JP2011028550A - Method and device for identifying system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a system identification method and a system identification device which generate M series signals which do not provide incorrect estimation and perform system identification. <P>SOLUTION: System identification is performed by generating a third M series signal and making it an input signal. The third M series signal is generated by combining a first M series signal including a first sampling period T<SB>1</SB>and a first shift register n<SB>1</SB>, and a second M series signal including a second sampling period T<SB>2</SB>which is different from the first sampling period T<SB>1</SB>and a second shift register n<SB>2</SB>. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a system identification method using an M-sequence signal and a system identification apparatus using an M-sequence signal.

  In industrial precision equipment such as machine tools and inspection devices, various control algorithms are used to drive components such as stages included in these equipment at high speed and accurately.

  For example, the control system 1 shown in FIG. 1 includes a stage 11 and a control device 12 that controls the stage 11. The stage 11 is used together with or incorporated in an industrial precision instrument such as a machine tool or an inspection apparatus to move a workpiece, a measurement object, or the like to an appropriate position. Further, for example, at the lower part of the stage 11, there may be provided a vibration isolation table 13 that blocks the stage from disturbance components (for example, vibration) from an external environment such as a floor. Naturally, it is necessary to change the control algorithm between a stage having a vibration isolation table and a stage having no vibration isolation table. Thus, it is necessary to design the control system reflecting the components included in the controlled object.

  In particular, in recent years, model-based control methods that are intended to express the characteristics of constituent elements to be controlled by mathematical formulas and actively reflect them in the design of a control system are frequently used.

  When designing a model-based control system, it is desirable to construct a model that accurately and concisely expresses the components included in the controlled object. For example, it is conceivable to construct a model suitable for the controlled object by building a differential equation based on physical considerations related to the controlled object or using a simulator incorporating a numerical calculation process. When building a model in this way, the knowledge of the control system designer's knowledge of the controlled object can be reflected in the model, but an appropriate model must be built for the controlled object with complex behavior. It becomes difficult.

  Therefore, in recent years, the application of a system identification method in which the dynamic characteristics of a controlled object is clarified by measurement and the result is used as a model for control system design is being recognized as an important technique. In the system identification method, as shown in FIG. 2, first, some input u is given to the controlled object and the model. When the input u is input to the controlled object, the output y is output from the controlled object, and when the input u is input to the model, the output Y is output from the model. Here, the model structure and / or parameters are determined so that the difference ε between the output y to be controlled and the output Y of the model becomes small.

  The amplitude and frequency characteristics of the input u are selected according to the characteristics to be controlled. Generally, a white signal, a sine wave frequency sweep signal, an M-sequence signal, or the like is used. The white signal is a signal that is generated irregularly with time, for example, using a random number, and includes a wide range of frequency components almost uniformly. The sine wave frequency sweep signal is a signal formed by sweeping (sweeping) the frequency of the sine wave. Here, since the white signal includes all frequency components uniformly, the low frequency component that is practically important in estimating the characteristics of the controlled object is relatively insufficient compared to the high frequency component. The problem that often occurs. When a sine wave frequency sweep signal is used, a signal having a desired frequency can be obtained by selecting an appropriate frequency sweep range, but the measurement time in the low frequency region is significantly increased.

  In contrast, an M-sequence signal is a combination of a binary signal (for example, a signal amplitude of 1 or 0) and a continuous signal of a certain width, ensuring a wide frequency band and an appropriate measurement time. Realization is possible.

  FIG. 5 of Patent Document 1 shows an M-sequence signal generation circuit using a flip-flop circuit and an EX-OR circuit. When a clock signal for a predetermined sampling pulse is input to the M-sequence signal generation circuit, an M-sequence signal that is a pseudo random binary signal is output. Here, by appropriately setting the number of flip-flop circuits (corresponding to the number of shift registers described later) and the period of the clock signal as parameters, a desired M-sequence signal can be obtained using a relatively simple circuit. Since it can be generated easily, its use in the field of system identification is also expanding.

JP-A-5-257505

  As will be described later, the present inventor has studied a method for selecting parameters of an M-sequence signal for generating an appropriate M-sequence signal as an input signal for estimating a frequency characteristic to be controlled. Specifically, an M-sequence signal generated with various parameters was input to a predetermined control target, and an output signal from the control target was measured. And the frequency characteristic of a control object was estimated for every M series signal generated with each parameter. As a result, the estimation results of the frequency characteristics of the controlled object in each parameter are compared with the actual frequency characteristics of the controlled object, and what parameters can be selected to obtain a highly reliable estimation result. It was investigated.

