the refrigerant inlet temperature _Twi used for cooling the raw material coincides with the refrigerant inlet temperature target value, and batch cooling crystallization A model storage means for storing in advance a crystallization process model expression that models the process, and a set of a crystallization temperature T _c , a refrigerant inlet temperature T _wi , a refrigerant outlet temperature T _wo, and a refrigerant circulation flow rate f _w Model adjustment means for adjusting the model parameters of the crystallization process model using actual data as series data as an input of the crystallization process model, and obtaining a transfer function model that linearly approximates the crystallization process model, and the transmission Crystallization after the steady-state control deviation from the ramp-like crystallization temperature target value and the crystallization temperature target value have shifted from the ramp-like change to a constant value using several models and predetermined control parameter setting rules The control parameter adjusting means for adjusting the control parameter of the first controller using the undershoot allowable value of the temperature T _c as an adjustment index, and a predetermined feedforward compensation law, the crystallization temperature T _c becomes a desired crystal. A target value change amount calculating means for obtaining a time pattern of the change amount of the refrigerant inlet temperature target value so as to coincide with the crystallization temperature target value, and before and after the switching point at which the crystallization temperature target value is switched from a ramp-like change to a constant value. The crystallization temperature target value change rate is moderated for a certain period of time, and the crystallization temperature target value with the gradual change rate is given to the first controller. Based on the time pattern of the chute suppression means and the change amount of the refrigerant inlet temperature target value, the change amount of the refrigerant inlet temperature target value corresponding to the batch elapsed time is output. Feedforward compensation means for providing the second controller with the addition result of the operation amount of 1 as the refrigerant inlet temperature target value.

According to the present invention, the batch operation result data is used as an input to the crystallization process model, the model parameters of the crystallization process model are adjusted, and the transfer function model and a predetermined control parameter setting rule are used to change into a ramp shape. The adjustment of the steady control deviation with respect to the target crystallization temperature value and the permissible undershoot value of the crystallization temperature T _c after the target crystallization temperature value has shifted from a ramp-like change to a constant value is used as an adjustment index. The control parameter is adjusted, and the time pattern of the change amount of the refrigerant inlet temperature target value is obtained by a predetermined feedforward compensation law so that the crystallization temperature T _c matches the desired crystallization temperature target value, and the refrigerant inlet An addition result of the change amount of the temperature target value and the first operation amount that is the output of the first controller is given to the second controller as the refrigerant inlet temperature target value. did. Further, in the present invention, the change rate of the crystallization temperature target value is made slow for a certain time before and after the switching point at which the crystallization temperature target value is switched from the ramp-like change to the constant value. As described above, in the present invention, it is possible to achieve high tracking performance with respect to the ramp-like target value change unique to the batch cooling crystallization process, so that the control of the B2B control method that is superior in practicality and generality compared to the past. A method can be realized.

  Moreover, in this invention, the control suitable for a batch cooling crystallization process can be performed by selecting a PI-D algorithm beforehand as a control algorithm of a 1st controller.

Further, in the present invention, under conditions to maintain the steady-state control deviation for the ramp target value change the specified value, PI setting to obtain the PI parameters as undershoot maximum value of the crystallization temperature T _c approaches most undershoot tolerance The control parameter adjustment rule suitable for the batch cooling crystallization process can be realized by using either the PID setting rule for converting the PI parameter obtained by the PI setting rule or the PID parameter into the PID parameter as the control parameter setting rule. it can.

It is an instrumentation diagram of a batch cooling crystallization process according to an embodiment of the present invention. It is a block diagram which shows the structure of the control apparatus which concerns on embodiment of this invention. It is a flowchart which shows operation | movement of the control apparatus which concerns on embodiment of this invention. It is a block diagram of the control system which concerns on embodiment of this invention. It is a figure which shows an example of the time pattern of the variation | change_quantity of the refrigerant inlet temperature target value in embodiment of this invention. It is a figure which shows one example of the time pattern of the crystallization temperature target value in embodiment of this invention. It is a figure which shows the example of the control amount response with respect to crystallization temperature target value change. It is a figure which shows one example of the crystallization temperature target value which the undershoot suppression part of the control apparatus which concerns on embodiment of this invention outputs. It is a figure which shows the PID control simulation result with respect to the crystallization temperature target value which the undershoot suppression part of the control apparatus which concerns on embodiment of this invention outputs. It is a figure which shows the example of the change of a crystallization heat and an overall heat transfer coefficient. It is a figure which shows the control simulation result of the control system which concerns on embodiment of this invention.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is an instrumentation diagram of a batch cooling crystallization process according to an embodiment of the present invention.
In the batch cooling crystallization process, the raw material liquid is quantitatively charged into the stirring crystallizer 100 via the valve 104, heated to a predetermined temperature, and then at a constant speed according to the time pattern (target value trajectory) of the crystallization temperature target value. Cooling. The stirring crystallizer 100 includes a jacket 101 for heating and cooling, a temperature sensor 102 for measuring the crystallization temperature of the raw material liquid, and a stirrer 103 for stirring the raw material liquid.

