WO1999051941A1

WO1999051941A1 - Method for forming an average value

Info

Publication number: WO1999051941A1
Application number: PCT/DE1999/000944
Authority: WO
Inventors: Wilfried Meyer
Original assignee: Mannesmann Rexroth Ag
Priority date: 1998-04-01
Filing date: 1999-03-26
Publication date: 1999-10-14
Also published as: DE19913753A1

Abstract

The invention relates to a method for forming the average value of a number of consecutive sampling values of a temporally variable signal. According to said method, a number of sampling values are combined with an appropriate calculation specification. In the case of periodical signals, the average value is usually calculated over an entire period of oscillation of the ground wave of the periodical signal. In the case of periodical signal variations, where the frequency of the ground oscillation can have different values between an upper limit and a lower limit, the time between two sampling operations is chosen to the effect that for the highest frequency, the minimum number of sampling values required within a period of the ground oscillation in order to calculate the average are stored.

Description

description

Process for forming the mean

The invention relates to a method for forming the mean value of a number of temporally successive samples of a time-varying signal, in which the mean value is calculated by mathematically linking a number of successive samples, according to the preamble of claim 1.

Averages generally serve to characterize a set of numbers. Here, for. B. differentiate between the arithmetic, the geometric and the quadratic mean. To form the arithmetic mean, the individual numbers are added and the sum divided by the number of added numbers. To form the geometric mean, the individual numbers are multiplied together and the root corresponding to the number of multiplied numbers is taken from the product. In order to form the quadratic mean, the squares of the numbers are added, the square root is taken from the sum and the result is divided by the number of numbers. to

Characterization of periodic waveforms, e.g. B. of electrical voltages or currents, in particular the temporally linear mean and the effective value are used. The linear mean in time corresponds to the arithmetic mean, and the effective value corresponds to the root mean square. For the formation of the mean value of a time-varying signal by means of a digital computing device, a predetermined number of temporally successive sample values of this signal are linked to one another by the digital computing device in accordance with a calculation rule. The calculated mean value is only output by the computing device when the predetermined number of samples has been taken into account when calculating the mean value. This ensures that a sufficient number of samples has always been taken into account for the calculation of the mean value. The greater the number of samples used for averaging, the better the mean is smoothed. However, an increase in the number of sample values used for averaging inevitably leads to an increase in the time period after which a new average value is output again if the time intervals between the sampling times are constant.

DE 43 37 388 AI discloses a method for averaging according to the preamble of claim 1. Temperature values determined at constant time intervals within a 24-hour period are added and the sum is divided by the number of added temperature values. A new updated mean value is available at the time intervals specified by the measurement value acquisition.

To characterize generally periodic signal curves, the mean value is usually formed in each case over a period of the fundamental wave of the signal curve. Should be the mean of periodic waveforms In which the frequency of the fundamental oscillation is not constant, but can assume values of different sizes between two limit values, additional demands are placed on the averaging. In the area of high frequencies of the fundamental wave, a sufficiently large number of samples must be acquired within one period. In contrast, in the range of low frequencies of the fundamental wave, short times between two sampling processes lead to a large memory requirement for the sample values occurring within one period of the fundamental wave.

DE 39 28 083 C2 discloses a circuit for measuring a measured variable derived from the root mean square of an AC voltage, in particular the effective value of an AC voltage. In order to allow a wide frequency range for the fundamental oscillation, the AC voltage to be measured is divided into a low-frequency and a higher-frequency voltage component. The low-frequency voltage component is digitally squared after digitization. The higher-frequency voltage component is squared using an analog squaring circuit and then digitized. The two digital values are added and the desired measured variable is calculated from the sum by averaging.

The invention is based on the object of specifying a method of the type mentioned at the outset in which a new mean value is available in short time intervals and for the averaging of time-varying ones periodic waveforms with a frequency of the fundamental oscillating between two limit values is suitable.

This object is achieved by the features characterized in claim 1. The method enables a moving averaging for periodic signal curves, in which the frequency of the fundamental wave can assume different values between two limit values, with a small memory requirement.

Advantageous developments of the invention are characterized in the subclaims. The subclaims relate to a further reduction in the memory requirement, the storage of the sample values and the use of the method according to the invention.

The invention is explained in greater detail below with its further details using an exemplary embodiment shown in the drawings. Show it

Figure 1 is a block diagram of a device for forming the average of a number of prematurely successive samples and

Figure 2 shows the course of a time-varying, periodic signal.

