JPH0535309A - Model prediction control device - Google Patents

Abstract

PURPOSE:To improve characteristics for the polar arrangement of a control system and a transient response, to set a response constant to the model prediction control system and to automatically set the suitable response time constant by evaluating stable tolerance by setting weight like an exponent to an evaluation function corresponding to the response constant. CONSTITUTION:A model prediction control operation part 2 is equipped with a cyclic frequency response characteristic calculating means 10, complementary sensitivity matrix calculating means 11 and stable tolerance parameter calculating means 12 or the like while completely covering the function of the model prediction control operation part 2. Further, a dynamic characteristic model setting means 3 is provided to set the dynamic characteristic of a controlled system for predicting a controlled variable, and an evaluation function setting means 4 to set the evaluation function meaning the purpose of control. A response time constant Tr from a terminal equipment 9 is held at a response time constant setting means 5. A stable tolerance parameter 5 is supplied to one input terminal of a response time constant adjusting means 8 and a storage device 13. The stable tolerance parameter 5 is displayed corresponding to the response time constant Tr inputted from the terminal storage device 9 by an operator.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a model predictive control device for predicting future movement of a control response on the basis of a dynamic characteristic model of a controlled object and calculating a manipulated variable while considering it.

[0002]

2. Description of the Related Art In recent years, model predictive control devices are often used in the field of process control. Model predictive control can realize a stable control response to a process with a long dead time. The followability can be improved by the foot-forward control using the future target value. 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, it is possible to expect fine control. Therefore, various predictive control methods have been proposed. Examples of these are, for example, (1) Nishitani: Application of model predictive control, measurement and control Vol.28,
No.11, pp.996-1004 (1989) (2) DWClarke & C. Mohtadi: Properties of Generaliz
ed PredictiveControl, Automatica 25-6 pp.859 (1989) etc. A configuration example of a general model predictive control system will be described with reference to FIG. First, when the manipulated variable u (k) is given from the model predictive control calculation unit 2 to a process, robot or the like which is the controlled object 1 at a certain time k, the controlled object 1 outputs the controlled variable y (k). The controlled variable y (k) and the manipulated variable u (k) at this time are written in the response data storage unit 26 of the model predictive control calculation unit 2. The prediction model 27 is
The predicted value y of the future control amount response is referred to by referring to a dynamic characteristic model selected in advance based on constant accumulated data of the operation amount u and the control amount y from the past to the present (time k) in the response data storage unit 26. (k + L), ..., Y (k + Np + L-1) is calculated, and the subtracter 3
1 to one input terminal. Here, L is the prediction start time, and Np is the prediction length.

On the other hand, the target value r (k) input from a terminal device (not shown) is given to the future target trajectory generation unit 28. The future target trajectory generation unit 28 uses the future target trajectory y ^* (k +
L), ..., Y ^* (k + Np + L-1) are generated and supplied to the other input terminal of the subtracter 31. The subtractor 31 uses a future control deviation signal y (k + i) −y ^* (k + i), which is the difference between the two, (i = L, ..., Np + L-
1) is calculated and supplied to the optimum manipulated variable calculation unit 29. As a typical example, the following quadratic form evaluation function is preset in the optimum manipulated variable calculating unit 29, and the optimum manipulated variable increment Δu (k) that minimizes J is calculated, and the first Δu ( Only k) is sent to the integrator 30.

[0004]

[Equation 2] Here, Nu represents the control length and λ represents the weighting coefficient. D (z ^-1 )
Represents a pole-placement polynomial, and D (z ^-1 ) = 1 + d ₁ z ^-1
+ ... + represented as d _n z ^-n. Δu (k + i) is an increment of the future manipulated variable, and is calculated as Δu (k + i) = u (k + i) −u (k + i−1). In the integrator 30, the arithmetic processing u (k) = u (k-1) + Δu (k) (2) is performed to calculate the actual manipulated variable u (k) including the predicted control amount given to the controlled object 1. It is calculated and supplied to the controlled object 1.

[0005]

In the model predictive control system described above, depending on how to select the so-called evaluation function parameters L, Np, Nu, λ, D (z ⁻¹ ) included in the evaluation function (1),
The characteristics of the control system, in particular, the stability and robustness against characteristic fluctuations, that is, the stability margin in the so-called Nyquist determination method, vary greatly, and therefore it is necessary to appropriately adjust (tune) them when starting the control device. In the conventional model predictive control device, these evaluation function parameters were given by the operator by trial and error, but the relationship between the parameters and the control characteristics was not clear, and the control device was designed so that the control system would be sufficiently stable. It took a lot of time to make adjustments, and it took time to start the control device.