  The raw material liquid exceeds the saturation concentration line and crystal precipitation starts, and is maintained for a certain period of time at a temperature in a metastable region where stable crystallization occurs. Thereafter, while maintaining the metastable region, the crystallization temperature is further lowered at a constant rate to grow and stabilize the crystal. After the lapse of the specified time, the crystallization operation is terminated, and the crystallization liquid is extracted from the stirring crystallizer 100 through the valve 105. The series of batch crystallization times is approximately several hours to one day.

The raw material liquid is cooled by a refrigerant (cold water) circulating at a constant flow rate through a jacket 101 provided in the stirring crystallizer 100. The refrigerant is supplied from the inlet side pipe 106 to the jacket 101 and discharged to the outlet side pipe 107. A part of the refrigerant discharged to the outlet side pipe 107 is cooled by a chiller 111, and the rest is returned to the inlet side pipe 106. The inlet side pipe 106 is provided with a temperature sensor 108 for measuring the refrigerant inlet temperature _Twi , and the outlet side pipe 107 is provided with a temperature sensor 109 for measuring the refrigerant outlet temperature _Two . Further, the inlet pipe 106, a flow sensor 110 for measuring the circulating flow rate f _w of the refrigerant is disposed.

  The control device 113 performs the refrigerant inlet temperature control and the crystallization temperature control so that the refrigerant inlet temperature matches the time pattern of the refrigerant inlet temperature target value and the crystallization temperature matches the time pattern of the crystallization temperature target value. Perform cascade control. The control device 113 also has a feed-forward control function that changes the target value of the refrigerant inlet temperature in accordance with the batch elapsed time. In order to change the crystallization temperature, the refrigerant inlet temperature is changed by adjusting the amount of refrigerant injected into the jacket 101. Thereby, the crystallization temperature can be controlled. Note that steam is injected into the jacket 101 when the raw material liquid is heated. By controlling the amount of steam injected into the jacket 101, the temperature during heating can be controlled.

FIG. 2 is a block diagram showing the configuration of the control device 113, and FIG. 3 is a flowchart showing the operation of the control device 113. The control device 113 has a model storage unit 1 for storing a crystallization process model, which is a dynamic characteristic model of the batch cooling crystallization process, and the batch operation performance data as an input to the crystallization process model, and sets model parameters of the crystallization process model. A model adjustment unit 2 that adjusts and obtains a transfer function model that linearly approximates the crystallization process model, a feedforward control execution unit 3 (feedforward compensation means) that executes feedforward control, and a transfer function model are predetermined. A control parameter adjustment unit 4 that adjusts a control parameter (PID parameter) for cascade control using a control parameter setting rule, a cascade control execution unit 5 that executes cascade control, and a predetermined feedforward compensation rule Accordingly, the crystallization temperature T _c is consistent with the desired crystallization temperature target value In addition, the refrigerant inlet temperature time pattern setting unit 6 that obtains the time pattern of the change amount of the refrigerant inlet temperature target value, and the crystallization temperature in a certain time before and after the switching point at which the crystallization temperature target value is switched from the ramp-like change to the constant value. There is provided an undershoot suppression unit 7 that moderates the change rate of the target value and provides the cascade control execution unit 5 with the crystallization temperature target value with the change rate being moderated.

  Before starting the batch operation, the model adjustment unit 2 adjusts the model parameters of the crystallization process model using the batch operation result data, and linearizes the crystallization process model to convert it into a transfer function model (see FIG. 3 step S1).

The control parameter adjusting unit 4 uses a transfer function model and a predetermined control parameter setting rule, and the steady control deviation and the crystallization temperature target value with respect to the crystallization temperature target value changing in a ramp shape are constant from the ramp shape change. and undershoot tolerance of crystallization temperature T _c after the transition to the value as an adjustment indicator to adjust the control parameters for cascade control (PID parameters) (Fig. 3 step S2).

The refrigerant inlet temperature time pattern setting unit 6 determines a time pattern {t, Δu _f } of the change amount of the refrigerant inlet temperature target value according to a predetermined feedforward compensation law (step S3 in FIG. 3).
When the batch operation for controlling the batch cooling crystallization process is started, the undershoot suppression unit 7 starts the crystallization temperature target value r ₁ at a certain time before and after the switching point at which the ramp-like change is changed from the ramp-like change. to moderate the rate of change crystallization temperature target value r _1, and outputs the the crystallization temperature target value r ₁ 'moderate the change speed cascade control execution unit 5 (FIG. 3 step S4).

Feedforward control execution unit 3 executes a feedforward control for outputting a change amount Delta] u _f of the refrigerant inlet temperature target value depending on the time pattern change amount of the refrigerant inlet temperature set point {t, Δu _f} (Fig. 3 step S5), and cascade control execution unit 5, the cascade control so that the refrigerant inlet temperature T _wi refrigerant inlet temperature target value r ₂ consistent with and crystallization temperature T _c matches the crystallization temperature target value r ₁ '( PID control) is executed (step S6 in FIG. 3). The processes in steps S4 to S6 as described above are executed every batch elapsed time t at regular intervals until the batch cooling crystallization process is completed (YES in step S7 in FIG. 3).

