JP2019152998A - Control method, control device, and program - Google Patents

Abstract

To achieve accurate and fast multivariable control with constraints even in equipment with limited computation resources.SOLUTION: A control method used in multivariable control making a plurality of controlled variables follow a target value causes a computer to execute a generation procedure and a calculation procedure. When a model expression representing a relationship between a variable representing a manipulated variable in a control target and a variable representing the controlled variables, an upper- and lower-limit constraints representing an upper limit and a lower limit of the variable representing the manipulated variable, and an evaluation function for evaluating the difference between the target value and the controlled variables are entered, the generation procedure generates a relation logic expression representing the relationship that the variable representing the target value and the variable representing the manipulated variable must satisfy in advance so that the evaluation function satisfies optimal conditions. The calculation procedure calculates a manipulated variable for making the plurality of controlled variables follow the target value on the basis of the target value and the relation logic expression each time the target value is entered.SELECTED DRAWING: Figure 3

Description

  The present invention relates to a control method, a control device, and a program.

  A method called Model Predictive Control (MPC) is known as a method for optimally controlling a multivariable system having complicated constraints. In model predictive control, the optimal input is calculated by solving the optimal control problem in a specific future period using the current value of the process state quantity at each sampling period. In model predictive control, optimal control is realized by repeatedly executing this state quantity observation and optimization calculation for solving the optimal control problem online (for example, Patent Document 1).

  On the other hand, multiparametric programming is known as a technique that extends model predictive control. In multiparametric programming, an optimal control problem is analyzed off-line to obtain a state feedback law for obtaining an optimal input for a state quantity. As a result, in the multiparametric programming method, online optimization calculation is not required, and optimal control can be realized at high speed (for example, Patent Documents 2 to 8, Non-Patent Documents 1 and 2).

  In addition, there are conventionally known techniques for expressing problems such as system control and circuit analysis by first-order predicate logical expressions and for optimizing the system by solving first-order predicate logical expressions (for example, non-patent Reference 3).

  Specifically, a quantifier represented by a universal symbol (∀) or an existence symbol (∃), and a logical symbol represented by a product (∧) or sum (∨) of a multivariable polynomial equation or inequality Combine the logical expressions combined using to obtain a first order predicate logical expression. Among variables appearing in a logical expression, a variable bound by a quantifier is called a bound variable, and a variable not bound by a quantifier is called a free variable. In the first order predicate logical expression, optimization is achieved by eliminating the bound variable and deriving a logical expression that the free variable should satisfy. Of the first-order predicate logical expressions, a method of eliminating a bound variable and deriving a logical expression to be satisfied by a free variable is called a quantifier elimination method.

  Further, a technique for performing control system design and control system analysis using a quantifier elimination method is known (for example, Patent Document 9). According to this method, the control system analysis / design apparatus formulates an input control problem as a linear matrix inequality (LMI) or a bilinear matrix inequality (BMI). . Then, the constraints such as design specifications formulated as LMI or BMI are transformed into constraints in the form of connecting inequalities with logical sums, and the control system is converted into a first-order predicate logical expression and bound by a quantifier. Analyze the control system from the expression with the variables deleted.

  Further, as a technique for analyzing the energy of the plant, a technique is known in which analysis is performed by generating a first-order predicate logical expression and solving the first-order predicate logical expression (for example, Non-Patent Document 4).

Japanese Patent Laid-Open No. 2004-20031 JP 2010-12889 A JP 2010-12890 A JP 2010-13990 A JP 2013-101472 A JP 2013-134741 A International Publication No. 2011/136160 International Publication No. 2013/077007 JP 11-328239 A

Alberto Bemporad, Manfred Morari, Vivek Dua, Efstratios N. Pistikopoulos "The explicit linear quadratic regulator for constrained systems" Automatica, Vol.38, pp.3-20 Junichi Imura, Shunichi Higashi, Izumi Masuka, “Control of Hybrid System”, Corona, 2014, pp. 142-154 Hirokazu Anai and Kazuhiro Yokoyama, “Calculation algorithm of QE and its application Optimization by mathematical expression processing”, University of Tokyo Press, 2011, pp. 214-221 Yoshio Tange, Satoshi Kiryu, Tetsuro Matsui, Yoshikazu Fukuyama, “Visualization of Supply / Demand Balance Optimization Problem Using Formula Processing Technology”, 13th ROMBUNNO. 8C2-5

  Here, in model predictive control disclosed in Patent Document 1, for example, optimal control is realized by solving an optimal control problem using mathematical programming. For this reason, a lot of calculation time is required for searching for the optimal solution, and a lot of calculation resources are required for solving the optimal control problem. For this reason, for example, it may be difficult to solve the optimal control problem with an edge device with limited calculation resources, and it may be difficult to control a control target with a short control cycle. In addition, for example, a case where an optimum input cannot be calculated because there is no solution of the optimum control problem cannot be determined in advance. Examples of the edge device include a built-in computing device and a control device such as a PLC (Programmable Logic Controller).

  On the other hand, for example, in the multiparametric programming methods disclosed in Patent Documents 2 to 8 and Non-Patent Documents 1 and 2, the target value is fixed in the state space model. In addition, when the prediction interval becomes long, the state variable region division becomes complicated, and it may be difficult to realize it with an edge device with limited computational resources.

  Furthermore, in the multiparametric programming method, optimization calculation is performed when an optimal control problem is analyzed offline to generate a state feedback law. For this reason, an accurate optimal control law (optimum state feedback law) may not be generated depending on numerical errors and optimization accuracy. That is, the state feedback rule cannot be generated in the state quantity region determined to have no feasible solution by the optimization calculation.

  An embodiment of the present invention has been made in view of the above points, and an object of the present invention is to realize accurate and high-speed limited variable control even in a device having limited calculation resources.

  In order to achieve the above object, in one embodiment of the present invention, there is provided a control method used for multivariable control in which a plurality of control amounts follow a target value. A model expression representing the relationship with the variable to be represented, upper and lower limit constraints representing the upper and lower limits of the variable representing the manipulated variable, and an evaluation function for evaluating the difference between the target value and the controlled variable are input. And a generation procedure for generating in advance a relational logical expression representing a relationship to be satisfied by the variable representing the target value and the variable representing the manipulated variable so that the evaluation function satisfies the optimality condition, and the target value is input A computer executing a calculation procedure for calculating the operation amount for causing the plurality of control amounts to follow the target value based on the target value and the relational logical formula each time And

  Even devices with limited computing resources can implement restricted multivariable control accurately and at high speed.

It is a figure which shows an example of a structure of the optimal control apparatus which concerns on 1st embodiment. It is a figure which shows an example of the hardware constitutions of the optimal control apparatus which concerns on 1st embodiment. It is a figure which shows an example of a function structure of the optimal control process part which concerns on 1st embodiment. It is a flowchart which shows an example of the production | generation process of the relational logical expression which concerns on 1st embodiment. It is a figure which shows an example of the area | region division which a relational logic expression represents. It is a flowchart which shows an example of the calculation process of the optimal operation amount which concerns on 1st embodiment. It is a figure which shows an example of the example of application of an optimal control process part. It is a figure which shows an example of a function structure of the optimal control process part which concerns on 2nd embodiment. It is a figure which shows an example of a cache. It is a flowchart which shows an example of the calculation process of the optimal operation amount which concerns on 2nd embodiment. It is a flowchart which shows the other example of the calculation process of the optimal operation amount which concerns on 2nd embodiment. It is a figure which shows an example of a function structure of the optimal control process part which concerns on 3rd embodiment. It is a flowchart which shows an example of the visualization process which concerns on 3rd embodiment. It is a figure which shows an example at the time of visualizing the set of evaluation values. It is a flowchart which shows the other example of the visualization process which concerns on 3rd embodiment. It is a figure which shows an example at the time of visualizing the area | region where deviation becomes 0. It is a figure which shows an example of a function structure of the optimal control process part which concerns on 4th embodiment. It is a flowchart which shows an example of the production | generation process of the relational formula which concerns on 4th embodiment. It is a figure which shows the heat pump model in Example 1. FIG. It is a figure which shows the area | region division | segmentation which the relational logical expression in Example 1 represents. It is a figure which shows an example of the plot result of 1000 target values. It is a figure which shows the comparative example of calculation time with a prior art. It is a figure which shows the time change of the control amount in Example 2, and the operation amount. It is a figure which shows an example of the area division | segmentation of each time in Example 2. FIG.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Hereinafter, the optimum control apparatus 10 that calculates the optimum operation amount for the operation target at high speed in multivariable control in which a plurality of control amounts follow the target value will be described. The optimum control device 10 is an edge device (for example, a built-in type computing device or a control device such as a PLC) having limited calculation resources. However, the optimal control apparatus 10 according to the present embodiment may be various devices or apparatuses having sufficient calculation resources, for example, other than the edge device.