Therefore, the applicant has filed Japanese Patent Application No. 3-04749.
No. 4 proposed a method to automatically adjust the evaluation function parameters so that the control system has sufficient stability. However, the response characteristics of the control system, such as the overshoot amount, the time constant, and the settling time, have not been positively taken into consideration.

For example, when a response within the time constant Tr [sec] is required for the control system, it is not clear what kind of evaluation function is specifically set to obtain the desired control system. . Moreover, it is difficult to deal with the specification of the response characteristic of the control system. As an example thereof, a transfer function model G (s) of the following equation having an extremely strong vibration characteristic will be described as a characteristic of a controlled object.

[0008]

[Equation 3] Here, assuming a mechanical system, the moment of inertia I = 16360 [Kg
-M ² ], damping factor ζ = 0.0025, resonance frequency ω = 0.2205 × 2π [rad / sec], torque admittance Φ ² = 7.49 × 10 ^-5 . With respect to this transfer function, the control cycle is 1.0 [sec], the parameters Np = 10, L = 1 and Nu of the equation (1) are Nu.
9 shows the control response by the model predictive control when = 5 is given. From this, it can be confirmed that although the control amount y follows the target value r, a fine vibration appears in the control response. Therefore, the poles of the control target of the control system (marked by X) and the poles of the control system (marked by ◯) are shown on the complex plane of FIG.
From this, it can be confirmed that poles near the unit circle corresponding to the vibration mode of the controlled object, that is, poles having extremely poor stability are left even in the pole arrangement of the closed loop system.
Thus, in the conventional model predictive control system, the evaluation function
Since the control calculation is performed with an emphasis on minimizing equation (1), it may happen that the closed loop poles that determine the transient response characteristics of the control system cannot be placed appropriately, and the control response is stable. Alternatively, even quickly, the problem that the response shape becomes oscillatory may occur. Therefore, an object of the model predicting device of the present invention is to provide a model predicting device in which the vibration of the controlled variable y in the rising response characteristic is suppressed.

[0009]

In order to achieve the above object, the model predictive control device of the present invention is provided with each means having the following functions in addition to the configuration of the conventional model predictive control device. That is, the first aspect of the present invention is based on a response time constant setting means having a function of setting a response time constant Tr [sec], which is a typical control specification, and a weighting factor parameter ρ = exp (-Δ / Tr) (4) where Δ [sec] is the control cycle. The stability margin parameter calculating means for calculating the stability margin parameter ρ and the stability margin parameter ρ are used to evaluate the exponentiation function with respect to time as a weighting coefficient.

[0010]

[Equation 4] And an evaluation function setting means for constructing.

The second aspect of the present invention further calculates the manipulated variable Δu (k) by referring to the above-mentioned evaluation function, and performs control using the above-mentioned evaluation function from the control constant used for calculating the manipulated variable and the dynamic characteristic model of the controlled object. The stability of the control system is maintained by calculating the open-loop frequency response characteristic L (jω) of the system and based on this open-loop frequency response characteristic L (jω) Stability margin parameter ε indicating the degree of, for example, a model prediction control system for a one-input one-output process, a gain margin, a phase margin, a peak value of a gain characteristic (so-called Mp value), and a model prediction for a multi-input multi-output process. In the control system, the peak value of the maximum singular value of the complementary sensitivity function matrix T (jω), which is a measure of robustness against model error

[0012]

[Equation 5] And the calculation means for calculating the stability margin parameter ε, and the stability margin parameter corresponding to the instantaneous value of the response time constant while changing the value of the response time constant set in the response time constant setting means. Simulation means for recording and accumulating values, accumulating response time constant Tr and stability margin parameter ε
And a display means for visually displaying the relationship between them.

According to a third aspect of the present invention, further, a stability margin parameter setting means for holding a stability margin parameter input as a control specification by an operator, and a stability margin specified so that the stability margin parameter is set. Therefore, the response time constant Tr is changed to derive the coefficient parameter ρ corresponding to the response time constant Tr, the evaluation function calculating means is caused to reconstruct the evaluation function, and the stability margin parameter of the control system is calculated. And a response time constant adjusting means for repeating the calculated stability margin parameter until the calculated stability margin parameter matches.

As a result, the model predictive control calculation is performed by the evaluation function weighted by the new weighting coefficient parameter ρ, and the optimum manipulated variables Δu (k) and u (k) are obtained, or the desired rising characteristic is determined. It becomes possible to specify.

[0015]

[Operation] Below, the conventional evaluation function (1) is applied to the present invention.
The reason why the response characteristics in model predictive control can be improved by changing to equation (5) is explained. First, 2 in equation (1)
The quadratic evaluation function is the prediction length Np, which is the time considered in the prediction.
If is chosen to be infinitely long, it corresponds to a special case of the evaluation function of the optimal regulator well known in control theory.

