JPH05173602A - Adaptive type model predictive controller - Google Patents

Abstract

PURPOSE:To speedily follow up variation in command and obtain response characteristic having small hunting by using plural dynamic models identified with data series having different sampling periods and calculating an optimum controlled variable from a prediction output and step responses which vary over a wide range. CONSTITUTION:The model predictive controller 2 is divided into an adaptive operation part 3 and a control arithmetic part 4. The adaptive operation part 3 inputs a manipulated variable (u) and the controlled variable (y) as input and output data of a process 1 and stores them in a response data storage part 71. At the same time, they are passed through N band-pass filters 5 having different passing bands and then made discrete by samplers 6, and response data obtained by the samplers 6 are stored in a response data storage part 72. Then a step response calculating means 9 calculates the step responses from the respective time-series models. Then the control arithmetic part 4 puts the step responses, calculated from the time-series moldes identified by Np identifying means 8, together while aligning the time bases to find one step response.

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 based on a dynamic characteristic model of a controlled object and calculating a manipulated variable in consideration of the future movement.

[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
Applicable to multi-variable processes, which can realize stable control response for processes with long dead time, can improve followability with feedforward control using future target values,
By including the physical laws and nonlinear characteristics of the plant in the prediction model, which does not require an accurate dynamic characteristic model of the controlled object that can realize decoupling control and can easily configure the control system from the step response, for example, There is a feature that you can expect fine control of.

Therefore, many predictive control methods have been proposed so far. 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 Predictive Control, Automatica 25-6 pp.859 (1989)
Etc.

An example of the configuration of a general model predictive control system is shown in FIG.
Shown in. In the model predictive control calculation unit 2, first, the controlled variable y (k) and the manipulated variable u (k) at the time k of the control target process 1 are fetched and written into the response data storage unit 7. The control amount predicting means 10 predicts a future control amount response y (k + L), ..., Y based on the operation amount u and the control amount y from the past to the present (time k) of the response data storage unit 7.
Calculate (k + Np + L-1). L and Np are predicted lengths. On the other hand, in the future target trajectory generation unit 15 to which the target value r (k) is input, the future target trajectory y ^* (k +
L), ..., Y ^* (k + Np + L-1), and the future control deviation signal y (k + i) −y ^* (k +
i) and (i = L, ..., Np + L−1) are calculated and sent to the optimum manipulated variable calculating unit 13. As a typical example, the optimum manipulated variable calculating unit 13 uses the following quadratic form evaluation function Is calculated, and only the first Δu (k) is sent to the integrator 14. Here, L and Np are prediction lengths, Nu is a control length, λ is a weighting coefficient, and D (z
^-1 ) is called a pole-placement polynomial, and D (z ^-1 ) = 1
+ D ₁ z ^-1 + ... + d _n z ^-n , Δu (k + i) is the future manipulated variable increment, and Δu (k + i) = u (k + i) −u (k + i)
-1). The integrator 14 calculates the actual manipulated variable u (k) from u (k) = u (k−1) + Δu (k) (2) and outputs it to the controlled object 1.

[0005]

In the above general model predictive control system, the predictive model is given in advance. However, in reality, the dynamic characteristics of the process may be unclear, or the prediction model may change due to aging or non-linear characteristics, and it may be difficult to always maintain good control performance with one prediction model. Therefore, an adaptive model predictive control method that sequentially identifies the process dynamic characteristic model from the input / output data of the process and sequentially modifies the predictive model is conceivable. This is a combination of the conventional adaptive control method and model predictive control method.

In the conventional discrete-time adaptive control system, since the sampling period of the observation data is one type, it is difficult to accurately identify the characteristics of the target over a very wide frequency band. For example, GCGoodwin, et.al .; “Indi
rect adaptive control: Anintegrated approach ”, Pro
ceedings of ACC, pp.2440-2445,1988, L. Ljung; “Syste
m Identification-Theory for the User ”, Prentice-H
In all, 1987, etc., the least squares method used in most adaptive control systems uses the frequency range 1 / 100τ to 1 / 5τ for identification based on observation data with a sampling period τ.
It has been pointed out that highly accurate identification is possible only in the range of [Hz]. Therefore, when starting the adaptive control, it was necessary to carefully select the sampling period τ according to the target characteristics. However, in reality, the target frequency characteristic is unknown in advance, and in a control system with multiple loops, when a loop with fast response and a loop with slow response are mixed, a wide frequency range that covers both design bands at the same time is used. It was difficult to identify the dynamic model accurately over the band.