Further, hereinafter, variables representing the operation amount in the system to be controlled are MV ₁ ,..., MV _M , variables representing the control amount are PV ₁ ,..., PV _N , and the control amount target value is represented. The variables are represented as SV ₁ ,..., SV _N. M and N are constants determined by the configuration of the system to be controlled.

[First embodiment]
<Configuration of Optimal Control Device 10>
First, the configuration of the optimal control apparatus 10 according to the present embodiment will be described with reference to FIG. FIG. 1 is a diagram illustrating an example of a configuration of an optimal control apparatus 10 according to the first embodiment.

  As shown in FIG. 1, the optimal control device 10 according to the present embodiment includes an optimal control processing unit 100. In the optimal control device 10 according to the present embodiment, the optimal control processing unit 100 calculates an optimal operation amount for the operation target in multivariable control in which a plurality of control amounts follow the target value. At this time, the optimal control apparatus 10 according to the present embodiment generates a relational logical expression that represents the relationship that the optimum operation amount should satisfy with respect to the target value in the offline state. That is, the optimal control apparatus 10 according to the present embodiment generates a relational logical expression in advance before online execution.

  And the optimal control apparatus 10 which concerns on this embodiment calculates the optimal operation amount for making a some control amount track a target value on the online by the relational logic formula produced | generated previously. As a result, the optimum control apparatus 10 according to the present embodiment can realize accurate and high-speed control even if the device or apparatus has limited calculation resources such as edge devices.

  The optimum control processing unit 100 is realized by a process that one or more programs installed in the optimum control apparatus 10 according to the present embodiment cause a CPU (Central Processing Unit) 17 described later to execute.

<Hardware Configuration of Optimal Control Device 10>
Next, the hardware configuration of the optimum control apparatus 10 according to the present embodiment will be described with reference to FIG. FIG. 2 is a diagram illustrating an example of a hardware configuration of the optimum control apparatus 10 according to the first embodiment.

  As shown in FIG. 2, the optimal control device 10 according to the present embodiment includes an input device 11, a display device 12, an external I / F 13, a communication I / F 14, a ROM (Read Only Memory) 15, and a RAM. (Random Access Memory) 16, a CPU 17, and an auxiliary storage device 18. These pieces of hardware are connected to each other via a bus 19 so that they can communicate with each other.

  The input device 11 is, for example, various buttons, a touch panel, a keyboard, a mouse, or the like, and is used to input various operations to the optimal control device 10. The display device 12 is, for example, a display and displays various processing results obtained by the optimum control device 10. The optimal control device 10 may not include at least one of the input device 11 and the display device 12.

  The external I / F 13 is an interface with an external device. The external device includes a recording medium 13a. The optimal control device 10 can read and write to the recording medium 13 a via the external I / F 13. Examples of the recording medium 13a include an SD memory card, a USB memory, a CD (Compact Disk), and a DVD (Digital Versatile Disk). Note that one or more programs for realizing the optimum control processing unit 100 may be stored in the recording medium 13a.

  The communication I / F 14 is an interface for the optimal control device 10 to perform data communication with other devices. Note that one or more programs that realize the optimum control processing unit 100 may be acquired (downloaded) from a predetermined server or the like via the communication I / F 14.

  The ROM 15 is a nonvolatile semiconductor memory that can retain data even when the power is turned off. The RAM 16 is a volatile semiconductor memory that temporarily stores programs and data. The CPU 17 is an arithmetic device that reads programs and data from the auxiliary storage device 18 and the ROM 15 to the RAM 16 and executes various processes, for example.

  The auxiliary storage device 18 is, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), or the like, and is a non-volatile memory that stores programs and data. The programs and data stored in the auxiliary storage device 18 include, for example, one or more programs that realize the optimum control processing unit 100, an OS (Operating System) that is basic software, and various application programs that operate on the OS. is there.

  The optimum control apparatus 10 according to the present embodiment has the hardware configuration shown in FIG. 2 and can implement various processes described later. In FIG. 2, an example of a hardware configuration in which the optimal control device 10 is realized by one computer is shown, but the optimal control device 10 may be realized by a plurality of computers.

<Functional Configuration of Optimal Control Processing Unit 100>
Next, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 3 is a diagram illustrating an example of a functional configuration of the optimum control processing unit 100 according to the first embodiment.

  As shown in FIG. 3, the optimal control processing unit 100 according to the present embodiment includes an offline processing unit 110 and an online processing unit 120. In addition, although this embodiment demonstrates the case where the one optimal control apparatus 10 has both the offline process part 110 and the online process part 120, it is not restricted to this. Different apparatuses may have the offline processing unit 110 and the online processing unit 120. In particular, for example, various devices or apparatuses having sufficient calculation resources may have the offline processing unit 110, while edge devices having limited calculation resources may have the online processing unit 120.

  The offline processing unit 110 calculates the relational logical expression 1400 by inputting the model formula 1100, the upper and lower limit constraints 1200, and the evaluation function 1300 offline.

The model formula 1100 is a model representing the relationship between the operation amount and the control amount in the system to be controlled. Model formula 1100, variable _MV 1 representing the operation amount, ..., and MV _M, the function representing the relationship between variable PV _n representing the controlled variable if _{f n, PV n: = f} n (MV 1 ,..., MV _M ), (n = 1,..., N).

The model formula 1100 can be created, for example, by regression analysis or the like using the actual value of the control amount with respect to the actual manipulated variable. f _n is not limited to linear, and may be piecewise linear or the like.

Further, the upper and lower limit constraint 1200 is a constraint that represents the upper limit and the lower limit of each operation amount in the system to be controlled. Upper and lower limit constraint 1200, the upper limit of each manipulation amount _{HMV 1, ···, HMV M,} LMV 1 the lower limit of each manipulation amount, ..., if _{LMV M, LMV m ≦ MV m} ≦ HMV m, (M = 1,..., M).

The evaluation function 1300 is a function for evaluating the difference between the target value and the control amount. Evaluation function 1300, a variable _SV 1 representing a target value, ..., and SV _N, variable _PV 1 representing a control amount, ..., if E function for evaluating the difference between the PV _N, It is represented by the following formula 1.

The relational logical expression 1400 is a variable SV ₁ that represents a target value when the optimality condition (KKT (Karush-Kuhn-Tucker) condition) based on the model expression 1100, the upper and lower limit constraints 1200, and the evaluation function 1300 is satisfied. ..., variable _MV 1 representing the operation amount with respect to SV _N, ..., a logical expression representing the relationship to be satisfied by MV _M. The relational logical expression 1400 is a logical expression that divides an N-dimensional space having variables SV ₁ ,..., SV _N representing target values into K regions Rk (k = 1..., K). It is represented by The division number K is a constant determined by performing the limit symbol elimination method.