In general, in the optimal regulator theory, a state space model, x (k + 1) = Ax (k) + Bu (k) (7a) y (k) = Cx (k) (7b), where x is a state Variable, y is a controlled variable, u is a manipulated variable, A,
B and C are matrix constants. For the controlled object represented by, the evaluation function

[0017]

[Equation 6] Can provide a minimized controlling law of ^{u (k) = k T ·} x (k) (9). Here, T represents a transposed matrix. The characteristic of the control system at this time is given by x (k + 1) = (A + Bk ^T ) x (k) (10) by substituting the equation (9) into the equation (7). That is, all the modes of the closed loop system are attenuated from the initial state to 0 with an attenuation rate determined by the eigenvalue of the matrix (A + Bk ^T ). Therefore, the eigenvalue closest to the unit circle becomes the dominant mode and corresponds to the response time constant of this control system.

Here, the parameter ρ of equation (4) (0 <ρ ≦
1), x (k + i) = ρ ^-i x ^* (k + i) (11a) u (k + i) = ρ ^-i u ^* (k + i) (11b) y (k + i) = ρ ^-i y ^* (k + i) (11c), the new state x ^* (k + i), input u ^* (k +)
i) and the output y ^* (k + i), and substituting them into Eqs. (7), (8), (9), and (10), the state space model x ^* (k + 1) = A'x ^{*, respectively.} (k) + B'u ^* (k) (7a ') y ^* (k) = Cx ^* (k) (7b') where A '= ρA and B' = ρB. Evaluation function

[0019]

[Equation 7] Control law u ^* (k) = k ^T · x ^* (k) (9 ') Control system characteristics x ^* (k + 1) = ρ (A + Bk ^T ) x ^* (k) (10') To be

That is, when the controlled object is originally given by the equations (7a ') and (7b'), the evaluation function (8 ') is set to design the optimum regulator, and the obtained equation (9') is obtained. When the control law is used, the pole arrangement of the closed loop system is the matrix ρ (A + Bk of Eq. (10 ').
It becomes the eigenvalue of ^T ). Here, the control law of the equation (9 ') is the same as the control law of the optimal regulator designed for the evaluation function equation (8) with respect to the virtual controlled objects of the equations (7a) and (7b). Because of the property of the optimal regulator, the virtual control system according to equation (10) is always stable, so all the eigenvalues of the matrix (A + Bk ^T ) fall within the unit circle of the complex plane. Therefore, (10 ')
All eigenvalues of the matrix ρ (A + Bk ^T ) of the equation fall within a circle with the origin at the center. This means that all modes in the control system of Eq. (10 ') are attenuated with a damping rate of ρ ⁱ (i is a discrete time) or more, and the response of the control system is faster than the corresponding time constant Tr. Become. Therefore, it is guaranteed that the response time constant of the control system by the optimum regulator using the evaluation function of the expression (8 ') is Tr or less. This relationship is shown in FIG.

This property holds even when the evaluation function J has a finite time length. In the evaluation function of the equation (8 '), Q = C
^{If T} C, R = λI (I is an identity matrix) and the section to be considered is i = L to Np + L-1 instead of i = 1 to ∞,
Matches the evaluation function of equation (5). Therefore, when the control for minimizing the evaluation function of the equation (5) is performed, the control response time constant is approximately Tr or less.

Based on the principle of the model predictive control method of the present invention, the response time constant setting means described above cannot set the response time constant Tr directly in the conventional model predictive control. It was made possible to be set by the operator. The stability margin parameter calculating means and the evaluation function setting means construct the above-mentioned evaluation function (5) and set it in the optimum manipulated variable calculating section so that the response time constant becomes Tr.
The following control response is realized. On the other hand, if the time constant Tr is made extremely small because the response characteristics are emphasized,
In general, the control system becomes excessively manipulated, and is sensitive to observation noise and model error of the controlled object, and sometimes the control system becomes unstable. Therefore, as a measure of stability of the control system, it is sufficient to check gain margin, phase margin, Mp value conventionally used, or complementary sensitivity function that means robustness to model error and sensitivity to observation noise. It is practically desirable to realize a control system with excellent robust stability. Even in a control system for multiple input / output processes, the stability margin can be evaluated by checking the peak value of the maximum singular value of the complementary sensitivity function matrix.

Therefore, the circuit frequency response characteristic calculation means is
Based on the set response time constant, the loop frequency response of the closed loop system for the model predictive control system designed in the evaluation function setting means is calculated, and the result is given to the stability margin parameter calculating means to calculate the above-mentioned stability margin parameter. And display it to inform the operator. As a result, the operator can be prompted to set an appropriate response time constant.

