JP3513633B2 - Method and apparatus for identifying unknown continuous-time system, and control system using the same - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention uses a method and apparatus for identifying parameters of an unknown continuous-time system, which can be described by differential equations, such as mechanical systems and electric motor systems, with high accuracy and efficiency, and uses the same apparatus. It was about the control system.

[0002]

2. Description of the Related Art In controlling a controlled object represented by a mechanical system and an electric motor system, a controller is generally designed based on this mathematical model. The actual controlled object is originally a continuous-time system, but conventionally, a differential equation is used as this mathematical model for the design of a discrete-time controller, and the parameters of this differential equation are Identification methods have been studied. However, in the model based on the difference equation, it is difficult to deal with the case where the control period and the identification period are different, the physical meaning of the parameter is unknown, it is not suitable for the design of a continuous-time controller, and it is difficult to apply it to a nonlinear system. Had a problem.

In order to solve these problems, it has been demanded to adopt a differential equation expression as a mathematical model of a controlled object and establish a method for identifying parameters on this equation. The traditional parameter identification method is differential equation
Continuous time input and continuous time of controlled object
Ensures linearity of output between parameters for identification
To avoid further differential processing caused by differential equations
Therefore, it is possible to use multiple analog filters according to the number of parameters.
Therefore, it is processed and an identification signal is generated. Identification
As an identification algorithm to obtain the parameter identification value from the
Has a continuous-time form and a discrete-time form, but generally the latter is
It's being used. For the latter use, of course
Time-splitting signal is required, which in turn leads to multiple analog filters.
The continuous time signal that is the output of the
You need to get this sample value. Such a traditional person
An invention using the method is disclosed in Japanese Patent Laid-Open No. 05-289703.
Japanese Patent Laid-Open No. 63-121904 and the like. former
Is an analog filter that processes continuous time input and output signals
State-space filter, the latter using a first-order filter
There is. However, this traditional method
Multiple (or higher) analog fills depending on the number of
It is difficult to realize the data evenly and accurately with an operational amplifier.
Difficulty, multiple samplers according to the number of parameters
It had two major problems, that is, a grab device was needed. Book
As a new method to solve the two major problems at the same time , I / O signals of the target system (basically independent of the number of parameters
The establishment of a method for identifying parameters of a continuous-time model represented by a differential equation has been particularly emphasized by the sample value of (i ) , that is, the discrete-time signal. As is well known,
For example, if the system is a 1-input / 1-output continuous time system, the input / output signal
The sampling device for obtaining
Two is sufficient regardless of the number of data.

An identification method of this kind that has already been studied is described in, for example, Document 1 (Identification by sampled data of a continuous-time system, Journal of Japan Society for Measurement and Control (Measurement and Control), No. 3).
Volume 2, No. 9, pp. 712-717, 1993), it is roughly divided into the indirect method and the direct method. The indirect method first identifies the parameters of the traditional discrete-time model (that is, the parameters on the difference equation) from the discrete-time signal, then converts these identified values into the parameters of the continuous-time model, and finally It is also trying to identify the parameters on the differential equation. However, in the case of this indirect method, in order to uniquely convert the discrete-time parameter to the continuous-time parameter, the object must be a linear system and the sampling period must be sufficiently small, but with the decrease of the sampling period, There is a contradictory problem that the identification accuracy of discrete time parameters decreases. This method, which requires the identification of discrete-time models by traditional difference equations, does not essentially solve the problems associated with the identification of discrete-time models described above.

On the other hand, the direct method uses a discrete-time signal obtained by sampling a continuous signal directly,
It seeks to identify a continuous time parameter (ie a parameter on a differential equation). According to the above-mentioned Document 1, it is pointed out that the reported direct method is capable of the following unified explanation.

For the sake of simplicity, the relationship between the input signal u (t) and the output signal y (t) of the unknown continuous-time system has a quadratic differential equation G (s) of the following equations (1) to (3). ).

[Equation 1] However, s is a differential operator, and

[Equation 2]

[Equation 3] And Here, for the differential operator s in equation (1),
By applying the bilinear transformation represented by the equation (4),

[Equation 4] Multiply this by P (z) ((1 + z-1) / 2) 2 T2,
An approximate difference equation Gd (z) is obtained as in equation (5).

[Equation 5] However, T is a sampling period, and the input signal u
(T) and the output signal y (t) are sampled at a cycle T, and the sample values at time t = kT are respectively u
It is expressed as (k) and y (k). Z-1 is a delay operator, P (z) is a digital filter transfer function,

[Equation 6]

[Equation 7]

[Equation 8] Is. In this example of the secondary system, the digital filter P (z) is selected from any of the following expressions (9) to (11).