Such a problem similarly exists in the adaptive model predictive control system. That is, from the prediction model, in order to accurately estimate the future control amount future value and the future control amount future value at the same time with high accuracy, the prediction model needs to be identified with high accuracy over a wide frequency band. But
Due to the above problems, such a prediction has been difficult.

Another problem is that even if a highly accurate prediction model is obtained over a wide frequency band, a fine control cycle and a long prediction range must be taken into consideration in constructing a control system that covers them. However, there is a problem that the number of predictive responses to be handled increases and the amount of control calculation becomes enormous.

[0009]

In order to achieve the above object, a control amount future value is predicted based on a dynamic characteristic model of the control target, and an operation amount that minimizes an evaluation function serving as a driving index is set to the control target. In the model predictive control device for calculating from the control amount and the future target value, the dynamic characteristic model is identified by using the time series data of the operation amount and the control amount collected in the first sampling period, and the first dynamic characteristic model is identified. A first identifying means for obtaining a characteristic model; and a second dynamic characteristic model for identifying the dynamic characteristic model using time series data of the manipulated variable and the controlled variable collected in a second sample period. Identification means, first step response characteristic calculation means for obtaining the first step response of the first dynamic characteristic model over a first range on the time axis, and second step of the second dynamic characteristic model
A second step response calculating means for obtaining a step response over a second range on the time axis, and the step responses obtained by the first and second step response calculating means are combined on the time axis to form a wider range. A step response synthesizing means for forming a step response over a time period, and time series data of the operation amount and the control amount are given to the first dynamic characteristic model to obtain a predicted control amount value over a first range on the time axis. Second control amount predicting means for determining, and second control for determining the control amount predicted value over the second range on the time axis by giving time series data of the operation amount and the control amount to the second dynamic characteristic model. Quantity forecasting means,
Control amount predictive value synthesizing means for combining control amount predictive values obtained by the first and second control amount predicting means on a time axis to form a control amount predictive value in a wider range, and the step response synthesizing An optimum manipulated variable calculating means for calculating and outputting an optimum manipulated variable that minimizes an evaluation function given by using the step response formed by the means and the control amount predicted value formed by the control amount predicted value combining means; It is characterized by including.

[0010]

[Function] For example, the minimum sampling period is τ [sec]
And From the data sampled in this cycle, the effective frequency characteristic estimation range of the time series model identified by the ordinary least squares method is 1 / 100τ to 1 / 5τ as described above.
It is around [Hz]. Similarly, the effective prediction range by this model is, for example, τ to 100τ [sec]. Therefore, the effective frequency characteristic estimation range of the time series model identified by the least square method from the data sampled at another sampling period of 10 τ [sec] is 1/1000 τ to 1
/ 50τ [Hz]. Similarly, the effective prediction range by this model is 10τ to 1000τ [sec].
Therefore, if combined with the former model, 1 / 1000τ ~
Frequency characteristic of 1 / 5τ [Hz] and τ to 1000τ
The prediction range of can be accurately estimated. In this way, by identifying a plurality of time series models with different sampling periods by a plurality of identifying means and connecting the obtained time series models, a highly accurate frequency characteristic over a wide range, or,
The prediction range can be estimated.