The simulation means obtains the relationship between the response time constant Tr and the stability margin parameter in advance by repeating the above processing, and the display means visually displays it in the form of a graph. , Helps the operator select an appropriate response time constant. The stability margin parameter setting means realizes a function in which an operator inputs a desired degree of stability by the stability margin parameter and an appropriate response time constant that satisfies the stability is automatically determined. As a result, the control system can be made to follow the response time constant determined by the operator, and the control system can be easily adjusted.

[0025]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the model predictive control device of the present invention will be described with reference to FIG. The model predictive control calculation unit 2 includes all the functions of the conventional model predictive control calculation unit 2 described above, and further includes a circuit frequency response characteristic calculation unit 10, a complementary sensitivity matrix calculation unit 11, and a stability margin parameter calculation unit 1.
It has 2 etc. Open-loop frequency response characteristic calculation means 10,
The complementary sensitivity matrix calculation means 11, the stability margin parameter calculation means 12 and the like correspond to the calculation means. The model predictive control calculation unit 2 controls the control amount y observed from the process 1 to be controlled.
(k) is fed back, and at the same time, the target value r (k) is taken in, and then the optimal manipulated variable u (k) is calculated based on the prediction model and the evaluation function and given to the controlled object 1.

In this embodiment, in order to give generality to model predictive control, the controlled object 1 is q manipulated variables u ₁ (k).
And a multi-output process with ~u _q (k) and p the controlled variable y ₁ a _{(k) ~y p (k)} . That, and outputs the manipulated variable u ₁ ~u _q for to follow the future target trajectory y ^* ₁ ~y ^* _p generated control amount y ₁ ~y _p process from the control target value r ₁ ~r _p successive . This model predictive control device is provided with a dynamic characteristic model setting means 3 for setting a dynamic characteristic model of a controlled object for predicting a controlled variable, and an evaluation function setting means 4 for setting an evaluation function meaning a control purpose. There is.

When the operator inputs the response time constant Tr from the terminal device 9, the response time constant Tr is held in the response time constant setting means 5 in an appropriate format. The weighting factor parameter calculating means 6 calculates the weighting factor parameter ρ corresponding to the held time constant Tr, and gives this to the evaluation function setting means 4. The evaluation function setting means 4 constructs an evaluation function in which the weighting factor parameter ρ is combined and sets it in the optimum manipulated variable calculation unit 29 (not shown) of the model prediction control calculation unit 2. Calculation means 10
The calculation means consisting of 12 calculates the stability margin parameter ε of the model predictive control system based on the new evaluation function. The stability margin parameter ε is supplied to one input terminal of the response time constant adjusting means 8 and the storage device 13. The calculated stability margin parameter ε of the control system is read from the storage device 13 to a display (not shown) of the terminal device 9, and the stability margin parameter ε corresponding to the response time constant Tr input by the operator from the terminal device 9 is displayed. It If the terminal device 9 gives a series of response time constants Tr to the response time constant setting means 5, a series of stability margin parameters corresponding thereto are accumulated in the storage device 13, and the response time constant Tr and the stability margin parameter ε are stored. Mutual relations are required.

On the other hand, when the operator inputs the stability margin parameter ε ₀ via the terminal device 9, the stability margin parameter ε ₀ is held in the stability parameter setting means 7. When the stability margin parameter ε ₀ is set in the stability parameter setting means 7, the response time constant adjusting means 8 sets the response time constant of the response time constant setting means to the initial value Tr ₀ and gradually changes it. Then, the value ρ of the weighting parameter calculated by the weighting factor parameter calculation means 6 also changes, and the evaluation function given to the model prediction control calculation section 2 by the evaluation function setting means 4 also changes. Correspondingly, the value of the stability margin parameter ε supplied from the stability margin parameter calculating means also changes. The response time constant adjusting means 8 calculates the set stability margin parameter ε ₀ by the calculated stability margin parameter ε.
The response time constant Tr is changed until it matches. When the set stability margin parameter ε ₀ matches the calculated stability margin parameter ε, the value of the response time constant Tr of the response time constant setting means at this time is fixed. These constants are given to the terminal device 9 via the storage device 13 and displayed in an appropriate form.

The function of each means will be described. The dynamic characteristic model for the multiple input / output process set in the model predictive control calculation unit 2 is given from the dynamic characteristic model setting means 3 by the pulse transfer function matrix of the following equation.

[0030]

[Equation 8] However, A _ij (z ^-1 ) = 1 + a ₁ ^ij z ^-1 + ... + a _n ^ij z ^-n B _ij (z ^-1 ) = b ₀ ^ij + b ₁ ^ij z ^-1 + ... + b _m ^ij z ^-m Is. Where p is the number of controlled variables, q is the number of manipulated variables,
It may be p ≠ q.

Here, it is assumed that the evaluation function of the following equation is given from the evaluation function setting means 4.

