JPH0883104A - Plant control equipment - Google Patents

Abstract

(57) [Abstract] [Purpose] To provide a plant control device capable of stably and smoothly performing unsteady operation of a plant. [Configuration] A model predictive control device, a plant dynamic characteristic model data output unit that outputs a function representing a dynamic characteristic of a controlled object, a control system adjustment unit that outputs a robust and stable control parameter based on the function, a control amount, and an operation amount It is configured by a constraint condition adjusting unit that determines a constraint condition. [Effect] The model predictive control device can be adjusted to a good state according to changes in the operating conditions of the plant, and it is possible to cope with the non-linear characteristics that occur during unsteady operation of the plant. In particular, when an attempt is made to suddenly change the controlled variable during unsteady operation, the automatic adjustment of the constraint condition brakes the changing speed of the controlled variable so that strong non-linear characteristics do not appear, and the stability of unsteady operation is maintained. be able to.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a non-linear plant in which the dynamic characteristics of a controlled object change greatly depending on operating conditions
The present invention relates to a proposal for a plant control device that enables stable unsteady operation.

[0002]

2. Description of the Related Art In various plants such as petrochemical, steel and electric power, various control devices are provided for stable and safe operation of the plant. These controllers are
In many cases, it is composed of a PID controller or a linear compensator based on modern control theory. These controllers are
It is designed and adjusted based on a dynamic model (linear model) when the plant is calm near a certain equilibrium point.

[0003]

However, with these control devices alone, stable operation of the plant is not possible during non-steady-state operation involving a large state change, such as when the plant is started or stopped, or when switching products. Have difficulty. This is because the plant dynamic characteristics change or a non-linear characteristic peculiar to the plant appears due to a drastic change in the control amount, the manipulated variable, etc. accompanying the unsteady operation. Therefore, in order to properly operate the plant, it is often necessary for the plant operator to manually monitor and control, which is one of the reasons for increasing the burden on the operator.

In order to solve the above problems, a plant controller capable of dealing with unsteady operation is required. For that purpose, it is necessary to make the controller correspond to the nonlinear dynamic characteristics of the plant. Therefore, in recent years, various nonlinear control techniques have been proposed. However, (a) systematically design a stable control system against all types of nonlinear dynamic characteristics, and (b) robust stability that does not impair the stability of the control system even if the nonlinear model has some errors. The general-purpose technology for having
Many problems remain for practical application.

On the other hand, in a control system based on a linear dynamic characteristic model of a plant, robust control is designed so that the stability of the control system is maintained against a model error generated when a nonlinear characteristic is approximated by a linear model. Technology is being researched. However, in the robust control method, it is necessary to know how much the model error with respect to the linear model of the plant at the design stage. If you overestimate the model error too much,
As a result, it becomes a passive control system with slow response, and conversely, if the model error is overestimated too small, the control system becomes unstable with little stability margin, so it is necessary to properly estimate the model error. However, in many plants, the model error that occurs when the dynamic characteristic model at that time is approximated by a linear model changes depending on the operating conditions, and it is difficult to accurately estimate it.

Therefore, the present invention solves the problem of robust stability against the above model error within the range of a practical linear control technique in which control system design, adjustment, and stability analysis are easy.
It is an object of the present invention to propose a plant controller capable of coping with nonlinear characteristics in plant unsteady operation.

[0007]

SUMMARY OF THE INVENTION In order to solve the above problems, the present invention proposes a plant unsteady operation control device. Among them, a control method called model predictive control is used.

As shown in FIG. 1, the model predictive control has a model representing the dynamic characteristics of the plant inside the controller, and predicts the future controlled variable for the manipulated variable using the model. Then, the operation amount that optimizes the evaluation function under the constraint condition that the future control amount is given in advance is obtained by the optimization calculation. This method requires a considerable amount of arithmetic processing in order to repeat the calculation for predicting the controlled variable and the calculation for optimizing the manipulated variable at every constant control cycle. For this reason, it has finally become practical with the increase in speed and cost of computers in recent years. Many methods have been proposed for model predictive control. For example, (1) Nishitani: Application of model predictive control, measurement and control Vol.2
8, No.11, pp.996-1004 (1989) (2) DWClarke & C. Mohtadi: Properties of Generaliz
ed Predictive Control, Automatica 25-6 pp.859 (198
9) etc. Especially in (2), the generalized predictive control method (Generali
zed Predictive Control (GPC) has been proposed.
This is because when the future target value vector y ^* (k + i) and i = 1, ..., Np are given, the controlled variable vector future value (y (k + i), i = 1, ..., Np) In this method, the manipulated variable increment vector Δu (k) that minimizes is calculated. As a technique related to this, Japanese Patent Laid-Open No. 4-118
Inventions such as 703 and Japanese Patent Laid-Open No. 4-256102 have been proposed.

A feature of the model predictive control system is that a stable control response can be realized for a control object having a long dead time. The feed-forward control using the future target value can improve the followability. It can also be applied to a multivariable control system. An accurate dynamic characteristic model of the controlled object is not required, and the control system can be easily configured from the step response, for example. By including physical laws and non-linear characteristics of the plant in the prediction model, fine grain control can be performed. Constraint conditions regarding the operation of the controlled object (for example, upper and lower limit limiters, change rate limiters, etc.) can be directly entered into the control law. And the like.

