JP6260214B2 - Information processing method, apparatus and program - Google Patents

Description

  The present technology relates to model predictive control.

  Model predictive control is a control method that determines the input to a controlled object by optimizing the response to a finite time future at each time. High control performance is expected as a control method that can explicitly handle inequality constraints such as manipulated variable saturation.

  Although application of this model predictive control is considered in various fields, application to intake system control of a diesel engine is also considered. The diesel engine intake system uses EGR (Exhaust Gas Recirculator) and VNT (Variable Nozzle Turbo), MAF (Mass Air Flow) and MAP (Manifold Absolute Pressure). In many cases, PID (Proportional, Integral and Differential) control is performed as SISO (Single Input Single Output) independently. However, since EGR and VNT share exhaust and interfere with each other, it is difficult for current methods to ensure sufficient target follow-up to achieve low environmental load performance.

  For this reason, 2-input 2-output MIMO (Multi-Input and Multi-Output) control for controlling MAF and MAP with EGR and VNT has been studied. Here, due to saturation of the operation amount of the EGR valve and VNT nozzle. Degradation of target value tracking performance is a major problem. As a solution to this problem, the model predictive control described above is expected.

  However, when model predictive control is applied to a fast-response target such as an intake system, a major issue is the calculation time required for optimization calculation performed at each sample time interval. Various approaches have been made to deal with this problem, and the technique used therein is a method of relaxing an optimization problem with a manipulated variable (also called control input) saturation condition using a penalty function.

  On the other hand, little consideration has been given to the case where a state constraint exists in a plant to be controlled such as an engine. And the point of how the calculation time in real-time processing can be suppressed is not specifically considered.

Yuhei Umeda, Tsutohito Maruyama, Tomohiro Shimura, Hirokazu Anai, “Efficient solution of model predictive control using algebraic simplification”, Proceedings of the 11th Annual Conference of the Society of Instrument and Control Engineers, 171-1-3 (2011 ) Y. Umeda, T. Maruyama, H. Anai, A. Ejiri and K. Shimotani, "A Fast Model Predictive Control Algorithm for Diesel Engines", Proceedings of 4th IFAC Nonlinear Model Predictive Control Conference International Federation of Automatic Control., Paper SuDR .6, 2012. Yuhei Umeda, Tsutohito Maruyama, Tomohiro Shimura, Hirokazu Anai, Junji Shimotani, “A Study on Setting a Penalty Function for Efficient Model Predictive Control of Diesel Engines”, Proc. , P0066 (2012) Yuhei Umeda, Tsutohito Maruyama, Tomohiro Shimura, Hirokazu Anai, Junji Shimotani, “Setting penalty functions for efficient model predictive control of diesel engines using GA”, Proceedings of the 3rd Japan Society for Evolutionary Computational Computing, P1-5 (2012)

  Accordingly, an object of the present technology is to provide a technology for appropriately handling a state constraint of a control target in model predictive control as one aspect.

  The off-line processing method according to the first aspect of the present invention includes (1) (a) a model predictive control evaluation function and a Lagrangian multiplier and a second function including a sum of a first function related to a state equation to be controlled. A first linear expression group obtained by partial differentiation of a function with respect to a Lagrange multiplier and including a state deviation of the controlled object and a linearized control input for the controlled object as variables; and (b) a state of the controlled object of the second function. A second linear expression group obtained by performing partial differentiation on the deviation and including the state deviation and Lagrangian multiplier of the controlled object as variables; and (c) partially differentiating the second function with respect to the linearized control input of the controlled object. And a third linear expression group including the Lagrange multiplier and the state deviation of the controlled object as variables, and (d) a penalty corresponding to the constraint condition on the controlled object of model predictive control The first linear expression group is read from the data storage unit that stores the number and (e) the relational expression related to the parameter restricted by the constraint condition, and the variable of the state deviation is eliminated except for the current value of the state deviation. Subsequent substitution is performed to transform the first linear expression group into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables, and (2) from the data storage unit to the second primary expression group. Read out the formula group, and sequentially substitute so as to eliminate the Lagrange multiplier variable, transform the second primary formula group into a fifth primary formula group including the state deviation as a variable, and (3) store data The third linear expression group is read from the unit, and the fourth linear expression group and the fifth linear expression group are substituted, so that the third linear expression group is converted into the current value of the state deviation, the linearization control input, Is transformed into a sixth primary expression group including as a variable, and (4) a sixth primary expression group The product of the first coefficient matrix and the vector for the linearization control input is transformed so as to be represented by the function vector of the current value of the state deviation, and (5) the penalty stored in the data storage unit Generate a first differential function obtained by first-order partial differentiation of the function with respect to the parameter and a second differential function obtained by second-order partial differentiation of the function, and (6) read out the relational expression from the data storage unit and relate the fourth primary expression group By substituting into the expression, the relational expression is transformed into a seventh linear expression group including the current value of the state deviation and the linearization control input as variables, and (7) the linearization control input from the seventh linear expression group. Is included, and a second coefficient matrix and a coefficient vector that are predetermined for the penalty function are calculated.

  The control method according to the second aspect of the present invention includes (1) (a) a function vector for a current value of a state deviation for a control target of model predictive control, and (b) linearization for the control target within a control period. The first coefficient matrix calculated in advance so that the product of the control input vector and the function vector is equal, and (c) the penalty function corresponding to the constraint condition in the control target of model predictive control is calculated in advance. A data storage unit for storing a second coefficient matrix and a coefficient vector, and (d) a first expression obtained by first-order partial differentiation of a penalty function and a second expression obtained by second-order partial differentiation with respect to a parameter restricted by the constraint condition The first value and the second value are read out, and the first value and the second value are calculated by substituting the value of the parameter base point obtained from the current value of the state deviation, 2) Read out the first coefficient matrix and the second coefficient matrix from the data storage unit, and obtain a first matrix that is the sum of the product of the second value and the second coefficient matrix and the first coefficient matrix. (3) From the first vector obtained by reading out the function vector from the data storage unit and substituting the current value of the state deviation into the function vector, ((first value) − (second value) And the third vector obtained by subtracting the product of the current value of the state deviation and the third value obtained from the current value of the state deviation or the value one unit time before the linearization control input)) and the coefficient vector (4) A vector of the linearization control input is generated by the product of the inverse matrix of the first matrix and the second vector, and (5) the first time among the elements of the vector of the linearization control input Including a process for extracting linearization control inputs for.

  According to one aspect, in the model predictive control, it is possible to appropriately handle the state constraint of the control target with the penalty function.

FIG. 1 is a diagram illustrating an example of an intake system of a diesel engine. FIG. 2 is a diagram illustrating an example of a block diagram of the engine control apparatus. FIG. 3 is a functional block diagram of the offline processing apparatus. FIG. 4 is a diagram showing a processing flow of processing executed by the offline processing device. FIG. 5 is a functional block diagram of the model prediction control unit. FIG. 6 is a diagram illustrating a processing flow of processing executed by the model prediction control unit. FIG. 7 is a diagram showing an equivalent circuit of the lithium ion battery. FIG. 8 is a diagram illustrating a first example of a penalty function according to the third embodiment. FIG. 9 is a diagram illustrating a second example of the penalty function according to the third embodiment. FIG. 10 is a diagram illustrating a processing flow of processing executed by the model prediction control unit according to the third embodiment. FIG. 11 is a diagram illustrating an example of a penalty function according to the fourth embodiment. FIG. 12 is a functional block diagram of a computer. FIG. 13 is a functional block diagram of the control device.

[Embodiment 1]
FIG. 1 shows a diesel engine intake system. The intake control system of the diesel engine includes an intake pressure control system and a new air volume control system. In order to reduce particulate matter (PM) in the exhaust, the intake pressure control system controls the nozzle diameter of the variable nozzle turbo VNT to control the intake pressure to follow the intake pressure target value. . On the other hand, in order to reduce nitrogen oxide (NOx) in the exhaust, the new air amount control system controls the valve opening degree of the exhaust gas circulator EGR that recirculates the exhaust gas into the cylinder, thereby reducing the fresh air amount. Control is performed to follow the quantity target value.

  That is, the engine body 1 includes an exhaust circulator EGR that supplies exhaust gas from the engine body 1 and a variable nozzle that rotates the turbine with the pressure of the exhaust gas to compress fresh air and supply the engine body 1 with the compressed air. Turbo VNT is connected. By adjusting the nozzle opening of the variable nozzle turbo VNT, the rotation of the turbine of the variable nozzle turbo VNT is adjusted, and the intake pressure (MAP) measured by the intake pressure (MAP) sensor is adjusted. On the other hand, the fresh air amount (MAF) measured by the fresh air amount (MAF) sensor is adjusted by adjusting the valve opening degree of the EGR valve provided in the exhaust gas circulator EGR.

  In the engine control apparatus 1000 according to the present embodiment, an intake pressure measurement value from the MAP sensor, a fresh air amount measurement value from the MAF sensor, a set value of the fuel injection amount given from the outside, and the same are given from the outside. And the set value of the engine speed to be input. Further, from the engine control apparatus 1000, the operation amount of the valve opening of the EGR valve is output to the EGR valve, and the operation amount of the nozzle opening of the VNT nozzle is output to the VNT nozzle.

  Hereinafter, although an engine is demonstrated as an example of a plant, the application range of this Embodiment is not restricted to an engine.

  FIG. 2 shows a block diagram of engine control apparatus 1000 according to the present embodiment. The engine control apparatus 1000 includes a planner 210, a model prediction control unit 220, and a conversion unit 225. The plant 240 corresponds to, for example, modeled engine characteristics, and since the opening of the EGR valve and the VNT nozzle is physically limited, a saturation element 230 is also provided. That is, the operation amount to the plant 240 is limited by the saturation element 230.

