JP3121651B2 - Adaptive model predictive controller - Google Patents

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 a future motion of a control response based on a dynamic characteristic model of a control object and calculating an operation amount while considering the predicted motion.

[0002]

2. Description of the Related Art In recent years, a model predictive control device is often used in the field of process control. Model predictive control is
It can be applied to multi-variable processes that can achieve stable control response to processes with long dead time, improve follow-up performance with feedforward control using future target values,
It does not require an accurate dynamic characteristic model of the controlled object that can realize decoupling control, and can easily configure a control system from, for example, step response.The prediction model includes the physical laws and non-linear characteristics of the plant. It can be expected that detailed control can be expected.

[0003] Therefore, a number of predictive control systems have been proposed. 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. are explained.

FIG. 3 shows a configuration example of a general model predictive control system.
Shown in The model predictive control operation unit 2 first takes in the control amount y (k) and the operation amount u (k) at time k of the process 1 to be controlled, and writes them into the response data storage unit 7. The control amount predicting unit 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) in the response data storage unit 7.
Calculate (k + Np + L-1). L and Np are predicted lengths. On the other hand, the future target trajectory generating unit 15 to which the target value r (k) is input is the future target trajectory y ^* (k +
L),..., Y ^* (k + Np + L−1), and the future control deviation signal y (k + i) −y ^* (k +
i), (i = L,..., Np + L-1) are calculated and sent to the optimum manipulated variable calculator 13. In the optimal operation amount calculation unit 13, as a representative example, the following quadratic form evaluation function

(Equation 1) 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 factor, and D (z
^-1 ) is called a pole assignment polynomial, and D (z ^-1 ) = 1
+ D ₁ z ⁻¹ +... + D _n z ⁻ⁿ , Δu (k + i) is a 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) and outputs it to the control target 1.

[0005]

In the general model predictive control system described above, the predictive model is assumed to be 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 nonlinear 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 a process dynamic characteristic model from input / output data of a process and sequentially corrects a prediction model can be considered. This is a combination of a conventional adaptive control method and a model predictive control method.

In the conventional discrete-time adaptive control method, since the sampling period of observation data is one, it is difficult to accurately identify characteristics of an object over an extremely 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
all, 1987, etc., in the least squares method used in most adaptive control systems, in the identification based on observation data of the sampling period τ, the frequency range 1 / 100τ to 1 / 5τ
It is pointed out that identification with high accuracy can be performed only in the range of [Hz]. Therefore, when starting the adaptive control, it is necessary to carefully select the sampling period τ according to the target characteristics. However, in reality, the frequency characteristics of the target are not known in advance, and in a control system having a plurality of loops, when a fast response loop and a slow response loop are mixed, a wide frequency band covering both design bands is simultaneously provided. It was difficult to accurately identify the dynamic characteristic model over the band.

[0007] Such a problem similarly exists in an adaptive model predictive control system. That is, in order to simultaneously and accurately estimate the future control amount future value and the distant future control amount future value from the prediction model, the prediction model needs to be identified with high accuracy over a wide frequency band. There is
Due to the above problems, such prediction was difficult.

Another problem is that even if high-precision prediction models are obtained over a wide frequency band, a fine control cycle and a long prediction range must be considered in order to construct a control system that covers them. Therefore, there is a problem that the number of predicted responses to be handled increases and the amount of control calculation becomes enormous.

[0009]

In order to achieve the above object, a dynamic characteristic model of the controlled object is identified using time series data of the manipulated variable and the controlled variable of the controlled object collected at a first sample period. To obtain the first dynamic characteristic model
Identification means; second identification means for identifying the dynamic characteristic model using time-series data of the manipulated variable and the control variable collected in a second sample period to obtain a second dynamic characteristic model; A first step response characteristic calculating means for obtaining a first step response of the one dynamic characteristic model over a first range on the time axis; and a second step response of the second dynamic characteristic model on a second axis on the time axis. A second step response calculation means for obtaining a step response over a range, and a step response synthesis for forming a step response over a wider range by combining each of the step responses obtained by the first and second step response calculation means on a time axis. Means, first control amount predicting means for providing the first dynamic characteristic model with the time-series data of the operation amount and the control amount to obtain a control amount prediction value over a first range on a time axis; 2nd dynamic characteristic A second control amount predicting means for obtaining the operation quantity and the second control amount prediction value over a range of the time giving series data axis when the control amount to Dell, the first
A control amount prediction value combining means for combining the control amount prediction values obtained by the second control amount prediction means on the time axis to form a control amount prediction value over a wider range; Optimum operation amount calculation means for calculating and outputting an optimum operation amount for minimizing the given evaluation function by using the step response obtained and the control amount prediction value formed by the control amount prediction value synthesizing means. It is characterized by.