In order to show this effect, the present method is applied to a controlled object having a step response having a complicated shape as shown in FIG. This object is expressed by G (S) = (1 + 4s) / (1 + 2s + s ² ) + 5e ^−0.25 / (1 + s + s ² ), and a fast response mode and a slow response mode are mixed. According to the above-mentioned method, the sampling cycle τ is selected from four kinds of 0.1 seconds, 0.2 seconds, 0.4 seconds, and 0.8 seconds for this object, and the model is identified by the data of each sampling cycle. The predicted step response of the above is combined with the true process response and is shown in FIGS. In the figure, the solid line shows the true process response and the dotted line shows the predicted step response. The model with a short sampling interval accurately represents the rising portion of the step response of the step, that is, the characteristics of the fast mode, and the model with a long sampling interval accurately represents the steady characteristics of the step response, that is, the characteristics of the slow mode. It can be seen that if these are connected together, the step response or the predicted response can be estimated with much higher accuracy than the conventional estimation using a single model.

Further, since each of the identifying means independently carries out the identification based on the amount of data necessary for the identification, for example, in the identification with a fine sampling period, the range on the time axis of the data used is narrowed. The adaptation speed can be increased, and the process characteristics over a long period of time can be modeled with a small amount of calculation by widening the range on the time axis of the data used in identification with a coarse sampling period.

In the model predictive control, the control amount prediction value and the step response over the set prediction range are necessary for the calculation of the optimum manipulated variable, but the above-mentioned method enables highly accurate control amount prediction values over a wide prediction range. And a step response is required.

Further, even when an appropriate value of the prediction range or the sampling cycle is not known in advance, good control can be expected if the minimum sampling cycle and the maximum prediction range are set as much as possible.

Further, how to select the actual sampling period will be described. Let τ [sec] be the minimum sampling period, and for example, 2τ [sec], 4τ [sec], ..., 2
^Np-1 τ [sec] and Np kinds of sampling periods are selected. These are evenly spaced when plotted on a graph of a logarithmic scale axis, and hence will be referred to as equal logarithmic spacing sampling. In response to this, Np identification means are prepared,
As a result, Np time series models are obtained. Y (t + τ) and y (t + 2) are calculated as the control amount prediction values of one point that are assumed to have the highest estimation accuracy from each model.
, τ, ..., Y (t + 2 ^Np-1 τ) (t is the current time) are estimated and these are used for the model predictive control calculation. In the model predictive control calculation, instead of the evaluation function for the prediction value at a constant time interval as in the conventional equation (1), the evaluation function for the prediction value at the equilogarithmic interval sampling interval is Is set, and the optimum manipulated variable that minimizes this is calculated for each control cycle.

As a result, it is possible to cover a long prediction range from τ to 2 ^Np-1 τ by handling prediction values at only Np points,
Moreover, since the required control calculation amount is at most Np ² order, it is suitable for a multivariable process including a loop with a fast time constant and a loop with a slow time constant.

Further, the weighting factors γ (i) and λ of the equation (2) are
By adjusting (i), the desired prediction range, that is, the control response speed, can be freely adjusted over a wide range.
For example, if you attach importance to the high frequency band and want to improve quick response,
The weight of the rising portion of the step response such as γ (1), γ (2), ... May be dominant. On the contrary, focusing on the low frequency band,
If you want a slow and stable response, γ (1) = γ
(2) = ... = 0, and the weight coefficient may be set so as to ignore the rising portion. In particular, in a multivariable system, by changing the weighting coefficient for each control loop, a multivariable model predictive control system having a different response speed for each loop can be easily realized.

[0018]

FIG. 1 shows a model predictive control device 2 of the present invention. The model predictive control device 2 is divided into an adaptive operation unit 3 and a control calculation unit 4. In the adaptive operation unit 3, the operation amount u and the control amount y, which are input / output data of the process 1, are input and stored in the response data storage unit 71, and at the same time, passed through Np band pass filters 5 having different pass bands. Thereafter, the response data obtained by each sampler is discretized by the sampler 6 having sampling periods τ, 2τ, ..., 2 ^Np-1 τ of different Np types, and stored in the response data storage unit 72. The Np identification means 8 cut out response data of an appropriate length from the data series of each sampling period, and use the least squares method to obtain the time series model A _i (z ⁻¹ ) y (k) = B _i (z ⁻¹ ) u (k) + e (k) (3) (i = 1, ..., Np) where A _i (z ⁻¹ ) = 1 + a _i1 z ⁻¹ + ... + a _in z ⁻ⁿ B _i (z ^{− 1} ) = b _i1 z ⁻¹ + ... + b _im z ^−m (where z ⁻¹ is a time transition operator) is estimated. For a multivariable process, A _i (z ⁻¹ ),
B _i (z ⁻¹ ) becomes a matrix.