The last item is a function called "constraint control", which is a feature of model predictive control not found in other control methods. By using this function during unsteady operation of the plant, stable plant operation can be expected to be achieved. This is because by confining the manipulated variable and the controlled variable in a certain operating condition region by the constraint function, it is possible to clearly estimate the model error of the linear model that approximates the characteristic in that region. If we ensure robust stability against the estimated model error,
This is because stable unsteady operation can be realized.

This situation will be described with reference to FIG. Assume unsteady operation in which the control point y of a certain plant is made to follow the target value r and the operating point is drastically changed from r ₀ to r ₂ . An upper limit value y _max and a lower limit value y _min are set as constraint conditions for the control amount, and the control amount y is changed while being restrained in a region between these constraint values by constraint control. At this time, the linear model G ₀ and its model error Δ ₀ in the constraint region A ₀ when the target value is r ₀ , and the linear model G ₁ and the model error thereof in the constraint region A ₁ when the target value is r ₁ delta _1, linear model G ₂ and the the model error delta ₂ in the constraint region a ₂ when the target value r _2, but if you know each linear model in each of the operating condition G _{i (i} = 0,1 , 2) to design the controller, and the model error Δ _{i (i} = 0,1,
By adjusting the control parameters so as to be robust and stable against 2) and switching these controllers according to changes in operating conditions, good unsteady operation is achieved while maintaining the stability of the entire control system. it can.

From the above description, in order to cope with the unsteady operation, it is effective to use the constraint control function and the robust control function against the model error based on the model predictive control method. Therefore, the present invention proposes a plant unsteady operation controller based on a model predictive controller based on a linear model. Its structure is as follows.

According to the first aspect of the invention, in addition to the model predictive control device, the dynamic characteristics of the controlled object within an operating condition limited by a preset equilibrium point concerning the controlled variable and the manipulated variable and a constraint condition. The plant dynamic characteristic model data output unit that outputs the linear transfer function and its maximum model error norm that approximately represent the above, and the prediction model is calculated based on the output linear transfer function, and it is robust to the maximum model error norm. And a control system adjusting unit for calculating such control parameters.

In the second aspect of the present invention, the allowable model error norm that guarantees the stability of the control system is calculated from the linear transfer function and the control parameter corresponding to the plant dynamic characteristic model in the current operating state, and the plant dynamic characteristic model is calculated. We propose a constraint condition adjustment unit that searches the allowable range of operating conditions where the maximum model error norm output by the data output unit is less than or equal to the allowable model error norm, and determines the constraint conditions for the controlled variable and manipulated variable based on that range.

A third aspect of the present invention proposes a configuration including the plant dynamic characteristic model data output unit, the control system adjustment unit, and the constraint condition adjustment unit described above.

In a fourth aspect of the present invention, the plant dynamic characteristic model data output unit used in the first to third aspects of the present invention is configured as a plant model expressing a nonlinear dynamic characteristic of a controlled object, and is given by using the plant model. The simulation calculation unit that calculates the control response to the control point and the equilibrium point of the operation amount and the change amount of the operation amount, and the linear transfer function that estimates the linear transfer function that approximates the control response obtained as a result. We propose a configuration that includes an estimation unit and a model error norm calculation unit that calculates the maximum model error norm from the fluctuation width of the linear transfer function under operating conditions within given constraints.

A mechanism for achieving favorable unsteady operation of the plant by the functions of the proposed parts will be described.

The plant dynamic characteristic model data output unit in the first aspect of the present invention approximates the plant dynamic characteristic in the operating region by inputting the equilibrium points of the controlled variable and the manipulated variable in a certain operating state and the constraint condition. A linear transfer function model represented by a symbol and the maximum norm (magnitude) of the model error when the actual plant dynamic characteristics are approximated by the model are output.

Further, the control system adjustment unit has a function of obtaining a prediction model used in the model predictive control device from the above-mentioned linear transfer function and a parameter relating to the evaluation function used in the model predictive control device (this is called a control parameter). )
Is configured by means for adjusting the control system so as to be robustly stable in consideration of the above-mentioned maximum model error norm.

By combining these two functions, the prediction model used in the model predictive control device can be optimally adjusted according to changes in the operating conditions of the plant, and the operating range determined by the set constraint conditions. At the inner,
The robust stability of the control system can always be ensured against the model error due to the linear dynamic characteristic model.

The constraint condition adjusting unit in the second invention is
From the standpoint of the first invention, first, to what extent the model prediction control system of the present condition can withstand without impairing the stability, the linear transfer function which is the source of the prediction model and the current controller Calculate from parameters. This is called the allowable model error norm. Next, while adjusting the constraint conditions for the controlled variable and the manipulated variable, that is, the operating region of the plant, the maximum model error magnitude (maximum model error norm) that can occur in that region is calculated using the model data output unit described above. Ask. Then, the maximum operation area in which the maximum model error norm is equal to or less than the allowable model error norm is searched and calculated, and the constraint conditions regarding the control amount and the operation amount determined as a result are output and set in the model predictive controller.

With these series of functions, it is possible to automatically adjust the maximum constraint condition (operating region) in which robust stability against model error is preserved, without changing the control parameters of the current model predictive control device. . In fact, when a strong nonlinear characteristic occurs when trying to rapidly change the control amount in the unsteady operation of the plant, this function automatically adjusts the constraint condition in the direction of narrowing the operating range,
As a result, the speed of change of the control amount is braked so that a strong nonlinear characteristic does not appear. With such a mechanism, the unsteady operation of the plant can be performed stably and smoothly.