The planning unit 210 of the engine control apparatus 1000 receives the fuel injection amount setting value and the engine speed setting value, and associates the fuel injection amount value and the engine speed value with the EGR valve. state target value and the VNT state target value Vref of the nozzles, the target value and the MAF target value X ^ref intake pressure MAP in association with the values and the value of the engine speed of the fuel injection amount is registered. In this embodiment, planner 210 outputs the state target value and the VNT state target value Vref of the nozzle of the EGR valve, and the target value and the MAF target value X ^ref intake pressure MAP.

A difference between the target value X ^ref and the output y (for example, MAF sensor output and MAP sensor output) from the plant 240 is input to the model prediction control unit 220. The model prediction control unit 220 performs model prediction control processing described below, and outputs a linearization control input u. The linearization control input u is converted into an EGR valve state and a VNT nozzle state v by a conversion unit 225 (g ⁻¹ ) described below. Then, the state v and the state target value Vref from the planner 210 are added to generate an operation amount, and the operation amount is input to the plant 240 via the saturation element 230. Such a process is repeated.

  Such an intake system of the engine body 1 is non-linear with respect to the EGR valve and the VNT nozzle, and the engine model also changes non-linearly according to the engine speed ω and the fuel injection amount σ.

  Here, assuming that the engine speed ω and the fuel injection amount σ are fixed, the engine model is formulated as follows.

Here, A _{ω (k), σ (k)} and B _{ω (k), σ (k)} are nonlinear 2 × 2 matrices that change depending on the operating condition (ω (k), σ (k)) at time k. It is a function. The rotational speed at time k is represented as ω (k), and the fuel injection amount is represented as σ (k). Further, the state deviation of MAF at time k is represented as x _maf (k), and the state deviation of MAP is represented as x _map (k). Further, the measured value of MAF at time k is expressed as y _maf (k), and the measured value of MAP is expressed as y _map (k). Further, the state of the EGR valve at time k is represented as v _egr (k), and the state of the VNT nozzle is represented as v _vnt (k). Further, the target value of the intake pressure MAP is expressed as X _map ^ref, and the target value of the fresh air amount MAF is expressed as X _maf ^ref .

Therefore, the state deviation vector x (k), the measurement value vector y (k), the target value vector X ^ref (k), and the state vector v (k) are expressed as follows.

The relationship between x (k), y (k) and X ^ref (k) is as follows.

  Further, the nonlinear function g is expressed as follows.

g ₁ and g ₂ are monotonically increasing functions. Based on experimental data, this assumption is valid. Since the nonlinear model is difficult to handle due to the calculation speed and the like, the nonlinear engine model is converted into a linear model below. Therefore, linearization is _performed by introducing the linearization control inputs u _egr and u _vnt described above.

  The linearization control input vector u (k) is expressed as follows.

In the present embodiment, typical operating conditions are selected and referred to as set points. Then, when the model prediction control unit 220 acquires the operating condition (ω (k), σ (k)), the model prediction control unit 220 selects the matrix A _{ω, σ} and B _{ω, σ} for ω and σ for the corresponding setpoint. Then, the linearization control input u is calculated by performing the processing described below. Also, the conversion function 225 converts the linearization control input u into a non-linear optimal state v using the conversion function g ⁻¹ . The optimum state v and the state target value Vref are added to generate an operation amount and output to the engine plant 240.

  The model prediction control unit 220 calculates an optimal linearization control input u for the set point according to the following linear model for each sample time.

  However, the constraint conditions for the linearization control input u are as follows.

For example, when ω = 2000 rpm and σ = 20 mm ³ / st, the following matrix is used.

  The linearization control input u for each time k is determined by minimizing an evaluation function J as shown below. Note that the predicted horizon Hp and the control horizon Hc are set in advance.

Here, Q ^T is a transposed matrix of the matrix Q. QεM (n, R), RεM (n, R), and SεM (n, R) are weight matrices and are set in advance. M (n, R) represents an n × n matrix. In Equation (9), the optimization problem for infinite horizon is changed to the optimization problem for finite horizon, and therefore, the weight matrix S is used as a matrix for solving the Ricatti algebraic equation.

  In the present embodiment, the model predictive control problem is transformed into solving a finite horizon optimal control problem.

  Here, x represents the current state deviation vector.

  Lagrange's undetermined multiplier method is efficient as a method for obtaining an optimal solution, but this method cannot be used as it is when there is an inequality constraint. Therefore, a penalty function is introduced instead of the inequality constraint to relax the evaluation function without the inequality constraint.

  That is, the evaluation function is relaxed to the following evaluation function Jb.

  Here, p (u (k + i)) is a penalty function, and when the input value u (k + i) approaches the boundary of the possible value range, a large value is added to the evaluation function J.

In general, the following penalty functions are used for the inequality constraint u ≦ u ^max .

  r is a coefficient of the penalty function and represents a weight for the inequality constraint.

  In the present embodiment, a simple penalty function such as (c) is preferable for the following calculation, and (c) will be used.

  In the case of a diesel engine, the following restrictions exist on the linearization control input u.

  When the penalty function having the form as shown in (c) is adopted, the penalty function is expressed as follows.

  When the constraint condition is relaxed using the equation (15), it results in solving the optimal control problem for the finite horizon as shown below.

In order to solve such an optimal control problem, Lagrange's undetermined multiplier method is used. Here, the Lagrange multiplier λ (j) = [λ _maf (j), λ _map (j)] ^T is used, and the Hamiltonian H is expressed as follows.

  Here, Х (capital letter of χ) is defined as follows.

If ∇x _{, u, λ} H = 0, the following equation is obtained.

  In the equation (20), 変 形 Jb / ∂x = ∂J / ∂x + ∂p (u) / ∂x = ∂J / ∂x.

  Note that ∂ / ∂x, ∂ / ∂u, and ∂ / ∂λ are the following calculations.

  The equations (20) to (22) are linear equations except for the portion of ∂p / ∂u. When で p / ∂u is linearized by Taylor expansion with the optimal linearization control input u ~ ("~" is added on u) of the immediately preceding step, it is expressed as follows.

  The EGR component of the first term of the equation (23) is expressed as follows. The VNT component is also expressed in the same manner.

  If such linear approximation is performed, the equations (20) to (22) become linear. Then, the linearly approximated equations (20) to (22) are expressed as follows.

Here, M is a matrix of (2H _p + H _c ) × (2H _p + H _c ), and U and b are (2H _p + H _c ) vectors. The vector U is expressed as follows.

Further, the vector b is expressed as follows. Note that b _maf , b _map, and b _const are (2H _p + H _c ) matrices calculated by matrix conversion.

b = x _maf b _maf + x _map b _map + b _const (27)

  The optimal linearization control input is obtained by solving this linear equation. However, if the size of the matrix M is large, the calculation time becomes long. Therefore, the size of the matrix M is reduced by offline preprocessing.

  First, the first to third equations of equation (22) are specifically written as follows.

The state deviations x _maf (k) and x _map (k) in the expressions (28-1) and (28-2) are current values. Therefore, according to the equation (28-1), x _maf (k + 1) is expressed by a linear equation of the linearization control input u (k). According to Expression (28-2), x _map (k + 1) is also expressed by a linear expression of the linearization control input u (k). Further, according to the equation (29), x _maf (k + 2) is expressed by a linear equation of state deviation and linearization control input. However, if the expressions (28-1) and (28-2) are substituted into the expression (29), x _maf (k + 2) can be expressed by the linearization control inputs u (k) and u (k + 1). become. If this is _repeated while increasing i, the state deviations x _maf (k + i) and x _map (k + i) are expressed as follows as a linear expression of the linearization control input.

On the other hand, the (2H _p −1) th and (2H _p -3) th equations of the equation (20) are specifically written as follows.

Here, s ₁₁ , s ₂₂ , and r ₁₁ represent matrix components of the weight matrices S and R.

It can be seen that the equations (31) and (32) are expressed by linear equations of λ _maf (H _p ) and λ _map (H _p ). Therefore, when the equations (31) and (32) are substituted into the equation (33), λ _maf (H _p −1) becomes the target value X ^ref _maf , the state deviation x (k + H _p ), and x (k + H _p −). 1). By sequentially performing such processing while decreasing i, the Lagrange multiplier λ (k + i) is expressed as follows.

  Further, by substituting equation (30) into equation (34), Lagrange multiplier λ (k + i) is transformed into a linear expression of linearization control input u (k).

  Finally, when the equations (30) and (35) are substituted into the equation (21), they are expressed as follows.

  In this way, the equation (21) can be expressed by the linear equation control input u and the initial value x (k) of the state deviation. Then, the expression (36) can be corrected to the following form.

Here, M ₂ is an H _c × H _c matrix. U ₂ and b ₂ are vectors of the form:

Note that b _2maf , b _2map, and b _2const are (2H _p + H _c ) matrices calculated by matrix conversion.

If such processing is performed off-line using mathematical expression processing, the engine control apparatus 1000 may perform an operation to solve Expression (37). Since the size of the matrix M ₂ is smaller than that of the matrix M and the amount of calculation is reduced, the control input can be obtained at high speed.

  Next, let us consider a case where a general state constraint is introduced in addition to the control input. For example, in a diesel engine, in order to improve fuel efficiency, the excess air ratio of gas sent to the engine body during operation (generally expressed using λ, but τ is used here to avoid duplication of symbols) is constant. It is required to keep above.