Next, the step response calculating means 9 calculates the step responses g _i (0), g _i (1), ..., G _i (N) (4) from the respective time series models (3). To do. The calculation method is Required by. In the case of a multivariable process, g and h are all matrices.

Further, in the control amount predicting means 10, the data u (t-2 ^i-1 τ), ..., U (t-) of the corresponding sampling period is extracted from the past response data stored in the response data storage unit 71. (M-1) 2 ^i-1 τ) y (t), y (t-2 ^i-1 τ), ..., y (t- (n-1) 2 ^i-1 τ) (where i = , ..., Np, t are current times), and the control amount predicted value y (t + 2 ^i-1 τ) when the manipulated variable is constant is calculated by the following calculation. Where i =
1, ..., Np.

Y (t + 2 ⁱ⁻¹ τ) = − a _i1 y (t) −a _i2 y (t−2 ⁱ⁻¹ τ) −... −a _in y (t− (n−1) 2 ⁱ⁻¹ τ) + b _i1 u (t-2 ^i-1 τ) + b _i2 u (t-2 ^i-1 τ) + ... + b _im u (t- (m-1) 2 ^i-1 τ) (6) where In a multivariable process, y and u are vertical vectors and a
_ij and b _ij are matrices of corresponding sizes. The above is the processing in the adaptive operation unit 3.

Next, in the control operation unit 4, among the step responses calculated from the Np time-series models identified by the Np identification units and the control amount prediction values, first, the step response synthesis unit 11 Individual step response (4)
Are combined with the time scales, and one step response of the minimum sampling period g (t), g (t + τ), g (t + 2τ), g (t + 3τ), ..., g (t + 2 ^Np-1 τ) (7 ). Here, i = 1, ..., Np, t is the current time.

As a concrete synthesizing method, an average value of overlapping portions in the equation (4) is adopted, and the lacking data is obtained by interpolation calculation from two points on both sides. This state will be described with reference to FIGS. 6 (a) to 6 (c). For example, it is assumed that the step responses of the four models estimated from the four types of sampling periods (when Np = 4) are as shown by g ₁ (t) to g ₄ (t) in FIG. 6A. .. At this time, the partial linear interpolation _{g (t) = αg i (} t) + (1-α) g i + 1 (t) (α overlapping, 1 at the left of the _{g i + 1 (t),} g i ( It is 0 at the right end of t) and is combined with each other to obtain the combined step response g (t) shown in FIG. 6 (c). The value of the weight α of each response g _i (t) at this time is as shown in FIG. 6B.

On the other hand, the effective step response estimate g _i (t)
Is intermittent, that is, when g ₁ (t) and g ₂ (t) are separated from each other as shown in FIG. Insert. The - (t ₁ t ₂₎ Thus, the step response g (t) g (t) = ((t 2 -t) g 1 (t 1) + (t- t 1) g 2 (t 2)) / To synthesize. By discretizing the step response estimation value g (t) synthesized by the above procedure, the step response sequence of the equation (7) is obtained.

Hereinafter, this step response is abbreviated as g ₀ , g ₁ , g ₂ , g ₄ , g ₈ , ..., G ₂ Np-1 (8). In a multivariable system, g _i becomes a matrix.

Next, in the control amount predicted value synthesizing means 12,
Prediction vectors y = [y (t + τ), y (t + 2τ), y (t + 4τ), ..., y (t + 2 ^Np-1 τ)] are arranged by arranging the control amount prediction values at equal logarithmic intervals obtained from the equation (6). Create ^T (9). Here, ^T represents the translocation value. This is a control amount prediction response sampled at equal logarithmic intervals as shown in FIG.