FIG. 4 is a block diagram of the control system of the present embodiment. F in FIG. 4 is a feedforward controller realized by the feedforward control execution unit 3. The feedforward control execution unit 3 refers to the time pattern {t, Δu _f } of the change amount of the refrigerant inlet temperature target value stored in the refrigerant inlet temperature time pattern setting unit 6 described later, and the current batch elapsed time t and outputs the change amount Delta] u _f of the refrigerant inlet temperature target value corresponding to. FIG. 5 shows an example of the time pattern {t, Δu _f } of the change amount of the refrigerant inlet temperature target value. The time pattern of the change amount of the refrigerant inlet temperature set point as is the time-series data consisting of a set of the change amount Delta] u _f batch elapsed time t and the coolant inlet temperature target value.

4, C ₁ is a crystallization temperature controller (PI-D controller) realized by the cascade control execution unit 5, C ₂ is a refrigerant inlet temperature controller (PI-D controller) also realized by the cascade control execution unit 5, P ₂ is a refrigerant inlet temperature process, P ₁ is a crystallization temperature process, and d ₁ and d ₂ are disturbances.

A crystallization temperature target value r ₁ ′ is given to the crystallization temperature controller C ₁ . FIG. 6 shows an example of the time pattern {t, r ₁ } of the crystallization temperature target value. As described above, the time pattern of the crystallization temperature target value is time-series data including a set of the batch elapsed time t and the crystallization temperature target value r ₁ . As shown in FIG. 6, the crystallization temperature target value r ₁ is continuously reduced at a constant change rate v _r after maintaining a constant value, it is preset to indicate a pattern such again stabilized at a constant value ing. Undershoot suppression unit 7 is output to the crystallization temperature target value r ₁ crystallization based on the temperature target value r ₁ ', the operation of the undershoot suppression unit 7 will be described later.

The crystallization temperature controller C ₁ calculates the manipulated variable u ₁ so that the crystallization temperature T _c matches the crystallization temperature target value r ₁ ′. And the operation amount u ₁ and the coolant inlet temperature set point of the change amount Delta] u _f are added, the addition result is provided to the refrigerant inlet temperature controller C ₂ as a refrigerant inlet temperature target value r _2. The refrigerant inlet temperature controller C ₂ calculates the operation amount u ₂ so that the refrigerant inlet temperature T _wi and the refrigerant inlet temperature target value r ₂ coincide. The opening degree of the valve 112 shown in FIG. 1 is determined according to the operation amount u _2, and the amount of refrigerant injected into the jacket 101 is controlled.

  Next, the operation of the model adjustment unit 2 will be described in more detail. In this embodiment, PID is used as an algorithm for cascade control of refrigerant inlet temperature control and crystallization temperature control. In order to design control by PID, an operation amount (refrigerant inlet temperature) and a control amount (crystallization temperature) are used. A linear dynamic characteristic model that represents the relationship between The model adjustment unit 2 adjusts model parameters of such a linear dynamic characteristic model. Specifically, the model adjustment unit 2 adjusts the model parameters of the crystallization process model using the batch operation result data, and linearizes the crystallization process model to convert it into a transfer function model (step S1 in FIG. 3). ).

The dynamic model of the batch cooling crystallization process is derived from the energy balance of the crystallization liquid and refrigerant under the following assumptions.
(A) The crystallization liquid in the crystallizer is completely mixed with a stirrer.
(B) Heat of stirring and heat radiation from the crystallizer surface can be ignored.
(C) The heat transfer area of the jacket is constant.
(D) Since the heat capacity of the crystallizer wall is very small, it is ignored.
(E) Cascade control of crystallization temperature The refrigerant inlet temperature control of the secondary loop has sufficiently fast target value response characteristics and can ignore dynamic characteristics.

Assuming that the crystallization temperature is T _c , the refrigerant average temperature is T _w , the refrigerant inlet temperature is T _wi , and the refrigerant outlet temperature is T _wo , the energy balance model is as follows.

In formulas (1) and (2), c _c is the specific heat of the crystallization liquid, W _c is the amount of residence in the crystallizer, c _w is the specific heat of the refrigerant, W _j is the amount of residence in the jacket, and Q _c is the crystallization. The amount of heat generated due to heat (crystallization heat amount), Q _w1 is the jacket heat removal amount, and Q _w2 is the refrigerant heat removal amount. The amount of heat generated by crystallization (the amount of heat of crystallization) Q _c acts as an uncertain disturbance. Note that the refrigerant circulation flow rate f _w is kept constant, and the temperature difference between the inlet and the outlet of the jacket 101 is small, so the refrigerant average temperature T _w = (T _wi + T _wo ) / 2. The jacket heat removal amount Q _w1 and the refrigerant heat removal amount Q _w2 can be expressed as follows.
Q _w1 (t) = UA (T _c (t) −T _w (t)) (3)
Q _w2 (t) = c _w f _w (T _wo (t) −T _wi (t))
= 2c _{w fw} (T _w (t) −T _wi (t)) (4)

  In the equations (3) and (4), U is the overall heat transfer coefficient of the jacket 101, and A is the heat transfer area of the jacket 101. From equations (1) to (4), the energy balance of the crystallization liquid and the refrigerant can be expressed by the following equation of state model.