FIG. 1 shows the block diagram of an apparatus for forming the mean value of a time-varying signal according to the invention. In this embodiment serves a voltage u (t) as a time-varying signal. The voltage u (t) has a generally periodic course, ie a fundamental oscillation U _Q (t) is superimposed on oscillations of a higher frequency. The time course of the voltage u (t) is shown on an enlarged scale in FIG. A scanning device 20 samples the amplitude of the voltage u (t) at equal time intervals. An analog / digital converter 21 converts the sample values present in analog form into corresponding digital values and transfers them to a first memory 22. The second memory 23 is followed by a second memory 23 serving as a buffer. In the exemplary embodiment under consideration, for reasons of clarity, the memories 22 and 23 each have only eight memory locations, each of which is designated by M1 to M8. In practice, however, the number of storage locations provided for storing the sample values is considerably larger. It is in the order of 4000 storage locations. A digital computing device 24, e.g. B. a microcontroller, calculates the mean value from the numbers stored in the memory locations of the memory 23 by mathematically linking these numbers using an algorithm for calculating the mean value. For the description of the exemplary embodiment, it is assumed that the effective value of the voltage u (t) is to be formed. In this case, the squares of the samples are added, the roots are taken from the sum and the result is divided by the number of samples used for averaging. The mean value of the voltage u (t) is still present in digital form at an output 25 of the computing device 24. The mean can either be processed further in digital form or in in a manner known per se can be converted into an analog value. A first control line 26 leads from the computing device 24 to the scanning device 20. Two further control lines 27 and 28 lead to the memories 22 and 23, respectively.

FIG. 2 shows the time profile of the voltage u (t) over two periods, which are denoted by T1 and T2. The voltage u (t) consists of a fundamental wave u ₀ (t) shown in dashed lines and this superimposed vibrations of higher frequency. Since the voltage u (t) has a periodic course, it is necessary to determine at least one period of the fundamental wave for the formation of the effective value. The amplitude of the voltage u (t) is detected at times t ₀ to t ₁₇ . The corresponding samples are designated A _Q to A ₁₇ . The period between two sampling times is constant, it is referred to as Δt below.

At the end of the period T1, that is to say between the times t and t ₉ , the memory locations M1 to M8 in the memory 22 contain the samples A- _j _ to A ₈ . The contents of the memories Ml to M8 of the memory 22 are transferred to the memories Ml to M8 of the memory 23, the memory locations that Ml to M8 of the memory 23 is also included after the samples A to Aη_. ₈ From the values contained in the memory 23, the computing device 24 calculates the effective value at the time t ₈ , which takes into account the sample values of the period T1, that is to say the sample values A 1 to A ₈ . After the sample values Aη_ to A _{8 have been} buffered in the memory 23, the sample values A ₂ to A _{8 are} shifted from the memory locations M2 to M8 of the memory 22 to the memory locations M1 to M7. In this case, the value stored in memory location Ml sample A _j _ from the sample A ₂ is overwritten. The contents of the storage locations M3 to M8 are shifted to the storage locations M2 to M7 in a corresponding manner. The memory location M8 is then available for storing a new sample value. The sample values A - _j _ to A ₈ provided for calculating the effective value at time t are still available in memory 23. At time tg, the computing device 24 causes the scanning device 20 to scan the voltage u (t) again via the control line 26. The sampled voltage value is converted into the digital value A _g and in that

Storage space M8 of the memory 22 is stored. The memory locations Ml to M8 of the memory 22 now contain the samples A ₂ to Ag, that is to say eight samples again, which cover the period of a period of the fundamental oscillation of the voltage u (t) up to the time tg. The contents of the memory locations M1 to M8 of the memory 22 are now transferred to the corresponding memory locations of the memory 23 by a control command from the computing device 24. As described above, the computing device 24 calculates a new effective value from the values transferred to the memory 23. This effective value is already a sampling time Δt after the previous effective value.