  As a result, the present inventor appropriately selects parameters such as the number of shift registers and the sampling period according to the control target, generates an M-sequence signal, and uses it as an input signal. Has been found to contain an erroneous estimation due to the input signal, leading to the present invention.

  The present invention has been made to solve the above problems, and an object of the present invention is to provide a system identification method for generating an M-sequence signal that does not give an erroneous estimation and performing system identification, and so on. It is an object of the present invention to provide a system identification apparatus that uses an M-sequence signal that does not give an incorrect estimation as an input signal.

According to a first aspect of the present invention, there is provided a system identification method for estimating a frequency characteristic of the controlled object, the first sampling period T _1, and, first characterized by first shift register number n ₁ And a second sampling period T ₂ different from the _first sampling period T ₁ and a second M series signal characterized by the second number of shift registers n ₂ are combined into a third M series signal. Generating an M-sequence signal, inputting a third M-sequence signal to the control object, measuring an output signal from the control object, and a third M-sequence signal input to the control object And a system identification method comprising: estimating a frequency characteristic of the control object using a measured output signal from the control object.

According to a second aspect of the present invention, there is provided a system identification device for estimating a frequency characteristic of the controlled object, the first sampling period T _1, and, first characterized by first shift register number n ₁ M and the first M-sequence signal output unit for outputting the sequence signal, the first sampling period T ₁ is different from the second sampling period T _2, and a second characterized by a second shift register number n ₂ The first and second M-sequence signals output from the second M-sequence signal output unit that outputs the M-sequence signal and the first and second M-sequence signal output units, respectively, A system comprising: a third M-sequence signal output unit that outputs an M-sequence signal; and a measurement unit that measures an output signal from the control object, which is obtained by inputting the third M-sequence signal to the control object. An identification device is provided.

  Here, when only one type of M-sequence signal is used as an input signal, even if the sampling period is selected so as to match the operating frequency band of the control target, the power spectrum density function of that M-sequence signal is A dip may occur in the operating frequency band, resulting in an erroneous estimation.

  On the other hand, according to the first and second aspects of the present invention, both M-sequence signals having different sampling periods are combined to generate a third M-sequence signal, which is controlled. Used as an input signal to be input to the target. Therefore, for example, even if the sampling period is selected so that one of the M-sequence signals is adapted to the operating frequency band to be controlled, the predetermined frequency band ( For example, the sampling period of the other M-sequence signal can be selected so that no dip occurs in the operating frequency band. Thereby, it is possible to avoid erroneous estimation while maintaining the estimation accuracy of the frequency characteristic to be controlled in a predetermined frequency band.

  By using the system identification method or system identification device of the present invention, a dip occurs in the power spectrum density function of the M-sequence signal used as the input signal in a predetermined frequency band (for example, the operating frequency band to be controlled). Can be avoided, and there is no possibility of erroneous estimation due to this. Therefore, it is possible to perform highly reliable system identification.

FIG. 1 is an example of a control system that controls a stage. FIG. 2 is a diagram showing the flow of the system identification method. FIG. 3 is a circuit diagram of the M-sequence signal generator. FIG. 4 is a waveform diagram of an M-sequence signal when the sampling period is 1 millisecond and the number of shift registers is six. FIG. 5 is a waveform diagram of an M-sequence signal when the sampling period is 10 milliseconds and the number of shift registers is eight. FIG. 6 is a schematic diagram illustrating a state in which the system identification device 500 is connected to the filter 200. FIG. 7 is a waveform diagram of an output signal from the filter 200 when the M-sequence signal shown in FIG. FIG. 8 shows an estimation result of the frequency characteristics of the filter 200 when the M-sequence signal shown in FIG. FIG. 9 is a waveform diagram of an M-sequence signal when the sampling period is 100 milliseconds and the number of shift registers is five. FIG. 10 shows an estimation result of the frequency characteristics of the filter 200 when the M-sequence signal shown in FIG. 9 is input to the filter 200. FIG. 11 is a power spectral density function of the M-sequence signal shown in FIG. FIG. 12 is a waveform diagram of an M-sequence signal obtained by combining the M-sequence signal shown in FIG. 5 and the M-sequence signal shown in FIG. 9 by the first combining method. FIG. 13 is a power spectral density function of the M-sequence signal shown in FIG. FIG. 14 is a schematic diagram illustrating a state where the system identification device 501 is connected to the filter 200. FIG. 15 shows an estimation result of the frequency characteristics of the filter 200 when the M-sequence signal shown in FIG. 16 is a waveform diagram of an M-sequence signal obtained by synthesizing the M-sequence signal shown in FIG. 5 and the M-sequence signal shown in FIG. 9 by the second synthesis method. FIG. 17 is a power spectral density function of the M-sequence signal shown in FIG. FIG. 18 is a schematic diagram illustrating a state where the system identification device 502 is connected to the filter 200. FIG. 19 shows an estimation result of the frequency characteristics of the filter 200 when the M-sequence signal shown in FIG. FIG. 20 is a diagram illustrating the rise time of the control target.