The model storage unit 1 stores in advance formulas (5) and (6) of the state equation model (crystallization process model 10) as described above.
The model adjusting unit 2 gives the batch operation result data as an input of the crystallization process model 10 to obtain the overall heat transfer coefficient U which is a model parameter, and the calorific value Q _c which is an uncertain disturbance. The batch operation record data used in the present embodiment is record data (previous record data) when a crystallization liquid of the same type as the crystallization liquid to be generated by the stirring crystallizer 100 is produced in the past. elapsed time t, crystallization temperature T _c, the refrigerant inlet temperature T _wi, coolant outlet temperature T _wo, time-series data of the circulating flow _{f w {t, T c,} T wi, T wo, f w} is. Such batch operation result data is given as an input of the crystallization process model 10, and the model parameters are adjusted. Note that known values are used for the heat transfer area A, the specific heat c _{c of the} crystallization liquid, the crystallizer internal retention amount W _c , the refrigerant specific heat c _w , and the jacket internal retention amount W _j .

Next, the model adjustment unit 2 obtains a transfer function model for crystallization temperature control from the crystallization process model 10 for which parameter adjustment has been completed. This transfer function model represents the dynamic characteristics of the manipulated variable u ₂ (refrigerant inlet temperature) and the controlled variable y (crystallization temperature T _c ). The state quantity (refrigerant average temperature T _w ) is x, and the operation quantity u ₂ is made dimensionless in the measurement range R _u , the control quantity y measurement range R _y , and the state quantity x measurement range R _x (= R _y ). When the manipulated variable u ₂ , the controlled variable y, and the state quantity x are used, the following relationship is established.
T _wi = R _u u ₂ (7)
T _c = R _y y (8)
T _w = R _x x (9)

  At this time, the transfer function model P (s) is as follows. Note that s is a Laplace operator.

The steady gain K _p and the time constants T _p1 and T _p2 are as follows. Here, a time constant that governs the dynamic characteristics of the batch cooling crystallization process is T _p1 (>> T _p2 ).

Equation (11), constants T _1, T ₂ of the formula _{(12), K x12, K} x21, K u are each expressed as follows.

Thus, the model adjusting unit 2 can linearize the crystallization process model 10 sequentially to obtain a transfer function model. Note that known values are used for the measurement ranges R _u , R _y , and R _x (= R _y ).
Table 1 shows numerical examples of operating conditions and transfer function model parameters of the batch cooling crystallization process. It can be seen that when R _y = R _u , K _p = 1 at all times, and the long time constant T _p1 dominates the dynamic characteristics of the batch cooling crystallization process, and T _p2 (<< T _p1 ) can be ignored.

Next, the crystallization temperature controller C ₁ realized by the cascade control execution unit 5 will be described. In the present embodiment, the PI-D algorithm is selected in advance as the crystallization temperature control algorithm. Hereinafter, the reason for selecting the PI-D algorithm will be described.
Here, the target value is r (s), the control amount is y (s), the control deviation is e (s) = r (s) -y (s), the operation amount is u (s), and the PID parameter is {K _{Let c} , T _i , T _d }. At this time, the PID controller C (s) is determined as follows.

The target value filter F (s) of the PID algorithm is as follows:
F (s) = 1 (19)
Further, the target value filter F (s) of the PI-D algorithm is as shown in Expression (20), and the target value filter F (s) of the I-PD algorithm is as shown in Expression (21).

  The target value response of PID control is expressed by the following equation.

Target value changing speed v _r of the ramp-shaped target value change _{r (s) = v r /} s stationary control deviation e of the PID algorithm for ² (∞) is expressed by the following equation.

  Similarly, the steady control deviation e (∞) of the PI-D algorithm is as shown in Expression (23), and the steady control deviation e (∞) of the I-PD algorithm is as shown in Expression (24).

Thus, the steady control deviation of the I-PD algorithm is very large compared to the PID algorithm and the PI-D algorithm. For example, when K _p = 1.0% /%, K _c = 10% /%, T _i = 10 min, v _r = −20% / 90 min, steady control deviation e (∞ of PID algorithm and PI-D algorithm ) = − 0.22%, the steady control deviation e (∞) of the I-PD algorithm is −2.44%, which is 11 times as large. For this reason, the most frequently used I-PD algorithm in process control cannot be used for crystallization temperature control. As an algorithm for controlling the crystallization temperature, it is preferable to apply a PI-D algorithm in which the differential operation does not act on the target value. When the differential gain is 1 / γ, the practical PI-D controller is expressed by the following equation.

Thus, in this embodiment, a PI-D controller as crystallization temperature controller C _1. The PID parameter of the crystallization temperature controller C ₁ is adjusted by the control parameter adjustment unit 4. Here, also for the coolant inlet temperature controller C _2, it is used PI-D controller. The PID parameter of the refrigerant inlet temperature controller C ₂ is assumed to be adjusted in advance.

Next, the operation of the control parameter adjustment unit 4 will be described. A model base setting rule frequently used in process control is an IMC (Internal Model Control) method. The IMC method is a method for uniquely determining a PID set value by defining a desired control amount response to a step-like target value change. Since the integration time is set to T _i = T _p1 + T _p2 , the steady control deviation with respect to the ramp target value change becomes very large. Therefore, the IMC method cannot be applied to the crystallization temperature control in which the ramp target value is always changed. In the present embodiment, a PID adjustment index suitable for crystallization temperature control is determined, and a model-based PID setting rule that satisfies this PID adjustment index is introduced.