After the samples A ₂ to Ag have been buffered in the memory 23, the samples A ₈ to A ₉ shifted from memory locations M2 to M8 of memory 22 to memory locations M1 to M7. The sample value A ₂ stored in the memory location M1 is overwritten by the sample value A ₃ . The contents of the storage locations M3 to M8 are shifted to the storage locations M2 to M7 in a corresponding manner. The memory location M8 is then available again for storing a new sample value. The sample values A ₂ to Ag provided for the calculation of the effective value are still available in the memory 23. At time t ^ o, the computing device 24 again causes the scanning device 20 to scan the voltage u (t). The sampled voltage value is converted into a digital value A ₁₀ and stored in the memory location M8. The memory locations M1 to M8 of the memory 22 now contain the sample values A3 to A _] _ _Q , that is to say eight sample values again, which cover the period of a period of the fundamental oscillation of the voltage u (t) from the time t ₃ to the time t ₁₀ . The contents of the memory locations M1 to M8 of the memory 22 are transferred to the corresponding memory locations of the memory 23 by a control command from the computing device 24. The calculating means calculates from the transmitted values in the memory 23, 24 - as described above ^'- a new RMS value. This RMS value is also already a sampling time Δt after the previous RMS value. This means that a new effective value of the voltage u (t) is present after each sampling time.

If the effective value is calculated in each case before the sample values are shifted in the memory 22, the memory 23 can be omitted. There is no need to shift the sample values in the memory 22 if the new sample value overwrites the respectively oldest sample value.

With each scan, the new sample replaces the oldest sample in memory. The other sample values are retained in the memory, so that the mean value is calculated on the basis of the latest sample values.

If the mean value of signals with a periodic course is to be formed, in which the frequency of the fundamental wave u ₀ (t) can assume different values within a range between two limit values fomin ^{un <} ^ ^ Omax, it must be ensured that at the highest frequency oma ' ^a l ^so if the period is minimum, a minimum number N _mj _ _n is from necessary for the averaging of samples are available. The relationship T (f _0max ) applies to the relationship between the period T (f _0max ) of the fundamental _wave with the greatest frequency fomax '^ ^{er time} it ^t between two sampling processes and the minimum number N _mj _ _n of the sampling values required for _averaging. = N _min x Δt (equation 1), where the period T (f _0max ) is the reciprocal of the frequency ^ Omax i ^st - If two of these quantities are given, the third quantity can be calculated from them. After the time .DELTA.t between two sampling processes for the greatest frequency o _{maχ is} fixed, the number of memory locations required for storing the sample values of a period increases with decreasing frequency of the fundamental _wave . Who are for 10

the number of memory spaces resulting in frequency is _hereinafter referred to as N _maχ . For the relationship between the period T (f _0m _ _n) of the fundamental frequency with the lowest frequency fomin '^ he ^Ze it ^At between two sample - operations and facilities required for the storage of samples Number of memory slots N _max applies the relation ^{τ (f} 0min ⁾ = ^N max ^{x Δt (} equation 2 ⁾ , the period T (f _0m i _n ) being the reciprocal of the frequency ^r _θ min i ^st • After the time Δt between two sampling processes has been determined in accordance with equation 1, the result is required number of memory slots N _max from the lowest frequency fo in ^{un <^} ^ he ^Ze it ^.DELTA.t •

Assuming a frequency range of the fundamental frequency of fomin = 1 Hz to fo ax ^{= 10} ° ^{Hz unc} ^ ^e i ^ner minimum number of N _mj _ _n = 40 samples at omax ⁼ 100 Hz made, resulting from the equation 1, the time Δt between two scans at 250 μs. For fo in = 1 Hz then at least N _maχ = 4000 memory locations are required according to equation 2. With a frequency range of the fundamental wave of z. B. ^f 0min ⁼ ° » ^{1 Hz} bi ^s ^ Omax ^{= 10} ° ^{Hz unc of a} minimum number of N _{m; j} _ _n = 40 samples with omax ^{= 1 (} ^ Hz, Equation 1 shows the time between two samples to Δt = 250 μis For fo i _n ⁼ ° ' ^{1 Hz s} ^ - ^{n <} ^ then at least N _maχ = 40,000 memory locations are required according to equation 2. In this example, more samples are taken for small frequencies during a period of the fundamental wave than actually According to a preferred development of the method according to the invention, for a 11

Partial range of the frequencies of the fundamental vibration, e.g. B. from fornin = 0.1 Hz to f ₀ * = 1 Hz, the time between two scanning processes compared to the time intended for the upper limit value o _{ma of} the frequency range Δt = 250 μs between two scanning processes by a factor of 10 to Δt * = 2 , 5 ms enlarged. If one considers the frequency f ₀ * = 1 Hz as the lower limit of the frequency range from 100 Hz to 1 Hz, then at the frequency of fg * = 1 Hz and the time Δt = 250 μs between two scanning processes 4000 memory locations are required. After increasing the time between two scanning processes to Δt * = 2.5 ms, the 4000 memory locations are sufficient up to a lower cut-off frequency, namely up to 0.1 Hz. By increasing the time between two scanning processes in the range of low frequencies of the fundamental, a lower lower limit frequency can be achieved without having to increase the number of memory locations.