[0010]

[Action] For example, the minimum sampling period is τ [sec].
And From the data sampled at this period, the effective frequency characteristic estimation range of the time series model identified by the ordinary least square method is 1 / 100τ to 1 / 5τ as described above.
[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 squares method from data sampled at another sampling period of 10τ [sec] is 1 / 1000τ to 1
/ 50τ [Hz]. Similarly, the effective prediction range based on this model is 10τ to 1000τ [sec].
Therefore, when combined with the former model, 1 / 1000τ ~
1 / 5τ [Hz] frequency characteristic, and τ to 1000τ
Can be accurately estimated. In this way, if a plurality of time series models with different sampling periods are identified by a plurality of identification means and the obtained plurality of time series models are connected, high-precision frequency characteristics over a wide range, or
The prediction range can be estimated.

In order to show this effect, the present method will be applied to a control object having a complicated step response as shown in FIG. The subject is represented by G (S) = (1 + 4s) / (1 + 2s + s 2) + 5e -0.25 / (1 + s + s 2), fast mode and slow mode response are mixed. For this object, according to the above-described method, the sampling period τ is selected from four types of 0.1 second, 0.2 second, 0.4 second, and 0.8 second, and the model identified by the data of each sampling period. 5 (a) to 5 (d) together with the true process response. In the figure, a solid line indicates a true process response, and a dotted line indicates a predicted step response. A model with a short sampling interval accurately represents the rising portion of the step response of the step, that is, a fast mode characteristic, and a model with a long sampling interval accurately represents the steady-state characteristic of the step response, that is, the characteristic of a slow mode. It can be seen that by combining these, the step response or the predicted response can be estimated with much more accuracy than the estimation using the conventional single model.

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

In the model predictive control, the control amount predicted value and the step response over the set prediction range are required for calculating the optimal manipulated variable. And a step response.

[0014] Even when the prediction range and the appropriate value of the sampling period are not known in advance, good control can be expected if the minimum sampling period and the maximum prediction range are set as much as possible.

Further, how to select an actual sampling period will be described. The minimum sampling period is τ [sec], and for example, 2τ [sec], 4τ [sec],.
^Np-1 τ [sec] and Np kinds of sampling periods are selected. These are equally spaced if plotted on a logarithmic scale axis graph, and will be referred to as equilogarithmic 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 the control amount prediction values of one point which are assumed to have the highest estimation accuracy from the respective models.
.tau.),..., y (t + 2 ^Np-1 .tau.) (t is the current time), and these are used for the model predictive control calculation. In the model predictive control operation, instead of the conventional evaluation function for the predicted value at fixed time intervals as in the equation (1), the evaluation function for the predicted value at the logarithmic sampling interval is used. Is set, and the optimal operation amount that minimizes this is calculated for each control cycle.

As a result, a long prediction range from τ to 2 ^{Np -1} τ can be covered by using only the predicted values at Np points.
In addition, the required control operation amount is at most on the order of Np ² , and 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 coefficients γ (i), λ in equation (2)
By adjusting (i), the prediction range to be noted, that is, the control response speed can be freely adjusted over a wide range.
For example, if you value the high frequency band and want to increase the responsiveness,
The weight of the rising portion of the step response such as γ (1), γ (2),. Conversely, emphasizing the low frequency band,
If you want a slow and stable response, γ (1) = γ
(2) =... = 0 and the weight count may be set so as to ignore the rising part. In particular, in a multivariable system, if the weight coefficient is changed for each control loop, a multivariable model predictive control system having a different response speed for each loop can be easily realized.