In this embodiment, crystals as the adjustment indication of precipitation temperature control, and the steady-state control error e _r for crystallization temperature target value r ₁ which changes in a ramp shape, the crystallization temperature target value r ₁ is a constant value from the ramp-like change to define two parameters undershoot tolerance e _u of the controlled variable y after the transition (crystallization temperature T _c) to. Stationary control deviation e _r is while the crystallization temperature target value r ₁ is changed in a ramp form, which is the control deviation when sufficient time has elapsed. After the target value change is completed and the process shifts to the constant value control, it is inevitable that the control amount y is excessive (undershoot). _eu is the maximum allowable value of the undershoot. FIG. 7 shows an example of the control amount response to this crystallization temperature target value change. According to FIG. 7, the existence of steady control deviation and undershoot can be confirmed. T _r in FIG. 7 crystallization temperature switching point of the target value r _1, the u _L is undershoot lower limit.

In the transfer function model shown in Expression (10), a short time constant T _p2 (<< T _p1 ) can be ignored, and thus approximates to the first-order lag characteristic. For this reason, the differential operation of the PI-D algorithm is not necessary, and the PI setting rule can be used as the PID parameter setting rule. Hereinafter, this PI setting rule will be described.

The steady-state control deviation e _r for the lamp-shaped target value change in the conditions keeping the prescribed value, so that undershoot maximum value is as close as possible to the allowable value e _u, determine the PI parameters. Derivation of the PI parameters, the steady-state control deviation e _r and equality constraints as an optimization problem of minimizing the quadratic form of the difference between the undershoot maximum value and its allowable value e _u, formula as follows Can be
_{{K c, T i} =} argmin (e max -e u) 2 ··· (26)

e _max = max {r ₁ (t) −y (t)} (t ≧ t _r ) (28)
In this way, the control parameter adjusting unit 4 uses the transfer function model obtained by the model adjusting unit 2 and the equations (26) to (28), so that the proportional gain K _c that is the PI parameter of the crystallization temperature controller C ₁ The integration time T _i can be obtained (step S2 in FIG. 3). As described above, in the PI setting rule, the differential time T _d is set to zero. Note that crystallization for precipitation temperature target value r ₁ can be used time pattern {t, r _1} predetermined value at the crystallization temperature target value, the target value change rate v _r also a known value However, in order to obtain the undershoot maximum value e _max of the equation (28), the control amount y (crystallization temperature T _c ) after the crystallization temperature target value r ₁ shifts to a constant value (t ≧ t _r ). Response is required. Hereinafter, how to obtain the response of the control amount y will be described.

  First, the equation of the transfer function model shown in Equation (10) is approximated to the equation of the first-order lag characteristic.

  A PI controller C (s) represented by the following equation is used.

The crystallization temperature target value r ₁ is given as follows.

Equation (31) shows the target crystallization temperature r ₁ when changing to a ramp shape (0 ≦ t <t _r ), and equation (32) is obtained after shifting to a constant value (t ≧ t _r ). shows the crystallization temperature target value r _1. At this time, the target value response characteristic W _c (s) is expressed by the following equation. Since the PI controller is used, the target value filter F (s) = 1.

The coefficients b ₁ , b ₀ , a ₁ and a ₀ are as follows.

  The conjugate complex root or real root of the characteristic equation is as follows. Since the set values are designed so that the control system is stable, α, β> 0.

  The controlled variable response is given by the following equation when the characteristic equation has a stable conjugate complex root.

Equation (39) shows the controlled variable y when the crystallization temperature target value r ₁ changes in a ramp shape (0 ≦ t <t _r ), and Equation (40) shows that the crystallization temperature target value r ₁ is constant. The control amount y after shifting to the value (t ≧ t _r ) is shown. In addition, the control amount response is as follows when the characteristic equation has a stable real root.

Equation (41) shows the controlled variable y when the crystallization temperature target value r ₁ changes in a ramp shape (0 ≦ t <t _r ), and Equation (42) shows that the crystallization temperature target value r ₁ is constant. The control amount y after shifting to the value (t ≧ t _r ) is shown. The second term on the right side of the equations (39) and (41) indicates the steady control deviation for the ramp-shaped target value change. The coefficients c, d, and φ are as follows.

  As described above, the control parameter adjustment unit 4 calculates the control amount y used in Expression (28) by Expression (40), Expression (43) to Expression (45), or Expression (42) to Expression (45). can do.

In some cases, the short time constant T _p2 of the transfer function model shown in Expression (10) cannot be ignored. In this case, the following PID setting rule is used instead of the PI setting rule as the PID parameter setting rule, and the following series compensation algorithm is used.

Hereinafter, “˜” attached to the head of the mathematical expression is referred to as a tilde. If the differential time tilde T _d is set to T _p2 , the first-order lag characteristic with a short time constant can be zero-zero canceled by the differential operation term of the controller. As a result, the proportional gain K _c obtained by the PI setting rule described above can be used as the proportional gain tilde K _c and the integration time T _i can be used as the integration time tilde T _i as it is. And it can convert into the parameter of a parallel compensation type PID algorithm by following Formula.