  Hereinafter, an M-sequence signal generation method and a system identification apparatus using the same according to the present invention will be described with reference to the drawings, but the present invention is not limited thereto.

The M-sequence signal can be expressed by, for example, the calculation shown in Expression (1), and can be generated by the M-sequence signal generation device (M-sequence signal generation circuit) 100 shown in FIG. The M-sequence signal generator 100 includes a pulse generator 51 that outputs a sampling clock pulse having a predetermined sampling period, n delay calculators 52 (denoted as D _{1 to} D _{n in} FIG. 3), comprises 0 or n number of amplifiers 53 to take a value of either 1 (denoted as FIG. 3 in _a 1 ~a _n), n pieces of exclusive oR calculator and (XOR circuit) 54. Note that n corresponds to the number of delay arithmetic units and the like, but generally, n is referred to as the number of shift registers. Therefore, n is hereinafter referred to as the number of shift registers in the present application.

Using the M-sequence signal generation apparatus 100 of FIG. 3, it is possible to generate an M-sequence signal with the number of data (also referred to as a period) N = 2 ⁿ −1. Here, the M-sequence signal defined by Equation 1 has a state in which n bits have the same value only once in one period. In other words, the generation circuit shown in FIG. 3 outputs a pulse signal having a pulse width that is n times the sampling period only once per period. Such a pulse signal having a pulse width of n clocks is called a maximum duration pulse, and the pulse width is called a maximum duration. Thus, it can be said that the M-sequence signal is a kind of white signal having both the upper limit band of the cycle N and the constant value component for n clocks.

  FIG. 4 shows an example of the M-sequence signal generated from the M-sequence signal generator 100 shown in FIG. 3 from the M-sequence signal generator when the sampling period is 1 millisecond and the number of shift registers is six. The obtained M-sequence signal is shown. The sampling clock pulse is input from the third millisecond. As shown in FIG. 4, after 3 milliseconds, the negative value continues for 6 clocks, and then transitions to a random signal region in which positive and negative are switched randomly. A pulse signal that appears first and lasts for 6 clocks is a signal composed of a low-frequency component called a maximum sustained pulse.

  Next, an example of a procedure for estimating the frequency characteristics of the control target using the M-sequence signal will be shown. Here, as an example of the control target, a low-pass filter 200 (see FIG. 6) having a break frequency of 4.5 Hz is considered. This filter 200 has a resonance mode of 25 Hz and a delay component of digital calculation of 50 milliseconds.

  When this filter 200 is mathematically expressed using the Laplace operator s, it can be expressed as Equation 2. Here, x indicates an input and y indicates an output.

  In order to estimate the frequency characteristic of the filter 200, the M-sequence signal generated with a sampling period of 10 milliseconds and the number of shift registers of 8 is repeated 6 times to generate an M-sequence signal of about 18 seconds as a whole. Input signal. The amplitude of the input signal is about ± 8V. FIG. 5 shows the first 3 seconds of the generated M-sequence signal. As shown in FIG. 6, the M-sequence signal output from M-sequence signal generator 100 is input to filter 200, and the output from filter 200 is input to predetermined measurement device 120. The output signal from the filter 200 measured by the measuring device 120 is shown in FIG. Here, system identification apparatus 500 is configured by combining M-sequence signal generation apparatus 100 and measurement apparatus 120.