[0018]

1 shows a model prediction control apparatus 2 according to the present invention. The model prediction control device 2 is divided into an adaptive operation unit 3 and a control operation unit 4. In the adaptive operation unit 3, the operation amount u and the control amount y, which are the 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 bandpass filters 5 having different pass bands. .., 2 ^{Np -1} τ, and the response data obtained by each sampler is stored in the response data storage unit 72. The Np identification means 8 cuts out response data of an appropriate length from the data sequence of each sampling period, and uses the least squares method to 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). For a multivariable process, A _i (z ⁻¹ ),
B _i (z ⁻¹ ) is 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). I do. The calculation method is Required by In the case of a multivariable process, g and h are all matrices.

Further, the control amount predicting means 10 uses the past response data stored in the response data storage unit 71 to store data u (t−2 ⁱ⁻¹ τ),..., U (t− (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 the current times.), And the following calculation is performed to calculate a predicted control value y (t + 2 ⁱ⁻¹ τ) when the manipulated variable is constant. 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) + _bi1u (t- _2i ^- 1τ) + _bi2u (t- _2i ^- 1τ) + ... + _bimu (t- (m-1) ^2i- 1τ) (6) In a multivariable process, y and u are vertical vectors, a
_ij and _bij are matrices of the corresponding size. The above is the processing in the adaptive operation unit 3.

Next, in the control operation unit 4, of the step response calculated from the Np time-series models identified by the Np identification means and the control amount prediction value, the step response synthesis means 11 first Individual step response (4)
Are combined with the same time scale, and a single step response 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.

In a specific synthesizing method, the overlapping portion in the equation (4) employs the average value thereof, and the missing data is obtained by interpolation calculation between two points on both sides. This situation will be described with reference to FIGS. For example, step responses of four models estimated from four types of sampling periods (in the case of Np = 4) are as shown in g ₁ (t) to g ₄ (t) shown in FIG. . 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 ( The right end of t) is 0.) The values are averaged and combined to obtain the combined step response g (t) shown in FIG. The value of the weight α of each response g _i (t) at this time is as shown in FIG.

On the other hand, the effective step response estimated value 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. g (t) = ((t ₂ −t) g ₁ (t ₁ ) + (t−t ₁ ) g ₂ (t ₂ )) / (t ₂ −t ₁ ) This makes the step response g (t) Combine. By discretizing the step response estimated value g (t) synthesized by the above procedure, the step response sequence of the equation (7) is obtained.

[0025] Hereinafter, the step response _{g 0, g 1, g 2} , g 4, g 8, ..., abbreviated as _{g 2 Np-1 (8)} . It should be noted that, in a multi-variable system, g _i is the matrix.

Next, the control amount predicted value synthesizing means 12
The control value predicted values at equal logarithmic intervals obtained from the equation (6) are arranged, and a predicted vector y = [y (t + τ), y (t + 2τ), y (t + 4τ),..., Y (t + 2 ^Np−1 τ)] Create ^T (9). Here, ^T represents a turning value. This is obtained by sampling the control amount prediction response at equal logarithmic intervals as shown in FIG.

At the same time, the future target value generator 15 receives the final target value r (t), and the 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), ..., and generates a ^{y * (t + 2 Np-} 1 τ) ] ^T (10). Here, ^T represents a turning 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 the multivariable system, each element of y and y ^* is a vertical vector, and the whole is also a vertical vector.

Next, the optimal manipulated variable calculating means 13 computes the optimal manipulated variable vector Δu = [Δu (t), Δu (t + τ),..., Δu (t + 2) for minimizing the evaluation function (2) by the following operation. ^Nu-1 τ)] ^T (12) is calculated by the following control operation 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) It 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 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.
× (Nu + 1) · q block matrix.

Finally, in the integrator 14, the first element Δu of the optimal manipulated variable vector obtained by the equation (13) is used.
Only (t) is taken out, and an optimal operation amount u (t) is calculated by an operation of u (t) = u (t−τ) + Δu (t) (15) and output to the process. Thus, adaptive model predictive control is performed.

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

In the configuration described in the claims of the present application, the first and second identification means are used. However, the same is true even if a single identification means performing both functions is used. First
And the second step response calculation means, but the same applies to the case where a single step response calculation means that performs both functions is used. Although the first and second step response calculation means are used, the same is true even if a single step response calculation means that performs both functions is used. Although the first and second control amount predicting means are used, the same applies even when a single control amount predicting means that performs both functions is used. These means can be realized by a known computer processing algorithm. Further, the technical configuration including at least the gist of the present invention, as well as the embodiments of the present application, is covered by the rights of the present application.