[Equation 9]

[Equation 10]

[Equation 11] Parameters on differential equation (a1, a2, b1, b2)
Is directly identified using the discrete-time signals u (k) and y (k) according to the approximate difference equation (5).

[0007]

However, in the above direct method, as is clear from the equation (4), the differential equation describing the characteristic of the unknown continuous-time system through the bilinear transformation is boldly applied to the difference equation. Approximate transformation is performed, and it does not essentially solve the error problem of the approximate transformation caused by the bilinear transformation used in the conventional indirect method.
That is, the error problem caused by the bilinear transformation is essentially the same as in the indirect method. In order to reduce the error of the approximate transformation, usually, a measure is taken to make the sampling period T sufficiently small. However, the reduction of the sampling period T increases the number of data required for identification, which in turn increases the identification calculation amount, and consequently accumulates more calculation errors due to the finite word length. This opposite phenomenon also holds. That is, in order to reduce the calculation error due to the finite word length, it is necessary to reduce the identification calculation amount, which requires a reduction in the number of data. The decrease in the number of data items makes the sampling period coarser, which in turn increases the approximate conversion error. As described above, in the conventional direct method, there is an essential problem that the reduction of the error of the approximation conversion causes the increase of the calculation error, and conversely the reduction of the calculation error causes the increase of the approximation error, It was difficult to obtain the identification value with high accuracy.

Further, as understood from the equations (5) to (11), the direct method requires a number of digital filters Fi (z) P (z) corresponding to the number of parameters to be identified ( The above example of identifying the 5 parameters requires 6 digital filters). Moreover, as the number of parameters to be identified increases, the order of the digital filter generally increases. For this reason, the calculation load required for the filtering increases rapidly as the identification parameter increases. As described above, the conventional direct method also has a problem of low calculation efficiency.

The present invention has been made to solve the above problems, and the inventions of claims 1, 2 and 3 provide a method and an apparatus capable of identifying an unknown continuous time system with high accuracy and high efficiency. The purpose is to It is another object of the present invention to provide a control system capable of controlling an unknown continuous time system with high control performance.

[0010]

In order to achieve the above object, the invention of claim 1 applies a continuous-time input signal to a continuous-time system which can be expressed by a differential equation, and a continuous-time output signal of the system. And sample- filter the sampled values of the input signal and the output signal , respectively.
A method for identifying a parameter on a differential equation of the system using the obtained filtered signal , a state space realization that can have a state variable that matches the sample value of the state variable of a stable analog filter realized in a state space to, stable group of digital filters, the sample value serving signal of the input signal and the output signal respectively input from each of the digital filters of the state variable, generates an identification signal corresponding to the parameters of the system, It is characterized in that the parameters of the system are identified by using the identification signal.

According to a second aspect of the present invention, in order to particularly balance the efficiency and accuracy of identification, in the identification method of an unknown continuous time system according to the first aspect, a discrete time signal is used as a digital filter for realizing the state space. state variables in the case of input, the state space of interpolated continuous time signal obtained by interpolating the zero-order or first-order or second-order, etc. functions by using the discrete-time signal
It is characterized in that the state-space realization digital filter is configured so as to match the sampled value of the state variable when input to the realization analog filter.

Further, the invention of claim 3 applies the continuous time input signal to a continuous time system which can be expressed by a differential equation, detects the continuous time output signal of the system, and detects the input signal and the output signal. Digital sample values of
An apparatus for identifying a parameter on a differential equation of the system using a filtered signal obtained by filtering can have a state variable that matches a sample value of a state variable of a stable analog filter realized in a state space. and the group of stable digital filters state space realization, from the digital filter group to the input signal and the output signal of the sample values serving signal each of the digital filter obtained by inputting the state variables, the parameters of the system Means for generating a corresponding identification signal and using the identification signal to identify a parameter of the system.

According to a fourth aspect of the present invention, there is provided a control system including a control target configured by a load and a drive unit for driving the load, and a control unit controlling the control target.
And a group of state-space realization and stable stable digital filters state space realization to a sample value of the state variable of the analog filter may have state variables that match, the control target of the input signal to the digital filter group and the output signal from the sample value serving signal each input obtained was the digital filter of the state variables and to generate the identification signal corresponding to該制the control target parameter, at least one of the control target parameter by using said identification signal It is characterized by comprising an identification device comprising means for identifying one of the two.