Next, the autocorrelation function R _xx of the input signal x shown in FIG. 5 is calculated by Equation 3, and the input signal x shown in FIG. 5 and the output signal y shown in FIG. The cross-correlation function R _xy is calculated. Thereafter, the power spectral density functions P _xx and P _xy were calculated by Equations 5 and 6, and the frequency response function was obtained by Equation 7 from the ratio thereof. FIG. 8 shows a frequency response function showing the frequency characteristics of the filter 200 thus obtained. According to FIG. 8, it is considered that the resonance mode of 25 Hz and the break frequency of 4.5 Hz can be generally estimated. However, it can be seen that the gain in the low frequency region of about 2 Hz or less exceeds 0 dB. This indicates that the estimation accuracy in the low frequency region is not sufficient.

  According to the inventor's consideration, as will be described later, in order to increase the estimation accuracy in the low frequency region, the number of shift registers is set so that the maximum duration is longer than the rise time (time constant) of the control target. It is desirable to adjust the sampling period. Therefore, in order to focus on the low frequency region, the maximum duration was increased by changing the sampling period from 10 milliseconds to 100 milliseconds. In this case, since the measurement time is extended ten times, the number of shift registers is changed from eight to six. The number of repetitions is six. The amplitude is ± 8 V as in the previous input signal. Here, since the cycle of the M-sequence signal can be shortened by reducing the number of shift registers, it is possible to suppress an increase in measurement time due to a long sampling cycle. Nevertheless, the maximum duration of this M-sequence signal is set longer than the maximum duration of the previous M-sequence signal.

  FIG. 9 shows a part of the M-sequence signal thus obtained. In the same manner as described above, the frequency response function of the filter 200 is derived from the M-sequence signal and the output signal obtained by inputting the M-sequence signal to the filter 200, and the result is shown in FIG. According to this, it can be seen that, unlike the frequency response function shown in FIG. 8, the gain in the low frequency region is equal to 0 dB. In this respect, it is considered that the accuracy of estimation in the low frequency region could be improved by extending the sampling period by 10 times in order to focus on the low frequency region.

  However, in the frequency response function shown in FIG. 10, it can be seen that a new resonance mode is generated at about 10 Hz, which was not found in the frequency response function shown in FIG. Since this resonance mode is not included in Equation 2 and does not appear in the frequency response function shown in FIG. 8, it is caused by how to select the parameters of the M-sequence signal, and is erroneously estimated. It is thought to be due to.

  Therefore, in order to analyze the characteristics of the M-sequence signal shown in FIG. 9, the power spectrum density function of the M-sequence signal is calculated using Equations 3 and 5, and the result is shown in FIG. According to FIG. 11, it can be seen that a dip (a spike-like sharp dent) is formed at a frequency of 10 Hz and an integer multiple thereof in the power spectral density function of the M-sequence signal. Here, according to Equation 7, the power spectral density function of the M-sequence signal that is the input signal is included in the denominator of the frequency response function. From this, when a dip is formed at a specific frequency as in the power spectrum density function of the M-sequence signal shown in FIG. 11, the frequency response function including the power spectrum function of the M-sequence signal in the denominator It can be seen that a peak is formed.

  As described above, even when the parameter of the M-sequence signal is appropriately adjusted according to the control target, the present inventor generates the frequency response function obtained by this by selecting the parameter of the M-sequence signal. It has been found that the peak of the resonance mode may appear due to incorrect estimation.

  As a result of intensive studies on this problem, the present inventor does not use a single M-sequence signal as an input signal, but combines two or more types of M-sequence signals generated with different parameters as described later. Has found that the above problem can be solved. Specifically, it is conceivable to combine a plurality of M-sequence signals by the following two methods.

As a first synthesis method, two M-sequence signals x ₁ (t) and x ₂ (t) designed with different parameters are sequentially output at different times, so that a new M-sequence signal x _A (t) is generated. Generation. For example, as shown in Equation 8, from the 0 seconds to _{T 1} seconds outputs _x 1 (t), from _{T 1} seconds _T to ₂ seconds and outputs a _x 2 (t).

As a second synthesis method, as shown in Expression 9, two M-sequence signals x ₁ (t) and x ₂ (t) designed with different parameters are added to obtain a new M-sequence signal x _B (t). Is generated. At this time, since the periods of the two M-sequence signals to be added are generally different, a zero-value signal is added to the M-sequence signal having a short period to make the lengths consistent with the M-sequence signal having a long period. It is also necessary to check that the added signal does not exceed the output limit.

