JPH07302101A - H-infinite norme measurement device and safety monitor device for control system - Google Patents

Abstract

PURPOSE:To measure the H-infinite norme of a controlled system in real time and also to automatically monitor the safety of the controlled system. CONSTITUTION:A safety monitor device 1 of a control system is provided with model response arithmetic means 4 which sequentially sequentially operates the estimated value of a controlled variable from the estimated value of a manipulated variable based on the linear model of a controlled system 70, a arithmetic means 5 which sequentially operates the signal series of the model difference, i.e., the difference between the estimated value of the controlled variable and measurement value. a filter means 6 which has a transmission function, T=(I+-CP)<-1>C where P shows the transmission function of the linear model of the system 70 with C meaning the transmission function of a controller 60 and I showing a unit matrix respectively and then uses the signal series of the model difference as an input signal, a measurement device 10 which measures H-indefinite norme of a system where the signal series of the model difference is used as an input signal and the input of the means 6 used as an output signal, a decider means 30 which decides that a feedback control system is set in a robust stable state and in a robust unstable state when the H-infinite norme is smaller and larger than 1 respectively.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an H infinity norm measuring device for measuring the H infinity norm, which is a characteristic of a control system of each industrial plant, and a stability monitoring device for a control system for monitoring the stability of the control system. Regarding

[0002]

2. Description of the Related Art In various industrial plants such as steel, petrochemical and electric power plants, various controllers are used to operate the plants optimally. In order to design a stable controller, it is necessary to optimally determine the controller parameters (control constants) according to the dynamic characteristics of the controlled object. However, even if the control is performed using the optimal control constant that has been determined once, the control performance decreases or the characteristics of the plant change during operation,
May lose stability. Since the influence of such a case appears in the output of the plant, the operator constantly monitors the output of the plant, and when the characteristic of the plant changes as described above, the operator re-adjusts the control constant.

[0003]

In such a plant whose characteristics change drastically, it is necessary for the operator to constantly monitor the state of the control system, which is a factor that increases the load on the operator.

Further, in order to reduce the load on the operator, in order to automatically monitor the stability of the controlled object against the dynamic characteristic variation, that is, the robust stability, it is necessary to estimate the degree of the dynamic characteristic variation of the controlled object online. For this purpose, it is necessary to perform a large amount of arithmetic processing using the input / output response data of the controlled object. Performing this large amount of arithmetic processing in real time inside the conventional controller has a problem of increasing the load on the processing device.

The present invention has been made in consideration of the above circumstances, and a first object thereof is an H infinity norm measuring device capable of measuring in real time the H infinity norm which is a dynamic characteristic of a controlled object. Is to provide.

A second object of the present invention is to provide a stability monitoring device for a control system capable of automatically monitoring the robust stability of the controlled object without imposing a load on the processing device of the operator or the controller body. Is.

[0007]

A first aspect of the H infinity norm measuring device according to the first invention outputs n (≧ 1) output signals based on m (≧ 1) input signals. For the system to identify, based on the time series data of the input signal and the output signal, the identification means for identifying the average value and fluctuation range of the parameters of the time series model of the system using the set membership identification method, and this identification means Estimating means for estimating the frequency response of the time series model based on the mean value and fluctuation range of the parameters of the identified time series model, and a frequency response matrix is constructed from the frequency response estimated by this estimating means. And a calculating means for calculating the maximum value of the maximum singular values of the frequency response matrix, and the maximum value calculated by this calculating means is the H infinity norm. That.

A second aspect of the H infinity norm measuring device according to the first invention is for a system which outputs n (≧ 2) output signals based on m (≧ 2) input signals. , A matrix U for the input signal sequence and a matrix Y for the output signal sequence based on the time-series data of the input signal and the time-series data of the output signal;
And an arithmetic means for calculating the maximum singular value of the product matrix U ⁻¹ Y of the inverse matrix of X and the matrix Y, and the maximum singular value is an H infinity norm.

A third aspect of the H infinity norm measuring device according to the first aspect of the invention is that for a system which outputs one output signal based on one input signal, time series data of the input signal and Fourier transform means for obtaining the Fourier transform of the input signal and the Fourier transform of the output signal at each frequency by applying the discrete time Fourier transform to the time-series data of the output signal, and the output signal for the Fourier transform of the input signal at all frequencies. And a calculating means for calculating the maximum value of the ratio of the Fourier transform, wherein the maximum value is the H infinity norm.