[0032]

[Equation 9] However, Δu _i (k) = u _i (k) −u _i (k−1) is the manipulated variable increment. Further, among the parameters in the equation (12), the prediction length L = 1, and Np, the control length Nu, and the weighting factor λ are set by an appropriate method, for example, Japanese Patent Application No. 3-04 considering the stability of the control system.
It is selected according to the method of 7494 so that the control system has sufficient stability. In addition, the pole-placement polynomial is set to D (z ⁻¹ ) = 1 for simplicity. These parameters L, Np, Nu, lambda is can vary the operation amount u ₁ ~u _q, for each controlled variable y ₁ ~y _p, showing a case where no distinction in this embodiment.

Calculated by the model predictive control calculation unit 2, (1
The optimum amount of operation that minimizes Eq. 2) is calculated by the following calculation. First, for the first to pth rows in the right-hand side matrix of Expression (11),
Divide the denominator in the line. For example, for the i-th row, B _i1 (z ⁻¹ ) / A _i1 (z ⁻¹ ) ... B _iq (z ⁻¹ ) / A _iq (z ⁻¹ ), B _i1 ′ (z ⁻¹ ) / A _i (z ^-1 ) ... B _iq '(z ^-1 ) / A _i (z ^-1 ). As a result, equation (11) becomes

[0034]

[Equation 10] Can be transformed into a shape. Here, the degree of A _i (z ⁻¹ ) is the n _i th order, and n max = max {n _i }. Next, for each row (i = 1 to p) and for j = 1 to Np,
The following equation D (z ⁻¹ ) = E _ji (z ⁻¹ ) (1-z ⁻¹ ) A _i (z ⁻¹ ) + z ^−j F _ji (z ⁻¹ ) (14) is solved to obtain the polynomial E _ji. (z ^-1 ) = 1 + e ₁ ^ji z ^-1 + ...
e _j-1 ^ji z ^{-j + 1} (j-1 order monic) (15a) F _ji (z ^-1 )
= F ₀ ^ji + f ₁ ^ji z ^-1 + ... + f _n ^ji z ^-nmax (nmax
Next, find (15b). Predictive value of this result, j step ahead of the controlled variable y ₁ ~y _p is

[0035]

[Equation 11] Given in. However, G _j−1 and G ₀ are p × q constant matrices, and H _j (z ⁻¹ ) is a p × q polynomial matrix with respect to z ^{−1 and} can be obtained from the following relational expression.

[0036]

[Equation 12] Note that G ₀ ... G _j-1 corresponds to the step response matrix of the controlled object formula (11).

Next, the expression (16) will be simply expressed as the following expression. D (z ^-1 ) y (k + j) = G _j-1 Δu (k + j-1) + ... + G ₀ Δu (k) + F _j (z ^-1 ) y (k) + H _j (z ^-1 ) Δu (k-1) (18) When this is expressed collectively for j = 1 to Np,

[0038]

[Equation 13] Therefore, it is further expressed as follows: D (z ⁻¹ ) y = GΔu + F (z ⁻¹ ) y (k) + H (z ⁻¹ ) Δu (k−1) (20) In this case, (12) the evaluation function of the ^{equation, J = (D (z -1} ) y-D (z -1) y *) T Q T Q (D (z -1) y -D (z -1 ) y ^* ) + λΔu ^T R ^T RΔu (21). However, Q and R are weight coefficient matrices, and for the weight coefficient parameter ρ,

[0039]

[Equation 14] Given in. Here, I in Q and R is p ×
It is a unit matrix of p and q × q. Here, instead of I, it is also possible to give a different weight to each control amount and operation amount by setting a different value for each element.

In addition,

[0041]

[Equation 15] Where y ^* _i (k + j) is j for the i-th controlled variable _yi .
This is the target value of the step destination. At this time, the optimum amount of operation to minimize the evaluation function (3) (or (13)) ^{is, Δu = (G T Q T} QG + λR T R) -1 G T Q T Q × {D (z -1 ) y ^* -F (z- ¹ ) y (k) -H (z- ¹ )? u (k-1)} (24). The actual manipulated variable is the first q element of the vector Δu Δu (k + 1) = G _{q *} {D (z ⁻¹ ) y ^* −F (z ⁻¹ ) y (k) −H (z ⁻¹ ). Δu (k-1)} (25) (where G _{q *} is (G ^T Q ^T QG + λR ^T R) ^-1 G ^T Q ^T Q, and q rows are taken out from the top, q × (p × Np ) Is taken out, and u (k) = u (k-1) + Δu (k) (26)

Is calculated by In this way, the model predictive control calculation unit 2 can obtain the optimum manipulated variable u (k) under the given conditions.
Is calculated.