A third aspect of the present invention is a composite system of two types of control, that is, control of the system that emphasizes robust stability by the control system adjustment unit and control of the system that emphasizes constraint conditions by the condition adjustment unit. Allows control. In this case, it is possible to perform the control in which one control is the main control and the other control is the sub control, and it is possible to realize a fine control mode.

A fourth aspect of the invention proposes a specific method of realizing the plant dynamic characteristic model data output section described above. First, it is assumed that there is a plant model or simulator that can approximate the dynamic characteristics including the nonlinear characteristics of the plant with sufficient accuracy. By using this, under any operating condition (equilibrium point of controlled variable and manipulated variable),
It is possible to simulate the response to a slight change in the manipulated variable from there. Next, a linear transfer function that approximates the dynamic characteristics near the equilibrium point in the operating state is estimated by the system identification method from the simulation response. Further, in order to evaluate the magnitude of the model error in the operating region, the linear transfer function is estimated by the above procedure while changing the range of change of the manipulated variable to various sizes in the operating region. Furthermore, the linear transfer function near the equilibrium point obtained above and the error dynamics of each of these linear transfer functions are calculated, and the maximum size (maximum model error norm) is calculated. Note that two linear transfer function matrices G ₁ (s) and G
The magnitude of the model error between ₂ (s) is obtained as a function of the frequency ω such that ε (ω) = σ _max {G ₁ (jω) −G ₂ (jω)} (2). Note that σ _max {A} means the maximum singular value of the matrix A, which is equal to the square root of the maximum eigenvalue of the matrix A ^T A.

According to the method of the third aspect of the present invention, even if the nonlinear dynamic characteristic of the controlled object is expressed by any model, if it can be realized in the form of a simulator capable of calculating the response under each operating condition, The linear transfer function and maximum model error norm can be approximately calculated by numerical calculation. Therefore, non-linear models are described by non-linear differential equations, fuzzy IF THEN rules, neural networks, model banks that interpolate several linear models, control Any form of model can be applied, such as a description of the dynamic characteristics of the object by an equation based on physical laws.

When the above three inventions are combined, the prediction model, the control parameters, and
The constraint condition can be appropriately adjusted according to the operating state, and as a result, the unsteady operation can be performed stably and smoothly.

[0027]

FIG. 3 shows an example of the configuration of the plant unsteady operation control system of the present invention. In the figure, the control amount y of the plant 1
Is fed back and is controlled by the model predictive control device 2 which outputs the manipulated variable u. The plant dynamic characteristic model data output unit 3 receives the current values of the controlled variable, the manipulated variable, and the constraint condition values considered in the model predictive control device 2, and from the current plant operating conditions determined by those values, The linear transfer function G (s) that approximates the plant dynamic characteristics, and the maximum model error norm ε that means the magnitude of the error between the transfer function and the actual dynamic characteristics of the plant
Calculate (ω).

In the control system adjusting section 4, the linear transfer function G calculated by the plant dynamic characteristic model data output section 3 is calculated.
(S), the maximum model error norm ε (ω) is input, and the prediction model used in the model predictive control device 2 and control parameters (parameters inside the evaluation function) are calculated. At this time, the control parameter is adjusted so that the model predictive control system is robustly stable with respect to the maximum model error norm ε (ω) for the current operating condition.

In the constraint condition adjusting unit 5, the linear transfer function G (s) and the maximum model error norm ε (ω) calculated by the plant dynamic characteristic model data output unit 3 and the control parameters used in the model predictive control device 2 are set. Is input, and the maximum model error norm ε (ω) under the current operating condition is searched for within a range of the allowable operating condition that does not exceed the allowable model error norm calculated by the linear transfer function and the control parameter. The range is output as constraint condition values for plant operation, that is, control variables, manipulated variables, and upper and lower limit constraint values for those change rate signals. The constraint condition value is given to the model predictive control device 2 and the plant dynamic characteristic model data output unit.

Next, a specific configuration and a method of realizing each functional block will be described.

(1) A configuration example of the plant dynamic characteristic model data output unit 3 shown in FIG. 3 will be described with reference to FIG. In the figure, the plant dynamic characteristic model data output unit 3 is composed of a plant dynamic characteristic model 3.1, a simulation calculation unit 3.2, a linear transfer function estimation unit 3.3, and a model error norm calculation unit 3.4. ing.

The dynamic characteristic model 3.1 of the plant to be controlled is described by the following non-linear differential equation. dx / dt = f (x, u) y = g (x, u) (3) where x is an n-dimensional vector representing the internal state quantity of the plant, u is a q-dimensional manipulated variable vector, and y is a p-dimensional vector. Control amount vector, dx / dt is a vector in which time differential values of each component of vector x are arranged, f (x, u) is an n-dimensional vector value function uniquely determined by vectors x and u, y (x, u) Is a p-dimensional vector valued function uniquely determined by the vectors x and u. In addition to general differential equations, these are models described by neural networks, models described by fuzzy models, or models that combine multiple linear models, or simply switch linear models according to the values of u and y. A model bank is also acceptable.