ここで、行列Ｃ及びＤは、１行２列行列である。 The excess air ratio τ uses the MAF and MAP state deviation vector x (k + i) and the linearized input vector u (k + i) for each time k + i according to each operating condition (that is, rotation speed and fuel injection charge). Is approximated as follows.

Here, the matrices C and D are 1 × 2 matrices.

In the MAF and MAP control of the diesel engine using the model predictive control, the following constraint condition of the excess air ratio τ is applied to each time.

τ₀は、空気過剰率の初期値である。 Therefore, the problem of model predictive control is expressed as follows.

τ ₀ is an initial value of the excess air ratio.

  However, since the model predictive control problem becomes a problem including inequality constraints and cannot be solved practically as it is, for example, by introducing a penalty function as shown below, the inequality constraint problem is reduced to an equality constraint problem .

Here, adding the penalty function of the equation (41) with respect to the evaluation function J _b. Then, it is expressed as follows.

  Further, from the equation (40-2), τ (k + i) at each time is specifically expressed as follows.

  Then, if equation (30) is substituted into equation (42), τ (k + i) is written as follows.

Then, τ (k + i) for all i, u (0) to u since it is a function of _{(H c -1), (42} ) equation u (0) is also the penalty function to u (H _c - It can be considered as a function of 1). Therefore, the optimization problem described in the equations (20) to (22) with respect to the input constraint is modified as follows.

In order to solve such equations (46) to (48), ∂q _b (x) / ∂u related to the penalty function for the state is linearized.

First, ∂q _b (τ (k + i)) / ∂u _egr (k + j) is expressed as follows. Further, the second line is also obtained from the equation (43).

Next, ∂q _b (τ (k + i)) / ∂τ (k + i) in the equation (51) is linearized. At that time, when the first-order Taylor expansion is performed with the following optimal linearization control input u˜, ∂q _b (τ (k + i)) / ∂τ (k + i) is expressed as follows.

  Moreover, it represents as follows similarly to (51) Formula.

  Therefore, the following approximate expression can be obtained.

  Therefore, the following approximate expression is obtained by combining the expressions (51) and (54).

Here, a base point of τ to be substituted as a variable of the penalty function portion is set for approximation. x ~ (k + i) ("~" is assumed to be on x) is set as a state deviation base point corresponding to u ~. And since the fluctuation | variation of the value of the state deviation in a short time is small, ^xbase (k) is represented as follows.

Therefore, from the equation (40-2), the base point τ ^base (k) of τ is expressed as follows. Note that u * (k−1) is an optimal linearization control input one unit time ago.

When such a base point τ ^base (k) is used, the equation (43) is transformed as follows.

  Here, the expression (57) is expressed as follows.

Furthermore, if τ (k + i) is approximated to τ ^base (k), {∂ ² q _b (τ (k + i)) / ∂τ (k + i) ² } (u˜) is τ ^base (k ) Is the same function. Similarly, {∂q _b (τ (k + i)) / ∂τ (k + i)} (u˜) is the same function with respect to τ ^base (k) for all i.

In the following, the first partial differential with respect to τ of the penalty function is represented as ∂ (τ), the second partial partial derivative is represented as ∂ ² (τ), and τ (τ ^base (k)) and τ = τ ^base (k) and By ∂ ² (τ ^base (k)), equation (55) is expressed as follows.

  From the equation (62), the following approximation is also performed.

  Furthermore, the following approximation is also performed from the equation (63).

Here, Λ ^l and ν ^l are expressed as follows.

Note that p in Λ ^l is fixed at 2j + 1, and q increases from 1 to H _c . That is, Λ ^l is a matrix of 1 row and H _c columns.

  Therefore, from the equations (64) and (37), the optimization problem with the penalty function for the state is mitigated as follows.

In order to solve the equation (65) by the engine control apparatus 1000, M ₂ , b ₂ , Λ ^l and ν ^l are prepared in advance offline, and the first-order partial differential に つ い て (τ) and τ of the penalty function The second-order partial differential ∂ ² (τ) is previously calculated offline. In the engine control apparatus 1000, τ ^base (k) is calculated by the equation (56), ∂ (τ ^base (k)) and ∂ ² (τ ^base (k)) are calculated, and d ^l (τ ^base (k)) is calculated by equation (58). Then, the equation (65) is solved.

  Next, a functional block diagram of the offline processing apparatus 100 according to the present embodiment is shown in FIG. In the present embodiment, the offline processing apparatus 100 includes an input unit 101, an input data storage unit 102, a first deformation processing unit 103, a first data storage unit 104, a second deformation processing unit 105, and a second Data storage unit 106, third transformation processing unit 107, third data storage unit 108, first matrix generation unit 109, fourth data storage unit 110, second matrix generation unit 111, and differentiation processing unit 112 And have.

Next, processing contents of the offline processing apparatus 100 will be described with reference to FIG. First, the input unit 101 receives input of values such as matrices A, B, C, D, S, and R, predicted horizon H _p, and control horizon H _c as input data from the user, and the input data storage unit 102 receives the input. Store (FIG. 4: step S1). When not stored in the input data storage unit 102, the data of the equations (46) to (48) are also stored in the input data storage unit 102 via the input unit 101. Similarly, the data of the expression relating to the input constraint (formula (24)) is also stored in the input data storage unit 102 and is input via the input unit 101 if not stored. . Further, the data of the expression related to τ (k + i) expressed using the state deviation vector x (k + i) and the linearized input vector u (k + i) is also stored in the input data storage unit 102 and stored. If not, it is input via the input unit 101.

  Next, the first transformation processing unit 103 executes the first transformation processing for the state deviation x using the data stored in the input data storage unit 102 and stores the processing result in the first data storage unit 104. (Step S3). The process of substituting the expressions (28-1) and (28-2) derived from the expression (22) into the expression (29) is repeatedly executed while increasing i to generate the expression (30) for the state deviation vector. Execute the process.

  In the present embodiment, the first deformation processing unit 103 further uses the data stored in the input data storage unit 102 to execute a deformation process on the excess air ratio τ, which is a restricted parameter, The result is stored in the first data storage unit 104 (step S4). By substituting equation (30) into equation (42), τ (k + i) is written down as shown in equation (43).

  In addition, the second transformation processing unit 105 executes the second transformation processing on the Lagrange multiplier λ using the data stored in the input data storage unit 102 and stores the processing result in the second data storage unit 106. (Step S5). The process of substituting the expressions (31) and (32) derived from the expression (20) into the expression (33) is repeatedly executed while decreasing i, and the process of generating the expression (34) is executed.

  Further, the third deformation processing unit 107 performs the third deformation processing on the Lagrange multiplier λ using the data stored in the first data storage unit 104 and the second data storage unit 106, and obtains the processing result as the first result. 3 is stored in the data storage unit 108 (step S7). A process of substituting Expression (30) into Expression (34) is executed to generate Expression (35).

Then, the first matrix generation unit 109 converts the equation (30) (stored in the first data storage unit 104) and the equation (35) (stored in the third data storage unit 108) into the equation (21). Substituting into (stored in the input data storage unit 102) generates the simultaneous equations (36), and transforms them into the form of (37) to calculate the matrices M ₂ and b ₂ , Store in the fourth data storage unit 110 (step S9). The processing so far other than step S4 is almost the same as the technique described in JP 2012-194960 A.

Thereafter, the second matrix generation unit 111 uses the result of the transformation process for τ stored in the first data storage unit 104 (equation (43)) according to the equation stored in the input data storage unit 102. , A coefficient matrix Λ ^l and a coefficient vector ν ^l are generated and stored in the fourth data storage unit 110 (step S11).

Furthermore, the differential processing unit 112 stores the first-order partial differential function ∂ (τ) and the second-order partial differential function ∂ ² (τ) for the penalty function τ stored in the first data storage unit 102. Is stored in the fourth data storage unit 110 (step S13). Since the generation of the first-order partial differential function and the second-order partial differential function is well known, the description thereof is omitted here.

  By executing the processing as described above, the processing load of the engine control apparatus 1000 can be greatly reduced, and the processing speed can be increased.

  Next, FIG. 5 shows a configuration example of the model prediction control unit 220 in the engine control apparatus 1000. The model prediction control unit 220 includes a differential value calculation unit 2201, a matrix calculation unit 2202, an output generation unit 2203, and a data storage unit 2205.

  The data storage unit 2205 stores data stored in the fourth data storage unit 110.

  Next, processing contents of the model prediction control unit 220 in the engine control apparatus 1000 will be described with reference to FIG.

First, the model prediction control unit 220 acquires x (k) (= X ^ref (k) −y (k)) (FIG. 6: step S21).

Then, the model predictive control unit 220, numerically vectorize function vector b ₂ by substituting x (k) to function vector b ₂ (step S23).

In addition, the differential value calculation unit 2201 calculates τ ^base (k) (equation (56)) that is the value of the base point of the constrained parameter, and the first-order bias of the penalty function stored in the data storage unit 2205. Substituting τ ^base (k) into the differential function ∂ (τ) and second-order partial differential function ∂ ² (τ) to obtain ∂ (τ ^base (k)) and ∂ ² (τ ^base (k)) (step S25).

Then, the matrix calculation unit 2202 calculates M ₃ and b ₃ (step S27).

(M ₂ + ∂ ² (τ ^base (k)) Λ ^l ) other than the vector U _{2 on} the left side of the equation (65) is M ₃ . Further, the right side of the expression (65) is b ₃ . That is, b ₃ = b ₂ − (∂ (τ ^base (k)) − ∂ ² (τ ^base (k)) d ^l (τ ^base (k)) ν ^{l In} order to calculate b ₃ , d ^l (τ ^base (k)) is calculated by equation (58).