A first aspect of the stability monitoring device for a control system according to the second aspect of the invention is a controlled object having m manipulated variables and p controlled variables, a set value of the controlled variable, and a fed-back control. In a feedback control system that includes a controller that outputs a manipulated variable based on an amount, an observing means that sequentially observes the manipulated variable and the controlled variable, and the observed value of the manipulated variable based on the linear model of the controlled object A model response calculation means for sequentially calculating a predicted value, a model error response calculation means for sequentially calculating a signal series of a model error, which is a difference between a predicted value of a control amount and an observed value, and a transfer function of a linear model to be controlled are P , when the transfer function of the controller C, a unit matrix I, T = (I + CP ) has a transfer function T represented by ^-1 C, the transfer function of the signal sequence of the model error as the input signal Filter means for calculating an output signal when the input signal is input to the device, and an H infinity norm measuring device for measuring an H infinity norm for a system in which an observed value of a manipulated variable is an input signal and an output of the filter device is an output signal. When the H infinity norm is smaller than 1, the feedback control system judges that it is robust stable, and when it is 1 or more, it judges that it is not robust stable.

A second aspect of the stability monitoring device for a control system according to the second aspect of the invention is the same as the first aspect of the second aspect of the invention, in which the manipulated variable of the controlled object and the control amount p. e. Reliability (sustainable excitability, persistently exciting property) and the reproducibility of the H-infinity norm signal, and a certainty factor for determining the certainty factor with respect to the stability determination result from the determination result, and the certainty factor is predetermined. When it is lower than the threshold value of, or when an external command is received, p. e. And a test signal generating means for generating a test signal satisfying the requirement and superimposing it on the manipulated variable of the controlled object or the set value of the controlled variable.

[0012]

With the H-infinity norm measuring device according to the first aspect of the invention configured as described above, the H-infinity norm can be measured in real time from the input / output data of the target system. Since the measurement of the H infinity norm can be performed independently of the controller to be controlled, no load is applied to the processing device of the controller body.

Further, according to the stability monitoring apparatus of the second aspect of the invention configured as described above, since the transfer function T of the filter means is T = (I + CP) ⁻¹ C, the operation amount of the controlled object is observed. When the H infinity norm with respect to the transfer function (system) from the value to the signal sequence of the output of the filter means is measured, this measured H infinity norm becomes an index of the stability of the feedback control system. As a result, the stability of the feedback control system can be sequentially and automatically monitored by successively measuring the H infinity norm, and no load is imposed on the operator. Further, since the above-described measurement is performed independently of the processing device of the controller body, the processing device of the controller body is not loaded.

[0014]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the H infinity norm measuring device according to the first invention will be described with reference to FIGS. As shown in FIG. 2, the H infinity norm measuring device 10 of this embodiment has p (≧ 1) based on m (≧ 1) manipulated variables u ₁ , ... U _m.
1) The transfer function G that outputs the number of controlled variables y ₁ , ... Y _p is G
H infinity norm | G | _∞ of the controlled system 70
Is _calculated based on the manipulated variables u ₁ , ... U _m and the controlled variables y ₁ , ... Y _p . The H-infinity norm measuring device 10 of this embodiment has analog data input terminals 11 ₁ , ... 11 _m and 12 ₁ , ... 12, as shown in FIG.
_p , A / D converters 13a and 13b, clock timer 14, digital data input terminal 15, buffer memories 16a and 16b, parameter setting terminal 17, data bus 18, program area 19a and data area 19b. A memory 19 having a CPU, a CPU 20 and a D
An A / A converter 21, a digital data output terminal 22,
And an analog data output terminal 23.

Next, the configuration and operation of the H infinity norm measuring device 10 of this embodiment will be described. The manipulated variable u _i input via the analog data input terminal 11 _i (i = 1, ... M) is sent to the A / D converter 13 a, and the analog data input terminal 12 _h (h = 1, ... P) is input. The control amount y _h input via the above is sent to the A / D converter 13b. The manipulated variables u ₁ , ... U _m and the controlled variables y ₁ ,.
y _p is A / D based on the output signal of the clock timer 14.
The signals are digitized in the converters 13a and 13b at regular intervals and sent to the buffer memories 16a and 16b, respectively. If the manipulated variables u ₁ , ... U _m and the controlled variables y ₁ , ... Y _p are digitized, they can be directly input to the buffer memories 16 a and 16 b via the digital input terminal 15. Buffer memory 1
Inside 6a and 16b, the latest signal data is input at every data observation cycle, and the data input before N (≧ 2) cycles are erased. For example, as shown in FIG. 4, the buffer memory 16a stores m pieces of data u before n cycles.
The memory of the address where ₁ (k−N), ... U _m (k−N) is stored is erased, and the latest m pieces of data u ₁ (k), ... U _m (k) are input to this address. . In the next cycle, the address of interest is moved to the next one, and the same processing is continued. As a result, the buffer memory 16a always stores Nm data from the present to N-1 steps before. Similarly, N is also stored in the buffer memory 16b.
・ P data is stored. Figure 1 again
Returning to, the buffer memories 16a, 16b,
The memory 19 and the CPU 20 are connected to the data bus 18. The CPU 20 extracts data from the buffer memories 16a and 16b in accordance with the program written in the program area 19a of the memory 19, and the memory 1
The H infinity norm is calculated on the data area 19b of No. 9. The result is sequentially output from the digital data output terminal 22 or the analog data output terminal 23 via the D / A converter 21. Further, parameters such as calculation conditions can be set and changed via the parameter setting terminal 17. In addition, H infinity norm | G | _∞ Figure 3
Is defined as the upper limit value of the gain frequency characteristic of the transfer function G of the controlled system.