[0014]

In the identification method according to claim 1 or the identification device according to claim 3, a continuous time input signal is applied to an unknown continuous time system, a continuous time output signal of this system is detected, and the detected input signal and output signal are detected. The sample values of are used to identify the parameters of the unknown continuous-time system.
At this time, the sampled value of the input / output signal (that is, the discrete time signal) is sent to a digital filter group composed of a plurality of stable digital filters and is input respectively. A plurality of digital filters in the digital filter group are individually realized in a state space, and in response to inputs to the filters, the same number of state variables as the filter order are simultaneously generated as output signals. At this time, since the digital filter is realized in the state space, the generation of the state variable is performed by the repeated calculation. Moreover, this state variable can be converted into an identification signal indispensable for identification. As a result, it is possible to obtain the effect of high efficiency that the identification signals of the same number as the filter order can be directly, simultaneously and repeatedly generated from the individual digital filters. In the digital filter group composed of a plurality of digital filters, the operation relating to the high efficiency is maintained as it is.

Moreover, since the state variable of the digital filter can be designed to match the sampled value of the state variable of the analog filter, it can be treated as the sampled value of the state variable of the analog filter itself. Accurate identification of continuous-time systems requires that the state variables of the analog filter be available with high accuracy. That is, according to the present invention, it is possible to directly generate the sample value of the state variable of the analog filter necessary for achieving high identification accuracy by the digital filter.

In particular, according to the identifying method of claim 2, the state variable when the interpolated continuous time signal obtained by interpolating by a rational function using the discrete time input signal of the digital filter is input to the analog filter. Since the digital filter is configured so that the sampled value of is completely equal to the state variable of the digital filter, the effect of achieving both the efficiency and the accuracy of identification in a balanced manner can be obtained.

In order to control the controlled object with high performance, a parameter indicating the characteristic of the controlled object is required. According to the control system of claim 4, even when an unknown continuous-time system is set as a control target, the parameter of the control target, which is indispensable for high-performance control, can be obtained from the identification device with high accuracy. It is possible to obtain the effect of realizing a matched controller with high accuracy.

[0018]

Embodiments of the present invention will now be described in detail with reference to the drawings. First, the overall configuration and operation of the unknown continuous time system and the identification device according to the present embodiment will be described with reference to FIG. In FIG. 1, 1 is an unknown continuous time system to be identified, to which a continuous time signal u (t) is input,
The continuous time signal y (t) is output. Here, 1
As an example, the system 1 is a single-input single-output system which is described by, for example, the following nth-order differential equation and whose parameters (ai, bi) are unknown.

[Equation 12] The relationship between the torque command value, speed, and position in many mechanical systems is expressed by the above equation. The same applies to the relationship between voltage and current in the DC motor system. In addition,
In FIG. 1, thin signal lines indicate scalar signal lines and thick signal lines indicate vector signal lines. This expression method is the same in the following drawings.

These input / output signals u (t) and y (t)
Are detected at each cycle T through the signal detector 2 including the input side signal detector 2a and the output side signal detector 2b.
That is, the function of the signal detector 2 is to detect the sampled values u (k) and y (k) for each cycle T. The sample value at this time may be obtained by directly sampling the continuous time signal, or may be obtained by sampling after analog filtering. The purpose of the filtering process in the latter is to remove strong noise mixed in the signal, etc., and the output signal of the detector may be basically regarded as u (k) and y (k). The detected discrete time signal is transferred to the identification device 3. The identification device 3 identifies the unknown parameters (ai, bi) using the discrete-time signals u (k), y (k), and identifies the identified values (αi (k),
β i (k)) is output as a vector signal.

FIG. 2 shows the internal structure of the identification device 3 according to the present invention. Reference numeral 4 in the figure denotes a digital filter group, which is an input side digital filter unit 4a.
And a digital filter section 4b on the output side. 4a and 4b, the state variable x (kT) that matches the sample value of the state variable x (t) of the stable analog filter realized in the state space at time t = kT (hereinafter, for simplicity, x (k) A digital filter for directly generating (indicated by the following) in a discrete time is realized in a state space according to the number of inputs (that is, in this example of single input and single output, one each). In this embodiment, the filter order m at this time is equal to or larger than the order n to be identified. That is, m ≧ n. Discrete-time signals u (k), y (k)
Are input to the digital filter units 4a and 4b, state variables xu (k) and xy (k) are generated as vector signals by the respective digital filters, and these are identification value determination units that implement identification value determination means. It is output to 5. In the identification value determination unit 5, first, the state variables xu (k), x
y (k) is sent to the identification signal generator 5a, and 5a synthesizes an identification signal ζ i (k) corresponding to the identification target parameters (ai, bi) as shown in the following equation, and this is combined into a vector signal ζ (k ) To the identification algorithm unit 5b.