Then, the output generation unit 2203 calculates the vector U by U = M ⁻¹ ₃ b ₃ (step S29). Further, the output generation unit 2203 extracts the linearization control input u (k) (i = 0) from the vector U and outputs it (step S31).

  Thereafter, the model prediction control unit 220 determines whether or not the process is finished (step S33). If the process is not finished, the process returns to step S21, and if the process is finished, the process is finished.

As can be seen from the above processing, since the data calculated by the offline processing can be utilized and the size of M ₃ is also reduced, steps S25 and S27 are added by introducing a penalty function for state constraints. Even if it is done, linearization control input can be obtained at high speed. Furthermore, the penalty function is appropriately approximated so that appropriate control can be performed with high accuracy.

Note that the present invention may be applied not only to engine control but also to charge / discharge control of a lithium ion battery, for example. An equivalent circuit of the lithium ion battery is shown in FIG. The terminal voltage V (k) of the lithium ion battery includes the product of the charging rate SoC (k) and the coefficient a, the voltage v (k) at the portion where the resistor R1 and the capacitor C1 are connected in parallel, and the series equivalent resistance R _0. And the product of the flowing current i (k). That is, it is expressed by the following formula.

  Further, the charging rate SoC (k) changes according to the following relational expression. Note that FC represents the maximum storage capacity of the storage battery.

  Further, the voltage v (k) changes according to the following relational expression.

  On the other hand, general model predictive control for a state, not a state deviation, is expressed as follows.

  Then, in the case of a lithium ion battery, if the voltage v (k) and the charging rate SoC (k) are treated as the state x, the terminal voltage V (k) as the output y, and the current i (k) as the input u (k), It is expressed as

Here, when the constraint condition y _min <y (k) <y _max is applied, the following penalty function is introduced.

  This has the same shape as the equation (41) described above.

  In addition, since an expression corresponding to the expression (30) is expressed as follows, the expression (101) is substituted into these expressions. Then, an expression corresponding to the expression (43) can be obtained.

  By doing so, it is possible to modify the same equation as described above.

[Embodiment 2]
In the diesel engine as described above, control for changing MAF and MAP is performed. However, it is preferable to avoid a sudden change in MAF and MAP from the viewpoint of durability.

  In the present embodiment, in the MAF and MAP control of a diesel engine using model predictive control, a restriction for suppressing a rapid change in MAF and MAP is added. However, in order to simplify the explanation, only the constraint for suppressing a rapid change in MAF is considered.

  Such a problem is expressed as follows.

For the equation (201-5), the penalty function q _c is expressed as follows.

  Then, the objective function of model predictive control is expressed as follows.

  As described above, since only MAF is handled, the following equation is obtained from equation (201-2).

  Then, when the equation (30) is substituted into the equation (203), an equation corresponding to the equation (43) is obtained.

Then, dx (k + i) for all i, u (0) to u since it is a function of _{(H c -1), (202} ) type u (0) also the penalty function to u (H _c - It can be considered as a function of 1). Therefore, the optimization problem described in the equations (20) to (22) with respect to the input constraint is modified as follows.

In order to solve these equations (204) to (206), ∂q _c (x) / ∂u related to the penalty function for the state is linearized.

First, ∂q _c (dx _maf (k + i)) / ∂u _egr (k + j) is expressed as follows.

Next, ∂q _c (dx _maf (k + i)) / ∂dx _maf (k + i) in equation (208) is linearized. At this time, when the first-order Taylor expansion is performed with the following optimal linearization control input u˜, ∂q _c (dx _maf (k + i)) / ∂dx _maf (k + i) is expressed as follows.

  Moreover, it represents as follows similarly to (208) Formula.

  Therefore, the following approximate expression can be obtained.

  Therefore, the following approximate expression can be obtained by combining the expressions (208) and (211).

Here, a base point of dx _maf to be substituted as a variable in the penalty function portion is set for approximation. In this case, the base point dx ^base _maf (k) is expressed as follows without approximation.

  Due to the characteristics of the diesel engine, the influence of the input is dominant in the change of the state, so that the influence of the influence of the initial value on the change of the state can be handled and approximated as extremely small. Therefore, the constant part of the equation (204) is approximated from the equation (211) as follows.

Further, if the approximate dx ~ _maf the (k + i) and _{^{dx base maf (k), {}} ∂ 2 q c (dx maf (k + i)) / ∂dx maf (k + i) 2} (u ~) , all i _{Is the} same function with respect to the ^base point dx ^base _maf (k). Similarly, {∂q _c (dx _maf (k + i)) / ∂dx _maf (k + i)} (u˜) is the same function with respect to the ^base point dx ^base _maf (k) for all i.

Hereinafter, the first-order partial differential for dx (here, dx _maf ) of the penalty function is represented as ∂ (dx), the second-order partial derivative is represented as ∂ ² (dx), and ∂ (dx = dx ^base _maf (k) (dx ^base _maf (k)) and ∂ ² (dx ^base _maf (k)), the expression (212) is expressed as follows.

  From the equation (215), the following approximation is also performed.

  Furthermore, the following approximation is also performed from the equation (216).

Here, Λ ^d and ν ^d are expressed as follows.

Note that p in Λ ^d is fixed at 2j + 1, and q increases from 1 to H _c . That is, Λ ^d is a matrix of 1 row and H _c columns.

  Therefore, from the equations (217) and (37), the optimization problem with the penalty function for the state is mitigated as follows.

In order to solve the equation (218) by the engine control apparatus 1000, M ₂ , b ₂ , Λ ^d and ν ^d are prepared in advance offline, and the first-order partial differential ∂ (dx) for dx _maf of the penalty function And second-order partial differential ∂ ² (dx) is previously calculated offline. The engine control apparatus 1000 calculates dx ^base _maf (k) using equation (213) and calculates ∂ (dx ^base _maf (k)) and ∂ ² (dx ^base _maf (k)). Then, the equation (218) is solved.

Although an example in which state constraints are provided for dx _{maf has been} described above, state constraints may be provided for dx _map , or state constraints may be provided for both of them. The basic processing is as described above.

  The offline processing apparatus 100 according to the present embodiment has the same configuration as that shown in FIG.

Next, the processing content of the offline processing apparatus 100 is substantially the same as that of the first embodiment, and will be described with reference to FIG. First, the input unit 101 accepts input of values such as matrices A, B, S and R, prediction horizon H _p and control horizon H _c as input data from the user, and stores them in the input data storage unit 102 (see FIG. 4: Step S1). When not stored in the input data storage unit 102, the data of the expressions (205) to (207) are also stored in the input data storage unit 102 via the input unit 101. Similarly, the data of the expression relating to the input constraint (formula (24)) is also stored in the input data storage unit 102 and is input via the input unit 101 if not stored. . Similarly, the data of the expression relating to the change amount dx (k + i) (= x (k + i) −x (k + i−1)) of the state deviation is stored in the input data storage unit 102 and is not stored. Is input via the input unit 101.

  Next, the first transformation processing unit 103 executes the first transformation processing for the state deviation x using the data stored in the input data storage unit 102 and stores the processing result in the first data storage unit 104. (Step S3). The process of substituting the expressions (28-1) and (28-2) derived from the expression (22) into the expression (29) is repeatedly executed while increasing i to generate the expression (30) for the state deviation vector. Execute the process.

  In the present embodiment, the first deformation processing unit 103 further uses the data stored in the input data storage unit 102 to execute a deformation process on the state deviation change amount dx that is a constrained parameter. The processing result is stored in the first data storage unit 104 (step S4). Since the constraint conditions are different, this step is different from the first embodiment. By substituting equation (30) into equation (203), dx (k + i) is written down as shown in equation (204).

  In addition, the second transformation processing unit 105 executes the second transformation processing on the Lagrange multiplier λ using the data stored in the input data storage unit 102 and stores the processing result in the second data storage unit 106. (Step S5). The process of substituting the expressions (31) and (32) derived from the expression (20) into the expression (33) is repeatedly executed while decreasing i, and the process of generating the expression (34) is executed.

  Further, the third deformation processing unit 107 performs the third deformation processing on the Lagrange multiplier λ using the data stored in the first data storage unit 104 and the second data storage unit 106, and obtains the processing result as the first result. 3 is stored in the data storage unit 108 (step S7). A process of substituting Expression (30) into Expression (34) is executed to generate Expression (35).

Then, the first matrix generation unit 109 converts the equation (30) (stored in the first data storage unit 104) and the equation (35) (stored in the third data storage unit 108) into the equation (21). Substituting into (stored in the input data storage unit 102) generates the simultaneous equations (36), and transforms them into the form of (37) to calculate the matrices M ₂ and b ₂ , Store in the fourth data storage unit 110 (step S9).

Thereafter, the second matrix generation unit 111 uses the result of the transformation process for dx stored in the first data storage unit 104 (formula (204)) according to the formula stored in the input data storage unit 102. , A coefficient matrix Λ ^d and a coefficient vector ν ^d are generated and stored in the fourth data storage unit 110 (step S11). This step is also different from the first embodiment.

Further, the differential processing unit 112 stores the first-order partial differential function ∂ (dx) and τ-order partial differential function ∂ for τ in the penalty function for the change amount of the state deviation stored in the first data storage unit 102. ² (dx) is generated and stored in the fourth data storage unit 110 (step S13). Since the generation of the first-order partial differential function and the second-order partial differential function is well known, the description thereof is omitted here.

  By executing the processing as described above, the processing load of the engine control apparatus 1000 can be greatly reduced, and the processing speed can be increased.