The simulation calculation section 3.2 uses the above-mentioned plant model, sets the control amount y ₀ and the manipulated variable u ₀ given at each time as initial values, and then manipulates the manipulated variable u (t).
= U ₀ , the future response y (t) at that time is calculated by numerically integrating the model of Equation (3), where t =
Calculate [0, t _max ]. Then the operation amount u manipulated variables plus minimal change Delta] u (t) to the j element of _{0 u (t) = u 0} + Δu (t)
However, Δu (t) = [0, ... 0, Δu, 0, ...
・, 0]… (4), by the same numerical integration calculation, future response y _j '(t)
To calculate. Then, a response difference signal vector Δy _j (t) = y _j '(t) -y (t) is obtained for each j. Thus, a matrix H (t) of size p × q representing the sensitivity of the minute change of each element of the control amount to the minute change of each element of the manipulated variable in the vicinity of a certain operating point y ₀ , u ₀ of the plant. [h _ij (t)] However, h _ij (t) = (i-th component of Δy _j (t)) / Δu is obtained, and this is output as response data.

The linear transfer function estimator 3.3 performs the response data matrix H (t) according to the procedure shown in the flowchart of FIG.
The linear transfer function matrix is obtained from as a dynamic model of the plant. The procedure is such that the individual elements h _ij (t) (i of H (t)
= 1, ..., p, j = 1, ..., q) is processed in the following steps.

Step 0: First, an initial value 1 is set to i and j.

Step 1: A discrete time response sequence h _dij (0), h _dij (1), ..., H _dij (N) obtained by sampling h _ij (t) at a period τ is _obtained . However, h _dij (k) = h _ij (τk), and N is an even number.

Step 2: From h _dij (k), the following coefficient corresponding to the impulse response sequence of the linear transfer function is obtained. g _dij (1), g _dij (2), ..., g _dij (N) where g _dij (k) = h _dij (k) −h _dij (k−
1) Step 3: Obtain the following two matrices G ₁ and G ₂ .

[0038]

[Equation 1] Step 4: Singular value decomposition of the matrix G ₁ to obtain a singular value σ ₁ ,
…, Find σ _{N / 2} . G ₁ = U Σ V However, Σ = diag {σ ₁ , ..., σ _{N / 2} } σ ₁ ≧ σ ₂ ≧ ... ≧ σ _{N / 2} . Step 5: For some threshold σ _ε > 0, σ _k ≧ σ
Find an integer k such that _ε and σ _{k + 1} <σ _ε .

However, when σ _{N / 2} ≧ σ _ε , k = N /
Set to 2. Then, the matrices U, V and Σ are decomposed as follows.

[0040]

[Equation 2] Where U _N is a matrix consisting of the first K columns of matrix U, V _N
Is a matrix consisting of the first K rows of the matrix V.

Step 6: The coefficient matrix of the discrete time state space model equivalent to the linear transfer function of interest is obtained by the following equation.

[0042] _{^{A = Σ N -1/2 U N T}} G2 V N T Σ N -1/2 B = Σ N 1/2 V N [I q 0] C = [I p 0] U N Σ N 1 ^{/ 2} However, I _q and I _p are identity matrices of sizes q and p, respectively.

Step 7: The matrix A is diagonalized by the diagonalization matrix T. A _d = T ^-1 AT = diag {λ ₁ , λ ₂ , ..., λ _k } B _d = T ^-1 B C _d = CT Step 8: Convert from discrete time model to continuous time model by the following procedure To do. A _c = diag {η ₁ , η ₂ , ..., η _k } where η _i = (α _i + jβ _i ) / τ (j is an imaginary unit) λ _i = exp (α _i + jβ _i ) (i = It is assumed that the relationship is 1, ..., k). B _C = (A _d −I _k ) ⁻¹ A _C B _d (I _k is the size k
Unit matrix of C _C = C _d Step 9: Obtain a continuous time transfer function.

G _ij (s) = C _C (sI _k −A _C ) ⁻¹ B _{C The} above procedure is repeated as shown in FIG. Note that these procedures are described in Japanese Patent Application No. 60-108316 "Plant Modeling Device".

If the transfer function is obtained by the above procedure for all the elements, the following transfer function matrix is obtained.
Step 10:

[0046]

(Equation 3) The above is the calculation procedure of the linear transfer function estimation unit 3.3.

Next, the model error norm calculation unit 3.4 will be described. This is the maximum fluctuation range of the linear transfer function within the operating condition range determined by the constraint condition currently set in the model predictive control device 2, that is, the inequality condition regarding the controlled variable and the manipulated variable below. Obtained as a function of frequency ω.

Y _min ≤ y ≤ y _max Δy _min ≤ Δy ≤ Δy _max u _min ≤ u ≤ u _max Δu _min ≤ Δu ≤ Δu _max (8) where y, Δy, u, and Δu are control amounts, respectively. rate of change, the manipulated variable, a vector of the change rate, the elements, for example y = [y (k + 1 ) T, ···, y (k + Np) T] T y (k + j) = [ y ₁ (k + j), ..., Y _p (k + j)] ^T. The inequality sign in the above expression is a collective expression of inequality signs for each element in the vector.

First, the model error norm calculation unit 3.4 gives various input fluctuation widths Δu to the simulation calculation unit 3.2, and as a result, the linear transfer function estimation unit 3.
The frequency response G (j) of the transfer function matrix G (s) obtained in
Find the fluctuation range of ω). The procedure is shown in the flowchart of FIG.

Step 0: First, k = 0, fluctuation range Δ
u (0) = Δu _min << 1, initial value of model error norm
Let ε (ω _i ) = 0 and i = 1, ..., m.

Step 1: Let the fluctuation range in the k-th trial be Δu (k). Control quantity response y (t) to this,
The manipulated variable response u (t) is obtained by the simulation calculation section 3.2.