Next, the first calculation of H infinity norm | G | _∞
A specific example of will be described. Now, the target system outputs p output signals (control quantities) y ₁ , ... Y _p based on _m input signals (manipulation quantities) u ₁ ,. Transfer function (discrete-time transfer function) matrix G
But

[0017]

[Equation 1] However

[0018]

[Equation 2] Shall be represented by. The current time is k + N. At this time

[0019]

[Equation 3] Input signal sequences u _h (k + i), (h = 1,
... m, i = 0, ... N) and the output signal sequence y _h (k +
i), (h = 1, ... P, i = 0, ... N), the H infinity norm | G | _∞ of the transfer function G is calculated by the following equation (4).

│G│ _∞ = σ _max (U ⁻¹ Y) (4) where σ _max (A) is the maximum singular value of the matrix A (the product of the conjugate transposed matrix A ^* of the matrix A and the matrix A). Represents the square root of the maximum eigenvalue of the matrix A ^* A, and the number of data N is N
+ 1 = m (n + 1) is an integer that holds the relationship, and the matrix U regarding the input signal sequence and the matrix Y regarding the output signal sequence are respectively

[0021]

[Equation 4] Is represented. That is, the matrix U is (N + 1) × (m (n
+1)) matrix, and the matrix Y is (N + 1) × (p (n +
1)) matrix.

The reason why the H infinity norm (approximate value) is calculated by the above equation (4) will be described below.

First, at time k + N, input / output data u ₁ (k) ... U _m (k), ... U ₁ (k + N), ... U from N steps before to the current time.
_{m (k + N) y 1} (k) ... y p (k), ... y 1 (k + N), ... y
Consider fitting the following nth-order impulse response model (or moving average model) to _p (k + N).

[0024]

[Equation 5] However, g _ih (z ⁻¹ ) = g _ih1 z ⁻¹ + g _ih2 z ⁻² + ... + g _ihn z ⁻ⁿ (8)

At this time, the following equation (9) holds between the observation data and the model parameters according to the definition of the impulse response model.

Y = UG (9) where G is

[0027]

[Equation 6] , G ^T (i) (i = 1, ... N) is a transposed matrix of the matrix G (i), and the matrix G (i) is

[0028]

[Equation 7] Is. As a result, G = U ^-1 Y (12) holds. When the impulse response up to the nth order of the target system whose pulse transfer function is expressed by the equations (1) and (2) is expressed by the equations (7) and (8), its H infinity norm | G | _∞ is (10 It is known that it must be greater than or equal to the maximum singular value of the matrix G of Therefore, if the order n of the impulse response model is sufficiently large, σ _max (G) = σ _max (U ⁻¹ Y) becomes H.
It gives a good approximation of the infinite norm | G | _∞ .

The number of input signals m = 1 and the number of output signals p =
The calculation method of the H infinity norm of the controlled system which is 1 is
“Time domain identi” by Tong Zhou and Hideki Kimura
fication for robust control ”, System & Control L
etlers 20 (1993) pp.167-178. That is, the time series data u (i) of the input signal u (i = 0, ...
N) and time series data y (i) of output signal y (i = 0, ...
N) from the matrix U, Y to the following equations (13) and (14)

[0030]

[Equation 8] And is calculated based on these matrices using | G | _∞ = σ _max (U ^-1 Y) (15).

Next, a second concrete example of the calculation of the H infinity norm will be described. First, the order n (<N) of time series data between input and output data is set. Here, n indicates the number of time series data of the same type fetched from the buffer memory. Then, a finite-dimensional time series model G (z ⁻¹ ) = G (1) z ⁻¹ + G (2) z ⁻² + ... + G (n) z ⁻ⁿ (16) and its frequency response are estimated. Where G (k),
(K = 1, ..., N) is a p × m matrix having elements g _ij (k). The above estimation is performed in the following procedure. Step 1: Input data u _h , (h
= 1, ... M) and output data y _i , (i = 1, ... P)
Past N data u _h (k) and y _i (k), (k
= 0, ... N-1) is taken out. Procedure 2: Hereinafter, the following steps 1 to 6 are repeated for i = 1, ... P.