  Further, the configuration example of the model prediction control unit 220 in the engine control apparatus 1000 is the same as that in the first embodiment.

  The data storage unit 2205 stores data stored in the fourth data storage unit 110.

  Next, the processing contents of the model prediction control unit 220 in the engine control apparatus 1000 are the same as those in the first embodiment, and will be described with reference to FIG.

First, the model prediction control unit 220 acquires x (k) (= X ^ref (k) −y (k)) (FIG. 6: step S21).

Then, the model predictive control unit 220, numerically vectorize function vector b ₂ by substituting x (k) to function vector b ₂ (step S23).

Also, the differential value calculation unit 2201 calculates dx ^base _maf (k) (equation (213)), which is the value of the base point of the constrained parameter, and the first order of the penalty function stored in the data storage unit 2205. Substituting dx ^base _maf (k) into the partial differential function ∂ (dx) and the second order partial differential function ∂ ² (dx), ∂ (dx ^base _maf (k)) and ∂ ² (dx ^base _maf (k)) Is obtained (step S25). This is different from the first embodiment.

Then, the matrix calculation unit 2202 calculates M ₃ and b ₃ (step S27).

(M ₂ + ∂ ² (dx ^base _maf (k)) Λ ^d ) other than the vector U _{2 on} the left side of the equation (218) is M ₃ . Further, the right side of the equation (218) is b ₃ . That is, b ₃ = b ₂ − (∂ (dx ^base _maf (k)) − ∂ ² (dx ^base _maf (k)) dx ^base _maf (k)) ν ^d . In order to calculate b ₃ , dx ^base _maf (k) is calculated by equation (213). This is different from the first embodiment.

Then, the output generation unit 2203 calculates the vector U by U = M ⁻¹ ₃ b ₃ (step S29). Further, the output generation unit 2203 extracts the linearization control input u (k) (i = 0) from the vector U and outputs it (step S31).

  Thereafter, the model prediction control unit 220 determines whether or not the process is finished (step S33). If the process is not finished, the process returns to step S21, and if the process is finished, the process is finished.

[Embodiment 3]
When the control is actually performed, the excess air ratio τ may exceed the limit value or may be allowed to slightly exceed the limit value. Even in this case, it is preferable to avoid exceeding the limit value as much as possible.

  In this case, for example, the following penalty function is adopted.

This penalty function is a function that changes as shown in FIG. In this way, q _b where τ is equal to or less than τ _min increases exponentially.

  Furthermore, some designers may perform control such that the excess air ratio τ changes around a desired target value.

In this case as well, in order to suppress excessive separation from the target value, the following penalty function may be adopted when the target value assumed transition section is changed from τ _min to τ _max .

This penalty function is a function that changes as shown in FIG. That is, q _b is “0” between τ _{min and} τ _max , but q _b increases exponentially as the interval is increased.

Furthermore, when it is desired to make the excess air ratio τ closer to the target value τ _ref , the following penalty function may be employed.

Even if such a penalty function is introduced, the offline processing described in the first embodiment is basically the same. However, since the form of the function differs depending on the range of the excess air ratio τ, the first-order partial differential function and the second-order partial differential function for τ (k + i) are calculated for each. That is, in step S13, a first-order partial differential function ∂ (τ) and a second-order partial differential function ∂ ² (τ) are generated for each application range.

Then, the application range of the penalty function is specified according to the value of τ (k + i), and the first-order partial differential function ∂ (τ) and the second-order partial differential function ∂ ² (τ) or “no constraint” according to the application range. (When the penalty function is “0”).

  Specifically, the processing contents of the model prediction control unit 220 will be described with reference to FIG.

First, the model prediction control unit 220 acquires x (k) (= X _ref (k) −y (k)) (FIG. 10: step S41).

Then, the model predictive control unit 220, numerically vectorize function vector b ₂ by substituting x (k) to function vector b ₂ (step S43).

  Also, the differential value calculation unit 2201 calculates τ (k) (= Cx (k−1) + Du (k−1)), which is the current value of the restricted parameter (step S44). Further, the differential value calculation unit 2201 specifies the application range of the penalty function from τ (k) (step S45).

  Then, the differential value calculation unit 2201 determines whether the specified application range is a range where the penalty function is 0 (step S47).

When the specified application range is not a range where the penalty function is 0, the differential value calculation unit 2201 calculates τ ^base (k) (expression (56)), which is a value at the base point of the constrained parameter. Then, τ ^base (k) is substituted into the first-order partial differential function ∂ (τ) and second-order partial differential function ∂ ² (τ) of the penalty function stored in the data storage unit 2205, and ∂ (τ ^base ( k)) and ∂ ² (τ ^base (k)) are obtained (step S51).

Then, the matrix calculation unit 2202 calculates M ₃ and b ₃ for the specified application range (step S53).

(M ₂ + ∂ ² (τ ^base (k)) Λ ^l ) other than the vector U _{2 on} the left side of the equation (65) is M ₃ . Further, the right side of the expression (65) is b ₃ . That is, b ₃ = b ₂ − (∂ (τ ^base (k)) − ∂ ² (τ ^base (k)) d ^l (τ ^base (k))) ν ^l . In order to calculate b ₃ , d ^l (τ ^base (k)) is calculated by equation (58). Then, the process proceeds to step S57.

On the other hand, if the specified application range is a range in which the penalty function is 0, the differential value calculation unit 2201 sets M ₃ = M ₂ and b ₃ = b ₂ (step S55). Penalty functions for state constraints are not applied. Thereafter, the process proceeds to step S57.

Then, the output generation unit 2203 calculates the vector U by U = M ⁻¹ ₃ b ₃ (step S57). Further, the output generation unit 2203 extracts the linearization control input u (k) (i = 0) from the vector U and outputs it (step S59).

  Thereafter, the model prediction control unit 220 determines whether the process is finished (step S61). If the process is not finished, the process returns to step S41, and if the process is finished, the process is finished.

  By executing such processing, an appropriate penalty function is applied, and overshoot and undershoot can be effectively suppressed.

[Embodiment 4]
The restriction on the amount of change in the state deviation also has the purpose of suppressing an excessive change. Therefore, depending on the control method, a change exceeding the restriction may be allowed. In this case as well, the following penalty function may be employed in order to suppress excessive restrictions.

  This penalty function is shown in FIG. 11 and is the same as that shown in FIG.

Therefore, as described in the third embodiment, the first-order partial differential function ∂ (dx) and the second-order partial differential function ∂ ² (dx) of the penalty function are set off-line for each application range of dx. Calculate it. Further, in the online processing, dx (k) (= x (k) −x (k−1)) is calculated, and the first-order partial differential function ∂ (dx) and the application range including dx (k) are included. The calculation may be performed using the second-order partial differential function ∂ ² (dx).

  Although the embodiment of the present technology has been described above, the present technology is not limited to this. For example, the functional block configuration described above may not match the program module configuration. Further, as long as the processing result does not change, the order of steps may be changed in the processing flow, or a plurality of steps may be executed in parallel.

  The offline processing device 100 described above is a computer device, and as shown in FIG. 12, a memory 2501, a CPU 2503, a hard disk drive (HDD) 2505, and a display control unit 2507 connected to the display device 2509. A drive device 2513 for the removable disk 2511, an input device 2515, and a communication control unit 2517 for connecting to a network are connected by a bus 2519. An operating system (OS) and an application program for executing the processing in this embodiment are stored in the HDD 2505, and are read from the HDD 2505 to the memory 2501 when executed by the CPU 2503. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing content of the application program, and performs a predetermined operation. Further, data in the middle of processing is mainly stored in the memory 2501, but may be stored in the HDD 2505. In an embodiment of the present technology, an application program for performing the above-described processing is stored in a computer-readable removable disk 2511 and distributed, and installed from the drive device 2513 to the HDD 2505. In some cases, the HDD 2505 may be installed via a network such as the Internet and the communication control unit 2517. Such a computer apparatus realizes various functions as described above by organically cooperating hardware such as the CPU 2503 and the memory 2501 described above and programs such as the OS and application programs. .

  The engine control apparatus 1000 described above is a computer apparatus, and as shown in FIG. 13, a RAM (Random Access Memory) 4501, a processor 4503, a ROM (Read Only Memory) 4507, and a sensor group 4515 are provided as a bus. 4519 is connected. A control program for executing the processing in the present embodiment and an operating system (OS: Operating System if present) are stored in the ROM 4507, and when executed by the processor 4503, the ROM 4507. To RAM4501. The processor 4503 controls a sensor group 4515 (for example, an intake pressure sensor and a fresh air amount sensor. In some cases, a fuel injection amount measurement unit, an engine speed measurement unit, and the like) to acquire a measurement value. Further, data in the middle of processing is stored in the RAM 4501. Note that the processor 4503 may include a ROM 4507, and may further include a RAM 4501. In the embodiment of the present technology, a control program for performing the above-described processing may be stored and distributed on a computer-readable removable disk and written to the ROM 4507 by a ROM writer. Such a computer device has various functions as described above by organically cooperating hardware such as the processor 4503, RAM 4501, and ROM 4507 described above and a control program (or OS in some cases). Is realized.

  The above-described embodiment can be summarized as follows.