Step 2: It is checked whether or not the controlled variable response y (t) and the manipulated variable response u (t) satisfy the constraint conditions of the equation (8). If satisfied, go to the next step, and if not satisfied, the model error norm ε (ω _i ) at that point, i =
1, ..., m are output as the maximum model error norm, and the process ends (step 7).

Step 3: The transfer function matrix G estimated by the kth trial by the linear transfer function unit 3.3.
_{Get k} (s). Step 4: For the frequency response ω ₁ , ..., ω _m , the model error norm ε _k (ω _i ) = σ _max {G _k (jω _i ) −G ₀ (jω _i )} (i = 1 ,.・ ・, M)… (9) is calculated. Here, σ _max {A} means the maximum singular value of the matrix A.

Step 5: For each ω _i , if ε (ω
_{If i} ) <ε _k (ω _i ), set ε (ω _i ) = ε _k (ω _i ). Step 6: With respect to the fluctuation width Δu _k , Δu _{k + 1} = −1.1 × Δu _k k ← k + 1, and the process returns to step 1.

In the above procedure, first, the recurrence formula in step 6 means that the variation width Δu of the manipulated variable is gradually increased in absolute value while alternately changing the sign between plus and minus. . While determining in step 2 whether or not each element of the control amount response y (t), the operation amount response u (t), the value at each time, and the change rate satisfy the constraint condition of the equation (8) at that time, The maximum magnitude of the model error within the operating condition range determined by (8) is obtained in steps 4 to 5 in the form of the maximum singular value of the frequency response of the model error transfer function at each frequency. The above is the processing procedure in the model error norm calculation unit 3.4.

As described above, in the process dynamic characteristic model data output unit 3, each operation of the plant model 3.1, the simulation unit 3.2, the linear transfer function estimation unit 3.3, and the model error norm calculation unit 3.4. By equilibrium points y ₀ and u ₀
And the linear transfer function G (s) and the maximum model error norm ε (ω _i ), i = 1, ..., m are calculated from the constraint condition expression (8) and output.

(2) A configuration example of the control system adjusting section 4 shown in FIG. 3 will be described with reference to FIG. As shown in the figure, the control system adjustment unit 4 is composed of a prediction model conversion unit 4.1 and a control parameter calculation unit 4.2.

In the predictive model conversion section 4.1, the linear transfer function G (
Based on s), a prediction model is created by the following procedure. Step 1: Convert G (s) into a discrete time transfer function model y (k) = A ^-1 (z ^-1 ) B (z ^-1 ) u (k). However, z is a time transition operator, y (k), u
(k) respectively controlled variable, manipulated variable discrete-time representation of a vector, A (z-1), B (z-1) is a coefficient matrix of the discrete-time transfer function, respectively ^{A (z -1) = 1 +} a 1 z ^-1 + ... + a _n z ^-n B (z ^-1 ) = b ₀ + b ₁ z ^-1 + ... + b _m z ^-m (a _i is a coefficient matrix of size p × p, b _i is size p × q)
Can be expressed as

Step 2: _{Let the} prediction range be N _p steps, and for j = 1 to N _p the following equation (this is the Diopha
ntine equation)). (I _p is a p × p identity matrix) I _p = E _j (z ⁻¹ ) (1-z ⁻¹ ) A (z ⁻¹ ) + z ^−j F _j (z ⁻¹ ), as a result, a polynomial matrix E _j (z ^-1 ) (j-1 order monic) and F _j (z ^-1 ) (n order) are obtained. further, And obtain the coefficient matrix b _eji Then, a polynomial matrix B _ej (z ⁻¹ ) is obtained. As a result, the predicted control value y (k + j) is y (k + j) = F _j (z ^-1 ) y (k) + B _ej (z ^-1 ) Δu (k-1) + S _j Δu (k) + ...・ + S ₁ Δu (k + j-1) is expressed as (9). However, here, Δu (k) = u (k) −u (k
-1) is the manipulated variable increment vector at each time, and S _j is the matrix of the j-th step of the step response sequence of the controlled object model. The z polynomial matrix F _j (z ⁻¹ ) and B _ej (z ⁻¹ ) of the equation (9) obtained by the above procedure and the step response sequence matrix S _j , (j = 1, ..., N _p ) is output as a parameter related to the prediction model.

In the control parameter calculation unit 4.2, the control parameter is calculated by the following procedure shown in the flowchart of FIG. Step 1: The linear transfer function G (s) and maximum model error norm ε (ω) are read from the plant dynamic characteristic model data output unit 3, and the coefficients of the prediction model are read from the above-mentioned prediction model conversion unit.

Step 2: Evaluation function Give the initial value of the weighting factor λ for. Where y ^* (k
+ i) is a control amount target value vector in the i step future from the current time k.

Step 3: A control rule for minimizing the evaluation function of the equation (10) without considering the constraint condition, Δu (k) = g
^T {y ^* -F (z ^-1 ) y (k) -H (z ^-1 ) Δu (k-1)} u (k) = u (k-1) + Δu (k) (11) . ^{However, y * = [y * (} k + 1) ··· y * (k + Np)] T F (z -1) = [F 1 (z -1) ··· F Np (z -1) ] ^T H (z ^-1 ) = [H ₁ (z ^-1 ) ... H _Np (z ^-1 )] ^T g ^T = (G ^T G + λI) ^-1 G ^T , the first line,

[0063]

[Equation 4] (S _i is the step response calculated from the dynamic characteristic model).