[Equation 13] In the identification algorithm unit 5b, a discrete time identification algorithm is implemented, the identification value of the unknown parameters (ai, bi) is determined from the identification signal ζ (k), and this is determined as a vector signal (α (k), β (k )) Is output outside the identification device.

As the discrete-time identification algorithm for identifying the unknown parameter from the identification signal ζ i (k) satisfying the relation of the equation (13), a known one may be used. In this regard, reference 2 (adaptive algorithm, p
p. 11 to 108, Industrial Books, 1990), detailed description thereof is omitted here. As is clear from the above description, in order to identify the unknown parameters (ai, bi) with high accuracy, the discrete time identification signal ζi (k) corresponding to these parameters is required with high accuracy, which will be described in detail later. However, the basic signal for this synthesis is the discrete time state variables xu (k), xy of the digital filter.
(K). Next, the discrete time state variable xu (k),
The realization of the digital filter units 4a and 4b, which is a key point for generating xy (k) with high accuracy and high efficiency, will be described in detail with the basic principle of identification according to the present invention.

Continuous time input signal u (t) and output signal y
(T) is an m-th order stable analog filter expressed by the following equation.

[Equation 14] UF (t) and output signal yF (t)

[Equation 15]

[Equation 16] think of. Regarding uF (t) and yF (t),
The following relationship similar to the expression (12) is established.

[Equation 17] However,

[Equation 18]

[Formula 19] (M + 1) continuous time signals xui (t) (i = 0, 1,
..., m) takes u (t) as an input if the analog filter F (s) is realized in a state space with an appropriate structure.
All analog filters F (s) can be generated all and simultaneously. FIG. 3 shows an example of this realization. In the figure, square blocks represent integrators, triangular blocks represent multipliers, and circular blocks represent adders.

If the m-dimensional vector xu (t) having the continuous-time signal xui (t) as an element is defined by the following equation,

[Equation 20] The analog filter F (s) in FIG. 3 can be expressed by the following continuous-time state equation having xu (t) as a state variable. Note that the prefix T in the equation (20) indicates transposition. The meaning of the prefix T is the same below.

[Equation 21] However,

[Equation 22]

[Equation 23]

[Equation 24] Is. Note that I in the equation (23) is (m-1) x (m-
The unit matrix of 1), and 0 indicates a zero vector of (m-1) x1. (Hereafter, margin)

(M + 1) continuous time signals xyi (t)
For (i = 0, 1, ..., M), the input signal is y
It is generated in the same manner as above, only by changing to (t). Since the relation of the equation (17) regarding the unknown system is a relation that holds at an arbitrary time, naturally the sampling time t = kT
But it holds. That is, the following relationship holds.

[Equation 25]

The relation of the equation (25) is similar to the equation (13) which is the basic equation of the identification value determining unit, and can be easily changed to this. That is, if the sample values xui (k), xyi
If (k) is obtained, the identification signal generator 5a can obtain the identification signal ζ i (k) required by the equation (13) by performing the following simple conversion,

[Equation 26]

[Equation 27]

[Equation 28] In the identification algorithm unit 5b, this identification signal ζi (k)
Can be used to determine the identification value without difficulty. As is clear from the above description, in order to identify unknown parameters with high accuracy and high efficiency, sample values xui (k), x in equation (25) are used.
Highly accurate and highly efficient generation of yi (k) is particularly important.

The sampled values are the state variables xui (t), x of the analog filter realized in the state space as shown in FIG.
It can be obtained by sampling yi (t), but in this case, (2n + 2) number of detectors with sampling function corresponding to the number of identification parameters and their balanced and precise adjustment are required. To be done. This inefficiency with increasing number of identification parameters is obvious.
Further, when the input signal of the identification device is a discrete time signal, naturally, this method of using a continuous time signal as an input signal cannot be used.

In the present invention, xui is directly calculated from the discrete-time signal u (k) of the unknown system, which is the discrete-time input signal of the identification device.
Similarly, xyi (k) is directly obtained from y (k) in (k). The method of obtaining xui (k) from u (k) is the same as the method of obtaining xyi (k) from y (k). Therefore, the method of obtaining xui (k) from u (k) will be described below as an example. I will explain to you.