At the same time, the future target value generation unit 15 receives the final target value r (t) and has a future target value trajectory y ^* = [y ^* (t + τ) at equal logarithmic intervals for causing the control amount to follow the final target value r (t). , Y ^* (t + 2τ), y ^* (t + 4τ), ..., Y ^* (t + 2 ^Np-1 τ)] ^T (10). Here, ^T represents the translocation value.

Specifically, for example, an appropriate time constant T is given, and y ^* (t + 2 ^i-1 τ) = y (t) + (r (t) -y (t)). (1-exp (- 2 ^i-1 τ / t)) (11) Here, i = 1, ..., Np, t is the current time. In a multivariable system, each element of y and y ^* is a vertical vector, and the whole is also a vertical vector.

Next, in the optimum manipulated variable calculating means 13, the optimum manipulated variable vector Δu = [Δu (t), Δu (t + τ), ..., Δu (t + 2) that minimizes the evaluation function (2) by the following calculation. ^Nu-1 τ)] ^T (12) is calculated by the following control arithmetic expression. Delta] u = ^{[G T Γ T ΓG + Λ T} Λ ] ^{-1 G T Γ T Γ (y} * -y) (13) However, gamma = diag [γ (1), γ (2 ), ..., γ (Np) ] Λ = diag [λ (1), λ (2),…, λ (Nu)]

[0030]

[Equation 1] Is.

In the case of a q-input p-output multivariable system, Γ = block · diag [γ (1) Ip, γ (2) Ip, ..., γ (Np) I
p] Λ = block ・ diag [λ (1) Iq, λ (2) Iq,…, λ (Np) I
q] Here, Ip is a p × p unit matrix, and Iq is a q × q unit matrix. The matrix G has a size Np · p in which each element is a P × q matrix
It becomes a block matrix of × (Nu + 1) · q.

Finally, in the integrator 14, the first element Δu in the optimum manipulated variable vector obtained by the equation (13) is calculated.
Only (t) is taken out, and the optimum manipulated variable u (t) is calculated by the calculation u (t) = u (t−τ) + Δu (t) (15) and output to the process. In this way, adaptive model predictive control is performed.

In order to show the effectiveness of the present method, the results of applying the present method to the controlled object having the step response shown in FIG. 4 are shown in FIGS. 8 (a) and 8 (b). The controlled object shown in FIG. 4 is a complicated process in which the fast mode and the slow mode degree are mixed as described above. When a curve of a target value whose value changes in a rectangular wave shape is given to this control target as shown by a dotted line in FIG. 8A, the adaptive model predictive control device of the present application is shown in FIG. 8B. Thus, the manipulated variable u (t) is given. As a result, the control amount y (t) satisfactorily follows the change of the rectangular wave-shaped target value indicated by the dotted line in FIG. 9A, as indicated by the solid line in FIG.

Although the first and second identifying means are used in the configuration described in the claims of the present application, the same is true even if a single identifying means that fulfills both functions is used. First
Although the second step response calculation means is used, the same is true even if a single step response calculation means that performs both functions is used. Although the first and second step response calculating means are used, the same is true by using a single step response calculating means that fulfills both functions. Although the first and second controlled variable predicting means are used, the same is true even if a single controlled variable predicting means that fulfills both functions is used. These means can be realized by a known algorithm of computer processing. Further, not to mention the embodiments of the present application, the technical scope including at least the gist of the invention of the present application is covered by the right of the present application.

Further, the adaptive model predictive control apparatus of the present invention can be similarly applied to the model predictive control system considering the control conditions shown in Japanese Patent Application No. 2-17527.

Further, the adaptive model predictive control device of the present invention can have the man-machine interface shown in, for example, Japanese Patent Application No. 3-75333.

In addition, the multivariable system has an advantage that it is possible to easily realize a control system that simultaneously considers a short loop and a long loop.