If a link of a control chain or a control circuit is acted upon by a time-varying signal, which consists of a periodic basic oscillation and higher-frequency oscillations superimposed on it, the output signal of this link is also a periodic signal, which consists of a basic oscillation and higher-frequency oscillations superimposed. In this case, the frequency of the fundamental wave of the output signal is equal to the known frequency of the input signal. The frequency of the basic oscillation of the output signal therefore does not need to be determined separately from the output signal for the change in the time between the scanning processes as a function of the frequency of the basic oscillation. 12

Since an updated mean value is again available at short time intervals in the method according to the invention for forming the mean value, the multiplicative correction of a setpoint signal fed to a control chain requires, depending on the quotient of the mean value of the setpoint signal and the mean value at the end of the control chain detected actual value signal takes place, no additional damping measures to be taken. This improves the effectiveness of the corrective action. For the multiplicative correction of the setpoint signal, it is advantageous to use an algorithm known as "LMS" as an abbreviation for "least mean square" to calculate the mean values instead of calculating the effective values, which essentially evaluates the fundamental wave of the setpoint signal and the actual value signal.

In a corresponding manner, the effectiveness of the correction intervention is improved even with an additive correction of a setpoint signal.

Claims

13 Patent claims

1. Method for forming the average of a number of temporally successive samples of a time-varying signal,

in which the mean value is calculated by mathematically combining a number of successive samples,

- After each sampling, the mean value is calculated from the last k samples, where k is for the

Calculation of the mean value is the intended number of samples,

- With each sampling process, the new sample value replaces the oldest sample value, characterized in that in the case of a time-varying signal (u (t)), which consists of a periodic fundamental wave (u ₀ (t)) and this superimposed vibrations of higher frequency, where the frequency of the fundamental oscillation (u ₀ (t)) can assume different values between two limit values (fomin _' ^ Omax ^, the time (Δt) between two scanning processes is selected so that at the greatest frequency (fomax ^ a minimum number (N _mj _ _n ) sample values required for calculating the mean value are stored within a period of the fundamental wave.

2. The method according to claim 1, characterized in that the number of memory locations provided for the samples (N _maχ ) is at least equal to the period ( ^τ (f _θ min ^ ^ ^er fundamental _wave at the lowest frequency 14

(f _0mj _ _n ) divided by the time (Δt) between two scans.

3. The method according to claim 1 or claim 2, characterized in that the time (Δt *) between two sampling operations for frequencies of the fundamental (u ₀ (t)) between the lower limit (fomin ^ of the frequency range and one between the two Limit values ⁽ fomin '^ Omax ^ ^ ^es frequency range lying frequency (fg *) are, compared to the time provided for the upper limit value (fomax ^ ^ ^es frequency range (Δt) between two scanning processes.

4. The method according to any one of the preceding claims, characterized in that for the calculation of the

Average values provided are transferred to a buffer (23) after each sampling process.

5. The method according to any one of claims 1 to 3, characterized in that the oldest before each scanning process

Sample is deleted and the remaining samples are each shifted by one memory location, so that the second oldest sample value up to then becomes the oldest sample value, and that the new sample value is stored in the memory location (M8) which has become free during the next sampling process.

6. Use of a method according to one of the preceding claims for calculating correction values for the correction of a setpoint signal with a predetermined time 15

Course by comparing the mean value of the setpoint signal with the mean value of the actual value signal, an algorithm being used as the basis for averaging, which essentially only evaluates the proportion of the fundamental wave of the setpoint signal and the actual value signal.

7. Use of a method according to one of claims 1 to 5 for calculating correction values for a multiplicative correction of a setpoint signal with a chronologically predetermined course from the quotient formed from the mean value of the setpoint signal and the mean value of the actual value signal, with a for the averaging Algorithm is used, which essentially evaluates the proportion of the fundamental wave of the setpoint signal and the actual value signal.