The sample value of the state variable xu (t), which is a continuous-time m-dimensional vector signal, at time t = kT is expressed as xu (k) for simplicity. In the present invention, this xu (k)
Is directly generated from the discrete-time input signal u (k) by, for example, a digital filter expressed by the following equation.

[Equation 29]

The digital filter represented by the equation (29) uses a discrete-time input signal, and directly targets only the discrete-time state variables, and further, m variables are simultaneously and repeatedly calculated. To generate.
As can be easily understood from the three features of the generation of the discrete-time state variable xu (k), which are directness, simultaneousness, and repeatability, this state variable generation method is extremely efficient from an arithmetic standpoint. The iterative calculation at this time is (k-
1) xu (k-1) at time T is the discrete-time input signal u that has the latest information and is available after time (k-1) T.
It is corrected with (k-1) and u (k), and has a sufficiently rational form. As described above, the state variable generation method of the present invention is extremely efficient and highly rational.

In order to generate a discrete-time state variable with high accuracy according to the digital filter of equation (29), it is important to select the filter parameters Ad1, bd1, bd0 used for this. This includes, for example, the following (30) to (3
Formula (1) is suitable.

[Equation 30]

[Equation 31]

[Equation 32] Where r is a scalar between zero and 1, which may include zero, one. That is, 0 ≦ r ≦ 1. Also, Aa,
ba is the matrix and vector of the analog filter described by the equations (21) to (24).

The digital filter expressed by the equations (29) to (32) uses the discrete time signal u (k) for the period (k-1) T≤t≤kT and the continuous time signal u.
Interpolate (t) with the following zero-order function,

[Expression 33] The continuous time state variable xu generated when this interpolation signal is input to the analog filters of equations (21) to (24)
A state variable exactly the same as the sample value of (t) can be generated. As described above, according to the present invention, it is possible to accurately generate sample values of continuous-time state variables in discrete time.

Digital filter parameters Ad1, bd
The following is also suitable as another selection example of 1 and bd0.

[Equation 34]

[Equation 35]

[Equation 36] The digital filter expressed by the equations (29) and (34) to (36) uses the discrete time signal u (k) for the period (k−1) T ≦ t ≦ kT and the continuous time signal u.
(T) is interpolated with a continuous time signal in the following linear relationship,

[Equation 37] The continuous time state variable xu generated when this interpolation signal is input to the analog filters of equations (21) to (24)
A state variable exactly the same as the sample value of (t) can be generated. As can be easily understood from the equation (37),
According to this second selection example, it is possible to more accurately generate the sample value of the continuous-time state variable in discrete time.

Digital filter parameters Ad1, bd
1 and bd0 may be determined in advance before using the digital filter of the equation (29). At this time, (3
0) to (32) and (34) to (36) show that exponential calculation of the matrix (TAa) is required when strict precision is pursued. Approximate calculation within the range is acceptable. There may be various approximation methods. For example, the following equation (38) may be used.

[Equation 38] As a matter of course, the digital filter parameters Ad1, bd1, bd0 have slightly different values depending on the approximation method used, but there is no problem if the error is within a permissible range. Since the exponential matrix exp (TAa) is exponentially stable, the error vanishes exponentially according to this eigenvalue.

It is pointed out that there are various methods other than the above several examples as methods for determining and approximating the parameters Ad1, bd1, bd0 of the digital filter shown in the equation (29), and these can be used. deep.

FIG. 4A is an example of hardware-based state space realization of the digital filter shown in equation (29). In the figure, a square block 4a1 is an mx1 vector delay device, 4a2 is a scalar delay device, and a triangular block 4a.
a3 is an mxm matrix multiplier, and triangular block 4a4 is mx
The 1-vector multiplier and the circle block represent the mx1 vector adder. The thick line between blocks is mx
One vector signal line and each thin line are scalar signal lines. FIG. 4B is a flowchart corresponding to FIG. 4A and showing an example of software-like state space realization of a digital filter. In S41, the discrete-time signal u (k) is received, and u (k-1), xu from the memory
(K-1) is taken out, the calculation of equation (29) is performed, and xu
Determine (k). In step S42, xu (k) is output, and xu (k) and u (k) are stored in the memory and prepared for the next calculation.