A) Step 1: For i = 1, ... P, amplitudes of noise A _i (1), ... A _i (A) (presumed to be included in the data y _i (1), ... Y _i (N)) n) is set.

B) Step 2: First, as an initial value, k = n θ (n) = [g _i1 (1) ... g _i1 (n) ... g _im (1) ... g
_im (n)] ^T = [0 ...... O] ^{T φ} (n) = _{[u 1 (n-1) ...} u 1 (0) ... u m (n-1) ... u m (0) ] ^T P (N) = γI is set. Here, I is a unit matrix of size n · m × n · m, and γ is a large positive value.

[0034] c) Step 3: a k = k + 1, φ ( k) = _{[u 1 (k-1) ...} u 1 (k-n) ... u m (k-1) ... u m (k-n) ] ^T g (k) = φ (k) ^T P (k−1) φ (k) ε (k) = y _i (k) −φ (k) ^T θ (k−1) c ₀ = (n− 1) A _i ² (k) g ² (k) c ₁ = {(2n−1) A _i ² (k) −g (k) + ε
^{2 (k)} g (k} ) c 2 = n (A i 2 (k) -ε 2 (k)) - calculates the g (k). Then, if c ₂ <0, a positive solution of the quadratic equation c ₀ ρ ² (k) + c ₁ ρ (k) + c ₂ = 0, that is,

[0035]

[Equation 9] Is calculated, and if c ₂ ≧ 0, ρ (k) = 0.

D) Step 4: The estimated parameter vector θ is updated by the following update formula.

[0037]

[Equation 10] e) Step 5: Repeat steps 3 and 4 until k equals N.

When the iteration for the variable k is completed,
Based on the information that the observed signal contains an unknown disturbance of amplitude A _i (k), the average value θ (N) and the fluctuation range of the parameter θ of the time series model represented by the equation (16) of the target system are observed. It can be determined from the data. This parameter θ is a set of ellipsoids satisfying (θ−θ (N)) ^T P ⁻¹ (N) (θ−θ (N)) ≦ 1, that is, the center has an average value θ (N).
And is expressed as a set of ellipsoids whose diameter is the reciprocal of the square root of the eigenvalues of the matrix P ⁻¹ (N). As a result, it is possible to estimate the model parameter including the fluctuation range of the target system, and it is possible to model the infinite dimensional system including the error due to the approximation by the finite dimensional model such as equation (16).

Obtaining the average value and the fluctuation range of the parameter θ as described above is known as a set membership identification method. For example, E. Fogel and YFHuang: On
theValue of Information in System Identification
: Bounded Noise Case, Automatica, Vol.18, pp229〜23
8 (1982).

F) Step 6: Estimate the frequency response of the model obtained as described above. When j is an imaginary unit, the frequency response G (jω) of the target system at a certain frequency ω (0 ≦ ω ≦ π) is Ψ (jω) = [exp (−jω) exp (−2jω) ... exp (− m jω)] ^T , the average value in the frequency domain is G _ihN (jω) = Ψ ^T (jω) θ _h (N). Where θ _h (N) is (h-1) · m of θ (N)
It is a vector reconstructed by taking out m elements from the + 1st to h · mth. Further, in the matrix P (N), the (h-1) · m + 1th row to the hmth row, the (h-1) · m + th row.
If the m × m matrix reconstructed by extracting the 1st to h · mth columns is P _ih (N), and the transformation of this matrix P _ih (N) into the frequency domain is Φ _ih (jω), then this Φ _ih (jω) is

[0041]

[Equation 11] Is represented. Where Re (A) and Im (A) are the matrix A
The matrix of the real part and the matrix of the imaginary part of are shown. That is, A = R
e (A) + j · (Im (A)).

Now, the frequency response G (jω) of the target system
_Let G _ih (jω) be the i-th row and h-th column of the component, and X _ih (jω) = G _ihn (jω) −G _ih (jω) be the fluctuation range from the average value G _ihN (jω). , The variation width X _ih (jω) of the i-th row and the h-th column component G _ih (jω) of the frequency response G (jω) is

[0043]

[Equation 12] Meet

The above calculation is performed by ω = 0, 2π / N, ... 2π
Find about (N-1) / N. Step 3: Frequency response G obtained as described above
_{From ih} (jω), i = 1, ... p, h = 1, ... m, frequency response matrix G (jω) = {G _ih (jω)} (ω = 0, 2π / N, ... 2π (N-1) / N). And G (jω) among all frequencies ω
The maximum value of the maximum singular values of is the H infinity norm.

Next, a third specific example of the calculation of the H infinity norm will be described. The third specific example is to calculate the H infinity norm of a system that outputs one output signal y based on one input signal u. The calculation procedure will be described below.