Next, the operation of the means added according to the present invention will be described with reference to the flowchart of FIG. Each means is specifically realized on software of a computer or the like. First, the operator receives a response time constant Tr from the terminal device 9.
When [sec] is input, it is held in the response time constant setting means 5. The response time constant setting means 5 sends the response time constant Tr [sec] to the weighting factor parameter calculating means 6 (step S1).
1). The weighting factor parameter calculating means 6 reads the given response time constant Tr [sec], and obtains the weighting factor parameter ρ by ρ = exp (-Δ / Tr) (where Δ [sec] is the control period) (27) This is given to the evaluation function setting means 4. The evaluation function setting means 4 constructs an evaluation function represented by the expression (12) using the weighting factor parameter ρ and gives it to the model prediction control operation unit 2 (step S
12). The model predictive control calculation unit 2 uses the control process (25) of the model predictive control system by the calculation process represented by the expressions (12) to (25).
Is calculated (step S13).

The model predictive control computing unit 2 is newly provided with a loop response frequency characteristic calculating unit 10, a complementary sensitivity matrix calculating unit 11, and a stability margin parameter calculating unit 12. The loop response frequency characteristic calculation means 10 uses the control equation (25) obtained in the above arithmetic processing to calculate the controlled object equation.
The closed loop system response frequency matrix L (j
ω) is calculated by the following equation.

[0045]

[Equation 16] However, A (z ^-1 ) and B (z ^-1 ) represent the A and B matrices shown on the left and right sides of equation (13), respectively. Δ (z ⁻¹ ) is a diagonal matrix, and Δ (z ⁻¹ ) = diag {(1-z ⁻¹ ) ... (1-
z ^-1 )}. I is a unit matrix, and τ is a control period.

Subsequently, the complementary sensitivity matrix calculating means 11 obtains a complementary sensitivity function matrix T (jω) = (I + L (jω)) ⁻¹ L (jω) (29). Then, the stability margin parameter calculation means 12 determines the stability margin parameter as

[0047]

[Equation 17] Ask for. However, σmax means the maximum singular value. This stability margin parameter is controlled from G (s) to G (s)
When it changes to (1 + Δ (s)),

[0048]

[Equation 18] As long as, the stability of the closed loop system is maintained. Therefore, ε
Is a kind of measure for the stability margin (step S1
4). The obtained stability margin parameter is displayed on the display of the terminal device 9 via the storage means 13 (step S1).
5) Encourage the judgment of operators such as plants. When the operator judges that the stability margin is sufficient and inputs Yes from the input means such as the keyboard (step S16), the weighting factor parameter corresponding to the response time constant Tr input to the response time constant setting means 5 is entered. The setting of ρ in the evaluation function setting means 4 is confirmed (step S17). On the contrary, when the operator judges that the stability margin is insufficient and inputs No (step S16), the process returns to step S11, and the model predictive control is performed based on the response time constant Tr newly input by the operator. The system is redesigned (steps S11 to 15).

The terminal device 9 has a kind of simulation function. This simulation function corresponds to each response time constant Tr by continuously changing the response time constant Tr given from the terminal device 9 to the response time constant setting means 5 in a certain range according to a simulation command from the operator. Obtain the stability margin parameter ε. That is, a certain value of the response time constant Tr, the weight coefficient parameter calculation means 6, the evaluation function setting means 4, the model prediction control calculation section 2, the open-loop frequency response characteristic calculation means 10, the complementary sensitivity function matrix calculation means 1
1. The stability margin parameter ε obtained by going through the stability margin parameter calculation means 12 is accumulated in the storage device 13.
The terminal device 9 uses the response time constant T stored in the storage device 13.
The relationship between r and the stability margin parameter ε is displayed on the screen in a graph as shown in FIG. 4, for example. FIG. 4 shows that the control system becomes stable when the response time constant is Tr _s or more and becomes unstable when the response time constant is less than Tr _s . By visually demonstrating the relationship between the two, it is possible to avoid in advance that the operator demands a faster response speed than the response time constant Tr _s and causes an unstable state of the control system, and There is an advantage that setting can be expected.