Next, using the M-sequence signal generated by these methods as an input signal, the frequency characteristics of the filter were estimated as described above. First, the estimation of the frequency characteristics of the filter using the M-sequence signal x _A (t) synthesized by the first synthesis method will be described.

For the first M-sequence signal x ₁ (t), the sampling period was 10 milliseconds, the number of shift registers was 8, and the number of repetitions was 6. For the second M-sequence signal x ₂ (t), the sampling period was 100 milliseconds, the number of shift registers was 6, and the number of repetitions was 5. The first M series signal x ₁ (t) was output for about 18 seconds, and about 2 seconds later, the second M series signal x ₂ (t) was output for about 20 seconds. FIG. 12 shows the waveform of the M-sequence signal x _A (t) generated by the first synthesis method in this way, and FIG. 13 shows its power spectral density function. Here, it can be seen that the 10 Hz dip present in FIG. 11 is not observed in the power spectral density function of the M-sequence signal x _A (t) generated by the first synthesis method shown in FIG. .

Furthermore, the frequency characteristics of the filter were estimated by the above-described method using the M-sequence signal x _A (t) generated by the first synthesis method as an input signal. As shown in FIG. 14, the system identification device 501 used here outputs a first M-sequence signal xA (t) (corresponding to a third M-sequence signal) synthesized by the first synthesis method. An M-sequence signal synthesis device 601 and a measurement device 120 to which a signal from the filter 200 is input are provided. Here, the first M-sequence signal synthesizer 601 outputs the first M-sequence signal output unit 101 that outputs the first M-sequence signal x1 (t) and the second M-sequence signal x2 (t). And a switching mechanism 103 that switches and outputs the outputs of the first and second M-sequence signal output units 101 and 102 at a constant time. Here, the configuration of first and second M-sequence signal output sections 101 and 102 is the same as that of M-sequence signal generation apparatus 100 described above, and a detailed description thereof will be omitted. In system identification device 501, switching mechanism 103 corresponds to the third M-sequence signal output unit of the present application.

The measurement results obtained by the system identification device 501 are shown in FIG. Looking at the frequency characteristics of the filter shown in FIG. 15, the resonance mode of 25 Hz and the breakpoint frequency of 4.5 Hz can be roughly estimated, and furthermore, the gain matches 0 dB in the low frequency region. Therefore, it is considered that sufficient estimation accuracy is secured. Also, there is no erroneous resonance mode peak at 10 Hz that appeared in FIG. From the above, it can be seen that by using the M-sequence signal x _A (t) generated by the first synthesis method as an input signal, it is possible to sufficiently ensure the estimation accuracy in the low frequency region without giving an erroneous estimation. It was.

Next, estimation of the frequency characteristics of the filter using the M-sequence signal x _B (t) generated by the second synthesis method will be described. The first M-sequence signal x1 (t) and the second M-sequence signal x2 (t) combined by the second synthesis method were the same as those in the first synthesis method described above. FIG. 16 shows the waveform of the M-sequence signal x _B (t) generated by the second synthesis method, and FIG. 17 shows its power spectral density function. As shown in FIG. 17, even in the power spectral density function of the M-sequence signal x _B (t) combined by the second combining method, the M-sequence signal x _A (combined by the first combining method described above). Similar to the power spectral density function of t), it can be seen that the 10 Hz dip present in FIG. 11 is not observed.

Further, the frequency characteristics of the filter were estimated by the above-described method using the M-sequence signal x _B (t) generated by the second synthesis method as an input signal. As shown in FIG. 18, the system identification device 502 used here includes a second M-sequence signal synthesizer 602 that outputs the M-sequence signal x _B (t) synthesized by the second synthesis method, and a filter. And a measuring device 120 to which a signal from 200 is input. Here, the second M-sequence signal synthesizer 602 includes a first M-sequence signal output unit 101 that outputs the _first M-sequence signal x ₁ (t), and a second M-sequence signal x ₂ (t). 2 and a signal adder 104 that adds the outputs of the first and second M-sequence signal output units 101 and 102. In system identification device 502, signal adder 104 corresponds to the third M-sequence signal output unit of the present application.