Step 4: From the control law of equation (11), the transfer function C (z ^-1 ) of the controller and the controlled object model A ^-1 (
The open loop transfer function L (z ^-1 ) of the control system is obtained from z ^-1 ) B (z ^-1 ). C (z ^-1 ) = (I-z ^-1 I) ^-1 (1+ g ^T H (z ^-1 )) ^-1 g ^T F (z ^-1 ) L (z ^-1 ) =-C (z ⁻¹ ) A ⁻¹ (z ⁻¹ ) B (z ⁻¹ ) ... (12) Step 5: It is determined whether or not the model predictive control system satisfies the robust stability condition of the following equation. σmax {ε (ω) (I + L (z ^-1 )) ^-1 C (z ^-1 ) |
_{z = exp (-jωτ)} } <1 If ω = ω ₁ , ..., ω _m is satisfied with all frequencies ω _i , then λ ← 0.99
X λ (step 6), and conversely the unsatisfied frequency ω
_{If i} is present, set λ ← 1.01 × λ (step 7),
Return to step 3 again.

Step 8: However, if some ω _i , σmax {ε (ω) (I + L (z ^-1 )) ^-1 C (z ^-1 ) |
_{z = exp (-jωτ)} } <1 ω = ω ₁ , _··· , ω _i-1 , ω _{i + 1} , _··· , ω _m , the control system at this time is considered to be robust stability limit , And the control parameters g ^T , F (z ⁻¹ ) of λ and the control law of the equation (11) at that time,
Output H (z ^-1 ).

The above is the processing procedure in the control system adjusting unit 4. With such a function, the parameters of the prediction model based on the linear transfer function of the plant under a certain operating condition
Furthermore, a control parameter that does not lose stability with respect to the maximum model error at that time, that is, is robust, is calculated and output.

(3) Constraint condition adjusting unit 5 shown in FIG.
An example of the configuration will be described with reference to FIG. As shown in the figure, the control condition adjusting unit 5 includes an allowable model error norm calculating unit 5.1, a comparator 5.2, and an allowable operating condition searching unit 5.3.

In the allowable model error norm calculation unit 5.1,
The allowable model error norm ε _max (ω) is calculated from the linear transfer function and the control parameters g ^T , F (z ⁻¹ ), and H (z ⁻¹ ) of the control law of Expression (11) by the following expression.

C (z ⁻¹ ) = (I−z ⁻¹ I) ⁻¹ ( ¹ + g ^T H (z ⁻¹ )) ⁻¹ g ^T F (z ⁻¹ ) L (z ⁻¹ ) = − C (z ^-1 ) A ^-1 (z ^-1 ) B (z ^-1 ) ε _max (ω) = σ _max {(I + L (z ^-1 )) ^-1 C (z ^-1 ) | _{z = exp ( -jωτ)} } ⁻¹ ω = ω ₁ , ..., ω _m (13) In the comparator 5.2, the maximum model error norm ε (ω) given from the plant dynamic characteristic model data output unit 3 and the above Allowable model error norm ε _max (ω) at each frequency ω = ω
₁ , ..., ω _m are compared.

In the permissible operating condition searching unit 5.3, the constraint condition expression (8) is adjusted according to the above comparison result by the following procedure shown in the flowchart of FIG. Step 1: The initial values of the upper and lower limit values of each of the constraint condition expression (8) are given.

Step 2: For the transfer function G (s) and the maximum model error norm ε (ω) calculated when the constraint conditions are given to the plant dynamic characteristic model data output unit 3, the above-mentioned allowable model error norm calculation is performed. The permissible model error norm ε _max (ω) is calculated by the section 5.1.

Step 3: ε (ω) by the comparator 5.2
And ε _max (ω) are compared.

Step 4: All frequencies ω ₁ , ...
If ε (ω) <ε _max (ω) with respect to ω _m , it is determined that the constraint condition is too narrow, and the constraint condition y _min ≤ y ≤ y _max Δy _min ≤ Δy ≤ Δy _max u _min ≤ u ≤ u _max Δu _min ≤ Δu ≤ Δu _max (8) The range is relaxed and the process returns to step 2.

Y _min ← y _min −0.1 × (y _max −y _min ) y _max ← y _max + 0.1 × (y _max −y _min ) Δy _min ← Δy _min −0.1 × (Δy _max − Δy _min ) Δy _max ← Δy _max + 0.1 × (Δy _max −Δy _min ) u _min ← u _min −0.1 × (u _max −u _min ) u _max ← u _max + 0.1 × (u _max −u _min ) Δu _min ← Δu _min −0.1 × (Δu _max −Δu _min ) Δu _max ← Δu _max + 0.1 × (Δu _max −Δu _min ) (14) Step 5: Conversely, ε at a certain frequency ω (Ω)> ε
_{If max} (ω), it is determined that the constraint condition is too wide, the constraint condition range is narrowed as follows, and the process returns to step 2. y _min ← y _min + 0.1 × (y _max −y _min ) y _max ← y _max −0.1 × (y _max −y _min) Δy _min ← Δy _min + 0.1 × (Δy _max −Δy _min ) Δy _max ← Δy _max −0.1 × (Δy _max −Δy _min ) u _min ← u _min + 0.1 × (u _max −u _min ) u _max ← u _max −0.1 × (u _max −u _min ) Δu _min ← Δu _min + 0.1 × (Δu _max −Δu _min ) Δu _max ← Δu _max −0.1 × (Δu _max −Δu _min ) (15) Step 6: ε (ω) = ε _max at a certain frequency ω (Ω) and at other frequencies, in the case of ε (ω) <ε _max (ω), the adjustment of the constraint condition is terminated, and the constraint value at that time is output to the model prediction control device 2.