FIG. 5 (a) shows another example of hardware state space realization of the digital filter shown in equation (29).
Here is an example. The meanings of components such as blocks and signal lines are shown in FIG.
It is similar to the case of (a). The present implementation example is characterized in that the number and arrangement of the multipliers and delay units are different from the example of FIG. 4A. FIG. 5B is a flowchart corresponding to FIG. 5A and showing another example of software-like state space realization of a digital filter. S51
When the discrete time signal u (k) is received at, first bd0u
(K) is calculated, and then the calculated (Ad1xu
(K-1) + bd1u (k-1)) is taken out and these are added to determine xu (k). In S52, (Ad1x
u (k) + bd1u (k)) is calculated, the calculation result is stored in the memory, and is prepared for the next calculation.

As a digital filter for directly generating the discrete-time state variable xu (k) from the discrete-time input signal u (k), the following equation can be given as another embodiment replacing the equation (29). .

[Formula 39]

The digital filter represented by the equation (39) uses a discrete-time input signal, and directly targets only discrete-time state variables, and further, m variables are simultaneously and repeatedly calculated by iterative calculation. To generate. This state variable generation method is extremely efficient from an arithmetic standpoint, as can be easily understood from the directness, simultaneousness, and repeatability in the generation of the discrete-time state variable xu (k). Moreover, it is possible to generate every two cycles if necessary.
From this point of view, the calculation efficiency can be improved about twice as much as the previous two embodiments. Further, the iterative calculation at this time is such that xu (k-2) at the time (k-2) T is (k-2)
It is corrected with the discrete-time input signals u (k-2), u (k-1), and u (k) that have the latest information and are available after time T, which is extremely rational. There is. As described above, the state variable generation method of the present invention is extremely efficient and highly rational.

It is important to select the digital filter parameters Ad2, bd2, bd1, bd0 used in the equation (39) in order to accurately generate the discrete-time state variables according to the digital filter represented by the equation (39) of the present invention. Becomes This includes, for example, the continuous-time signal u (k) over the period (k−2) T ≦ t ≦ kT with the discrete-time signal u (k).
Interpolating (t) with a quadratic function represented by the following equation (40),

[Formula 40] The continuous time state variable xu generated when this interpolation signal is input to the analog filters of equations (21) to (24)
The digital filter parameters Ad2, bd2, bd are generated so as to generate a state variable that is exactly the same as the sample value of (t).
It is sufficient to set 1 and bd0. According to such a digital filter parameter based on the quadratic interpolation, it is possible to generate the sample value of the continuous-time state variable in a discrete time with higher accuracy than that of the above-described embodiment by the zero-order and linear interpolation.

These parameters are defined in the following (41)-
Equation (44) is obtained.

[Formula 41]

[Equation 42]

[Equation 43]

[Equation 44]

Digital filter parameters Ad2, bd
2, bd1 and bd0 may be determined in advance before using the digital filter of the equation (39). At this time,
When strict accuracy is pursued, it is sufficient to execute the expressions (41) to (44) with high accuracy. In practice, approximation calculation within the allowable range of error is sufficiently permitted. As a matter of course, the digital filter parameters Ad2, bd2, bd1, and bd0 have slightly different values depending on the approximation used, but there is no problem if the error is within a permissible range.
Since the eigenvalues of the exponential matrix exp (2TAa) used in this embodiment are twice smaller than the eigenvalues of the exponential matrix exp (TAa) used in the previous embodiment, the error is reduced at a double exponential speed. . That is, this embodiment is also excellent in the error of the filter parameter, and the discrete time state variable can be generated with high accuracy.

It should be pointed out that there are various methods other than the above-mentioned examples as methods for determining and approximating the parameters Ad2, bd2, bd1, bd0 of the digital filter shown in the equation (39), and these can be used. .

FIG. 6A shows an example of hardware-based state space realization of the digital filter shown in equation (39). The meaning of the block and signal line components is shown in FIG.
It is similar to the case of. FIG. 6B is a flowchart corresponding to FIG. 6A and shows an example of software-like state space realization of a digital filter. S61
Receives the discrete-time signal u (k) at
-2), u (k-1), xu (k-2) are taken out,
Equation (39) is calculated to determine xu (k). S6
In step 2, xu (k) is output and xu is stored in the memory.
(K) and u (k) are stored and prepared for the next calculation.

The method for generating the discrete-time state variable xu (k) with high efficiency and accuracy and the digital filter as this device have been described above with reference to the embodiments. Sampled value y of output signal of unknown continuous-time system
The method of generating the discrete-time state variable xy (k) related to (k) and the apparatus are the same as in the case of xu (k). That is, the same digital filter may be used to generate xy (k), and y (k) may be input instead of the discrete-time signal u (k).