  Here, the offline processing unit 110 includes a first-order predicate logical expression generation unit 111 and a quantifier elimination unit 112. The first order predicate logical expression generation unit 111 generates a first order predicate logical expression ψ from the model expression 1100, the upper and lower limit constraints 1200, and the evaluation function 1300. The quantifier elimination unit 112 generates a relational logical expression 1400 from the first-order predicate logical expression ψ generated by the first-order predicate logical expression generation unit 111 by a quantifier elimination method.

  The online processing unit 120 inputs the relational logical expression 1400 and the target value 1500 online to calculate the optimum operation amount 1600.

Target value 1500 is variable _PV 1 representing a control amount, ..., the target value _p 1 of PV _N, ..., a _{p N.}

The optimum operation amount 1600 is the optimum operation amount s ₁ ,..., S _M for causing the control amount to follow the target value.

Here, the online processing unit 120 includes an area determination unit 121 and an operation amount calculation unit 122. Area determination unit 121 determines whether the target value _p 1, ···, _{p N} are regions Rk (k = 1, ···, K) is included in any area of the. Control input calculation unit 122, according to the determination result by the area determination unit 121, a target value _p 1, ..., _{p N} optimum manipulated variables _s 1 by the function corresponding to the region Rk containing the, ..., s Calculate _M.

<Relational logic generation process>
Hereinafter, the process of generating the relational logical expression 1400 will be described with reference to FIG. FIG. 4 is a flowchart illustrating an example of the generation process of the relational logical expression 1400 according to the first embodiment. Note that the processing shown in FIG. 4 is executed in advance offline, for example, before the optimal operation amount calculation processing described later.

  First, the first-order predicate logical expression generation unit 111 of the offline processing unit 110 receives the model expression 1100, the upper and lower limit constraints 1200, and the evaluation function 1300, and generates the first-order predicate logical expression ψ (step S101).

Here, the first order predicate logical expression generation unit 111 generates the first order predicate logical expression ψ as follows. That is, first-order predicate logical expression generation unit 111 arranges upper and lower limit constraints 1200 so that the right side is 0, that is, LMV _m −MV _m ≦ 0 and MV _m −HMV _m ≦ 0. Next, the first-order predicate logical expression generation unit 111 adds, to the evaluation function E, an expression obtained by multiplying LMV _m -MV _m and MV _m -HMV _m by a Lagrange multiplier (λ1 _m , λ2 _m ), respectively. A Lagrangian function L is generated.

Next, the first-order predicate logical expression generation unit 111 generates the following conditional expressions so that the optimality condition (KKT condition) is satisfied for m = 1,. In other words, the first-order predicate logical expression generation unit 111 generates the following conditional expressions so as to satisfy the optimality condition (KKT condition) by the number M of constraints.

Then, first-order logic formulas generator 111, all conditional expressions .psi.1 m was produced _above, .psi.2 _m, to produce a .psi.3 _m and [Psi] 4 _m a logical bound following conditional expressions Pusai5.

Then, the first-order predicate logical expression generation unit 111 assigns an existence symbol (∃) to the Lagrange multipliers (λ1 _m , λ2 _m ) with respect to the conditional expression ψ5, and generates the following first-order predicate logical expression ψ. .

Thereby, the first order predicate logical expression generation unit 111 generates the first order predicate logical expression ψ.

  Next, the quantifier elimination unit 112 of the offline processing unit 110 generates a relational logical expression 1400 from the first order predicate logical expression ψ by a quantifier elimination method (step S102). Here, if the relational logical expression 1400 is represented as φ, the quantifier elimination unit 112 generates the following relational logical expression φ by erasing the Lagrange multiplier by the quantifier elimination method. For the quantifier elimination method, see Non-Patent Document 3, for example.

Here, the region Rk (k = 1,..., K) indicates a region in which the divided logical expression φ ^Rk (SV ₁ ,..., SV _N ) is true. In other words, the above-described relational formula φ divides an N-dimensional space having SV ₁ ,..., SV _N as axes into K regions Rk (k = 1..., K).

  Also,

Calculates the optimum operation amount when the target values p ₁ ,..., P _N are inside the region Rk (that is, when the target values p ₁ ,..., P _N are included in the region Rk). An operation amount determination function is represented. This expression is determined by performing the quantifier elimination method on the first order predicate logic expression ψ.

Thus, the relationship formulas phi, variable _SV 1 representing a target value, ..., dividing the logical expression phi ^Rk to divide the space the SV _N and each axis _{(SV 1, ···, SV N} ) and , Target values p ₁ ,..., P _N are represented by the logical sum of the logical products of the operation amount determination functions for calculating the optimum operation amount when the region Rk is included.

As a result, the relational symbol φ is generated by the quantifier elimination unit 112. Here, as described above, the relational logical formula φ divides the N-dimensional space with SV ₁ ,..., SV _N as axes into K regions Rk (k = 1..., K). is doing. Therefore, as an example, in the case of K = 5, regions R1 to R5 on a plane constituted by a certain axis SV _n and SV _{n + 1} are shown in FIG. FIG. 5 is a diagram illustrating an example of area division represented by the relational logical expression. As shown in FIG. 5, each of the regions R1 to R5 is represented by a region that divides an N-dimensional space with SV ₁ ,..., SV _N as axes.

<Optimum operation amount calculation processing>
Hereinafter, a process for calculating the optimum operation amounts s ₁ ,..., S _M for the target values p ₁ ,..., P _N using the relational logical expression 1400 will be described with reference to FIG. . FIG. 6 is a flowchart illustrating an example of an optimum operation amount calculation process according to the first embodiment. Note that the processing shown in FIG. 6 is executed online, for example, every control cycle of the system that is the control target.

  First, the online processing unit 120 initializes k for specifying the region Rk (this k is also referred to as “region number”) to 1 (step S201).

Next, the area determination unit 121 of the online processing unit 120 inputs the relational logical expression 1400 and the target value 1500, and whether or not the divided logical expression φ ^Rk (p ₁ ,..., P _N ) = True. Is determined (step S202). Note that the target value 1500 input to the online processing unit 120 may have a different value for each control cycle, for example.

That is, the region determination unit 121 substitutes the target values p ₁ ..., P _N for the divided logical expressions φ ^Rk (SV ₁ ,..., SV _N ) included in the relational logical expression φ, and It is determined whether or not ^Rk (p ₁ ,..., P _N ) = True. In other words, the region determination unit 121 determines whether or not the target values p ₁ ..., P _N are included in the region Rk.

If it is determined in step S202 that φ ^Rk (p ₁ ,..., P _N ) = True (that is, the target values p ₁ ,..., P _N are not included in the region Rk), online The processing unit 120 adds 1 to the area number k (step S203). And the online process part 120 returns to the process of step S202. Thus, the above step S202 is repeatedly executed until φ ^Rk (p ₁ ,..., P _N ) = True for a certain area number k.

If it is determined in step S202 that φ ^Rk (p ₁ ,..., P _N ) = True (that is, the target values p ₁ ,..., P _N are included in the region Rk), online control input calculation block 122 of the processing unit 120 calculates a target value _p 1, · · ·, optimal manipulated variable _s 1 by the operation amount determination function corresponding to the region Rk containing the _{p N,} · · ·, a _{s M} (Step S204).

That is, the operation amount calculation unit 122 calculates the optimum operation amount s ₁ ,..., S _M for each m = 1,.

Thus, by the operation amount calculation unit 122, a target value _p 1, · · ·, optimal manipulated variable _s 1 for to follow the _{p N,} · · ·, _{s M} is calculated a controlled variable of the controlled object of the system The

  As described above, the optimal control apparatus 10 according to the present embodiment calculates the optimum operation amount for the target value online after generating the relational logical expression φ in advance offline. Thus, by generating the relational logical expression φ in advance offline, the optimal control apparatus 10 according to the present embodiment can optimize the operation amount online at high speed even when, for example, calculation resources are limited. Can be calculated.