  The off-line processing method according to the first aspect of the present embodiment includes (1) (a) a model predictive control evaluation function and a Lagrange multiplier and a sum of a first function related to a state equation to be controlled. A first linear expression group obtained by partially differentiating a function of 2 with respect to a Lagrange multiplier and including a state deviation of the controlled object and a linearized control input for the controlled object, and (b) a second function as the controlled object A second linear expression group obtained by partial differentiation with respect to the state deviation of the control object and including the state deviation and Lagrange multiplier of the controlled object as variables, and (c) the partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear expression group that includes the Lagrange multiplier and the state deviation of the controlled object as variables, and (d) a pena that corresponds to the constraint condition on the controlled object of model predictive control. The first linear expression group is read from the data storage unit that stores the tee function and (e) the relational expression related to the parameter restricted by the constraint condition, and the state deviation variable is eliminated except for the current value of the state deviation. And the first linear expression group is transformed into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables, and (2) from the data storage unit to the second linear expression group The primary expression group is read out and sequentially substituted so as to eliminate the variable of the Lagrangian multiplier, and the second primary expression group is transformed into a fifth primary expression group including the state deviation as a variable. (3) Data The third primary expression group is read from the storage unit, and the fourth linear expression group and the fifth primary expression group are substituted, so that the third primary expression group is changed to the current value of the state deviation and the linearization control input. To the sixth group of linear expressions including (4) sixth one The expression group is transformed so that the product of the first coefficient matrix and the vector for the linearization control input is expressed by an equation with the function vector of the current value of the state deviation, and (5) stored in the data storage unit A first differential function obtained by first-order partial differentiation of the penalty function and a second differential function obtained by second-order partial differentiation with respect to the parameters, and (6) a relational expression is read out from the data storage unit to obtain a fourth linear expression By substituting the group into the relational expression, the relational expression is transformed into a seventh linear expression group including the current value of the state deviation and the linearization control input as variables, and (7) linear from the seventh linear expression group. Including a process of extracting a coefficient for the optimization control input and calculating a second coefficient matrix and coefficient vector predetermined for the penalty function.

  By executing such processing offline, it is possible to perform model predictive control in which various state constraints are introduced.

  The parameter described above may be a parameter expressed from the state deviation and the linearization control input. In such a case, a constraint condition can be set for the excess air ratio of the diesel engine.

  Furthermore, the parameter described above may be a change amount of the state deviation. In such a case, it becomes possible to prevent a change in the state deviation from occurring suddenly.

  Furthermore, the penalty function described above may be represented by a function that is different for each parameter range. In this case, the first and second differential functions described above may be generated for each parameter range. In this way, the first function and the second function can be switched and used during control execution.

  The control method according to the second aspect of the present embodiment includes (1) (a) a function vector for a current value of a state deviation for a control target of model predictive control, and (b) for a control target within a control period. The first coefficient matrix calculated in advance so that the product of the vector of the linearization control input becomes equal to the function vector, and (c) the penalty function corresponding to the constraint condition in the control target of model predictive control is calculated in advance. The second coefficient matrix and coefficient vector, and (d) data that stores a first expression obtained by first-order partial differentiation of a penalty function and a second expression obtained by second-order partial differentiation with respect to parameters restricted by the constraint condition The first value and the second value are calculated by reading the first and second equations from the storage unit and substituting the value of the parameter base point obtained from the current value of the state deviation. (2) The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the first coefficient matrix is the sum of the product of the second value and the second coefficient matrix and the first coefficient matrix. (3) From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation into the function vector, ((first value) − (first The product of the value of 2 and the third value obtained from the current value of the state deviation or the value one unit time before the linearization control input)) and the coefficient vector. (4) a vector of the linearization control input is generated by the product of the inverse matrix of the first matrix and the second vector, and (5) of the elements of the vector of the linearization control input The process includes extracting a linearization control input for the first time.

  By executing such processing, model predictive control with state constraints can be executed at high speed.

  The control method according to the second aspect may further include a process of determining whether the current value of the parameter calculated from the current value of the state deviation is within a predetermined range. In this case, if the current value of the parameter is within a predetermined range, a process for calculating the first value and the second value, a process for calculating the first matrix, a process for calculating the second vector, You may make it perform the process which produces | generates the vector of a linearization control input, and the process which extracts a linearization control input. This is because depending on the control target, it may not be preferable to perform processing based on state constraints.

  Furthermore, the data storage unit described above may store the first expression and the second expression corresponding to the range of the current value of the parameter. In this case, the process of calculating the first value and the second value specifies the value range to which the current value of the parameter belongs, and reads the first expression and the second expression corresponding to the specified value range May be included. Appropriate control can be performed by separating and using appropriate expressions according to the situation.

  Further, if the current value of the parameter described above is outside the predetermined range, the function vector and the first coefficient matrix are read from the data storage unit, and the current value of the state deviation is substituted into the function vector. The product of the vector of 1 and the inverse of the first coefficient matrix generates a second vector of the linearization control input, for the first time of the elements of the second vector of the linearization control input A process of extracting a linearization control input may be further included. Model predictive control without considering state constraints can be executed at high speed.

  In addition, when the parameter described above is a parameter represented by the state deviation and the linearization control input, the third value described above is linearized with the matrix used in the state equation to be controlled. It may be calculated from a value one unit time before the control input. For example, such calculation is performed in the case of the excess air ratio.

  Further, when the above-described parameter is a change amount of the state deviation, the third value may be a difference between the current value of the state deviation and a value one unit time before the state deviation. Such calculation is performed when there is a restriction on the amount of change in the state deviation.

  It is possible to create a program for causing a processor (or computer) to perform the processing according to the above method, and the program can be read by a computer such as a flexible disk, CD-ROM, magneto-optical disk, semiconductor memory, hard disk, Stored in a storage medium or storage device. The intermediate processing result is temporarily stored in a storage device such as a main memory.

  The following supplementary notes are further disclosed with respect to the embodiments including the above examples.

(Appendix 1)
(A) obtained by partially differentiating the second function including the evaluation function of model predictive control and a Lagrange multiplier and including the sum of the first function related to the state equation of the controlled object with respect to the Lagrange multiplier and the control A first linear expression group including a target state deviation and a linearized control input for the control target as variables; and (b) obtained by partial differentiation of the second function with respect to the control target state deviation and A second linear expression group including the state deviation of the controlled object and the Lagrange multiplier as variables; and (c) the Lagrange multiplier obtained by partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear equation group including the state deviation of the controlled object as a variable, and (d) a penalty corresponding to a constraint condition on the controlled object of the model predictive control The first linear expression group is read from a data storage unit that stores a number and (e) a relational expression related to a parameter restricted by the constraint condition, and the variable of the state deviation is excluded except for the current value of the state deviation. Subsequent substitution is performed so that the first linear expression group is transformed into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables,
The second primary expression group is read from the data storage unit and sequentially substituted so as to eliminate the variable of the Lagrange multiplier, and the second primary expression group includes the state deviation as a variable. Transformed into a linear group of
By reading the third primary expression group from the data storage unit and substituting the fourth primary expression group and the fifth primary expression group, the third primary expression group is changed to the state deviation. Transformed into a sixth linear expression group including the current value and the linearization control input as variables,
Transforming the sixth linear equation group so that the product of the first coefficient matrix and the vector for the linearization control input is expressed by an equation with the function vector of the current value of the state deviation;
Generating a first differential function obtained by first-order partial differentiation of the penalty function stored in the data storage unit with respect to the parameter and a second differential function obtained by second-order partial differentiation;
By reading the relational expression from the data storage unit and substituting the fourth primary expression group into the relational expression, the relational expression is used with the current value of the state deviation and the linearization control input as variables. Transformed into a seventh group of primary formulas,
A program for causing a computer to execute a process of extracting a coefficient for the linearization control input from the seventh linear expression group and calculating a second coefficient matrix and a coefficient vector predetermined for the penalty function .

(Appendix 2)
The program according to claim 1, wherein the parameter is a parameter represented by the state deviation and the linearization control input.

(Appendix 3)
The program according to claim 1, wherein the parameter is a change amount of the state deviation.

(Appendix 4)
The penalty function is represented by a different function for each range of the parameter,
The program according to any one of appendices 1 to 3, wherein the first and second differential functions are generated for each value range of the parameter.

(Appendix 5)
(A) The product of the function vector for the current value of the state deviation for the control target of model predictive control and (b) the vector of the linearization control input for the control target within the control period is equal to the function vector. (C) a first coefficient matrix that is calculated in advance, (c) a second coefficient matrix and coefficient vector that are calculated in advance for a penalty function corresponding to a constraint condition in the control target of the model predictive control, and (d) The first equation and the second equation are stored in a data storage unit that stores a first equation obtained by first-order partial differentiation of the penalty function and a second equation obtained by second-order partial differentiation for the parameters restricted in the constraint condition. By reading the equation and substituting the value of the base point of the parameter obtained from the current value of the state deviation, the first value and the second value are calculated,
The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the product of the second value and the second coefficient matrix and the sum of the first coefficient matrix Calculate the matrix of 1
From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation for the function vector, ((the first value) − (the second value) And the third value obtained from the current value of the state deviation or the value of one unit time before the linearization control input))) and the coefficient vector are subtracted. Calculate a second vector;
A vector of the linearization control input is generated by a product of an inverse matrix of the first matrix and the second vector;
A program for causing a processor to execute a process of extracting a linearization control input for the first time among vector elements of the linearization control input.

(Appendix 6)
A process of determining whether the current value of the parameter calculated from the current value of the state deviation is within a predetermined range;
If the current value of the parameter is within the predetermined range, a process for calculating the first value and a second value, a process for calculating the first matrix, and a process for calculating the second vector The program according to claim 5, wherein: a process for generating a vector of the linearization control input and a process for extracting the linearization control input are executed.