Procedure 1: From the buffer memories 16a and 16b, the past n pieces of data u (i), y (i), (i
= 0, ... N-1) is taken out.

Step 2: Discrete-time Fourier transform is applied to each data series.

[0048]

[Equation 13] Step 3: The maximum value of gain is

[0049]

[Equation 14] And the maximum value is the H infinity norm.

As described above, according to the H infinity norm measuring apparatus of this embodiment, the input / output response data u _i (i = 1, ... M), y _h (h = 1, ... ) Can be stored in the buffer memories 16a and 16b, and the H infinity norm can be measured from a finite number of data. Since this H infinity norm is measured using a dedicated device, the H infinity norm of the controlled object can be measured in real time without imposing a load on the processing device of the controller body.

FIG. 5 shows the configuration of the first embodiment of the stability monitoring device 1 for the control system according to the second invention. The stability monitoring device 1 of this embodiment includes a model response calculating means 4, a model error response calculating means 5, a filter 6, an H infinity norm measuring device 10, and a judging means 30. The stability monitoring device 1 includes the control parameter adjusting means 50.
Parameters and set values r ₁ , ...
Output y ₁ of _p and the plant 70, ... the operation amount u ₁ controller 60 to the plant 70 based on the y _p, ... u _m
To output the control amount y ₁ , ...
_It is used in a feedback control system for controlling _p so that it becomes the set value r ₁ , ... R _p .

The configuration of the stability monitoring apparatus of this embodiment will be described below together with the operation. Note that the manipulated variables u ₁ , ... U _m and the controlled variables y ₁ , ... Y _p are such that their time-series data are input to the stability monitoring device 1 of this embodiment every certain observation period. A preset transfer function model P of the plant 70 and a manipulated variable u which is an output of the controller 60.
_{Based on 1} (k), ... U _m (k), the model response calculation means 4 calculates the following equation.

[0053]

[Equation 15] Is used to calculate model responses η ₁ (k), ... η _p (k), which are predicted values of the controlled variables y ₁ (k), ... Y _p (k).
Here, P _ih (i = 1, ... P, h = 1, ... M) is represented by a discrete time transfer function.

Next, this model response η ₁ (k), ... η _p
(K) and the actual control variables y ₁ (k), ... Y _p (k), the model error response ε ₁ (k), ... ε _p (k) is ε _i (k) = y _i (k) −η _i (k) (i = 1,
.. p) is used to successively calculate in the model error response calculation means 5.

Next, in the filter 6, the model error response ε ₁ (based on the filter transfer function F = (I + CP) ⁻¹ C composed of the transfer function model P to be controlled and the transfer function C of the controller 60 at that time point. k), ... ε _p (k)

[0056]

[Equation 16] Is used to obtain the filter operation output e ₁ (k), ... E _m (k). Here, F _ih (i = 1, ... M, h = 1, ... P) is each element of the filter transfer function F and is represented by a discrete time transfer function.

Next, the manipulated variables u ₁ (k), ... U _m observed
(K) and the filter operation output e ₁ (k), ... E _m (k), the manipulated variables u ₁ (k), ... U _m (k) are used as input signals, and the filter operation output e ₁ (k) , ... E _m (k) as an output signal, that is, a system including the plant 70, the model response calculation means 4, the model error response calculation means 5 and the filter 6 is G, and its H infinity norm | G | _∞ It is determined by the H infinity norm measuring device 10. This H infinity norm | G | _∞ can be obtained by the procedure described in the above first invention.

Then, the measured H infinity norm | G
_│∞ is sequentially sent to the judging means 30, and the judging means 3
At 0 at each time, if | G | _∞ <1, it is determined that the current control system is robust stable, and if | G | _∞ ≧ 1, it is determined that the current control system is not robust stable,
The determination result is sequentially sent to the operator terminal 40 and displayed.

Next, the reason why the control system is determined to be robust stable when the H infinity norm | G | _∞ measured as described above is smaller than 1 will be described. Now, Fig. 6
, A system 81 having a transfer function Δ and a transfer function T
Considering a closed loop system consisting of a system 82 having
A sufficient condition for this closed loop system to be stable is given by | TΔ | _∞ <1 (17). This means that when the signal goes around the closed loop system shown in FIG. 6, the gain becomes 1 or less, so that the energy of the signal is surely attenuated, and as a result, the above-mentioned closed loop system has any bounded disturbance. It means that the signal of the closed loop system is bounded and stable even if it is disturbed by. Based on this, the stability of the feedback control system shown in FIG. 7 will be considered. In FIG. 7, C
Is the transfer function of the controller 83, P is the transfer function of the model 84 to be controlled, and Δ is the transfer function of the system 81 that calculates the error between the actual controlled object and the model 84. In the control system shown in FIG. 7, that stability is maintained even if there is a model error is called robust stability. When the feedback control system shown in FIG. 7 is converted to the closed loop system shown in FIG. 6 as seen from the system 81, T = (I + CP) ⁻¹ C (18) Here, I represents an identity matrix.