  Further, the optimum control apparatus 10 according to the present embodiment generates the relational logical expression φ by the quantifier elimination method. Thereby, in the optimal control apparatus 10 which concerns on this embodiment, the exact optimal control law (namely, relational logic formula (phi)) without a numerical error can be produced | generated.

  The relational logical expression generation process shown in FIG. 4 is performed once before the optimum operation amount calculation process shown in FIG. 6 unless at least one of the model expression 1100, the upper and lower limit constraints 1200, and the evaluation function 1300 is changed. It only has to be executed.

<Application Example of Optimal Control Processing Unit 100>
Here, an application example of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIGS. 7A and 7B. FIG. 7 is a diagram illustrating an example of application of the optimum control processing unit 100.

In FIG. 7A, the host controller C <b> 11 has the optimum control processing unit 100. The upper controller C11 calculates the optimum operation amount (MV ₁ and MV ₂ ) from the target values (SV ₁ and SV ₂ ) by the optimum control processing unit 100, and outputs it to the lower controllers C12 and C13. Then, the lower controllers C12 and C13 receive and control the optimum operation amounts (MV ₁ and MV ₂ ) as target values (SV ′ ₁ and SV ′ ₂ ). As described above, the upper controller C11 may pass the optimum operation amount to the lower controllers C12 and C13, and the lower controllers C12 and C13 may perform control using the optimum operation amount as a target value.

In FIG. 7B, the upper controller C11 calculates the optimum operation amount (MV ₁ and MV ₂ ) from the target values (SV ₁ and SV ₂ ) by the optimum control processing unit 100, and uses the model equation from the optimum operation amount. The control amounts (PV ₁ and PV ₂ ) calculated by 1100 are output to the lower controllers C12 and C13. Then, the lower controllers C12 and C13 receive the control amounts (PV ₁ and PV ₂ ) as target values (SV ′ ₁ and SV ′ ₂ ) and perform control. As described above, the upper controller C11 may pass the control amount for the optimum operation amount to the lower controllers C12 and C13, and the lower controllers C12 and C13 may perform control using the control amount as a target value.

[Second Embodiment]
Next, a second embodiment will be described. In the first embodiment, in the calculation process of the optimum operation amount shown in FIG. 6, the region including the target values p ₁ ,..., P _N among the regions R1 to RK is searched in order from k = 1. . For this reason, it may take time to search for a region including the characteristic values p ₁ ,..., P _N. Therefore, in the second embodiment, a case will be described in which a search for a region including target values p ₁ ,..., P _N is performed based on priority.

  In the second embodiment, differences from the first embodiment will be mainly described, and description of components that are substantially the same as those in the first embodiment will be omitted or simplified.

<Functional Configuration of Optimal Control Processing Unit 100>
First, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 8 is a diagram illustrating an example of a functional configuration of the optimum control processing unit 100 according to the second embodiment.

As shown in FIG. 8, the online processing unit 120 of the optimal control processing unit 100 according to the present embodiment further includes a cache mechanism unit 123. The online processing unit 120 according to the present embodiment determines whether or not the target values p ₁ ,..., P _N are included in the region Rk indicated by the region number k corresponding to the priority Y in ascending order of the priority Y. Determine. At this time, the cache mechanism unit 123 refers to the cache 1700 and converts the priority Y to the area number k.

  Here, the cache 1700 will be described with reference to FIG. FIG. 9 is a diagram illustrating an example of the cache 1700.

As shown in FIG. 9, the priority 1 and the area number k are associated with the cache 1700. For example, the priority Y = 1 is associated with the area number k = 5. Similarly, the priority Y = 2 and the region number k = 4 are associated with each other. The same applies to the case of priority Y = 3 or later. Accordingly, the online processing unit 120 according to the present embodiment sets the target value p in the region Rk indicated by the corresponding region number k in the order of the region number k = 5, 4, 1, 3, 2 in accordance with the priority Y. ₁ ,..., P _N can be determined.

<Optimum operation amount calculation processing>
Hereinafter, the optimum operation amount calculation process according to the present embodiment will be described with reference to FIG. FIG. 10 is a flowchart illustrating an example of an optimum operation amount calculation process according to the second embodiment. Note that steps S202 and S204 in FIG. 10 are the same as those in FIG.

First, the online processing unit 120 initializes the priority Y to 1 (step S301). Next, the cache mechanism unit 123 of the online processing unit 120 refers to the cache 1700 and converts the priority Y to the area number k (step S302). That is, the cache mechanism unit 123 refers to the cache 1700 and converts the priority Y to the area number k associated with the priority Y. Thereby, in step S202, it is determined whether or not φ ^Rk (p ₁ ,..., P _N ) = True using the region number k. Note that k: = cache [Y] is a function that refers to the cache 1700 and converts the priority Y to the area number k.

If it is determined in step S202 that φ ^Rk (p ₁ ,..., P _N ) = True, the online processing unit 120 adds 1 to the priority Y (step S303). Then, the online processing unit 120 returns to the process of step S302. As a result, step S202 is repeatedly executed until φ ^Rk (p ₁ ,..., P _N ) = True for a certain area number k in ascending order of priority Y.

Thus, in the optimal control apparatus 10 according to the present embodiment, the region Rk including the target values p ₁ ,..., P _N is searched in descending order of priority. Thus, by appropriately creating the cache 1700, it is possible to reduce the time required for searching for the region Rk including the target values p ₁ ,..., P _N.

<Another example of calculation processing of optimum operation amount>
Hereinafter, another example of the calculation process of the optimum operation amount according to the present embodiment will be described with reference to FIG. FIG. 11 is a flowchart illustrating another example of the optimum operation amount calculation process according to the second embodiment. Note that steps S301 to S303 and S204 in FIG. 11 are the same as those in FIG.

When it is determined in step S202 that φ ^Rk (p ₁ ,..., P _N ) = True, the cache mechanism unit 123 updates the cache 1700 so that the priority of the area number k becomes higher. (Step S304).

For example, the cache mechanism unit 123 updates the priority Y associated with the area number k to 1 and subtracts 1 from the priority Y associated with the other area number k. Thereby, the priority Y of the region number k determined as φ ^Rk (p ₁ ,..., P _N ) = True in step S202 can be made highest.

However, the present invention is not limited to this. For example, the cache mechanism unit 123 increases the priority Y of the area number k determined as φ ^Rk (p ₁ ,..., P _N ) = True in step S202 by one. You may do it.

As described above, the optimal control device 10 according to the present embodiment may update the cache 1700 according to the determination result of the region determination unit 121. Thereby, the priority Y corresponding to the area number k of the area Rk determined to include the target values p ₁ ,..., P _N can be dynamically increased. Therefore, further reduction in the time required for searching for the region Rk including the target values p ₁ ,..., P _N can be expected.

[Third embodiment]
Next, a third embodiment will be described. In the third embodiment, for example, when a target value for each control cycle i (that is, a set of target values) is input, a set of target values and a set of control amounts calculated from the optimum manipulated variable A case will be described in which evaluation values such as deviations are calculated and a set of calculated evaluation values is visualized. Thereby, for example, the user of the optimal control device 10 can check the deviation between the control amount and the target value when the operation of the optimal operation amount is performed on the operation target.

  Note that in the third embodiment, differences from the first embodiment will be mainly described, and description of components that are substantially the same as those in the first embodiment will be omitted or simplified.

<Functional Configuration of Optimal Control Processing Unit 100>
First, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 12 is a diagram illustrating an example of a functional configuration of the optimal control processing unit 100 according to the third embodiment.

  As shown in FIG. 12, the online processing unit 120 of the optimal control processing unit 100 according to the present embodiment inputs the relational logical expression 1400 and the set of target values 1800 online, and sets the optimal manipulated variable set 1900. Is calculated.