(Appendix 7)
The data storage unit
Storing the first equation and the second equation according to the range of the current value of the parameter;
The process of calculating the first value and the second value includes:
The program according to appendix 5 or 6, including a process of specifying a range to which a current value of the parameter belongs and reading the first expression and the second expression according to the specified range.

(Appendix 8)
If the current value of the parameter is outside the predetermined range,
The function vector and the first coefficient matrix are read from the data storage unit, and the first vector obtained by substituting the current value of the state deviation into the function vector and the inverse of the first coefficient matrix Generating a second vector of said linearization control inputs by multiplication with a matrix;
The program according to any one of appendices 5 to 7, further including a process of extracting a linearization control input for a first time among elements of a second vector of the linearization control input.

(Appendix 9)
When the parameter is a parameter represented by the state deviation and the linearization control input,
The program according to any one of appendices 5 to 8, wherein the third value is calculated from a matrix used in the state equation of the control target and a value one unit time before the linearization control input.

(Appendix 10)
When the parameter is a change amount of the state deviation,
The program according to claim 1, wherein the third value is a difference between a current value of the state deviation and a value one unit time before the state deviation.

(Appendix 11)
(A) obtained by partially differentiating the second function including the evaluation function of model predictive control and a Lagrange multiplier and including the sum of the first function related to the state equation of the controlled object with respect to the Lagrange multiplier and the control A first linear expression group including a target state deviation and a linearized control input for the control target as variables; and (b) obtained by partial differentiation of the second function with respect to the control target state deviation and A second linear expression group including the state deviation of the controlled object and the Lagrange multiplier as variables; and (c) the Lagrange multiplier obtained by partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear equation group including the state deviation of the controlled object as a variable, and (d) a penalty corresponding to a constraint condition on the controlled object of the model predictive control The first linear expression group is read from a data storage unit that stores a number and (e) a relational expression related to a parameter restricted by the constraint condition, and the variable of the state deviation is excluded except for the current value of the state deviation. Subsequent substitution is performed so that the first linear expression group is transformed into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables,
The second primary expression group is read from the data storage unit and sequentially substituted so as to eliminate the variable of the Lagrange multiplier, and the second primary expression group includes the state deviation as a variable. Transformed into a linear group of
By reading the third primary expression group from the data storage unit and substituting the fourth primary expression group and the fifth primary expression group, the third primary expression group is changed to the state deviation. Transformed into a sixth linear expression group including the current value and the linearization control input as variables,
Transforming the sixth linear equation group so that the product of the first coefficient matrix and the vector for the linearization control input is expressed by an equation with the function vector of the current value of the state deviation;
Generating a first differential function obtained by first-order partial differentiation of the penalty function stored in the data storage unit with respect to the parameter and a second differential function obtained by second-order partial differentiation;
By reading the relational expression from the data storage unit and substituting the fourth primary expression group into the relational expression, the relational expression is used with the current value of the state deviation and the linearization control input as variables. Transformed into a seventh group of primary formulas,
An off-line executed by a computer, including processing for extracting a coefficient for the linearization control input from the seventh linear expression group and calculating a second coefficient matrix and coefficient vector predetermined for the penalty function; Processing method.

(Appendix 12)
(A) The product of the function vector for the current value of the state deviation for the control target of model predictive control and (b) the vector of the linearization control input for the control target within the control period is equal to the function vector. (C) a first coefficient matrix that is calculated in advance, (c) a second coefficient matrix and coefficient vector that are calculated in advance for a penalty function corresponding to a constraint condition in the control target of the model predictive control, and (d) The first equation and the second equation are stored in a data storage unit that stores a first equation obtained by first-order partial differentiation of the penalty function and a second equation obtained by second-order partial differentiation for the parameters restricted in the constraint condition. By reading the equation and substituting the value of the base point of the parameter obtained from the current value of the state deviation, the first value and the second value are calculated,
The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the product of the second value and the second coefficient matrix and the sum of the first coefficient matrix Calculate the matrix of 1
From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation for the function vector, ((the first value) − (the second value) And the third value obtained from the current value of the state deviation or the value of one unit time before the linearization control input))) and the coefficient vector are subtracted. Calculate a second vector;
A vector of the linearization control input is generated by a product of an inverse matrix of the first matrix and the second vector;
A control method executed by a processor, including a process of extracting a linearization control input for a first time among elements of a vector of the linearization control input.

(Appendix 13)
(A) obtained by partially differentiating the second function including the evaluation function of model predictive control and a Lagrange multiplier and including the sum of the first function related to the state equation of the controlled object with respect to the Lagrange multiplier and the control A first linear expression group including a target state deviation and a linearized control input for the control target as variables; and (b) obtained by partial differentiation of the second function with respect to the control target state deviation and A second linear expression group including the state deviation of the controlled object and the Lagrange multiplier as variables; and (c) the Lagrange multiplier obtained by partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear equation group including the state deviation of the controlled object as a variable, and (d) a penalty corresponding to a constraint condition on the controlled object of the model predictive control The first linear expression group is read from a data storage unit that stores a number and (e) a relational expression related to a parameter restricted by the constraint condition, and the variable of the state deviation is excluded except for the current value of the state deviation. Means for sequentially substituting to eliminate the first linear expression group into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables;
The second primary expression group is read from the data storage unit and sequentially substituted so as to eliminate the variable of the Lagrange multiplier, and the second primary expression group includes the state deviation as a variable. Means for transforming into a linear group of
By reading the third primary expression group from the data storage unit and substituting the fourth primary expression group and the fifth primary expression group, the third primary expression group is changed to the state deviation. Means for transforming the current value and the linearization control input into a sixth group of linear expressions including variables,
Means for transforming the sixth linear equation group so that a product of a first coefficient matrix and a vector for the linearization control input is expressed by an equation with a function vector of the current value of the state deviation; ,
Means for generating a first differential function obtained by first-order partial differentiation of the penalty function stored in the data storage unit with respect to the parameter and a second differential function obtained by second-order partial differentiation;
By reading the relational expression from the data storage unit and substituting the fourth primary expression group into the relational expression, the relational expression is used with the current value of the state deviation and the linearization control input as variables. Means for transforming into a seventh group of primary formulas including:
Means for extracting a coefficient for the linearization control input from the seventh linear equation group, and calculating a second coefficient matrix and coefficient vector predetermined for the penalty function;
An off-line processing apparatus.

(Appendix 14)
(A) The product of the function vector for the current value of the state deviation for the control target of model predictive control and (b) the vector of the linearization control input for the control target within the control period is equal to the function vector. (C) a first coefficient matrix that is calculated in advance, (c) a second coefficient matrix and coefficient vector that are calculated in advance for a penalty function corresponding to a constraint condition in the control target of the model predictive control, and (d) The first equation and the second equation are stored in a data storage unit that stores a first equation obtained by first-order partial differentiation of the penalty function and a second equation obtained by second-order partial differentiation for the parameters restricted in the constraint condition. Means for calculating a first value and a second value by reading an equation and substituting the value of the base point of the parameter obtained from the current value of the state deviation;
The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the product of the second value and the second coefficient matrix and the sum of the first coefficient matrix Means for calculating a matrix of 1;
From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation for the function vector, ((the first value) − (the second value) And the third value obtained from the current value of the state deviation or the value of one unit time before the linearization control input))) and the coefficient vector are subtracted. Means for calculating a second vector;
Means for generating a vector of the linearization control input by a product of an inverse matrix of the first matrix and the second vector;
Means for extracting a linearization control input for a first time among vector elements of the linearization control input;
Control device.

101 Input unit 102 Input data storage unit 103 First modification processing unit 104 First data storage unit 105 Second modification processing unit 106 Second data storage unit 107 Third modification processing unit 108 Third data storage unit 109 First matrix generation unit 110 Fourth data storage unit 111 Second matrix generation unit 112 Differentiation processing unit

Claims (14)