However, the above y, Δy, u, and Δu are vectors of the control amount, its change rate, the manipulated variable, and its change rate, and each element is, for example, y = [y (k + 1) ^T , ..., y (k + N _p ) ^T ] ^T y (k + j) = [y ₁ (k + j), ..., y _p (k + j)] ^T . The inequality sign in the above expression is a collective expression of inequality signs for each element in the vector.

With the configuration of the constraint condition adjusting unit 5 as described above, the operating range, that is, the constraint, that guarantees that the model error of the plant dynamic characteristic model is within the robust stability range of the current model predictive control system The conditions can be determined automatically.

(4) The configuration of the model predictive control device 2 shown in FIG. 3 is the same as the configuration example shown in FIG. 1, and the predictive model 2.1 and the operation amount optimization determined from the plant dynamic characteristic model are used. It is configured by the calculation unit 2.3.

[0078] In the plant dynamics model 2.1, predictive model y (k + j) the prediction model conversion unit 4.1 shown in Figure 5 and output ^{_{= F j (z -1) y}} (k) + B ej (z - ¹ ) Δu (k ⁻¹ ) + S _j Δu (k) + ... + S ₁ Δu (k + j-1) (9) (where Δu (k) = u (k) −u (k-1) is The manipulated variable increment vector at each time, S _j is the matrix of the j-th step of the step response matrix of the controlled object model.), And the manipulated variable vector u (k) of the plant 1 observed in each control cycle is read. , The future control response prediction value vector 2.2 y _p (k) = [y ^T (k + 1), y ^T (k + 2), ..., using the prediction model from the control amount vector y (k). y ^T (k
+ N _p )] ^T is calculated.

In the operation amount optimization calculation section 2.3, given constraint conditions y _min ≤ y ≤ y _max Δy _min ≤ Δy ≤ Δy _max u _min ≤ u ≤ u _max Δu _min ≤ Δu ≤ Δu _max (8 ), The given evaluation function (Y ^* (k + i) is the control amount target value vector in the i step future from the current time k) Δu = [Δu ^T (k), Δu ^T (k + 1), ... ., Δu ^T (k
+ Nu-1)] ^T is calculated and the optimal manipulated variable vector u (k) = u (k-1) + Δu (k) is output to the plant 1.

[0080] constraints of the above formula (8), the upper and lower limit constraint value vector _{ymax, ymin, Δy max, Δy} min, u
_{Using max} , u _min , Δu _max , Δu _min , and the matrix G of equation (11)

[0081]

(Equation 5)

[0082]

(Equation 6) Is.

[0083] On the other hand, the evaluation function equation (10) can be deformed and ^{J = Δu T [G T G} + λI] Δu + 2 (y p (k) -y *) T GΔu ... (17). Under the constraint condition of Expression (16), Expression (1
The optimum operation amount vector Δu that minimizes the quadratic form evaluation function of 7) is obtained for each control cycle by the following procedure using a quadratic programming method which is a kind of optimization calculation method. Secondary programming (Q
P: Quadratic Programming) is a concrete solution, for example, Iwanami Computer Science "optimized programming" Author Ibaraki, Fukushima April 10, 1991 p87
~ P132. In addition, the above equations (16) and (1
The procedure of 7) is described in, for example, Japanese Patent Application No. 2-111800 “Model Predictive Control Device” and Japanese Patent Application No. 3-17527 “Model Predictive Control Device”.

By repeating the above processing for each control cycle, the evaluation function expression (1
The control operation is performed so that the controlled variable optimally follows the target value so as to minimize 0).

In this way, the plant dynamic characteristic model data output unit 3, the control system adjustment unit 4, the constraint condition adjustment unit 5, and the model prediction control device 2 which constitute the plant unsteady operation control device of the present invention are specifically realized. To be done. With these configurations, the magnitude of the model error of the linear model caused by changes in nonlinear characteristics and dynamic characteristics is sequentially evaluated, and the model predictive control system is robustly stable against the model error even when the plant is in unsteady operation. Function to self-adjust the control parameters, or to self-adjust the operating condition range, that is, the constraints on the controlled variable, manipulated variable, and its rate of change, so that the model error falls within the range that the model predictive control system can withstand. Is realized, and the control system can always be operated stably and satisfactorily.

The control system adjusting unit 4 and the constraint condition adjusting unit 5 shown in FIG. 3 can execute only one of the operations according to an instruction from the plant operator, or both of them can be executed simultaneously. It is possible. In the latter case, it is also possible to give priority to each adjustment function, and one of the control system adjustment unit 4 and the constraint condition adjustment unit 5 is the main control, and the other control is added to this. Control is realized.

[0087]

As described above, in the plant operation controller of the present invention, the plant transfer characteristic model for calculating the linear transfer function model and its maximum model error norm in each operating state of the plant is based on the model predictive controller. Since the data output unit and the control system adjustment unit that calculates the prediction model and the control parameters used in the model predictive control device or the constraint condition adjustment unit that calculates an appropriate constraint condition are provided, it is possible to prevent changes in the operating conditions of the plant. Accordingly, the model predictive control device can be adjusted to a good state, and the non-linear characteristic that occurs during unsteady operation of the plant can also be dealt with.