  A set of target values 1800 is, for example, a set of target values for each control cycle i, where n = 1,..., N, i = 1,.

It is represented by

  The set of optimum manipulated variables 1900 is a set of optimum manipulated variables for each control cycle i, for example, and m = 1,..., M, i = 1,.

It is represented by

  Further, the optimal control processing unit 100 according to the present embodiment illustrated in FIG. 12 includes a visualization processing unit 130. The visualization processing unit 130 calculates an evaluation value such as a deviation between the control amount calculated from the optimum operation amount and the target value, and visualizes the calculated evaluation value.

  Here, the visualization processing unit 130 includes a control amount calculation unit 131, an evaluation value calculation unit 132, and a visualization unit 133. The control amount calculation unit 131 calculates a set of control amounts from the optimal operation amount set 1900 using the model formula 1100. The set of controlled variables is n = 1,..., N, i = 1,.

Is calculated by

  The evaluation value calculation unit 132 calculates a set of evaluation values based on the set of control amounts calculated by the control amount calculation unit 131 and the set of target values 1800. The visualization unit 133 visualizes the set of evaluation values calculated by the evaluation value calculation unit 132.

<Visualization processing>
Hereinafter, a process of visualizing the evaluation value set after calculating the evaluation value set will be described with reference to FIG. FIG. 13 is a flowchart illustrating an example of a visualization process according to the third embodiment.

  First, the online processing unit 120 inputs a set of target values 1800 and calculates a set of optimum manipulated variables 1900 (step S401). The online processing unit 120 calculates the optimum operation amount set 1900 by repeatedly executing the optimum operation amount calculation processing shown in FIG. 6, for example, every control cycle i.

  Next, the control amount calculation unit 131 of the visualization processing unit 130 calculates a set of control amounts from the optimal operation amount set 1900 using the model formula 1100 (step S402). That is, the control amount calculation unit 131 calculates a set of control amounts according to the equation shown in Equation 11 above.

  Next, the evaluation value calculation unit 132 of the visualization processing unit 130 calculates a set of evaluation values (step S403).

  Here, as the evaluation value, for example, (1) deviation between the target value and the control amount corresponding to the optimum manipulated variable, (2) mean square error (RMSE), (3) evaluation function E Can be used.

(1) Deviation between target value and control amount corresponding to optimum manipulated variable When using a deviation as an evaluation value, evaluation value calculation unit 132 has n = 1,..., N, i = 1,. , I, the deviation err _n ⁱ is calculated by the following equation.

As a result, a set of deviations err _n ⁱ is obtained as a set of evaluation values.

(2) Mean square error (RMSE)
When the mean square error is used as the evaluation value, the evaluation value calculation unit 132 sets i = 1. .., RMSE ⁱ is calculated from the following equation.

Thereby, a set of mean square errors RMSE ⁱ is obtained as a set of evaluation values.

(3) Function Value of Evaluation Function E When the function value of the evaluation function E is used as the evaluation value, the evaluation value calculation unit 132 sets i = 1. .., ^I is calculated by the following formula for I.

Thereby, a set E ^{i of} evaluation function values is obtained as a set of evaluation values.

  Next, the visualization unit 133 of the visualization processing unit 130 visualizes the set of evaluation values calculated by the evaluation value calculation unit 132 (step S404).

Here, FIG. 14 shows an example when the set of evaluation values is visualized. FIG. 14A is a graph visualizing the deviation err ₁ on the plane composed of SV ₁ and SV ₂ . FIG. 14B is a graph visualizing the mean square error RMSE on the plane composed of SV ₁ and SV ₂ . FIG. 14C is a graph visualizing the evaluation function value E on the plane constituted by SV ₁ and SV ₂ .

  As described above, by visualizing the set of evaluation values, the user or the like of the optimal control device 10 according to the present embodiment can determine the deviation between the target value and the control amount corresponding to the optimal operation amount, the mean square error, or the evaluation. The function value can be confirmed. Thereby, the user etc. can specify how much it deviates from a target value, for example, when optimal control is performed with respect to the target value for every i. In addition, the visualization processing in the present embodiment can be performed on a set of assumed target values offline before the control is performed. For this reason, the presence or absence of a solution or a situation in which a control deviation occurs can be grasped in advance before performing control by visualization.

<Other examples of visualization processing>
Hereinafter, as another example of the visualization process, a process for visualizing a region in which an evaluation value becomes a predetermined value when optimal control is performed (that is, when an operation with an optimal operation amount is performed) will be described. This will be described with reference to FIG. FIG. 15 is a flowchart illustrating another example of the visualization process according to the third embodiment. Hereinafter, as an example, it is assumed that the evaluation value is a deviation. Note that the visualization process shown in FIG. 15 is executed offline, for example.

  First, the first-order predicate logical expression generation unit 111 of the offline processing unit 110 generates a first-order predicate logical expression ψ ′ corresponding to a region where the deviation is a predetermined value from the model expression 1100 and the relational logical expression 1400. (Step S501). Hereinafter, as an example, a case where a first-order predicate logical expression corresponding to a region where the deviation is 0 will be described.

  In this case, the first-order predicate logical expression generation unit 111 generates the first-order predicate logical expression ψ ′ shown in the following Expression 15.

For example, when the first-order predicate logical expression ψ ′ corresponding to the region where the deviation is a is generated, the following Expression 16 may be generated.

Further, for example, when generating the first order predicate logical expression ψ ′ corresponding to the region where the deviation is not less than a and not more than b, the following Expression 17 may be generated.

Next, the quantifier elimination unit 112 of the offline processing unit 110 generates a controllable logical expression φ ′ (SV ₁ ,..., SV _N ) from the first-order predicate logical expression ψ ′ by the quantifier elimination method ( Step S502).

Next, the visualization processing unit 130 visualizes the controllable logical expression φ ′ (SV ₁ ,..., SV _N ) generated by the quantifier elimination unit 112 (step S503). That is, the visualization processing unit 130 draws a region where the controllable logical expression φ ′ (SV ₁ ,..., SV _N ) becomes True, thereby controlling the controllable logical expression φ ′ (SV ₁ ,. , SV _N ).

Here, FIG. 16 shows an example when a region where the deviation is 0 is visualized. In FIG. 16, a region where the deviation is 0 on the plane composed of SV ₁ and SV ₂ (that is, a region where φ ′ (SV ₁ ,..., SV _N ) = True) is visualized. .

  Thereby, the user etc. of the optimal control apparatus 10 which concerns on this embodiment can confirm the area | region of the target value from which deviation becomes a predetermined value (for example, deviation is 0). Thereby, the user etc. can set an appropriate target value, for example.

[Fourth embodiment]
Next, a fourth embodiment will be described. In the fourth embodiment, a case will be described in which there is a change rate constraint on the change in the control amount. When there is a change rate constraint, it is necessary to satisfy the change rate constraint, and a change in the control amount (PV _n ) that does not satisfy the change rate constraint (for example, a rapid temperature increase or a rapid temperature decrease) can be performed. Can not.

  Therefore, in the fourth embodiment, a case will be described in which an optimal operation amount that satisfies the change rate constraint is calculated when the system to be controlled has the change rate constraint. However, the fourth embodiment is applied not only when there is a restriction on the change in the controlled variable, but also when there is a change rate restriction on the manipulated variable or when there is a change rate restricted on both the manipulated variable and the controlled variable. Is possible.

  Note that in the fourth embodiment, differences from the first embodiment will be mainly described, and description of components that are substantially the same as those in the first embodiment will be omitted or simplified.

<Functional Configuration of Optimal Control Processing Unit 100>
First, the functional configuration of the optimum control processing unit 100 according to the present embodiment will be described with reference to FIG. FIG. 17 is a diagram illustrating an example of a functional configuration of the optimal control processing unit 100 according to the fourth embodiment.