[0038]

As described above, the adaptive model predictive control method of the present invention uses a plurality of dynamic models identified by data series with different sampling periods, and is obtained by using each of these dynamic models. The predicted output and step response are combined to obtain a predicted output and step response over a wider range, and the optimum controlled variable is calculated using this wide range of predicted output and step response. Good response characteristics can be obtained which follow and have less hunting. Further, by selecting each sampling period so as to be evenly spaced on the time axis represented by logarithm, it is possible to predict the control amount with high accuracy over a wide range with a relatively small amount of control calculation. Furthermore, in the case of the conventional model identification with a single sampling period, it was necessary to be careful because the selection of the sampling period at the start of the control system has a great influence on the characteristics of the model identified by this. In the invention, since the prediction range is wide, good control can be expected from the start even if a plurality of sampling periods are roughly determined.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an adaptive model predictive control device of the present invention.

FIG. 2 is a graph showing a prediction interval according to the present invention.

FIG. 3 is a configuration diagram of a conventional model predictive control device.

FIG. 4 is a graph showing an example of a step response.

FIG. 5 is a graph showing the predicted step response of a model identified by data at different sampling periods.

FIG. 6 is an explanatory diagram illustrating a synthesizing method when step responses overlap.

FIG. 7 is an explanatory diagram illustrating a synthesizing method when step responses are separated.

FIG. 8 is a graph illustrating the effect of the adaptive model predictive control device of the present application.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Control object 2 Model predictive control device 3 Adaptive operation part 4 Control calculation part 5 Bandpass filter 6 Sampler 7 Response data storage part 8 Identification means 9 Step response calculation means 10 Control amount prediction means 11 Step response synthesis means 12 Control amount predicted value Combiner 13 Optimal manipulated variable calculator 14 Integrator 15 Future target value generator 16 Subtractor

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 operation amount that minimizes an evaluation function serving as a driving index from the controlled variable of the controlled object and a future target value. A predictive control device, comprising: first identifying means for identifying the dynamic characteristic model by using time series data of the manipulated variable and the controlled variable collected in a first sampling period to obtain a first dynamic characteristic model. Second identifying means for obtaining the second dynamic characteristic model by identifying the dynamic characteristic model using time series data of the manipulated variable and the controlled variable collected in a second sample period, and the first dynamic characteristic A first step response characteristic calculating means for obtaining a first step response of the model over a first range on the time axis; and a second step response of the second dynamic characteristic model over a second range on the time axis. Second step A step response calculation means, a step response combination means for combining the step responses obtained by the first and second step response calculation means on a time axis to form a step response over a wider range, and the first step response calculation means. A first controlled variable predicting means for determining a controlled variable predicted value over a first range on the time axis by giving time series data of the manipulated variable and the controlled variable to the dynamic characteristic model; and the second dynamic characteristic model. A second controlled variable predicting means for giving a time series data of the manipulated variable and the controlled variable to obtain a predicted controlled variable value over a second range on the time axis; and the first and second controlled variable predicting means. Control amount predicted value synthesizing means for combining the obtained control amount predicted values on the time axis to form a control amount predicted value over a wider range, and the step response and the control amount formed by the step response synthesizing means. Prediction value synthesis Adaptive model predictive control apparatus, characterized in that it comprises an optimum operating amount calculating means which calculates and outputs the optimum manipulated variables to minimize the evaluation function given by using the control amount predicted value formed by the step. 2. The adaptive model predictive control device according to claim 1, wherein the first and second sample periods are set to have equal intervals on a time axis displayed in logarithm. 3. The step response synthesizing means, when the first range and the second range on the time axis overlap each other, averages the step responses of the overlapping ranges of the first and second step responses. When the first range and the second range are separated from each other, the step response of the separated section is calculated by linear interpolation of the first and second step responses. 2. The adaptive model predictive control device described in 2. 4. The control amount predicted value synthesizing means, when the first range and the second range on the time axis overlap, sets the control amount predicted values of the overlapping range to the first and second ranges. Obtained by averaging the control amount prediction values, and when the first range and the second range are separated, the control amount prediction values of the separated sections are obtained by linear interpolation of the first and second control amount prediction values. The adaptive model predictive control device according to claim 1, 2 or 3, which is obtained.