Thus, the control parameter adjustment unit 4 obtains the proportional gain K _c and the integration time T _i by using the transfer function model obtained by the model adjustment unit 2 and the equations (26) to (28), and further calculates the proportionality. The gain K _c is set as a proportional gain tilde K _c , and the integration time T _i is set as the integration time tilde T _i , and the proportional gain K _c that is a PID parameter of the crystallization temperature controller C ₁ is integrated by the equations (47) to (49). Time T _i and differential time T _d can be obtained (step S2 in FIG. 3).

Examples of crystallization temperature transfer function parameters and PID adjustment indices are shown in Table 2, and the crystallization temperature target value r ₁ is switched at the time t _r = 90 min, the target value changing rate v _r = −20 ° C./90 min = −20%. Table 3 shows examples of PID parameters obtained by the PI setting rule and the PID setting rule at / 90 min.

Next, the operation of the refrigerant inlet temperature time pattern setting unit 6 will be described. The refrigerant inlet temperature time pattern setting unit 6 includes a target value change amount calculation unit 60 and a time series table storage unit 61.
When the target value changing speed v _r of the crystallization temperature control and, more time differentiating the state equation model for dT _c (t) / dt, it is found equal to even v _r change rate of the refrigerant average temperature T _w. That is, the following equation is established.

Conditions applied to the state equations of the equation (50), to obtain the target value trajectory tilde T _wi coolant inlet temperature T _wi.

As the target value trajectory tilde T _c of crystallization temperature can be realized in combination with the feedback control, feedforward compensation constituting the control system to provide a target value change amount Delta] u _f of the refrigerant inlet temperature control. That is, the feedforward compensation law is defined as follows:

Target value change amount calculation unit 60, the feed forward compensation law of Formula (53), the crystallization temperature T _c is the time pattern {t, tilde T _c} of the desired crystallization temperature target value refrigerant inlet to match the A time pattern {t, Δu _f } of the change amount of the temperature target value is determined. The time series table storage unit 61 stores a time pattern {t, Δu _f } of the change amount of the refrigerant inlet temperature target value determined by the target value change amount calculation unit 60.

Under the operating conditions shown in Table 1, when the crystallization temperature target value switching time t _r = 1.5 h and the target value changing speed v _r = −20% / 1.5 h, the refrigerant inlet temperature target value by feedforward compensation the amount of change Δu _f is as follows.

Next, the operation of the undershoot suppressing unit 7 will be described. It has already been described that the undershoot occurs in the controlled variable y (crystallization temperature T _c ) after the crystallization temperature target value r ₁ shifts from a ramp-like change to a constant value. To obtain higher control performance, it is necessary to minimize undershoot. In this embodiment, the PID control system with PID parameters by PID setting rules as described above, the crystallization temperature change rate of the target value r ₁ at a predetermined time before and after the crystallization temperature target value r ₁ of the switching time t _r By relaxing, the undershoot of the controlled variable y (crystallization temperature T _c ) is minimized.

  A method has already been proposed to determine a modified target value that optimizes the control performance, taking into account the constraints on the manipulated variable and state variables of the closed-loop system (referring to the documents “Shunji Sugie, Hiroyuki Yamamoto,“ Considering state and input constraints. Target value generation of closed loop system ", Transactions of the Society of Instrument and Control Engineers, Vol. 37, No. 9, 849/855, 2001"). However, the technique disclosed in this document is that (1) the objective is to improve the control performance in a range that satisfies the constraint conditions, (2) the control target is a positioning servo system, and (3) the desired target. The present embodiment differs from the present embodiment in that the value trajectory is limited to a step shape, (4) a step-like signal in which the shape of the correction target value changes in small increments, and (5) no PID control is used. Different.

The crystallization temperature target value r ₁ defined in advance by the time pattern {t, r ₁ } is given as follows, for example.
r ₁ (t) = r ₁₀ + v _r t (0 ≦ t <t _r ) (55)
r ₁ (t) = r ₁₁ (t _r ≦ t) (56)
Here, r ₁₀ is the crystallization temperature target value r _1, r ₁₁ before changing in a ramp form is crystallization temperature target value r ₁ after the transition from the ramp-like change in a constant value (r _10> r ₁₁ ).

Thus with respect to crystallization temperature target value r ₁ to a predetermined undershoot suppression unit 7, the rate of change of crystallization temperature target value r ₁ at a predetermined time before and after the crystallization temperature target value switching time t _r And the target value of the crystallization temperature at which the change rate is reduced is output to the cascade control execution unit 5 as r ₁ ′. Crystallization temperature target value r ₁ of the change rate relaxation start point of t _s, changes to slow at a predetermined time between change rate relaxation end point _{t e (t s <t r} <t e), t s and t _e When the speed is v _s (| v _r |> | v _s |), the target crystallization temperature value r ₁ ′ output from the undershoot suppressing unit 7 is expressed by the following equation.
r ₁ ′ (t) = r ₁₀ + v _rt (0 ≦ t <t _s ) (57)
r ₁ ′ (t) = r _s + v _s (t−t _s ) (t _s ≦ t <t _e ) (58)
_{r 1 '(t) = r} 11 (t e ≦ t) ··· (59)

Here, the starting point r _s of crystallization temperature target value r ₁ to slow changes speed becomes _{r s = r 10 + v r} t s. An example of the crystallization temperature target value r ₁ ′ output from the undershoot suppressing unit 7 is shown in FIG. Thus, by moderating the rate of change of crystallization temperature target value r _1, it is possible to suppress the overshoot of the manipulated variable u ₁ at the crystallization temperature target value switching time t _r, the controlled variable y (crystallization temperature T _c ) Undershoot can be minimized.