  As illustrated in FIG. 17, the offline processing unit 110 of the optimal control processing unit 100 according to the present embodiment inputs a model formula 1100, an upper / lower limit constraint 1200, an evaluation function 1300, and a change rate constraint 2000 offline. Then, the relational logical expression 1400 is calculated.

The change rate constraint 2000 is a constraint condition indicating a control amount or an operation amount that can change per unit time when the control amount (PV _n ) or the operation amount (MV _m ) in the system to be controlled is changed. . If the current control amount is P _n ⁰ , the upper limit of the change rate with respect to the control amount P _n is δ _n ^u , and the lower limit of the change rate with respect to the control amount P _n is δ _n ^l , n = 1, .., N is expressed by the following equation (18).

The first-order predicate logical expression generation unit 111 of the offline processing unit 110 according to the present embodiment generates a first-order predicate logical expression ψ from the model expression 1100, the upper and lower limit constraints 1200, the evaluation function 1300, and the change rate constraint 2000. As a result, the first-order predicate logical expression ψ in consideration of the change rate constraint 2000 is generated. Then, the quantifier elimination unit 112 generates a relational logical expression 1400 from the first-order predicate logical expression ψ in consideration of the change rate constraint 2000 by the quantifier elimination method.

<Relational logic generation process>
Hereinafter, a process of generating the relational logical expression 1400 from the first order predicate logical expression ψ in consideration of the change rate constraint 2000 will be described with reference to FIG. FIG. 18 is a flowchart illustrating an example of a generation process of the relational logical expression 1400 according to the fourth embodiment. Note that the process shown in FIG. 18 is executed in advance offline, for example, before the process of calculating the optimum operation amount.

  First, the first-order predicate logical expression generation unit 111 of the offline processing unit 110 inputs the model expression 1100, the upper and lower limit constraints 1200, the evaluation function 1300, and the change rate constraint 2000, and generates a first-order predicate logical expression ψ Step S601).

Here, the first order predicate logical expression generation unit 111 generates the first order predicate logical expression ψ as follows. That is, the first-order predicate logical expression generation unit 111 arranges the upper and lower limit constraints 1200 so that the right side becomes 0, that is, LMV _m −MV _m ≦ 0, MV _m −HMV _m ≦ 0, and changes The rate constraint 2000 is arranged so that the right side becomes 0, that is, PV _n ⁰ −δ _n ¹ −PV _n ≦ 0 and PV _n −PV _n ⁰ −δ _n ^u ≦ 0. Next, the first-order predicate logical expression generation unit 111 multiplies LMV _m −MV _m and MV _m −HMV _m by a Lagrange multiplier (λ1 _m , λ2 _m ), and PV _n ⁰ −δ _n ^l −PV. An expression obtained by multiplying _n and PV _n −PV _n ⁰ −δ _n ^u by a Lagrangian multiplier (λ 3 _n , λ 4 _n ) is added to the evaluation function E, thereby generating the following Lagrangian function L.

Next, the first-order predicate logical expression generation unit 111 satisfies the following conditions so as to satisfy the optimality condition (KKT condition) for m = 1,..., M, n = 1,. Generate an expression. In other words, the first-order predicate logical expression generation unit 111 satisfies the optimality condition (KKT condition) by the number of constraints (m = 1,..., M, n = 1,..., N). The following conditional expression is generated.

Next, the first-order predicate logical expression generation unit 111 includes the following conditional expression ψ5 obtained by combining the conditional expressions ψ1 _m , ψ2 _m , ψ3 _m, and ψ4 _m generated above with a logical product, and the conditional expression ψ6 generated above. _The following conditional expression ψ9 is generated by combining _n , ψ7 _n, and ψ8 _n with a logical product.

Then, the first-order predicate logical expression generation unit 111 performs Lagrange multipliers (λ1 _m , λ2 _m , λ3 _n , λ4 _n ) for the logical expression ψ5 ∧ ψ9 obtained by combining the conditional expression ψ5 and the conditional expression ψ9 with a logical product. Is given an existence symbol (∃) to generate the following first-order predicate logical expression ψ.

Thereby, the first order predicate logical expression generation unit 111 generates the first order predicate logical expression ψ.

  Next, the quantifier elimination unit 112 of the offline processing unit 110 generates the relational logical expression 1400 from the first-order predicate logical expression ψ by the quantifier elimination method (step S602). Here, if the relational logical expression 1400 is represented as φ, the quantifier elimination unit 112 generates the following relational logical expression φ by erasing the Lagrange multiplier by the quantifier elimination method.

As a result, the relational logical expression φ is generated from the first-order predicate logical expression ψ in consideration of the change rate constraint 2000.

Here, for n = 1,..., N, PV _n ⁰ is a variable representing the current value of the controlled variable, and the region R _k (k = 1,..., K) is a divided logical expression φ ^Rk (SV ₁ ,..., SV _N , PV ₁ ⁰ ,..., PV _N ⁰ ) indicates a region where the ^value is true. That is, the above-described relational logical formula φ is obtained by dividing a 2N-dimensional space with SV ₁ ,..., SV _N , PV ₁ ⁰ ,..., PV _N ⁰ as respective axes into K regions Rk (k = 1. ..., K).

Also, the operation amount determination function _g ^{m Rk} is, the target value _p 1, ..., if the current value _q 1 of _{p N} and the controlled variable, ..., and the _{q N} inside the region Rk (i.e., the target the value p _1, ..., the current value q ₁ of p _N and the controlled _variable, ..., and a q _N represents the manipulated variable determining function for calculating the optimum operation amount in the case) included in the region Rk . This equation is determined by performing the quantifier elimination method on the first order predicate logical expression ψ in consideration of the change rate constraint.

Thus, the relationship formulas phi, variable _SV 1 representing a target value, ..., variable _PV ¹ 0 representing the current value of the SV _N and the controlled variable, ..., a _PV ^{N 0} and the axis split logical expression phi ^Rk dividing the space ^{_{(SV 1, ···, SV N}} , PV 1 0, ···, PV N 0) and the target value _p 1, ···, _{p N} and the controlled variable of the current An operation amount determining function g _m ^Rk (SV ₁ ,..., SV _N , PV ₁ ⁰ ,... For calculating an optimum operation amount when the values q ₁ ,..., Q _N are included in the region Rk. ., PV _N ⁰ ) is expressed as a logical sum of logical products. As a result, the relational symbol φ is generated by the quantifier elimination unit 112.

<Optimum operation amount calculation processing>
Area determining portion 121 of the line processing unit 120, a target value _p 1 to the split logical expression, ..., and _{p N,} control of the current value _q 1, ..., and inputs the _{q N,} logically divided It is determined whether or not the expression φ ^Rk (p ₁ ,..., P _N , q ₁ ,..., Q _N ) = True. Note that the target value 1500 and the current value 2100 input to the online processing unit 120 may be different for each control cycle, for example.

When the region determination unit 121 of the online processing unit 120 determines that the divided logical expression φ ^Rk (p ₁ ,..., P _N , q ₁ ,..., Q _N ) = True, the online processing unit 120 control input calculation block 122, the target value _p 1, ..., and _{p N,} the current value _q 1 of the controlled variable, ..., the target value of the operation amount determination function corresponding to the region Rk containing the a _{q N p 1,} ···, p _N and the current value _q 1, ···, by substituting the _{q N,} optimal manipulated variable _s 1, ···, by which to calculate the _{s M,} optimal manipulated variable In the calculation process, it is possible to calculate the optimum operation amount considering the change rate constraint 2000. The calculation process of the optimum operation amount is the same as that in the first embodiment, and the description thereof is omitted.