In particular, when an attempt is made to rapidly change the control amount in unsteady operation, the control amount is braked so that a strong nonlinear characteristic does not appear due to automatic adjustment of constraint conditions, and unsteady operation is stabilized. You can keep your sex. Further, as the dynamic characteristic model of the plant, any type of model can be applied to the present control device as long as the control response under each operating condition can be calculated.

[Brief description of drawings]

FIG. 1 is a block diagram showing the configuration of a model predictive control device.

FIG. 2 is an explanatory diagram for explaining the effect of constraint control in plant unsteady operation.

FIG. 3 is a block diagram showing the overall configuration of a plant unsteady operation control device of the present invention.

FIG. 4 is a block diagram showing a configuration of a process dynamic characteristic model data output unit.

FIG. 5 is a block diagram showing a configuration of a control system adjustment unit.

FIG. 6 is a block diagram showing a configuration of a constraint condition adjusting unit.

FIG. 7 is a flowchart showing a processing procedure of a linear transfer function estimation unit.

FIG. 8 is a flowchart showing a processing procedure of a model error norm calculation unit.

FIG. 9 is a flowchart showing a processing procedure of a control parameter calculation unit.

FIG. 10 is a flowchart showing a processing procedure of an allowable operating condition search unit.

[Explanation of symbols]

 1 Control object (plant) 2 Model predictive control device 2.1 Plant dynamic characteristic model (prediction model) 2.2 Control amount predictive response 2.3 Manipulation amount optimization calculation unit 3 Process dynamic characteristic model data output unit 3.1 Plant Model 3.2 Simulation calculation unit 3.3 Linear transfer function estimation unit 3.4 Model error norm calculation unit 4 Control system adjustment unit 4.1 Prediction model conversion unit 4.2 Control parameter calculation unit 5 Constraint condition adjustment unit 5.1 Allowable model error norm calculation unit 5.2 Comparator 5.3 Allowable operating condition search unit

Claims (4)

[Claims] 1. A future value of a controlled variable is predicted using a dynamic characteristic model of a controlled object that outputs a controlled variable corresponding to an input manipulated variable, and while the controlled variable and the manipulated variable satisfy a constraint condition, A plant control device having a model predictive control device for performing control while sequentially calculating an operation amount for optimizing an evaluation function related to a deviation signal from a future target value and an operation amount, is preset. The plant dynamics that output the linear transfer function and its maximum model error norm that approximately represent the dynamics of the controlled object within the operating conditions limited by the equilibrium points regarding the controlled variables and the manipulated variables and the constraint conditions. Calculate the prediction model based on the model data output section and the output linear transfer function,
A plant control apparatus, comprising: a control system adjusting unit that calculates a control parameter that is robust and stable with respect to the maximum model error norm, and applies the control parameter to the model predictive control apparatus. 2. A controlled object future value is predicted using a dynamic characteristic model for a controlled object that outputs a controlled variable according to an input manipulated variable, and a constraint condition given the controlled variable and the manipulated variable is set. In a plant control device having a model predictive control device that performs control while sequentially calculating an operation amount that optimizes an evaluation function related to a deviation signal from a future target value and an operation amount while satisfying , Outputs a linear transfer function and its maximum model error norm that approximately represent the dynamic characteristics of the controlled object within the preset equilibrium points regarding the controlled variables and manipulated variables, and the operating conditions limited by the constraint conditions. The plant dynamic characteristic model data output section and the allowable model that guarantees the stability of the control system from the linear transfer function and control parameters corresponding to the plant dynamic characteristic model in the current operating state. Of the operating conditions in which the maximum model error norm output by the plant dynamic characteristic model data output unit is equal to or less than the allowable model error norm is calculated, and the control amount and the operation amount are restricted based on the range. A plant control device, comprising: a constraint condition adjusting unit that determines a condition and applies the condition to the model predictive control device. 3. A future value of a controlled variable is predicted by using a dynamic characteristic model of a controlled object that outputs a controlled variable according to an input manipulated variable, and while the controlled variable and the manipulated variable satisfy a constraint condition given, A plant control device having a model predictive control device for performing control while sequentially calculating an operation amount for optimizing an evaluation function related to a deviation signal from a future target value and an operation amount, is preset. The plant dynamics that output the linear transfer function and its maximum model error norm that approximately represent the dynamics of the controlled object within the operating conditions limited by the equilibrium points regarding the controlled variables and the manipulated variables and the constraint conditions. Calculate the prediction model based on the model data output section and the output linear transfer function,
A control system adjusting unit that calculates a control parameter that is robustly stable with respect to the maximum model error norm and gives the control parameter to the model predictive controller, a linear transfer function corresponding to the plant dynamic characteristic model in the current operating state, and the Calculate the allowable model error norm that guarantees the stability of the control system from the control parameters, and search for the allowable range of operating conditions where the maximum model error norm output from the plant dynamic characteristic model data output unit is less than or equal to the allowable model error norm. And a constraint condition adjusting unit that determines a constraint condition regarding a control amount and an operation amount based on the range and gives the constraint condition to the model predictive control device. 4. The plant dynamic characteristic model data output unit includes a plant model expressing a nonlinear dynamic characteristic of a controlled object, each equilibrium point of a control amount and a manipulated variable given using the plant model, and an manipulated variable A simulation calculation unit that calculates a control response to the amount of change, a linear transfer function estimation unit that estimates a linear transfer function that approximately represents the control response obtained by the simulation calculation unit, and within a given constraint condition A model error norm calculation unit that calculates a maximum model error norm from the fluctuation range of the linear transfer function under operating conditions, and the plant control device according to any one of claims 1 to 3.