Since r ₁₀ , r ₁₁ , v _r and _tr are known values, the operation of the undershoot suppression unit 7 can be determined by setting t _s , t _e and v _s . The crystallization temperature target value trajectory parameters _{{t s, t e, v} s} for method of determining the will be described. As in the case of the PI parameter, the value of the parameter {t _s , v _s } is obtained by optimization based on the control simulation. The method for deriving the parameters {t _s , v _s } can be formulated as an optimization problem for minimizing the square of the control deviation e (t) as follows.

Thus, by using the equation (60), the parameters {t _s , v _s } of the crystallization temperature target value trajectory can be obtained in advance. In this control simulation, control deviation e (t) = r ₁ ′ (t) −y (t), process transfer function model {P (s) | K _p , T _p1 , T _p2 }, PI-D controller {C (S) | K _c , T _i , T _d } follows the PID setting rule. The control amount y used in Expression (60) can be calculated by Expression (40), Expression (43) to Expression (45), or Expression (42) to Expression (45). Further, the change rate relaxation end time t _e is uniquely determined from r ₁ (t _e ) = r ₁ ′ (t _e ) = r _{11 as} follows.

Thus, the parameters _{{t s, t e, v} s} can be set, it can be predetermined operation of the undershoot suppression unit 7.
The operating conditions are as shown in Table 1, the process transfer function model and the PID adjustment index as shown in Table 2, and the PID set values as shown in Table 3. The crystallization temperature target value switching time t _r = 90 min and the target value changing speed v _r = −20% / 90 min = −0.222% / min. At this time, parameters of the crystallization temperature target value trajectory that minimize the undershoot of the control amount y (crystallization temperature T _c ) are as shown in Table 4.

The PID control simulation result for this crystallization temperature target value trajectory is shown in FIG. The feedforward compensation is not used here. y ₀ is a control amount y for the crystallization temperature target value r ₁ in which the change rate is not relaxed. According to FIG. 9, it can be seen that by providing the undershoot suppressing unit 7, the undershoot of the controlled variable y (crystallization temperature T _c ) is reduced to ６ from −0.40 ° C. to −0.061 ° C. .

As described above, according to the present embodiment, batch operation result data is used as an input to a crystallization process model, model parameters of the crystallization process model are adjusted, and a transfer function model and a predetermined control parameter setting rule ( Using the PI setting rule or PID setting rule), the crystallization temperature T _c after the steady control deviation with respect to the ramp-like crystallization temperature target value and the crystallization temperature target value shift from the ramp-like change to a constant value. The control parameter of the crystallization temperature controller C ₁ is adjusted using the permissible undershoot allowable value as an adjustment index, and the crystallization temperature T _c matches the desired crystallization temperature target value by a predetermined feedforward compensation law. Thus, the time pattern of the change amount of the refrigerant inlet temperature target value is obtained, and the addition result of the change amount of the refrigerant inlet temperature target value and the operation amount u ₁ which is the output of the crystallization temperature controller C ₁ The result was given to the refrigerant inlet temperature controller C ₂ as the refrigerant inlet temperature target value. Further, in the present embodiment, the crystallization temperature target value r ₁ is as crystallization temperature change rate of the target value r ₁ at a predetermined time before and after the switching time to switch to a fixed value from the change in the ramp-like becomes gentle . As described above, according to the present embodiment, it is possible to realize a high value-added control performance with respect to the ramp-like target value change unique to the batch cooling crystallization process, so that B2B superior in practicality and generality compared to the past. A control method of the control method can be realized.

The effectiveness of the present embodiment is numerically verified by a control simulation. The batch cooling crystallization process is expressed by the state equation model shown in Equation (5) and Equation (6), and the operating conditions shown in Table 1 are used. The target value orbit of the crystallization temperature T _c is changed in two stages of 70 ° C. → 50 ° C. → 30 ° C., and the change rate is v _r = −20 ° C./1.5 h. As the PID parameter, the value of the PI setting rule shown in Table 3 is used, and the result of the numerical example shown in the equation (54) is applied to the feedforward compensation.

As disturbance, changes in the crystallization heat quantity Q _c [kcal / h] and the overall heat transfer coefficient U [kcal / (m ² hK)] are given as shown in FIG. 10 (A) and FIG. 10 (B). In order to compensate for this disturbance, it is necessary to adjust the refrigerant inlet temperature _Twi by about −15 ° C.
FIG. 11 shows a control simulation result by PID cascade control and feedforward compensation. According to FIG. 11, it can be seen that high control performance that satisfies the required performance of the control system design (target value within ± 0.50 ° C.) can be realized.

  The control device 113 described in the present embodiment can be realized by a computer having a CPU, a storage device, and an interface, and a program that controls these hardware resources. The CPU executes the processing described in the present embodiment in accordance with a program stored in the storage device.

  The present invention can be applied to batch cooling crystallization process control.