  As a result of considering the change rate constraint 2000, even if the operation target is operated with an optimal operation amount, the control amount may not reach the target value with a single operation. In such a case, for example, by repeating the calculation of the optimum operation amount and the operation on the operation target for each control cycle, the control amount can reach the target value while the change rate constraint 2000 is satisfied. .

[Example 1]
Hereinafter, Example 1 of the optimum control apparatus 10 according to the present embodiment will be described. In Example 1, the case where the heat pump model shown in FIG. 19 is controlled as a system to be controlled will be described. The heat pump model shown in FIG. 19 includes a compressor 200, an expansion valve 300, a condenser 400, and an evaporator 500. When the operation amount (MV ₁ : compressor motor rotation rate) of the compressor 200 is increased, the control amount (PV ₁ : condensation temperature) of the condenser 400 becomes high, and the control amount (PV ₂ : evaporation temperature) of the evaporator 500 increases. ) Becomes cold. On the other hand, when the operation amount (MV ₂ : expansion valve opening) of the expansion valve 300 is increased, the control amount (PV ₁ : condensation temperature) of the condenser 400 becomes low, and the control amount (PV ₂ : Evaporation temperature) becomes high. In the first embodiment, the operation amount of the compressor 200, the operation amount of the expansion valve 300, the control amount of the condenser 400, and the control amount of the evaporator 500 are modeled in the following relationship. .

At this time, the operation amount of the compressor 200 and the operation amount of the expansion valve 300 are adjusted, and the control amount of the condenser 400 and the control amount of the evaporator 500 are controlled to the target values (SV ₁ and SV ₂ ). Shall.

Further, the operation amount of the compressor 200 and the operation amount of the expansion valve 300 have upper and lower limit constraints of 1800 ≦ MV ₁ ≦ 3400 and 500 ≦ MV ₂ ≦ 700, respectively, and an error between the target value and the control amount is determined. The evaluation function E to be evaluated is as follows.

At this time, in step S101 of FIG. 4, the first-order predicate logical expression generation unit 111 generates the following Lagrangian function L.

Next, the first-order logic formulas generator 111, optimality satisfies conditional expressions _{ψ1 1, ψ1 2, ψ2 1} , ψ2 2, ψ3 1, ψ3 2, ψ4 1, ψ4 2 is generated. Then, conditional expressions _{ψ1 1, ψ1 2, ψ2 1} , ψ2 2, ψ3 1, ψ3 2, ψ4 1, ψ4 2 is generated ψ5 joined by logical, that exist in the Lagrange multiplier symbols are given First-order predicate logical expression ψ: = ∃λ1 ₁ ∃λ1 ₂ ∃λ2 ₁ ∃λ2 ₂ (ψ5) is generated.

Thereafter, in step S102 of FIG. 4, the quantifier erasure unit 112 generates the relational logical expression φ from the first-order predicate logical expression ψ by the quantifier elimination method. Here, FIG. 20 shows the area division represented by the division logical expression ^φRk of the relational logical expression φ in the first embodiment. In FIG. 20, the case where it divided | segmented into the some area | region containing area | region R1-R7 is shown. An operation amount determination function g _m ^Rk for calculating an optimum operation amount is determined for each region shown in FIG.

Next, a case where the optimum operation amount is determined will be described. As an example, the target values are p ₁ = 63 and p ₂ = 0. In this case, in step S202 of FIG. 6, the region determination unit 121 determines that the target value (p ₁ , p ₂ ) is included in the region R7. Therefore, the operation amount calculation unit 122 calculates the optimum operation amount using the following equation.

By substituting target values (p ₁ = 63, p ₂ = 0) for SV ₁ and SV ₂ of the operation amount determination function shown in the above equation 27, the following optimum operation amounts s ₁ and s _{2 are obtained.} Is calculated.

On the other hand, when the manipulated variables MV ₁ and MV ₂ are (56950004) / 25877 and (45129733) / 77631, respectively, the controlled variables PV ₁ and PV ₂ are 63 and 0, respectively, which coincide with the target value.

Here, in the first embodiment, 1000 target values SV ₁ and SV in a case where an optimal control amount (that is, an optimal operation amount) is calculated by the optimal control device 10 using a certain 1000 target values. A plot result obtained by plotting ₂ is shown in FIG. Further, FIG. 22 shows a comparative example with the prior art at this time. As shown in FIG. 21, it can be seen that these plot results are concentrated in a specific area. For this reason, for example, when the cache mechanism unit 123 is used, it is easy to hit an area with higher priority, and high speed can be expected. Further, in the example shown in FIG. 22, when the optimum operation amount is calculated by the optimization function (Mathematica) using the interior point method as the conventional technique, the optimum operation amount is obtained by the optimum control device 10 according to the present embodiment. The calculated case is shown. As shown in FIG. 22, it is 0.022122 [sec] in the conventional technique, but 0.000255 [sec] in the optimum control apparatus 10 according to this embodiment, and the calculation time is about 1/87. You can see that it has been shortened. As described above, according to the optimal control device 10 according to the present embodiment, the optimal operation amount for causing the control amount to follow the target value can be calculated at a higher speed than in the conventional technique.

  In addition, when the optimal control apparatus 10 which concerns on this embodiment has the cache mechanism part 123, it was 0.000203 [sec], and it was 1.26 times faster.

[Example 2]
Hereinafter, Example 2 of the optimum control apparatus 10 according to the present embodiment will be described. In the second embodiment, a case where there is a change rate constraint on the control amount of the heat pump model of the first embodiment will be described. This change rate constraint is as follows.

Specifically, the change rate constraint is a constraint condition in which the controlled variables (PV ₁ and PV ₂ ) change only 1 ° C. in one control cycle. PV ₁ ⁰ and PV ₂ ⁰ represent the values of PV ₁ and PV ₂ at the time of control, respectively.

  At this time, in step S101 of FIG. 4, the first-order predicate logical expression generation unit 111 generates the following Lagrangian function L.

Next, the first-order logic formulas generator 111, condition .psi.1 ₁ so as to satisfy the optimality _{condition, ψ1 2, ψ2 1, ψ2} 2, ψ3 1, ψ3 2, ψ4 1, ψ4 2, ψ5, ψ6 1 , Ψ6 ₂ , ψ7 ₁ , ψ7 ₂ , ψ8 ₁ , ψ8 ₂ , ψ9 are generated. Then, for ψ5∧ψ9 obtained by combining ψ5 and ψ9 with a logical product, an existence symbol is present in a Lagrange multiplier (λ1 ₁ , λ1 ₂ , λ2 ₁ , λ2 ₂ , λ3 ₁ , λ3 ₂ , λ4 ₁ , λ4 ₂ ). As a result, the first-order predicate logical expression ψ: = ∃λ1 ₁ ∃λ1 ₂ ∃λ2 ₁ ∃λ2 ₂ ∃λ3 ₁ ∃λ3 ₂ ∃λ4 ₁ ∃λ4 ₂ (ψ5∧ψ9) is generated.

  Thereafter, in step S102 of FIG. 4, the quantifier erasure unit 112 generates the relational logical expression φ from the first-order predicate logical expression ψ by the quantifier elimination method. As a result, the optimum operation amount that satisfies the change rate constraint is calculated in the optimum operation amount calculation process.

Here, FIG. 23 shows a temporal change when the control amount is controlled by repeatedly executing the optimum operation amount calculation process for each control cycle. 23 (a) shows the time change of PV ₁ , FIG. 23 (b) shows the time change of PV ₂ , FIG. 23 (c) shows the time change of MV ₁ , and FIG. 23 (d) shows the time change of MV _2. Yes. As shown in FIG. 23A to FIG. 23D, the operation amount at each time is set so that the control amount approaches the target value while satisfying the change rate condition (the change in the control amount is within 1 ° C.). It has been calculated.