Substituting this into the above sufficient condition for stability gives | (I + CP) ^-1 CΔ | _∞ <1 (19), and this equation (19) is robust to the feedback control system shown in FIG. 7. It becomes a condition for becoming stable.

Returning to FIG. 5 again, now, the system including the plant 70, the model response calculation means 4 and the model error response calculation means 5, that is, the manipulated variables u ₁ (k), ... U _m
With (k) as an input signal, the model error response ε ₁ (k), ...
Letting Δ be the transfer function of the system that uses ε _p (k) as an output signal, the H infinity norm | G | of the system G including the plant 70, the model response calculation means 4, the model error response calculation means 5, and the filter 6 _∞ is expressed as | G | _∞ = | (I + CP) ^-1 CΔ | _∞ (20). Therefore, the H infinity norm measuring device 1
H infinity norm | G | _∞ is calculated by 0, and (19),
If | G | _∞ is smaller than 1 from the equation (20), it can be determined that the control system that performs feedback control of the plant 70 by the controller 60 is robust and stable.

In this way, in the stability monitoring device 1,
A manipulated variable and a controlled variable of a plant to be controlled are sequentially input, and a determination result signal regarding robust stability and an H infinity norm signal | G | that means the degree of robust stability
Output _∞ sequentially. These signals are transmitted to the operator terminal 4
It is always displayed at 0. Further, when it is determined that the robustness is not stable, the operator terminal receiving the signal emits an alarm sound and displays an alarm message on the screen to notify the operator of an abnormality in the plant control system. The operator can determine the degree of robust stability by seeing how small the H infinity norm signal | G | _∞ is from 1 or how much it exceeds 1. FIG. 8 shows a screen configuration example of the operator terminal for displaying them. FIG. 8 (a) shows a case where the robust flow is stable, and the plant flow 91 displayed on the screen is shown.
When the desired control system is designated, the status for the control system is displayed in the message window 92, and the value of | G | _∞ is displayed in the robust stability display meter 93. on the other hand,
FIG. 8B shows a case where robust stability is not achieved, an alarm sound is emitted, an alarm sign 94 blinks, and a control loop in the plant flow 91 that does not satisfy robust stability is blinked. Further, a message is displayed on the message window 92, and the robust stability display meter 93 indicates that the value of | G | _∞ exceeds 1.

The determination result signal, the H infinity norm signal and the like output from the stability monitoring device 1 are also input to the control parameter adjusting means 50. When the controller 60 is in the automatic adjustment mode, the robust stability is determined by the following procedure. The control parameters are adjusted to be optimal.

Procedure 1: Take in the H infinity norm signal | G | _∞ . Step 2: If | G | _∞ <η, increase the control gain K _p a little. K _p ← K _p × 1.1 If | G | _∞ > η, the control gain K _p is slightly decreased. K _p ← K _p ÷ 1.1 If | G | _∞ = η, the control gain remains unchanged. Step 3: Set the control gain K _p in the controller 60 and return to step 1. However, η (0 <η <1) is a parameter for designing a preferable robust stability of the control system and is set from the operator terminal 40.

As described above, according to the stability monitoring apparatus of the present embodiment, the H of the control system is changed from the observation data of the operation amount u and the control amount y of the control system without imposing a load on the processing unit of the controller body. Measure the infinity norm in real time,
Whether or not the control system is robustly stable is determined based on the magnitude of this H infinity norm. Then, it is possible to inform the operator of the judgment result, issue an alarm when robust stability is not satisfied, and take appropriate measures such as adjusting the gain of the controller.As a result, the load of the operator who monitors the control system can be reduced. The safety of platonic operation can be reduced.

Next, FIG. 9 shows the configuration of the second embodiment of the stability monitoring apparatus 1 according to the second invention. The stability monitoring device 1 of this embodiment is the same as the stability monitoring device 1 of the first embodiment shown in FIG.
And are newly provided. Confidence determination means 2 is the first
Monitoring means and second monitoring means. The first monitoring condition is the p. e (peristentl
y exciting) property, that is, whether or not the input / output signal contains a sufficiently large number of frequency components, and the second monitoring means monitors the reproducibility of the H infinity norm.

In the first monitoring means, first, the input / output signal of the controlled object, that is, the controlled variable y _i (i = 1, ... P),
The manipulated variable u _h (h = 1, ... M) is observed in real time at a time k in each predetermined cycle, and the next vector φ _i (k) = [y _i (k-1 ), ... Y _i (k−n), u
_{1 (k-1), ...} u 1 (k-n), ..., u m (k-
1), ... U _m (k−n)] ^{T is obtained} for each i (i = 1, ... M).