  DESCRIPTION OF SYMBOLS 1 ... Model storage part, 2 ... Model adjustment part, 3 ... Feedforward control execution part, 4 ... Control parameter adjustment part, 5 ... Cascade control execution part, 6 ... Refrigerant inlet temperature time pattern setting part, 7 ... Undershoot suppression part , 60 ... target value change amount calculation unit, 61 ... time series table storage unit, 100 ... stirring crystallizer, 101 ... jacket, 102 ... temperature sensor, 103 ... stirrer, 104, 105, 112 ... valve, 106 ... inlet side Pipes, 107 ... outlet side pipes, 108, 109 ... temperature sensors, 110 ... flow sensors, 111 ... chillers.

Claims (6)

Actual data, which is time-series data consisting of a set of the crystallization temperature T _c of the raw material in the crystallizer, the refrigerant inlet temperature T _wi , the refrigerant outlet temperature T _wo used for cooling the raw material, and the refrigerant circulation flow rate f _w A model adjustment step of adjusting a model parameter of the crystallization process model as an input of a crystallization process model that models a batch cooling crystallization process, and obtaining a transfer function model that linearly approximates the crystallization process model;
The control parameter of the first controller for calculating the first manipulated variable so that the crystallization temperature T _c matches the crystallization temperature target value is determined using the transfer function model and a predetermined control parameter setting rule. , adjusting the undershoot tolerance of crystallization temperature T _c after the steady-state control deviation and crystallization temperature target value for the crystallization temperature target value which changes in a ramp shape is shifted to a constant value from the change in the ramp-like as an adjustment indicator Control parameter adjustment step to
A target value change amount calculation step for obtaining a time pattern of the change amount of the refrigerant inlet temperature target value so that the crystallization temperature T _c matches the desired crystallization temperature target value by a predetermined feedforward compensation law;
The crystallization temperature target value is set to a gradual change rate by slowing the change rate of the crystallization temperature target value for a fixed time before and after the switching point at which the crystallization temperature target value switches from a ramp-like change to a constant value. An undershoot suppressing step applied to the first controller;
Based on the time pattern of the change amount of the refrigerant inlet temperature target value, the change amount of the refrigerant inlet temperature target value corresponding to the batch elapsed time is output, and the change amount of the refrigerant inlet temperature target value and the first operation amount A feedforward compensation step with the addition result of the refrigerant as a refrigerant inlet temperature target value,
And a control step in which the second controller calculates a second operation amount and adjusts the refrigerant injection amount so that the refrigerant inlet temperature _Twi matches the refrigerant inlet temperature target value. . The control method according to claim 1,
A control method, wherein a PI-D algorithm is selected in advance as a control algorithm of the first controller. The control method according to claim 1 or 2,
The control parameter setting law, the conditions to maintain the steady-state control deviation for the ramp target value change the prescribed value, the PI parameters as undershoot maximum value of the crystallization temperature T _c approaches most to the undershoot tolerance A control method, which is either a PI setting rule to be obtained or a PID setting rule for converting a PI parameter obtained by the PI setting rule into a PID parameter. A first controller for calculating a first manipulated variable so that the crystallization temperature T _c of the raw material in the crystallizer coincides with the target crystallization temperature in the batch cooling crystallization process;
A second controller that calculates the second manipulated variable so as to adjust the refrigerant injection amount so that the refrigerant inlet temperature _Twi used for cooling the raw material matches the refrigerant inlet temperature target value;
Model storage means for storing in advance a formula of a crystallization process model that models a batch cooling crystallization process;
The actual data is time-series data consisting of a set of the crystallization temperature T _c and the coolant inlet temperature T _wi and the coolant outlet temperature T _wo and circulation flow rate f _w of the refrigerant as the input of the crystallization process model, the crystallization process A model adjusting means for adjusting a model parameter of the model and obtaining a transfer function model obtained by linear approximation of the crystallization process model;
Using the transfer function model and a predetermined control parameter setting rule, the steady control deviation for the crystallization temperature target value changing in a ramp shape and the crystallization temperature target value after shifting from a ramp change to a constant value Control parameter adjusting means for adjusting a control parameter of the first controller using an undershoot allowable value of the crystallization temperature T _c as an adjustment index;
A target value change amount calculation means for obtaining a time pattern of the change amount of the refrigerant inlet temperature target value so that the crystallization temperature T _c matches the desired crystallization temperature target value by a predetermined feedforward compensation law;
The crystallization temperature target value is set to a gradual change rate at a constant time before and after the switching point at which the crystallization temperature target value switches from a ramp-like change to a constant value. An undershoot suppressing means applied to the first controller;
Based on the time pattern of the change amount of the refrigerant inlet temperature target value, the change amount of the refrigerant inlet temperature target value corresponding to the batch elapsed time is output, and the change amount of the refrigerant inlet temperature target value and the first operation amount And a feedforward compensation means for providing the second controller with the result of the addition as a refrigerant inlet temperature target value. The control device according to claim 4, wherein
A control device, wherein a PI-D algorithm is selected in advance as a control algorithm of the first controller. The control device according to claim 4 or 5,
The control parameter setting law, the conditions to maintain the steady-state control deviation for the ramp target value change the prescribed value, the PI parameters as undershoot maximum value of the crystallization temperature T _c approaches most to the undershoot tolerance A control apparatus, which is either a PI setting rule to be obtained or a PID setting rule for converting a PI parameter obtained by the PI setting rule into a PID parameter.

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