The result obtained by the system identification device 502 is shown in FIG. Looking at the frequency characteristics of the filter shown in FIG. 19, the resonance mode of 25 Hz and the breakpoint frequency of 4.5 Hz can be roughly estimated, and further, the gain matches 0 dB in the low frequency region. Therefore, it is considered that sufficient estimation accuracy is secured. Further, there is no erroneous resonance mode peak of 10 Hz that appeared in FIG. From the above, it can be seen that by using the M-sequence signal x _B (t) generated by the second synthesis method as an input signal, it is possible to sufficiently secure the estimation accuracy in the low frequency region without giving an erroneous estimation. It was.

  In this way, regardless of which of the first and second synthesis methods is used, an input signal that does not give an erroneous estimation is obtained while ensuring the estimation accuracy in a desired frequency region according to the frequency characteristics of the control target. I found out that I could do it. As described above, when the two M-sequence signals are combined by the first combining method and when the two M-sequence signals are combined by the second combining method, the M-sequence signal in which the latter is generated rather than the former is generated. Can be shortened, and an increase in measurement time can be avoided.

As described above, in each of the first and second combining methods, at least two M-sequence signals are combined to newly generate an M-sequence signal. It is a problem whether to combine them. Therefore, in the following, a method for selecting parameters of an M-sequence signal to obtain an input signal that does not give erroneous estimation while ensuring estimation accuracy in a desired frequency region according to the frequency characteristics of the control target will be described in detail. Specifically, consideration will be given to how to select the amplitude of the M-sequence signal, the number of shift registers, the sampling period, and the number of repetitions. In the following description, a case will be described in which the first and second M-sequence signals X ₁ and X ₂ are combined by any one of the two synthesis methods to generate a new M-sequence signal X. Similar guidelines can be followed when two or more M-sequence signals are combined.

The amplitudes of the M-sequence signals X ₁ and X ₂ are determined according to the characteristics of the controlled object. As shown in Equation 7, since the frequency response is calculated by the ratio of the output signal to the input signal, the estimation result of the frequency response depends on the input amplitude when the input / output relationship of the control target is linear. Absent. On the other hand, for example, when the control target does not respond to an input below a certain level (when it has a dead zone), the amplitudes of the M-sequence signals X ₁ and X ₂ are set so as to sufficiently exceed the dead zone. To do. An example where the control target has such a dead zone is when the stage cannot be moved unless an input signal of a certain level or more is input when a frictional force is acting on the drive part of the stage. Can be mentioned.

Next, the number of shift registers and the sampling period will be considered. As described above, the maximum duration is an amount determined by the product of the number of shift registers and the sampling period. Here, in order to ensure the estimation accuracy of the control target, particularly in the low frequency region, the maximum duration of at least one M-sequence signal among the _two M-sequence signals X ₁ and X _{2 to} be combined is set as the control target. It is desirable to set it to be approximately equal to the rise time τ (time constant of the control target) or longer than the rise time τ. Here, the rising time τ of the controlled object means the time from when the output exceeds 10% until it reaches 90% when an input signal of a certain level is input to the controlled object, as shown in FIG. is doing. Here, by setting the maximum duration of at least one M-sequence signal to be approximately equal to or longer than the rise time τ of the control target, the control target is sufficiently responsive to the input signal. The output signal can be measured. Thereby, it is possible to ensure the estimation accuracy particularly in the low frequency region.

Here, in order to adjust the maximum duration according to the rise time of the controlled object, it is conceivable to simply increase or decrease the number n of shift registers. However, as described above, the number N of data of the M-sequence signal is N = 2 ⁿ −1. Therefore, if the number of shift registers is greatly increased, the number of data of the M-sequence signal significantly increases and the measurement time is greatly increased. Resulting in. Therefore, it is necessary to set the number of shift registers n so that the number N of data does not become too large, and adjust the length of the sampling period as will be described later.