Further, the adaptive model predictive control device of the present invention can be similarly applied to a model predictive control method in consideration of control conditions described in Japanese Patent Application No. 2-17527.

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

Further, the multivariable system has an advantage that a control system that simultaneously considers a loop having a short time constant and a loop having a long time constant can be easily realized.

[0038]

As described above, the adaptive model predictive control system of the present invention uses a plurality of dynamic models identified by data sequences with different sampling periods, and is obtained by using each of these dynamic models. By combining the predicted output and the step response, the predicted output and the step response over a wider range are obtained, and the optimal control amount is calculated using the predicted output and the step response over the wider range. Good response characteristics that follow and have little hunting can be obtained. In addition, by selecting each sampling cycle so as to be equally spaced on a time axis expressed by a logarithm, it is possible to accurately predict the control amount over a wide range with a relatively small control calculation amount. Furthermore, in the case of the conventional model identification based on a single sampling period, it was necessary to exercise caution because the selection of the sampling period at the start of the control system had a large effect on the characteristics of the model identified thereby. In the present invention, since the prediction range is wide, good control can be expected from the start even if a plurality of sampling periods are roughly set.

[Brief description of the 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 section according to the present invention.

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

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

FIG. 5 is a graph showing a 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]

 REFERENCE SIGNS LIST 1 control object 2 model prediction control device 3 adaptive operation unit 4 control operation unit 5 bandpass filter 6 sampler 7 response data storage unit 8 identification unit 9 step response calculation unit 10 control amount prediction unit 11 step response synthesis unit 12 control amount prediction value Synthesizing means 13 Optimal manipulated variable calculating means 14 Integrator 15 Future target value generator 16 Subtractor

Continuation of the front page (56) References JP-A-3-217901 (JP, A) JP-A-2-292601 (JP, A) JP-A-4-309101 (JP, A) Shuichi Adachi, two other students, System Identification Method Using Multiple Decimations ”, Proceedings of the Society of Instrument and Control Engineers, The Society of Instrument and Control Engineers, September 30, 1990, Vol. 26, No. 9, p. 1029-1035 Junji Ome and three others, “Study on application of indirect adaptive control using decimation to robot arm”, 10th Adaptive Control Symposium, Society of Instrument and Control Engineers, 85-88 Koichi Nishitani, “Application of Model Predictive Control,” Measurement and Control, Japan Society for Instrument and Control Engineers, November 1989, Vol. 996-1004 (58) Field surveyed (Int. Cl. ⁷ , DB name) G05B 13/00-13/04 JICST file (JOIS)

Claims (3)

(57) [Claims] A first identification for obtaining a first dynamic characteristic model by identifying a dynamic characteristic model of the controlled object using time series data of the manipulated variable and the controlled variable of the controlled object collected at a first sample period. Means for identifying the dynamic characteristic model using time-series data of the manipulated variable and the control amount collected in a second sample period to obtain a second dynamic characteristic model; and the first identification means. First step response characteristic calculating means for obtaining a first step response of the dynamic characteristic model over a first range on the time axis; and a second step response on the time axis of the second step response of the second dynamic characteristic model. Step-response calculating means for obtaining a step response over a range of time, and combining step responses obtained by the first and second step-response calculating means on a time axis to form a step response over a wider range. Means, first control amount predicting means for giving time-series data of the operation amount and the control amount to the first dynamic characteristic model to obtain a control amount prediction value over a first range on a time axis; Second control amount predicting means for giving a time series data of the operation amount and the control amount to a second dynamic characteristic model to obtain a control amount prediction value over a second range on a time axis; (2) a control amount prediction value synthesizing means for combining the control amount prediction values obtained by the control amount prediction means on a time axis to form a control amount prediction value over a wider range; An optimal operation amount calculating means for calculating and outputting an optimal operation amount for minimizing a given evaluation function using a step response and a control amount predicted value formed by the control amount predicted value synthesizing means. Adaptive Model Predictive Control apparatus. 2. The adaptive model prediction control apparatus according to claim 1, wherein said first and second sample periods are determined so as to be equally spaced on a logarithmic time axis. 3. The step response synthesizing means, when the first range and the second range on the time axis overlap, calculates a step response of the overlapping range as an average of the first and second step responses. The step response is obtained by linear interpolation of the first and second step responses when the first range and the second range are separated from each other. 3. The adaptive model predictive control device according to 2.