The operator can directly set the stability margin parameter ε ₀ in the stability margin parameter input means 7 from the terminal device 9. In such a case, the process is performed according to the flowchart of FIG. First, when the operator inputs the stability margin parameter ε ₀ from the terminal device 9 (step S21), the input stability margin parameter ε ₀ is set in the stability margin parameter setting input means 7. When the response time constant adjusting means 8 detects that the initial stability margin parameter has been set in the stability margin parameter setting input means 7, the response time constant setting means 5 is caused to set the initial value Tr ₀ . The initial value Tr ₀ is set to a sufficiently large value as the initial value (step S22). The initial value Tr ₀ is converted into the weight coefficient ρ by the weight coefficient parameter calculating means 6 and given to the evaluation function setting means 4. The evaluation function setting means 4 forms a new evaluation function (12) formula (step S23). With reference to this evaluation function (12), the model predictive control calculation unit 2 performs the calculation processing represented by the formulas (12) to (25) in the same manner as in step 13 described above, by the control formula (25 ) Is calculated (step S24). Further, the open-loop frequency response characteristic calculation means 10, the complementary sensitivity matrix calculation means 11, and the stability margin parameter calculation means 12 perform arithmetic processing based on the above-described equations (28), (29), (30) to obtain the stability margin parameter ε. Is calculated (step S25). The calculated stability margin parameter ε is given to the response time constant adjusting means 8. The response time constant adjusting means 8 compares the calculated ε with the designated ε ₀ (step S26). The response time constant adjusting means 8 determines that the current stability margin is small if (i) ε <ε _{0 as} a result of the comparison, and the response time constant is slightly increased, for example, Tr ← Tr × 1.1. Then, the process returns to step S23 (step S27). (ii) If ε> ε _0, it is determined that the current stability margin is too large, the response time constant is made slightly smaller, for example, Tr ← Tr / 1.1, and the process returns to step S23 (step S28). (iii) If ε is substantially equal to ε ₀ , it is determined that the current stability margin is satisfactory, and the response time constant Tr at that time is displayed as an optimum value on the terminal device 19 via the storage device 13, and After checking the operator or automatically, the weighting factor parameter ρ corresponding to the response time constant Tr is input to the evaluation function setting means 4 (step S29). The evaluation function setting means 4 uses the input weighting factor parameter ρ to set the evaluation function of the expression (12) for the model prediction control calculation unit 2.

The dynamic characteristic model setting means 3 sets the model (11) to be controlled in the model predictive control calculation section 2. Here, the dynamic characteristic model of the controlled object is input from the terminal device 9 or an external storage device (not shown), and the time series analysis such as the recursive least squares method from the controlled variable y (k) and the manipulated variable u (k). In some cases, the one estimated by real-time processing using the method is used.

Next, FIG. 5 shows the control response (target value tracking response) when the model predictive control device of the present invention is applied to the controlled object represented by the transfer function of equation (3). The pole arrangement of the system is shown in FIG.

In this case, the prediction length Np, the control length Nu, the weighting factor λ, the control cycle, etc. are the same as those in the above-mentioned example. The control response of FIG. 5 shows that the response more quickly follows the target value than the control response of the conventional method shown in FIG. Also,
The pole arrangement of the control system in FIG. 6 (circle in the figure) also has poles on the unit circle according to the conventional method shown in FIG. 10, whereas it has poles inside the unit circle and has sufficient stability. You can see that you keep it.

In the embodiment of the present invention, the evaluation function (5) or the corresponding expression (12) is used as the evaluation function, but the same applies to evaluation functions other than this form. By setting an exponential weighting coefficient, the response characteristic can be improved approximately. By adding an exponential weighting coefficient to the evaluation function, control is performed so that the range in which the control amount y (k) should converge gradually narrows as the prediction time elapses, and the control amount y (k) becomes the target value. It is possible to prevent the process leading to to become oscillatory.

Further, in the stage of calculating the optimum manipulated variable, for example, Iino, Ohya: “Multivariable model predictive control system with limiting conditions considering stability”, Japan Society of Instrument and Control Engineers, Adaptive Control Symposium pp.75 (1991). ), That is, a model predictive control method that sequentially calculates an optimal operation amount that minimizes the evaluation function while satisfying the limiting conditions using the quadratic programming method, considering the limiting conditions. The model predictive control device of the present invention can also be used for model predictive control in which the limiting conditions regarding the control amount and the manipulated variable are taken into consideration.

Even when the process prediction model is non-linear, the response characteristics can be improved by the model prediction control system using the same evaluation function.

Further, in the case of a multi-input multi-output process, different response time constants Tr _i can be set in each control loop and each can be controlled by an individual response speed. In this case, instead of equation (27), ρ _i = exp (-Δ / Tr _i ) (where Δ [sec] is the control period) (27 ') is used to obtain the weighting factor parameter ρ _i , and the evaluation function is ,

[0058]

[Formula 19] And set it.

[0059]

As described above, in the model predictive control device of the present invention, when the response time constant is input, the weight coefficient of the exponential function corresponding to this time constant is determined, and this weight coefficient is added to the evaluation function. Therefore, it becomes possible to specify the response time constant of the model predictive control system, and the poles of the control system in the complex plane that determines the stability can be placed in the stable region.
It is possible to effectively improve the transient response characteristic, particularly the damping rate. Further, since the stability margin of the control system can be evaluated with respect to the designated response time constant, an appropriate response time constant can be set in consideration of stability. Furthermore, if a stability margin is given as a control specification, the response time constant can be automatically adjusted so as to obtain a control system that satisfies it, so that it is possible to realize appropriate stability and transient response characteristics.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of a model predictive control device of the present invention.