Therefore, first, for one M-sequence signal (here, the first M-sequence signal X ₁ ), the maximum duration (sampling period T ₁ × number of shift registers n ₁ ) is about the same as the rise time of the control target, Alternatively, the shift register number n ₁ and the sampling period T ₁ are set so as to be longer. Then, as described above, as estimated erroneous by dipping generated in the first of the power spectral density function of the M series signal X ₁ is not performed, the second M-sequence signal X ₂ sampling period T ₂ the It is set to be different from the sampling period T ₁ of one M-sequence signal. Here, the first sampling period T ₁ of the M series signal X ₁ is set in consideration of the rise time of the controlled object. In other words, in order to ensure the estimation accuracy of the low frequency range of the controlled object, the sampling period T ₁ of the first M-sequence signal X ₁ is set longer. Therefore, the sampling period T ₂ of the second M-sequence signal is desirably set shorter to than the sampling period T ₁ of the first M-sequence signal X _1. Thus, the sampling period T ₂ of the second M-sequence signal X _2, by setting shorter than the sampling period T ₁ of the first M-sequence signal X _1, first, second M-sequence signal X It is possible to prevent a dip from occurring in the low frequency region of the power spectral density function of the M-sequence signal X generated by combining ₁ and X ₂ by the above method.

At this time, the shift register number n ₁ of the first M-sequence signal X _1, when the shift register number n ₂ of the second M-sequence signal X ₂ in the same period of the second M-sequence signal X ₂ is shorter than the first period of the M series signal X _1. Therefore, in order to prevent a large difference between the periods of the first and second M-sequence signals, the shift register number n ₂ of the _second M-sequence signal X ₂ is shifted by the shift of the first M-sequence signal X ₁ . it may be set larger than the register number n _1. At this time, as shown in Equation 10 may be set so that the maximum duration of the first M-sequence signal X ₁ becomes shorter than the maximum duration of the second M-sequence signal X _2. That is, the number n ₂ of shift registers for the second M-sequence signal X ₂ may be set within the range of Equation 11. Thus, while set to the maximum duration of the first M-sequence signal X ₁ becomes shorter than the maximum duration of the second M-sequence signal X _2, the period of the first, second M-sequence signal Large differences can be avoided.

Alternatively, the parameters of the first and second M-sequence signals may be determined as follows. As described above, first, for one M-sequence signal (here, the first M-sequence signal X ₁ ), the maximum duration (sampling period T ₁ × number of shift registers n ₁ ) is the same as the rise time of the controlled object. The number of shift registers n ₁ and the sampling period T ₁ are set so as to be about or longer. Next, the sampling period T _{2 of} the second M-sequence signal and the number of shift registers n ₂ are set to dip in a predetermined frequency band (for example, operating frequency band) of the power spectral density function of the synthesized M-sequence signal. Choose not to occur. In this case, for various combinations of the sampling period T ₂ and the number of shift registers n ₂ , the power spectrum density function of the synthesized M-sequence signal is repeatedly calculated, and the sampling period T is such that no dip occurs in a predetermined frequency band. ₂ and the combination of the number of shift registers n ₂ is searched.

Note that the number of repetitions of the first and second M-sequence signals X ₁ and X ₂ can be determined according to the degree of noise (observation noise) included in the output signal. When there is a lot of noise, an effect of averaging the influence of noise in the output signal can be expected by increasing the number of repetitions.

As described above, at least two M-sequence signals having different sampling periods are synthesized by the above-described first or second synthesis method to generate a new M-sequence signal, and this is used as an input signal to be controlled. Thus, it is possible to eliminate erroneous estimation caused by the input signal and to accurately estimate the frequency characteristic of the control target in a desired frequency band. However, the present invention is not limited to the above-described embodiments. In the above description, in the first synthesis method, after the first M-sequence signal x ₁ (t) is completely output, the second M-sequence signal x ₂ (t) is output. The time series for outputting the second M-sequence signal can be arbitrarily set. For example, after a part of the first M-sequence signal x1 (t) is output for a certain time, the second M-sequence signal x ₂ (t) is output, and then the first M-sequence signal x ₁ (t ) May be output.

Further, when the first and second M-sequence signals x ₁ (t) and x ₂ (t) having different lengths are synthesized by the second synthesis method, in the above description, the longer M-sequence signal is converted into the longer M-sequence signal. In addition, a zero-value signal is added to the shorter M-sequence signal. However, it is not always necessary to add a zero-value signal. For example, the shorter M-sequence signal may be repeated until the signal becomes the same length as the longer M-sequence signal.

  In the first synthesis method described above, the two M-sequence signals are synthesized so that they do not overlap in time, and in the second synthesis method, the shorter M-sequence signal is temporally combined. The synthesis was performed so as to completely overlap the longer M-sequence signal. However, the present invention is not limited to this. For example, a part of one M-sequence signal and a part of the other M-sequence signal may be combined so as to overlap in time. That is, the synthesized M-sequence signal includes a portion that outputs only one M-sequence signal, a portion that outputs only the other M-sequence signal, and a portion that outputs a signal obtained by superimposing both M-sequence signals. You may have.