FIG. 24 shows a case where the divided logical expression φ ^Rk of the relational logical expression φ is visualized for each control period t when the optimal control by the optimal control apparatus 10 according to the present embodiment is repeatedly executed for each control period t. Show. In the example shown in FIG. 24, the current value of the controlled variable at each control cycle t is observed, and the divided logical expression ^φRk to which the observed value is substituted is visualized. In t = 1 to t = 4, for example, it can be seen that the region R1 has changed greatly. On the other hand, the region R1 hardly changes at t = 5 to t = 7. This is because, as shown in FIGS. 23A and 23B, when t = 5 to t = 7, PV ₁ and PV ₂ approach the target values p ₁ and p _2. is there.

<Summary>
As described above, the optimal control apparatus 10 according to the present embodiment generates a relational logical expression offline in multivariable control in which a plurality of control amounts follow a target value, and then online the relational logical expression and the target The optimum operation amount is calculated from the value. As a result, the optimum control apparatus 10 according to the present embodiment can perform multivariable control even with a device having relatively few calculation resources such as an edge device.

  Further, the optimum control apparatus 10 according to the present embodiment generates a relational logical expression using quantifier elimination when the relational logical expression is generated. Thereby, in the optimal control apparatus 10 which concerns on this embodiment, the exact optimal control law (namely, relational logic formula (phi)) without a numerical error can be produced | generated.

  The present invention is not limited to the specifically disclosed embodiments, and various modifications and changes can be made without departing from the scope of the claims.

DESCRIPTION OF SYMBOLS 10 Optimal control apparatus 100 Optimal control processing part 110 Offline processing part 111 First-order predicate logical expression generation part 112 Limit symbol elimination part 120 Online processing part 121 Area determination part 122 Operation amount calculation part

Claims (13)

A control method used for multivariable control in which a plurality of control amounts follow a target value,
A model expression representing the relationship between a variable representing the manipulated variable and the variable representing the controlled variable in the controlled object, upper and lower limit constraints representing the upper and lower limits of the variable representing the manipulated variable, and the target value and the controlled variable When an evaluation function for evaluating the difference is input, a relational logical expression representing a relationship that the variable representing the target value and the variable representing the manipulated variable should satisfy so that the evaluation function satisfies the optimality condition A generation procedure for generating in advance,
A calculation procedure for calculating the operation amount for causing the plurality of control amounts to follow the target value based on the target value and the relational logical formula each time the target value is input;
A control method characterized in that a computer executes. The generation procedure is as follows:
A Lagrangian function is generated from the model formula, the upper and lower limit constraints, the evaluation function, and a Lagrange multiplier,
The Lagrangian function generates a conditional expression that satisfies the optimality condition;
A first-order predicate logical expression is generated by assigning an existence symbol to the Lagrange multiplier of the conditional expression, and a quantifier elimination method is applied to the first-order predicate logical expression to be configured by a variable representing the target value. Generating a relational logical expression composed of a division logical expression that divides the space into a plurality of areas and an operation amount determination function that calculates the optimum operation amount for each of the divided areas; The control method according to claim 1. The calculation procedure is as follows:
By searching for a region including the target value among a plurality of regions divided by the division logical formula, and substituting the target value into an operation amount determination function corresponding to the searched region, the manipulated variable is obtained. The control method according to claim 2, wherein the control method is calculated. The generation procedure is as follows:
A Lagrangian function is generated from the model formula, the upper and lower limit constraints, the evaluation function, a Lagrange multiplier, and a rate-of-change constraint of the control amount per unit time,
The Lagrangian function generates a conditional expression that satisfies the optimality condition;
An existence symbol is assigned to the Lagrange multiplier of the conditional expression to generate a first order predicate logical expression,
Applying a quantifier elimination method to the first-order predicate logical expression, a divided logical expression that divides a space constituted by a variable representing the target value and a variable representing the current value of the controlled variable into a plurality of regions; For each divided area, generate the relational logical expression composed of an operation amount determination function for calculating the optimum operation amount,
The calculation procedure is as follows:
A search is made for a region including the target value and the current value of the control amount among a plurality of regions divided by the division logical expression, and the target value and the control value determination function corresponding to the searched region are searched for. Substituting the current value of the controlled variable to calculate the manipulated variable,
The control method according to claim 1. The generation procedure is as follows:
A Lagrangian function is generated from the model formula, the upper and lower limit constraints, the evaluation function, a Lagrange multiplier, and a unit time change rate constraint of the manipulated variable,
The Lagrangian function generates a conditional expression that satisfies the optimality condition;
An existence symbol is assigned to the Lagrange multiplier of the conditional expression to generate a first order predicate logical expression,
Applying a quantifier elimination method to the first order predicate logical expression, a divided logical expression that divides a space constituted by a variable representing the target value and a variable representing the current value of the manipulated variable into a plurality of regions; For each of the divided areas, generate the relational logical expression constituted by an operation amount determination function that calculates the optimum operation amount,
The calculation procedure is as follows:
A search is made for a region including the target value and the current value of the manipulated variable among a plurality of regions divided by the division logical formula, and the target value and the manipulated value determination function corresponding to the searched region are searched for. Substituting the current value of the manipulated variable to calculate the manipulated variable,
The control method according to claim 1. The calculation procedure is as follows:
Searching for a region including the target value among a plurality of regions divided by the division logical expression according to the priority by referring to a cache storing the priority of the region to be searched. The control method according to claim 3, wherein:   The computer executes an update procedure for updating the cache so that the priority of the searched area becomes higher when an area including the target value is searched. Control method.   A visualization procedure for calculating a predetermined evaluation value from the control amount calculated using the operation amount calculated by the calculation procedure and the model formula, and the target value, and visualizing the calculated evaluation value, The control method according to claim 1, wherein the control method is executed by a computer.   When optimal control is performed from the relational logical expression and the model expression, a first-order predicate logical expression corresponding to a region where the deviation becomes a predetermined value is generated, and the region corresponding to the deviation becomes a predetermined value A visualization procedure for generating a controllable logical expression representing a region where the deviation is a predetermined value by applying a quantifier elimination method to the first-order predicate logical expression, and visualizing the generated control ability logical expression; The control method according to claim 1, wherein the control method is executed.   An output procedure for outputting either the operation amount calculated by the calculation procedure or the control amount calculated using the operation amount and the model formula to another device connected to the computer; The control method according to claim 1, wherein the control method is executed.   The said model formula is produced | generated by regression analysis using the actual value of the manipulated variable, and the actual value of the control amount corresponding to the actual value of the manipulated variable. The control method according to one item. A control device that performs multi-variable control for causing a plurality of control amounts to follow a target value,
A model expression representing the relationship between a variable representing the manipulated variable and the variable representing the controlled variable in the controlled object, upper and lower limit constraints representing the upper and lower limits of the variable representing the manipulated variable, and the target value and the controlled variable When an evaluation function for evaluating the difference is input, a relational logical expression representing a relationship that the variable representing the target value and the variable representing the manipulated variable should satisfy so that the evaluation function satisfies the optimality condition Generating means for generating in advance;
Calculation means for calculating the operation amount for causing the plurality of control amounts to follow the target value based on the target value and the relational logical formula each time the target value is input;
A control device comprising: A computer that performs multivariable control that allows multiple control amounts to follow a target value,
A model expression representing the relationship between a variable representing the manipulated variable and the variable representing the controlled variable in the controlled object, upper and lower limit constraints representing the upper and lower limits of the variable representing the manipulated variable, and the target value and the controlled variable When an evaluation function for evaluating the difference is input, a relational logical expression representing a relationship that the variable representing the target value and the variable representing the manipulated variable should satisfy so that the evaluation function satisfies the optimality condition Generation procedure for generating in advance,
A calculation procedure for calculating the operation amount for causing the plurality of control amounts to follow the target value based on the target value and the relational logical expression each time the target value is input.
A program characterized by executing