FIG. 2 is a flowchart illustrating a processing procedure in stability margin parameter calculation means 6.

FIG. 3 is a flowchart illustrating a processing procedure in a response time constant calculation means 8.

FIG. 4 is a graph showing the relationship between the response time constant Tr and the stability margin parameter ε.

FIG. 5 is a graph showing an example of control response characteristics by the model predictive control device of the present invention.

6 is a graph showing a closed-loop pole arrangement of the control system in the example of FIG.

FIG. 7 is a diagram illustrating improvement in closed-loop pole placement and control response by weighting the evaluation function.

FIG. 8 is a block diagram of a conventional model predictive control device.

FIG. 9 is a graph showing an example of control response characteristics by a conventional model predictive control device.

10 is a graph showing a closed-loop pole arrangement of the control system in the example of FIG.

[Explanation of symbols]

1 controlled object 2 Model predictive control calculation unit 3 Dynamic characteristic model setting means 4 Evaluation function setting means 5 Response time constant setting means 6 Weighting factor parameter calculation means 7 Stability margin parameter setting means 8 Response time constant adjustment matching detection means 9 Terminal device 10 Circular Response Characteristic Calculation Means 11 Complementary sensitivity matrix calculation means 12 Stability margin parameter calculation means 13 Storage device 26 Response data storage unit 27 Prediction model 28 Future Target Trajectory Generation Unit 29 Optimal manipulated variable calculator 30 integrator

Claims (4)

[Claims] 1. A model for predicting a controlled variable future value based on a dynamic characteristic model of a controlled object and calculating an optimum manipulated variable that minimizes a value of an evaluation function representing control performance from the controlled variable and a future target value. In the predictive control device, a response time constant setting means for setting a response time constant representing the rise time that the controlled object should operate, and an exponential part for the response time constant, and a weighting coefficient whose value increases with the passage of time. A model predictive control device comprising: a weighting factor parameter calculating means for calculating; a new evaluation function incorporating the calculated weighting coefficient; and an evaluation function setting means for setting the new evaluation function as the evaluation function. . 2. A model for predicting a controlled variable future value based on a dynamic characteristic model of a controlled object, and calculating an optimum manipulated variable that minimizes the value of an evaluation function representing control performance from the controlled variable and a future target value. In the predictive control device, a response time constant setting means for setting a response time constant representing the rise time that the controlled object should operate, and an exponential part for the response time constant, and a weighting coefficient whose value increases with the passage of time. A weighting factor parameter calculating means for calculating and a new evaluation function incorporating the calculated weighting coefficient, and an evaluation function setting means for setting this as the evaluation function, and a model predictive control system in which the new evaluation function is set. The calculation means for calculating the stability margin parameter indicating the stability with respect to the fluctuation of the controlled object, and the response time constant while changing the value of the response time constant set in the response time constant setting means. A simulation means for recording the value of the stability margin parameter corresponding to the instantaneous value of the constant; and a display means for visually displaying the relationship between the value of the recorded response time constant and the value of the stability margin parameter. A model predictive control device characterized by: 3. A model for predicting a controlled variable future value based on a dynamic characteristic model of a controlled object, and calculating an optimum manipulated variable that minimizes the value of an evaluation function representing control performance from the controlled variable and a future target value. In the predictive control device, a response time constant setting means for setting a response time constant representing the rise time that the controlled object should operate, and an exponential part for the response time constant, and a weighting coefficient whose value increases with the passage of time. A weighting factor parameter calculating means for calculating and a new evaluation function incorporating the calculated weighting coefficient, and an evaluation function setting means for setting this as the evaluation function, and a model predictive control system in which the new evaluation function is set. A calculation means for calculating a stability margin parameter indicating the stability with respect to the fluctuation of the controlled object, a stability margin parameter setting means for holding a designated stability margin parameter, Response time constant adjustment for changing the value of the response time constant held in the response time constant setting means until the value of the issued stability margin parameter matches the value of the stability margin parameter held in the stability margin parameter setting means And a model predictive control device. 4. The new evaluation function comprises a control variable y (k + j), a target value y ^* (k + j), a manipulated variable increment Δu (k + j), and a polynomial D (z ^-1 ) in terms of ρ ^-2j , ρ
= Exp (-Δ / Tr), Δ is the control cycle, and Tr is the evaluation function obtained by multiplying by the weighting coefficient which is the response time constant and integrating. The model predictive control device according to claim 1, 2 or 3, wherein