  In the above description, when two or more M-sequence signals are combined, the amplitude of each M-sequence signal may be adjusted so that the combined M-sequence signal does not exceed a predetermined signal level.

  In the above description, the M-sequence signal generator 100 is shown as the mechanism for generating the M-sequence signal, but the present application is not limited to this. For example, the pulse generation circuit may be integrated into the M-sequence signal generation device or may be formed as a separate body. Further, the M-sequence signal generator is not limited to the one composed of the delay calculator as described above, and a known M-sequence signal generator can be used. Further, the control target is not limited to the above-described filter, and the present invention can be applied to any control target.

  In the above-described system identification device 501 (502), the measurement device 120 and the M-sequence signal synthesis device 601 (602) are provided independently, but the present invention is not limited to this, and the measurement device 120 is not limited thereto. And the M-sequence signal synthesizer 601 (602) may be provided integrally.

  By using the system identification method and the system identification device of the present invention, a control system that drives components such as stages included in industrial precision equipment such as machine tools and inspection devices at high speed and easily can be easily constructed. Can do.

DESCRIPTION OF SYMBOLS 51 Pulse generation circuit 52 Delay calculator 54 Exclusive OR calculator 100 M series signal generator 101 1st M series signal output part 102 2nd M series signal output part 103 Switching mechanism 104 Signal adder 120 Measuring apparatus 200 Filter 500, 501, 502 System identification device 601 First M-sequence signal synthesizer 602 Second M-sequence signal synthesizer

Claims (7)

A system identification method for estimating frequency characteristics of a controlled object,
A first M-sequence signal characterized by a _first sampling period T ₁ and a first shift register number n _{1; a} second sampling period T ₂ different from the _first sampling period T ₁ ; Combining a second M-sequence signal characterized by _two shift register numbers n ₂ to generate a third M-sequence signal;
Inputting a third M-sequence signal to the controlled object and measuring an output signal from the controlled object;
A system identification method comprising: estimating a frequency characteristic of the control target using a third M-sequence signal input to the control target and a measured output signal from the control target.   The system identification method according to claim 1, wherein the first M-sequence signal and the second M-sequence signal are combined while being shifted in time so as not to overlap with each other to generate a third M-sequence signal.   The first M-sequence signal and the second M-sequence signal are added together in the state where at least a part of the first M-sequence signal and the second M-sequence signal overlap each other in time. The system identification method according to claim 1, wherein an M-sequence signal is generated. A product T ₁ × n ₁ of the first sampling period T ₁ of the first M-sequence signal and the first shift register number n ₁ is set to a length equal to or longer than the rise time τ of the control target,
A second sampling period T _2, the system identification method as claimed in any one of claims 1 to 3 is set shorter than the first sampling period T _1. The second shift register number n ₂ is
n ₁ <n ₂ <log ₂ {(2 ⁿ¹ −1) × (T ₁ / T ₂ ) +1}
The system identification method according to claim 4, wherein the system identification range is set to a range that satisfies the above. A product T ₁ × n ₁ of the first sampling period T ₁ of the first M-sequence signal and the first shift register number n ₁ is set to a length equal to or longer than the rise time τ of the control target,
The second sampling period T ₂ of the second M-sequence signal and the second shift register number n ₂ are set to values that do not cause a dip in a predetermined frequency region of the power spectrum density function of the third M-sequence signal. The system identification method as described in any one of Claims 1-5 to set. A system identification device for estimating frequency characteristics of a controlled object,
A first M-sequence signal output unit that outputs a first M-sequence signal characterized by a _first sampling period T ₁ and a first shift register number n ₁ ;
A second M-sequence signal output unit that outputs a second M-sequence signal characterized by a _second sampling cycle T ₂ different from the _first sampling cycle T ₁ and a second shift register number n ₂ ;
A third M-sequence signal output unit that combines the first and second M-sequence signals output from the first and second M-sequence signal output units, respectively, and outputs a third M-sequence signal;
A system identification apparatus comprising: a measurement unit that measures an output signal from the control target, which is obtained by inputting a third M-sequence signal to the control target.

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