Next, the covariance matrix Γ (k) is updated at each time k according to the following equation.

Γ _i (k) = λ _i Γ _i (k−1) + φ
_i (k) φ ^T _i (k) where 1 ≧ λ _i > 0, Γ (0) is a positive definite matrix.
Then, at each time, p. e. The measure of sex pe (k) is

[0070]

[Equation 17] Calculate using. Where σ _max (A) and σ
_min (A) means the maximum singular value and the minimum singular value of the matrix A, respectively. In equation (21), pe (k) means the reciprocal of the condition number of the covariance matrix for the input / output signal vector φ (k) of the control target. If this value is small, the dynamic characteristic model of the control target from the input / output signal. Means that it becomes difficult to estimate.

In the second monitoring means, the H infinity norm estimation result signal | G | _∞ , which is the output of the H infinity norm measuring device, is observed at each time k, and the average of the past N step results is obtained. The value AH (k) and variance BH (k) are

[0072]

[Equation 18] In real time. Then, the reciprocal number re (k) = (BH (k) / AH (k)) ⁻¹ of the signal obtained by normalizing the variance BH (k) is used as a measure of the reproducibility of the H infinity norm. When the output signal of the H infinity norm measuring device 10 is fluctuating due to disturbance or observation noise received by the controlled object, the variance BH (k) of the result of the expression (22) becomes large and the signal re (k) becomes small. . Therefore, the magnitude of re (k) becomes a measure of the reproducibility of the H infinity norm of the model error estimated in the stability monitoring device 1.

P. Of the input / output signal of the control target estimated by the above procedure. e. The scale pe (k) of the sex or the scale re (k) of the reproducibility of the H-infinity norm of the model error is output as the scale of the certainty factor of the determination result in the stability monitoring device 1. This result is first displayed on the operator terminal 40 to inform the plant operator of the reliability of the stability monitoring function. Secondly, when the certainty factor is sent to the control parameter adjusting means 50 and is lower than a certain threshold value, the automatic adjustment of the control parameter is suppressed even if it is determined that the robust stability is poor. This makes it possible to avoid adversely affecting the control system by forcibly adjusting the control parameters when the stability of the control system is erroneously determined.

Next, in the test signal generating means 3, p. e.
Sex determining means (determining means 1) to p. e. When a certainty level signal is received or a certainty level signal is received from the certainty level determination means 2 and becomes less than a certain threshold value, or the plant operator confirms those certainty levels and determines that it is necessary. Only when a command is input, p. e. Satisfying test signal δ _1, ... δ _m or d _1, ... operation amount _{u i (i = 1, ...} m) of the control system of d _p or setpoint signal r _i
(I = 1, ... P). As the test signal, an arbitrary signal is examined from among a pulse signal, a rectangular wave signal, an M series signal, and a pseudo white signal. Examples of these signals are shown in FIG.
Shown in (a), (b), (c) and (d).

In the embodiment of the H infinity norm measuring device according to the first invention and the first embodiment of the stability monitoring device according to the second invention, the estimation of the H infinity norm of the model error and the feedback control system are performed. All of the stability criteria are based on the manipulated variable of the controlled object and the observed value of the controlled variable. However, when the set value is constant over a long period of time, both the manipulated variable and the controlled variable are constant, and it is difficult to obtain meaningful information on model error and stability from those signals. Further, when the control system receives a large disturbance or observation noise, the model error estimated from the observation data and the stability judgment result have low reliability. Therefore, the pe property and the reproducibility of the H infinity norm are monitored as in the second embodiment described above,
If necessary, the control parameters are automatically adjusted, or the test signal is superimposed on the setting signal and the manipulated variable, whereby the reliability of stability monitoring can be improved more than in the case of the first embodiment.

[0076]

According to the H-infinity norm measuring device of the first invention, the H-infinity norm can be measured in real time based on the input signal and the output signal of the controlled system. Since this measurement can be performed independently of the controller to be controlled, it does not put a load on the processing device of the controller body.

Further, according to the stability monitoring apparatus of the second invention, the robust stability with respect to the change in the dynamic characteristics of the controlled object can be automatically judged in real time, and the load on the plant monitoring work of the plant operator can be increased. Can be reduced. Moreover, by adjusting the control system according to the result, the reliability of the control system can be improved.

[Brief description of drawings]

FIG. 1 is a block diagram showing the configuration of an embodiment of an H infinity norm measuring device according to the first invention.

FIG. 2 is a block diagram illustrating a relationship between an H infinity norm measuring device and a controlled object.

FIG. 3 is a graph illustrating the meaning of H infinity norm.