Discrete-time state variable x as a vector signal
A method for generating an identification signal and a method for determining an identification value after u (k) and xy (k) are obtained with high efficiency and high accuracy, and these devices, and further, for identification with high efficiency and high accuracy, discrete time As described above with reference to FIG. 2 and the like, it is particularly important to generate the state variables xu (k) and xy (k) with high efficiency and high accuracy.

In the above description of the embodiments relating to the identifying method and the identifying apparatus, a single-input / single-output linear system is used as the unknown continuous-time system for the sake of simplicity.
It is pointed out that the identification method and the identification device according to the present invention can be used for identification of a multi-input multi-output or non-linear system such as a multi-degree-of-freedom mechanical system and an AC electric motor, as can be easily understood by those skilled in the art. Keep it.

FIG. 7 schematically shows the configuration of an embodiment of a typical control system incorporating the identification device according to the present invention. The control system includes a control target 10 including a load 11 and a drive device 12 that drives the load, and a control device 13 that controls the control target 10. The control device 13 includes a controller 14 that is an essential component of the control device, an identifier 15 that identifies a control target, and a parameter converter 16 that converts the identified control target parameter into a parameter of the controller. .

The controller 14 has an external command signal y (t) *.
And the output signal y (t) of the controlled object are captured.
The controller of this embodiment is configured digitally, and takes the deviation between the external command signal sample value y (k) * and the sample value (k) of the output signal to be controlled, and P is taken for this deviation.
The control process represented by the I controller is digitally performed,
Finally, the control input signal u is converted to analog by a hold circuit or the like.
(T) is generated and is output to the drive device 12. The drive device 12 drives the load 11 according to u (t). The driven amount at this time is observed as y (t) and is fed back to the controller 14.

The control input signal u (t) is output from the controller 14.
In addition, sample values u (k), y of u (t) and y (t)
(K) is output to the identifier. In this embodiment,
Since the controller is constructed digitally, sample values u (k), y (k) have already been obtained inside the controller. Therefore, no special sample value detector for the identifier is needed. The identifier 15 has a configuration similar to that of the identifying device 3 of the embodiment of FIG. 2, and has sample values u (k) and y (k).
The parameter to be controlled is further identified, and the identified value is output as a vector signal to the parameter converter 16. The identification parameters at this time do not have to be all parameters to be controlled. If unknown and known parameters are mixed, only the unknown parameters need to be identified. Further, when a parameter that easily fluctuates and a parameter that does not fluctuate depending on the operating state coexist, only the parameter that fluctuates may be identified. When the parameter converter 16 receives the identification value of the controlled object, the parameter converter 16 converts it into a controller parameter and outputs it to the controller 14. The controller 14 performs control processing according to the latest controller parameter received from the parameter converter to generate a control input u (t) to the controlled object.

By incorporating such an identifier in the control device, even when the characteristics of the controlled object are unknown or ambiguous, or when the characteristics of the controlled object fluctuate, the characteristics of the controlled object can be accurately controlled while being controlled. Since it can be identified, it is possible to obtain the controller parameter that matches the characteristics of the controlled object in real time. As a result, it is possible to realize a control system that always guarantees high control performance even when the characteristics of the controlled object are unknown or ambiguous or change.

As a method of using the identifier in the control device,
In some cases, as in the above embodiment, it is not necessary to always operate the control during execution. For example, if the characteristics of the controlled object are unknown or ambiguous, but it does not change depending on the operating condition of the controlled object, the identifier operates only at the initial stage of control, and if the optimal controller parameters are determined, it is suspended. Good. Even in this case, high control performance can always be guaranteed. This embodiment is one application example of the identifier that matches the characteristics of the controlled object. As can be easily understood from the two embodiments shown here, by utilizing the highly accurate and highly efficient identifier provided in the control device in a form according to the characteristics of the controlled object, high control performance is obtained. Can be applied to the control system.

Although the preferred embodiments of the present invention have been described above, it will be apparent to those skilled in the art that the present invention is not limited to the above embodiments, and various modifications and changes can be made within the technical scope thereof. In addition, it can be implemented.

[0053]

Since the present invention is configured as described above, it has the following effects.

According to the identification method of claim 1 or the identification device of claim 3, the sampled signals (that is, discrete-time signals) of the continuous-time input signal and the continuous-time output signal of the unknown continuous-time system to be identified are determined. , Inputting to a stable digital filter group realized in the state space, taking out the state variable of the digital filter realized in the state space as an output signal, and further converting this state variable into an identification signal indispensable for identification. Therefore, it is possible to generate the identification signals of the same number as the filter order directly, simultaneously, and repeatedly by using a single filter, that is, with high efficiency.