(A) obtained by partially differentiating the second function including the evaluation function of model predictive control and a Lagrange multiplier and including the sum of the first function related to the state equation of the controlled object with respect to the Lagrange multiplier and the control A first linear expression group including a target state deviation and a linearized control input for the control target as variables; and (b) obtained by partial differentiation of the second function with respect to the control target state deviation and A second linear expression group including the state deviation of the controlled object and the Lagrange multiplier as variables; and (c) the Lagrange multiplier obtained by partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear equation group including the state deviation of the controlled object as a variable, and (d) a penalty corresponding to a constraint condition on the controlled object of the model predictive control The first linear expression group is read from a data storage unit that stores a number and (e) a relational expression related to a parameter restricted by the constraint condition, and the variable of the state deviation is excluded except for the current value of the state deviation. Subsequent substitution is performed so that the first linear expression group is transformed into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables,
The second primary expression group is read from the data storage unit and sequentially substituted so as to eliminate the variable of the Lagrange multiplier, and the second primary expression group includes the state deviation as a variable. Transformed into a linear group of
By reading the third primary expression group from the data storage unit and substituting the fourth primary expression group and the fifth primary expression group, the third primary expression group is changed to the state deviation. Transformed into a sixth linear expression group including the current value and the linearization control input as variables,
Transforming the sixth linear equation group so that the product of the first coefficient matrix and the vector for the linearization control input is expressed by an equation with the function vector of the current value of the state deviation;
Generating a first differential function obtained by first-order partial differentiation of the penalty function stored in the data storage unit with respect to the parameter and a second differential function obtained by second-order partial differentiation;
By reading the relational expression from the data storage unit and substituting the fourth primary expression group into the relational expression, the relational expression is used with the current value of the state deviation and the linearization control input as variables. Transformed into a seventh group of primary formulas,
A program for causing a computer to execute a process of extracting a coefficient for the linearization control input from the seventh linear expression group and calculating a second coefficient matrix and a coefficient vector predetermined for the penalty function . The program according to claim 1, wherein the parameter is a parameter represented by the state deviation and the linearization control input. The program according to claim 1, wherein the parameter is a change amount of the state deviation. The penalty function is represented by a different function for each range of the parameter,
The program according to any one of claims 1 to 3, wherein the first and second differential functions are generated for each value range of the parameter. (A) The product of the function vector for the current value of the state deviation for the control target of model predictive control and (b) the vector of the linearization control input for the control target within the control period is equal to the function vector. (C) a first coefficient matrix that is calculated in advance, (c) a second coefficient matrix and coefficient vector that are calculated in advance for a penalty function corresponding to a constraint condition in the control target of the model predictive control, and (d) The first equation and the second equation are stored in a data storage unit that stores a first equation obtained by first-order partial differentiation of the penalty function and a second equation obtained by second-order partial differentiation for the parameters restricted in the constraint condition. By reading the equation and substituting the value of the base point of the parameter obtained from the current value of the state deviation, the first value and the second value are calculated,
The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the product of the second value and the second coefficient matrix and the sum of the first coefficient matrix Calculate the matrix of 1
From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation for the function vector, ((the first value) − (the second value) And the third value obtained from the current value of the state deviation or the value of one unit time before the linearization control input))) and the coefficient vector are subtracted. Calculate a second vector;
A vector of the linearization control input is generated by a product of an inverse matrix of the first matrix and the second vector;
A program for causing a processor to execute a process of extracting a linearization control input for the first time among vector elements of the linearization control input. A process of determining whether the current value of the parameter calculated from the current value of the state deviation is within a predetermined range;
If the current value of the parameter is within the predetermined range, a process for calculating the first value and a second value, a process for calculating the first matrix, and a process for calculating the second vector The program according to claim 5, wherein: a process of generating a vector of the linearization control input and a process of extracting the linearization control input are executed. The data storage unit
Storing the first equation and the second equation according to the range of the current value of the parameter;
The process of calculating the first value and the second value includes:
7. The program according to claim 5, further comprising: a process of specifying a value range to which a current value of the parameter belongs, and reading the first expression and the second expression according to the specified value range. If the current value of the parameter is outside the predetermined range,
The function vector and the first coefficient matrix are read from the data storage unit, and the first vector obtained by substituting the current value of the state deviation into the function vector and the inverse of the first coefficient matrix Generating a second vector of said linearization control inputs by multiplication with a matrix;
The program according to any one of claims 5 to 7, further comprising: extracting a linearization control input for a first time among elements of a second vector of the linearization control input. When the parameter is a parameter represented by the state deviation and the linearization control input,
The program according to any one of claims 5 to 8, wherein the third value is calculated from a matrix used in the state equation of the control target and a value one unit time before the linearization control input. When the parameter is a change amount of the state deviation,
The program according to claim 5, wherein the third value is a difference between a current value of the state deviation and a value one unit time before the state deviation. (A) obtained by partially differentiating the second function including the evaluation function of model predictive control and a Lagrange multiplier and including the sum of the first function related to the state equation of the controlled object with respect to the Lagrange multiplier and the control A first linear expression group including a target state deviation and a linearized control input for the control target as variables; and (b) obtained by partial differentiation of the second function with respect to the control target state deviation and A second linear expression group including the state deviation of the controlled object and the Lagrange multiplier as variables; and (c) the Lagrange multiplier obtained by partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear equation group including the state deviation of the controlled object as a variable, and (d) a penalty corresponding to a constraint condition on the controlled object of the model predictive control The first linear expression group is read from a data storage unit that stores a number and (e) a relational expression related to a parameter restricted by the constraint condition, and the variable of the state deviation is excluded except for the current value of the state deviation. Subsequent substitution is performed so that the first linear expression group is transformed into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables,
The second primary expression group is read from the data storage unit and sequentially substituted so as to eliminate the variable of the Lagrange multiplier, and the second primary expression group includes the state deviation as a variable. Transformed into a linear group of
By reading the third primary expression group from the data storage unit and substituting the fourth primary expression group and the fifth primary expression group, the third primary expression group is changed to the state deviation. Transformed into a sixth linear expression group including the current value and the linearization control input as variables,
Transforming the sixth linear equation group so that the product of the first coefficient matrix and the vector for the linearization control input is expressed by an equation with the function vector of the current value of the state deviation;
Generating a first differential function obtained by first-order partial differentiation of the penalty function stored in the data storage unit with respect to the parameter and a second differential function obtained by second-order partial differentiation;
By reading the relational expression from the data storage unit and substituting the fourth primary expression group into the relational expression, the relational expression is used with the current value of the state deviation and the linearization control input as variables. Transformed into a seventh group of primary formulas,
An off-line executed by a computer, including processing for extracting a coefficient for the linearization control input from the seventh linear expression group and calculating a second coefficient matrix and coefficient vector predetermined for the penalty function; Processing method. (A) The product of the function vector for the current value of the state deviation for the control target of model predictive control and (b) the vector of the linearization control input for the control target within the control period is equal to the function vector. (C) a first coefficient matrix that is calculated in advance, (c) a second coefficient matrix and coefficient vector that are calculated in advance for a penalty function corresponding to a constraint condition in the control target of the model predictive control, and (d) The first equation and the second equation are stored in a data storage unit that stores a first equation obtained by first-order partial differentiation of the penalty function and a second equation obtained by second-order partial differentiation for the parameters restricted in the constraint condition. By reading the equation and substituting the value of the base point of the parameter obtained from the current value of the state deviation, the first value and the second value are calculated,
The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the product of the second value and the second coefficient matrix and the sum of the first coefficient matrix Calculate the matrix of 1
From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation for the function vector, ((the first value) − (the second value) And the third value obtained from the current value of the state deviation or the value of one unit time before the linearization control input))) and the coefficient vector are subtracted. Calculate a second vector;
A vector of the linearization control input is generated by a product of an inverse matrix of the first matrix and the second vector;
A control method executed by a processor, including a process of extracting a linearization control input for a first time among elements of a vector of the linearization control input. (A) obtained by partially differentiating the second function including the evaluation function of model predictive control and a Lagrange multiplier and including the sum of the first function related to the state equation of the controlled object with respect to the Lagrange multiplier and the control A first linear expression group including a target state deviation and a linearized control input for the control target as variables; and (b) obtained by partial differentiation of the second function with respect to the control target state deviation and A second linear expression group including the state deviation of the controlled object and the Lagrange multiplier as variables; and (c) the Lagrange multiplier obtained by partial differentiation of the second function with respect to the linearized control input of the controlled object. And a third linear equation group including the state deviation of the controlled object as a variable, and (d) a penalty corresponding to a constraint condition on the controlled object of the model predictive control The first linear expression group is read from a data storage unit that stores a number and (e) a relational expression related to a parameter restricted by the constraint condition, and the variable of the state deviation is excluded except for the current value of the state deviation. Means for sequentially substituting to eliminate the first linear expression group into a fourth linear expression group including the current value of the state deviation and the linearization control input as variables;
The second primary expression group is read from the data storage unit and sequentially substituted so as to eliminate the variable of the Lagrange multiplier, and the second primary expression group includes the state deviation as a variable. Means for transforming into a linear group of
By reading the third primary expression group from the data storage unit and substituting the fourth primary expression group and the fifth primary expression group, the third primary expression group is changed to the state deviation. Means for transforming the current value and the linearization control input into a sixth group of linear expressions including variables,
Means for transforming the sixth linear equation group so that a product of a first coefficient matrix and a vector for the linearization control input is expressed by an equation with a function vector of the current value of the state deviation; ,
Means for generating a first differential function obtained by first-order partial differentiation of the penalty function stored in the data storage unit with respect to the parameter and a second differential function obtained by second-order partial differentiation;
By reading the relational expression from the data storage unit and substituting the fourth primary expression group into the relational expression, the relational expression is used with the current value of the state deviation and the linearization control input as variables. Means for transforming into a seventh group of primary formulas including:
Means for extracting a coefficient for the linearization control input from the seventh linear equation group, and calculating a second coefficient matrix and coefficient vector predetermined for the penalty function;
An off-line processing apparatus. (A) The product of the function vector for the current value of the state deviation for the control target of model predictive control and (b) the vector of the linearization control input for the control target within the control period is equal to the function vector. (C) a first coefficient matrix that is calculated in advance, (c) a second coefficient matrix and coefficient vector that are calculated in advance for a penalty function corresponding to a constraint condition in the control target of the model predictive control, and (d) The first equation and the second equation are stored in a data storage unit that stores a first equation obtained by first-order partial differentiation of the penalty function and a second equation obtained by second-order partial differentiation for the parameters restricted in the constraint condition. Means for calculating a first value and a second value by reading an equation and substituting the value of the base point of the parameter obtained from the current value of the state deviation;
The first coefficient matrix and the second coefficient matrix are read from the data storage unit, and the product of the second value and the second coefficient matrix and the sum of the first coefficient matrix Means for calculating a matrix of 1;
From the first vector obtained by reading the function vector from the data storage unit and substituting the current value of the state deviation for the function vector, ((the first value) − (the second value) And the third value obtained from the current value of the state deviation or the value of one unit time before the linearization control input))) and the coefficient vector are subtracted. Means for calculating a second vector;
Means for generating a vector of the linearization control input by a product of an inverse matrix of the first matrix and the second vector;
Means for extracting a linearization control input for a first time among vector elements of the linearization control input;
Control device.

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