FIG. 4 is a schematic diagram illustrating the structure of a buffer memory according to the embodiment shown in FIG.

FIG. 5 is a block diagram showing the configuration of a first embodiment of a stability monitoring device according to the second invention.

FIG. 6 is a block diagram illustrating stability of a closed loop system.

FIG. 7 is a block diagram illustrating robust stability of a feedback control system.

8 is a schematic diagram showing an example of a display screen on the operator terminal of the embodiment shown in FIG.

FIG. 9 is a block diagram showing the configuration of a second embodiment of the stability monitoring device according to the second invention.

10 is a waveform diagram showing a waveform of a test signal generated by the test signal generating means according to the embodiment shown in FIG.

[Explanation of Codes] 1 Stability monitoring device 2 Confidence determination means 3 Test signal generation means 4 Model response calculation means 5 Model error response calculation means 6 Filter 10 H Infinity norm measurement device 11 _i (i = 1, ... m) Analog data input terminal 12 _i (i = 1, ... p) Analog data input terminal 13a, 13b A / D converter 14 Clock timer 15 Digital data input terminal 16a, 16b Buffer memory 17 Parameter setting terminal 18 Data bus 19 Memory 19a Program Area 19b Data area 20 CPU 21 D / A converter 22 Digital data output terminal 23 Analog data output terminal

Claims (6)

[Claims] 1. n (≧ 1) based on m (≧ 1) input signals
1) For a system that outputs a number of output signals, the average value and the fluctuation range of the parameters of the time series model of the system are set based on the time series data of the input signal and the output signal by using the membership identification method. Identifying means for identifying, estimating means for estimating the frequency response of the time series model based on the average value and fluctuation range of the parameters of the time series model identified by the identifying means, and the frequency response estimated by this estimating means And a calculation means for calculating the maximum value of the maximum singular values of the frequency response matrix among all frequencies, and the maximum value calculated by this calculation means is the H infinity norm. H infinity norm measuring device characterized by the following. 2. Based on m (≧ 2) input signals, n (≧ 2)
2) For a system that outputs a plurality of output signals, a configuring means that configures a matrix U regarding the input signal sequence and a matrix Y regarding the output signal sequence based on the time-series data of the input signal and the time-series data of the output signal. , An inverse matrix of the matrix U and a matrix Y, and a calculating means for calculating a maximum singular value of the product matrix U ⁻¹ Y, and the maximum singular value is an H infinity norm. An H infinity norm measuring device characterized in that 3. A system for outputting one output signal based on one input signal, wherein discrete time Fourier transform is applied to the time series data of the input signal and the time series data of the output signal, respectively. Fourier transform means for obtaining the Fourier transform of the input signal and the Fourier transform of the output signal at each frequency, and a computing means for computing the maximum value of the ratio of the Fourier transform of the output signal to the Fourier transform of the input signal at all frequencies. And an H infinity norm measuring apparatus having the maximum value as an H infinity norm. 4. A controlled object having m (≧ 1) manipulated variables and p (≧ 1) controlled variables, and a manipulated variable output based on the set value of the controlled variable and the fed back controlled variable. In a feedback control system including a controller, an observing unit that sequentially observes the manipulated variable and the controlled variable, and a predicted value of the controlled variable from the observed value of the manipulated variable based on the linear model of the controlled object. Model response calculation means for calculating, model error response calculation means for sequentially calculating a model error signal sequence which is a difference between the predicted value and the observed value of the controlled variable, P the transfer function of the linear model of the controlled object, When the transfer function of the controller is C and I is a unit matrix, it has a transfer function T represented by T = (I + CP) ⁻¹ C, and the transfer function using the signal series of the model error as an input signal. Filter means for calculating an output signal when input to T, and an H infinity norm measuring device for measuring an H infinity norm for a system in which an observed value of the manipulated variable is an input signal and an output of the filter means is an output signal And a judging means for judging that the feedback control system is robust stable when the H infinity norm is smaller than 1, and judging that the feedback control system is not robust stable when the norm is 1 or more. Control system stability monitoring device. 5. The stability monitoring device according to claim 4, wherein the manipulated variable of the controlled object and the p. e. Reliability (sustainable excitability, persistently exciting property) and the reproducibility of the H infinity norm signal, and the reliability determination means for determining the reliability with respect to the stability determination result from the determination result; When it is lower than a predetermined threshold value or when an external command is received, p. e. And a test signal generating means for generating a test signal satisfying the above requirement and superimposing it on the manipulated variable of the controlled object or the set value of the controlled variable, and a stability monitoring device for a control system. 6. The stability of a control system according to claim 4, wherein the H infinity norm measuring device is the H infinity norm measuring device according to any one of claims 1 to 3. Monitoring equipment.