Moreover, since the state variable of the digital filter at this time can be designed so as to match the sample value of the state variable of the analog filter indispensable for highly accurate identification of the continuous time system, the state variable of this digital filter is used. By doing so, the effect that the unknown continuous-time system can be identified with high accuracy is obtained.

In particular, according to the identification method of claim 2, the state variable when the interpolated continuous time signal obtained by interpolating by a rational function using the discrete time input signal of the digital filter is input to the analog filter. Since the digital filter is configured so that the sampled values of are exactly the same as the state variables of the digital filter, both the efficiency and the accuracy of identification are achieved in a balanced manner (that is, the accuracy / computation ratio is the highest or The effect is that unknown continuous-time systems can be identified.

According to the control system of the fourth aspect, even when the unknown continuous time system is set as the control target, the control target can be identified with high accuracy by the identification device, and therefore the control target is matched with high accuracy. The effect that a controller can be realized and, by extension, high control performance can be achieved is obtained.

[Brief description of drawings]

FIG. 1 is a block diagram showing a relationship between an unknown continuous time system and an identification device according to an embodiment of the present invention.

FIG. 2 is a block diagram showing a schematic configuration of the inside of the identification device in FIG.

FIG. 3 is a block diagram showing an example of an analog filter realized in a state space.

FIG. 4 is a hardware block diagram (a) and a software flow diagram (b) showing an example of a state space-implemented digital filter in the digital filter unit of FIG.

FIG. 5 is a hardware block diagram (a) and a software flow diagram (b) showing an example of a state space-implemented digital filter in the digital filter unit of FIG.

FIG. 6 is a hardware block diagram (a) and a software flow diagram (b) showing an example of a state space-implemented digital filter in the digital filter unit of FIG. 2.

FIG. 7 is a block diagram showing an example of a control system including an identification device.

[Explanation of symbols]

1 Unknown continuous time system 2 signal detector 3 identification device 4 Digital filter group 5 Identification value determination unit 10 controlled objects 11 load 12 Drive 13 Control device 14 Controller 15 Identifier 16 parameter converter

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Claims (4)

(57) [Claims] 1. A continuous-time input signal is applied to a continuous-time system that can be represented by a differential equation, a continuous-time output signal of the system is detected, and sample values of the input signal and the output signal are digitally filtered. The processed file
In the method for identifying the parameters on the differential equations of the system using the filtered signal, the state space realized stable state that can have a state variable matching the sample value of the state variable of the stable analog state realized space filter such a group of digital filters, the sample value serving signal of the input signal and the output signal respectively input from each of the digital filters of the state variable, generates an identification signal corresponding to the parameters of the system, said identification signal A method for identifying an unknown continuous-time system, characterized in that the parameters of the system are identified by using. 2. Interpolation continuity obtained by interpolating a state variable when a discrete-time signal is input to the state-space realization digital filter using a function of 0th order, 1st order, or 2nd order using the discrete time signal. The unknown continuous time according to claim 1, wherein the state-space realization digital filter is configured so as to coincide with a sample value of a state variable when a time signal is input to the state-space realization analog filter. System identification method. 3. A continuous time input signal is applied to a continuous time system that can be represented by a differential equation, a continuous time output signal of the system is detected, and sample values of the input signal and the output signal are digitally filtered. The processed file
In a device for identifying a parameter on a differential equation of the system using a filtered signal , a state space realized stable state that can have a state variable that matches the sample value of the state variable of a stable analog filter realized in a state space and a group of digital filters, were sampled value of the input signal and the output signal to the digital filter group
From the state variables of the digital filter obtained by inputting each of the signals to be generated, an identification signal corresponding to a parameter of the system is generated, and a parameter of the system is identified by using the identification signal. Characterizing device of unknown continuous time system. 4. A control system comprising a control target composed of a load and a drive unit for driving the load, and a control unit controlling the control target, comprising a stable analog filter realized in a state space. and the group of stable digital filters state space realization to a sample value of the state variable may have state variables that meet, respectively input sample values serving signal between the input signal and the output signal of the controlled object to the digital filter group From the state variable of the digital filter obtained as described above, and an identification signal corresponding to the parameter of the control target, and using the identification signal, at least one of the parameters of the control target is identified. A control system comprising: