DE102023210871A1 - Method and arrangement for generating a Bode diagram for a dynamic system - Google Patents

Abstract

The invention relates to a method for generating a Bode diagram (B) for a dynamic system (10), comprising the steps:
- Exciting (S1) the dynamic system (10) by means of at least one input signal (1), the at least one input signal (1) being designed as a jump signal,
- Detecting (S2) the at least one input signal (1) and at least one output signal (2),
- converting (S3) the at least one input signal (1) and the at least one output signal (2) from the time domain to the frequency domain,
- determining (S4) at least one transfer function based on the converted input signal and the converted output signal,
- determining (S5) at least one amplitude response (A) and at least one phase response (P) using the determined at least one transfer function,
- Generating (S6) the Bode diagram (B) based on the determined at least one amplitude response (A) and the determined at least one phase response (P), and a corresponding arrangement (100).

Description

The invention relates to a method for generating a Bode diagram for a dynamic system and a corresponding arrangement.

A Bode diagram is used to represent the transmission behavior of a dynamic system, such as an electric motor with a current, speed and/or position control loop. The transmission behavior is also referred to as frequency behavior. The Bode diagram usually includes two function graphs, with one function graph representing the so-called amplitude response and another function graph representing the so-called phase response depending on the frequency.

To generate a Bode diagram, the dynamic system is conventionally excited one after the other by a large number of harmonic oscillations, for example sine oscillations with a frequency in a range from 10 Hz to 5000 Hz being generated one after the other as an excitation signal. This type of excitation is also known as a sine sweep and can be generated, for example, using a signal generator. For each frequency to be examined, an excitation signal and a response signal from the dynamic system are recorded and the transmission behavior for the frequency range being examined is determined from the recorded signals.

To conventionally generate the Bode diagram, for example, a sinusoidal excitation signal, for example as a control voltage, is applied to the aforementioned electric motor of the coordinate measuring machine for each frequency to be examined, with the excitation signal and an associated response signal being recorded over a certain period of time. Since the recorded signals must have a high resolution and the signals must be recorded individually for each excited frequency, a corresponding amount of time is required to record the signals. In addition, a considerable amount of data is created, which also makes further processing of the signals more difficult. A further disadvantage of this conventional procedure is that the signal generators used for this purpose generally have difficulties in generating high excitation frequencies and thus the resolution of the Bode diagram generated decreases with increasing frequency.

The technical problem therefore arises of creating a method for generating a Bode diagram for a dynamic system and a corresponding arrangement, which enable the Bode diagram to be generated quickly and accurately in time.

• - Anregen des dynamischen Systems mittels mindestens eines Eingangssignals, wobei das mindestens eine Eingangssignal als Sprungsignal ausgebildet ist,
• - Erfassen des mindestens einen Eingangssignals und mindestens eines Ausgangssignals,
• - Konvertieren des mindestens einen Eingangssignals und des mindestens einen Ausgangssignals aus der Zeitdomäne in die Frequenzdomäne,
• - Ermitteln mindestens einer Übertragungsfunktion ausgehend von dem konvertierten Eingangssignal und dem konvertierten Ausgangssignal,
• - Bestimmen mindestens eines Amplitudengangs und mindestens eines Phasengangs mittels der ermittelten mindestens einen Übertragungsfunktion,
• - Erzeugen des Bode-Diagramms ausgehend von dem bestimmten mindestens einen Amplitudengang und dem bestimmten mindestens einen Phasengang.

A method for generating a Bode diagram for a dynamic system is proposed, comprising the steps:

• - Exciting the dynamic system by means of at least one input signal, the at least one input signal being designed as a jump signal,
• - detecting the at least one input signal and at least one output signal,
• - converting the at least one input signal and the at least one output signal from the time domain to the frequency domain,
• - determining at least one transfer function based on the converted input signal and the converted output signal,
• - determining at least one amplitude response and at least one phase response using the determined at least one transfer function,
• - Generating the Bode diagram based on the determined at least one amplitude response and the determined at least one phase response.

When exciting using a jump signal, all frequencies of the dynamic system are excited simultaneously. This means that to generate a Bode diagram it is sufficient to record only one input signal and one output signal. The captured signals contain all the information needed to generate the Bode diagram. By converting the captured signals into the frequency domain, the information contained in the captured signals can be displayed in a frequency-dependent manner. The Bode diagram generated in this way therefore requires the detection of an input signal and an output signal for the entire frequency range to be examined. This significantly reduces the time to capture the relevant signals. Because all frequencies of the dynamic system are excited simultaneously using the jump signal, the recorded data can be recorded with a correspondingly high resolution Input and output signals also have higher frequencies in the Bode diagram. This improves the resolution of the generated Bode diagram.

The dynamic system can, for example, include a drive device, in particular an electric motor, of a coordinate measuring machine or be designed as such. Alternatively or cumulatively, the dynamic system can comprise a movable part of a coordinate measuring machine, wherein a driving force for moving the movable part can be generated by the drive device.

The input signal can, for example, include the time course of an input variable of the dynamic system in the time domain. The input variable can be, for example, a control voltage of the electric motor. The input or jump signal can be designed, for example, as a square wave signal or as a Dirac pulse. In this way, the system can be stimulated in shocks or jumps. The stimulation can be done, for example, by means of a device for stimulation. The excitation device can, for example, be designed as a signal generator or include one.

The output signal can, for example, include the time course of an output variable of the dynamic system in the time domain. The output variable can be, for example, a motor current, a speed and/or angular position of an output element, for example a rotor, of the drive device. In particular, the output signal arises based on the sudden excitation explained above. Therefore the output signal can also be referred to as a step response.

The input signal and/or the output signal can be detected, for example, by means of at least one detection device. The detection device can, for example, include at least one sensor or be designed as such. The sensor can be, for example, a voltage sensor, a current sensor, a speed sensor and/or a position sensor. The input signal can in particular be detected at an input of the dynamic system, such as at a voltage connection of the drive device. The output signal can in particular be detected at an output of the dynamic system, such as in a phase line of a current-controlled drive device or on an output shaft of the electric motor. Of course, different output signals can also be selected and recorded with a corresponding detection device. The input and/or output signal can in particular be detected with a sampling rate with a value in a range from 1 kHz to 200 kHz, in particular in a range from 1 kHz to 20 kHz. This sampling rate of the input and/or output signal can ensure that the Bode diagram generated thereby has an improved resolution.

The conversion can be done, for example, using a control device. The control device can be designed, for example, as a microcontroller or integrated circuit or include one. Converting the input and output signals can be done, for example, using a Fast Fourier Transformation. Converting includes in particular that a vector with a large number of signal values is generated for the respective signal. In particular, the vector can have a signal value for each detected frequency. The signal value can, for example, be designed as a complex number that has a real part and an imaginary part. The converted signals in particular have the same number of signal values, so that for each detected frequency there is at least one pair of signal values, consisting of a converted input signal value and a converted output signal value.

bestimmt wird, um einen positiven Signalvektor zu bestimmen. Dieser umfasst also Signalwerte, die positiven Frequenzen zugeordnet sind. Um die Wertigkeit der Signalwerte im positiven Signalvektor zu erhalten, werden die entsprechenden Einträge, also z.B. die Real- und der Imaginärteile der Signalwerte, mit dem Faktor 2 multipliziert. Der erste und der letzte Eintrag vom jeweiligen Signal muss jedoch nicht zwingend mit diesem Faktor multipliziert werden. Diesem positiven Signalvektor ist also ein einseitiges, positives Frequenz-Spektrum zugeordnet, welches Frequenzen insbesondere von 0 Hz bis zur Frequenz der halben Abtastrate umfasst.In particular, the signal values of the respective signals can be generated in a so-called two-sided frequency spectrum, that is, for each positive frequency determined during the conversion, a signal value for the corresponding negative frequency, which has the same magnitude as the positive frequency but a negative sign, is also determined . In order to convert such a two-sided frequency spectrum into a so-called one-sided frequency spectrum, for example only the signal values of the positive frequencies, which usually correspond to the entries in one half of the respective signal vector, can be taken into account. For this purpose, for example, the entries of the respective signals in the entire signal vector are cut off up to an intersection limit, the intersection limit being determined, for example, using the formula $$\text{Cutting boundary}=\left(\text{complete L}\ddot{\text{a}}\text{nge of the respective signal/}2\right)+1$$

is determined to determine a positive signal vector. This therefore includes signal values that are assigned to positive frequencies. In order to obtain the significance of the signal values in the positive signal vector, the corresponding entries, for example the real and imaginary parts of the signal values, are multiplied by a factor of 2. However, the first and last entry of the respective signal does not necessarily have to be with this one factor can be multiplied. This positive signal vector is therefore assigned a one-sided, positive frequency spectrum, which includes frequencies in particular from 0 Hz to the frequency of half the sampling rate.

bestimmt werden. Die Maximalfrequenz kann z.B. vom Nutzer als Integer vorgegeben werden und somit vorbestimmt sein und kann dem Betrag der Frequenz entsprechen, bis zu welcher das Bode-Diagramm erzeugt werden soll. Dieser Betrag kann insbesondere kleiner als der Betrag der halben Abtastrate sein. Durch die Variable Ignore kann z.B. durch den Nutzer festgelegt werden, wie viele (Signalwert-)Einträge am Anfang des jeweiligen Signalvektors entfernt bzw. ignoriert werden. Die Relevanzlänge kann auf einen Integer gerundet werden. Dies erleichtert die weitere Verarbeitung. Die Relevanzlänge kann genutzt werden, um aus den jeweiligen positiven Signalvektoren solche Einträge zu extrahieren, welche von dem Index, der der Ignore-Variablen entspricht, bis zu dem Index, der der Relevanzlänge entspricht, im jeweiligen Signalvektor enthalten sind. Die restlichen Einträge können unberücksichtigt bleiben. Auf diese Weise können die konvertierten Signale zur weiteren Verarbeitung vorbereitet werden.Since a frequency of 0 Hz is usually not represented in a Bode diagram, for example the first signal value or the first two signal values can be removed in a positive signal vector. This can be done by, for example, only taking into account the relevant entries from the respective (positive) signal vectors that are assigned to frequencies greater than zero or greater than a predetermined minimum value. The number of relevant entries of a positive signal vector can be determined, for example, using the formula $$\text{Relevancel}\ddot{\text{a}}\text{nge}=\text{Cutting boundary}/\left(\text{sampling rate}/2\right)/\text{Maximum frequency}))-\text{Ignore}$$

be determined. The maximum frequency can, for example, be specified by the user as an integer and can therefore be predetermined and can correspond to the frequency up to which the Bode diagram is to be generated. This amount can in particular be smaller than the amount of half the sampling rate. Using the Ignore variable, the user can, for example, specify how many (signal value) entries are removed or ignored at the beginning of the respective signal vector. The relevance length can be rounded to an integer. This makes further processing easier. The relevance length can be used to extract from the respective positive signal vectors those entries which are contained in the respective signal vector from the index that corresponds to the ignore variable to the index that corresponds to the relevance length. The remaining entries can be ignored. In this way, the converted signals can be prepared for further processing.

ermittelt werden. G(s) kann hierbei z.B. ein Wert der Übertragungsfunktion für ein jeweiliges Signalwertepaar der konvertierten Signale / Signalvektoren sein. Y(s) entspricht hierbei einem konvertierten Ausgangssignalwert und U(s) entspricht einem konvertierten Eingangssignalwert. Die Variable s wird auch als Laplace-Variable bezeichnet und entspricht hierbei der komplexen Kreisfrequenz s = j*omega, wobei omega proportional zu der jeweils erfassten Frequenz ist. Zum Ermitteln der Übertragungsfunktion können weiter z.B. jeweils die Signalwerte des Ausgangssignalvektors durch die jeweiligen Signalwerte des Eingangssignalvektors mit dem gleichen Index dividiert werden, beispielsweise mit der Formel $$\left(\text{a}+\text{b}*\text{j}\right)/\left(\text{c}+\text{d*j}\right)=\left(\text{a*c}+\text{b*d}\right)/\left(\text{c}2+\text{d}2\right)+\text{j}*\left(\text{b*c}-\text{a*d}\right)/\left(\text{c}2+\text{d}2\right),$$

wobei a und b z.B. der Real- und Imaginärteil eines Signalwerts des Ausgangssignalvektors und c und d z.B. der Real- und Imaginärteil eines Signalwerts des Eingangssignalvektors mit dem gleichen Index sind. Um eine effiziente Division der komplexen Zahlen zu erreichen, kann z.B. zuerst der Nenner aus Formel 4 bestimmt werden. Anschließend kann geprüft werden, ob der Wert des Nenners kleiner als ein vorbekannter Schwellwert ist, um eine Division durch Null zu vermeiden. Falls der bestimmte Wert vom Nenner kleiner als der Schwellwert ist, kann das Ergebnis der Division von des vorherigen Signalwerts nochmals verwendet. Auf diese Weise wird z.B. ein vollständiger Übertragungsvektor der Übertragungsfunktion erzeugt. Die Elemente dieses ermittelten Übertragungsvektors können jeweils einen Übertragungswert für eine erfasste Frequenz repräsentieren.The transfer function can be determined by determining a ratio between the converted input and output signals, i.e. the corresponding positive signal vectors. The transfer function can be determined, for example, using the previously explained control device. For example, the transfer function can be determined using the formula $$\text{G}\left(\text{s}\right)=\text{Y}\left(\text{s}\right)/\text{U}\left(\text{s}\right)$$

be determined. G(s) can be, for example, a value of the transfer function for a respective pair of signal values of the converted signals/signal vectors. Y(s) corresponds to a converted output signal value and U(s) corresponds to a converted input signal value. The variable s is also referred to as the Laplace variable and corresponds to the complex angular frequency s = j*omega, where omega is proportional to the frequency recorded in each case. To determine the transfer function, the signal values of the output signal vector can, for example, be divided by the respective signal values of the input signal vector with the same index, for example with the formula $$\left(\text{a}+\text{b}*\text{j}\right)/\left(\text{c}+\text{d*j}\right)=\left(\text{a*c}+\text{b*d}\right)/\left(\text{c}2+\text{d}2\right)+\text{j}*\left(\text{b*c}-\text{a*d}\right)/\left(\text{c}2+\text{d}2\right),$$

where a and b are, for example, the real and imaginary parts of a signal value of the output signal vector and c and d are, for example, the real and imaginary parts of a signal value of the input signal vector with the same index. In order to achieve efficient division of the complex numbers, the denominator from Formula 4 can first be determined. It can then be checked whether the value of the denominator is smaller than a previously known threshold value in order to avoid division by zero. If the determined value of the denominator is smaller than the threshold value, the result of division from the previous signal value can be used again. In this way, for example, a complete transfer vector of the transfer function is generated. The elements of this determined transmission vector can each represent a transmission value for a detected frequency.

Determining the amplitude response and the phase response can also be done, for example, using the previously explained control device. Determining the amplitude response and the phase response may include determining a frequency vector, a phase vector and an amplitude vector.

erfolgen, wobei i jeweils ein Element des Phasenvektors ist.The phase vector can be determined in degrees, for example, by determining each element of the transfer vector of the transfer function with the arctan2. This can be done, for example, using the formula $$\text{Phase vector}\left[\text{i}\right]=\text{arctan}2(\text{G}\left(\text{Imagine}\ddot{\text{a}}\text{rpart}\left[\text{i}\right]\right),\text{G}\left(\text{Real part}\left[\text{i}\right]\right)\ast \left(180°\text{/pi}\right)$$

take place, where i is an element of the phase vector.

wobei i jeweils ein Element des Amplitudenvektors mit dem Index i ist.The amplitude vector can be determined, for example, in decibels by, for example, applying the logarithm with base 10 to each individual element of the transfer vector of the transfer function, for example using the formula $$\text{Amplitude vector}\left[\text{i}\right]=20*{\text{log}}_{10}(\text{G}(\text{Real part}\left[\text{i}\right])2+\text{G}\left(\text{Imagine}\ddot{\text{a}}\text{rpart}\left[\text{i}\right]2\right),$$

where i is an element of the amplitude vector with the index i.

wobei i jeweils ein Element des Frequenzvektors ist und Ignore wiederum der Anzahl der Einträge entspricht, welche am vom konvertierten Signal entfernt wurden (vgl. Formel 2).The frequency vector can be determined in Hertz, for example using the formula $$\text{Frequency vector}\left[\text{i}-\text{Ignore}\right]=\text{i}*(\text{Sampling rate/}\left(2*\text{Cutting boundary}\right),$$

where i is an element of the frequency vector and Ignore corresponds to the number of entries that were removed from the converted signal (see Formula 2).

The Bode diagram can be generated starting from the specific amplitude vector and the specific phase vector, for example by graphically representing or plotting the amplitude vector and the phase vector over the frequency vector. However, generating can also mean that the specific amplitude response and the specific phase response are stored in a storage device. The Bode diagram is therefore not necessarily displayed graphically.

The proposed method advantageously enables the Bode diagram for a dynamic system to be generated quickly and accurately. This can then be used, for example, to design the controller parameters of a controller.

In one embodiment, the at least one input signal and the at least one output signal are detected in a period of less than one second. This period is sufficient to capture the information needed to generate the Bode diagram. For the conventional procedure explained at the beginning, the time period for recording all relevant signals is usually between one minute and two minutes. This represents a significant and therefore advantageous reduction in the time required for recording.

In one embodiment, a time interval between stimulation of the dynamic system and detection of the at least one output signal has a value of 1 millisecond to 1000 milliseconds. In this way, the dynamic system can be given time to settle. This improves the accuracy of the generated Bode diagram.

In one embodiment, an offset is further removed from the detected at least one input signal and/or from the detected at least one output signal.

The offset can in particular be a constant component or offset. In this way, the conversion of the input and output signals can be improved, since the offset, particularly when converting using a fast Fourier transformation, can generate an undesirable noise component in the converted signal. The offset can in particular be an amplitude offset in the input signal and/or output signal. In particular, in order to remove the offset, an average value of at least a portion of the signal values of the respective detected signal can be determined. The determined mean value can then be subtracted from all signal values of the respective detected signal. The proportion of the signal values used for averaging can, for example, correspond to the first 20 signal values of the respective detected signal.

In one embodiment, the detected, at least one output signal is differentiated in time at least once. In this way, the influence of time-integrating elements, which can be part of a controlled system, on the output signal can be reduced and does not have to be taken into account separately, for example when converting the output signal from the time to the frequency domain. Through this Experience has shown that converting the output signal is made easier. However, the influence of such integrating elements can - if necessary - be taken into account when determining the amplitude and phase response, for example by adding an element-specific factor.

In one embodiment, the detected at least one input signal and/or the detected at least one output signal is smoothed using filtering. In this way, any noise in the captured signals can be smoothed out before conversion. This in turn has a beneficial effect on the Bode diagram generated. The filtering can be done, for example, by means of the control device. The filtering can, for example, include low-pass filtering. The filtering can in particular be phase-correct filtering.

• - Bestimmen eines gemittelten Eingangssignal aus mindestens zwei konvertierten Eingangssignalen und/oder,
• - Bestimmen eines gemittelten Ausgangssignals aus mindestens zwei konvertierten Ausgangssignalen,
• - Ermitteln der Übertragungsfunktion mittels des gemittelten Eingangssignals und/oder des gemittelten Ausgangssignals.

In one embodiment, the method further comprises the steps:

• - Determining an averaged input signal from at least two converted input signals and/or,
• - determining an averaged output signal from at least two converted output signals,
• - Determining the transfer function using the averaged input signal and/or the averaged output signal.

By averaging at least two converted input and output signals, the accuracy of the transfer function determined from this can be improved. Averaged input signals and/or averaged output signals can be determined from and in the form of positive signal vectors explained previously. This in turn has a beneficial effect on the quality of the Bode diagram generated. In particular, the transfer function becomes more independent of individual influences on the converted signal. For example, at least two input signals and at least two output signals can be recorded for the dynamic system. Here, properties, in particular the frequency and amplitude, of the input signal can be left constant. By repeatedly recording the relevant signals, adverse effects of the dynamic system settling on the recorded signals can be reduced and measurement errors can be reduced. Determining an averaged input signal and/or output signal can of course include converting the at least two input and/or output signals as previously explained. The converted signals or positive signal vectors determined by the conversion can in particular have the same length. In this way, averaging can be carried out in a particularly simple manner. In particular, the mean value of the signal values assigned to this index can be determined for each index of the positive input or output signal vectors. In particular, the length of the averaged input and/or output signal vector can also correspond to the respective length of the at least two input and/or output signal vectors.

In one embodiment, at least a first portion of the specific phase response and/or at least a first portion of the specific amplitude response is smoothed by means of a first filtering and at least a further portion of the specific phase response and/or at least one further portion of the specific amplitude response is smoothed by means of a further filtering . The first and further portions may be different portions that may or may not overlap. In this way, for example, noise in the phase response and/or amplitude response can be reduced and the quality of the Bode diagram generated can thus be improved. This can also be referred to as partial smoothing of the phase response and/or the amplitude response. It can happen, for example, that signal values of the phase and/or amplitude response hardly need to be smoothed at smaller frequencies such as up to 1000 Hz and, for example, strong noise occurs from 1000 Hz onwards. Such a frequency of e.g. 1000 Hz can also be referred to as a transition frequency. In such a case, for example, signal values in a phase and/or amplitude response that are assigned to frequencies smaller than the transition frequency can form the at least a first portion of the phase and/or amplitude response. Further, for example, signal values in a phase and/or amplitude vector that are assigned to frequencies greater than or equal to the transition frequency can form the at least one further portion of the phase and/or amplitude response. For example, a first low-pass average value filter with, for example, a first corner frequency can be applied to the first component and, for example, a further low-pass average value filter with a further corner frequency can be applied to the further component. The first corner frequency can be higher than the further corner frequency. In this way, for example, the first part is smoothed less than the other part. Of course, a large number of components of the phase response and/or the amplitude response can also be smoothed, each with different degrees of filtering, in order to obtain a particularly smooth transition between the differently filtered components.

1. (1) Ein Vektorfenster mit n Elementen kann erstellt werden, wobei die Anzahl n kleiner ist als die Anzahl der Elemente des Phasenvektors;
2. (2) Ein erstes Element des Phasenvektors wird in alle n Elemente des Vektorfensters eingetragen;
3. (3) Eine phasenvektorspezifische Zählvariable i und eine vektorfensterspezifische Zählvariable j wird jeweils mit dem Wert 1 initialisiert,
4. (4) Es wird ein i-ter Mittelwert für die n aktuellen Elemente des Vektorfensters bestimmt;
5. (5) Weiter kann eine i-te Differenz zwischen dem bestimmten i-ten Mittelwert und dem i+1-ten Element des Phasenvektors bestimmt werden;
6. (6) Das i+1-te Element des Phasenvektors kann um einen vorbekannten Korrekturfaktor, beispielsweise um +360° oder um -360°, korrigiert werden, wenn die bestimmte i-te Differenz größer als ein vorbekannter Schwellwert ist; ist die im Schritt (5) bestimmte Differenz z.B. negativ, so kann der Korrekturfaktor ein negatives Vorzeichen aufweisen, ist die im Schritt (5) bestimmte Differenz z.B. negativ, so kann der Korrekturfaktor ein positives Vorzeichen aufweisen;
7. (7) Das i+1-te und gegebenenfalls korrigierte Element kann in das j+1-te Element des Vektorfensters eingetragen werden und das an dieser Stelle bis zu diesem Zeitpunkt eingetragene Element ersetzen; erreicht die vektorfensterspezifische Zählvariable j den Wert der n, so kann als Wert j+1 der Wert 1 gesetzt werden;
8. (8) Die Zählvariablen i, j können inkrementiert werden, insbesondere um den Wert 1; hat die vektorspezifische Zählvariable den Wert n, so kann diese auf den Wert 1 gesetzt werden,
9. (9) Die Schritte (4) bis (8) können wiederholt werden, bis jeder Signalwert des Phasenvektors einmal in das Vektorfenster eingetragen wurde und somit gegebenenfalls korrigiert werden konnte.

In one embodiment, signal values of the phase response are corrected using a moving average method. In this way, for example, disadvantageous phase jumps in the phase response can be corrected and thus the accuracy of the Bode diagram generated can be improved. The phase response can, for example, have N signal values, whereby the signal values can correspond, for example, to the entries in the phase vector explained at the beginning. To correct the phase response, the following averaging steps can be carried out using a moving average method:

1. (1) A vector window with n elements can be created, where the number n is smaller than the number of elements of the phase vector;
2. (2) A first element of the phase vector is entered into all n elements of the vector window;
3. (3) A phase vector-specific counting variable i and a vector window-specific counting variable j are each initialized with the value 1,
4. (4) An ith mean value is determined for the n current elements of the vector window;
5. (5) Furthermore, an i-th difference between the determined i-th mean value and the i+1-th element of the phase vector can be determined;
6. (6) The i+1th element of the phase vector can be corrected by a previously known correction factor, for example by +360° or by -360°, if the determined ith difference is greater than a previously known threshold value; if the difference determined in step (5) is, for example, negative, then the correction factor can have a negative sign; if the difference determined in step (5) is, for example, negative, then the correction factor can have a positive sign;
7. (7) The i+1-th and, if necessary, corrected element can be entered into the j+1-th element of the vector window and replace the element entered at this point up to this point in time; If the vector window-specific counting variable j reaches the value of n, the value 1 can be set as the value j+1;
8. (8) The counting variables i, j can be incremented, in particular by the value 1; If the vector-specific counting variable has the value n, it can be set to the value 1,
9. (9) Steps (4) to (8) can be repeated until each signal value of the phase vector has been entered once into the vector window and can therefore be corrected if necessary.

• - mindestens eine Einrichtung zur Anregung des mindestens einen dynamischen Systems,
• - mindestens eine Erfassungseinrichtung zur Erfassung mindestens eines Eingangssignals und mindestens eines Ausgangssignals,
• - mindestens eine Steuereinrichtung zur Verarbeitung der erfassten Signale,

wobei die Anordnung dazu ausgebildet ist, ein Verfahren gemäß einer in dieser Offenbarung beschriebenen Ausführungsform auszuführen. Die Anordnung kann auch das dynamische System oder Elemente davon umfassen.Also proposed is an arrangement for generating a Bode diagram for a dynamic system, comprising:

• - at least one device for stimulating the at least one dynamic system,
• - at least one detection device for detecting at least one input signal and at least one output signal,
• - at least one control device for processing the detected signals,

wherein the arrangement is designed to carry out a method according to an embodiment described in this disclosure. The arrangement can also include the dynamic system or elements thereof.

The advantages and technical effects mentioned for the method in this disclosure also apply in particular to the proposed arrangement. The arrangement for generating a Bode diagram for a dynamic system can in particular be designed to carry out one, several or all steps of the method described in this disclosure.

• 1 eine schematische Darstellung einer Anordnung zur Erzeugung eines Bode-Diagramms für ein dynamisches System,
• 2 eine Flussdiagramm eines Verfahrens zur Erzeugung eines Bode-Diagramms für ein dynamisches System,
• 3-A eine schematische Darstellung eines Bode-Diagramms, welches gemäß dem Stand der Technik bestimmt wurde, und
• 3-B eine schematische Darstellung eines Bode-Diagramms, welches gemäß einer Ausführungsform eines erfindungsgemäßen Verfahrens bestimmt wurde.

The invention is explained in more detail using exemplary embodiments. The figures show:

• 1 a schematic representation of an arrangement for generating a Bode diagram for a dynamic system,
• 2 a flowchart of a method for generating a Bode diagram for a dynamic system,
• 3-A a schematic representation of a Bode diagram, which was determined according to the prior art, and
• 3-B a schematic representation of a Bode diagram, which was determined according to an embodiment of a method according to the invention.

Below, the same reference numbers designate elements with the same or similar technical features.

1 shows an embodiment of an arrangement 100 for generating a Bode diagram B for a dynamic system 10.

The arrangement 100 includes a device 20 for stimulating the dynamic system 10. The dynamic system 10 includes an electric motor, which forms a drive device for generating a driving force for the movement of a movable part of a coordinate measuring machine. The device 20 for excitation can be designed, for example, as a signal generator. The device 20 for excitation generates, for example, a control voltage S, which is present as a sudden square-wave voltage at an input E of the dynamic system 10. The time course of this control voltage S can be referred to as input signal 1.

To detect the input signal 1, a detection device 30 designed as a voltmeter is arranged, for example, at the input E of the dynamic system 10. The input signal 1 is suitable for exciting the dynamic system 10 with a variety of frequencies simultaneously. The arrangement 100 includes the detection device 30.

As a result of the excitation using the input signal 1, an output signal 2 can be output, for example, at an output G of the dynamic system. The output signal 2 can, for example, be a time course of a speed D of a shaft (in 1 marked by a double arrow) of the dynamic system 10 designed as an electric motor.

To detect the output signal 2, a detection device 31 designed, for example, as a speed sensor is arranged at the output G of the dynamic system 10. The arrangement 100 includes the detection device 30, 31.

The arrangement 100 further comprises a control device 40 designed, for example, as a microcontroller. The detected input signal 1 and the detected output signal 2 can be transmitted from the detection devices 30, 31 to the control device 40. Furthermore, the control device 40 can control the device 20 explained at the beginning for excitation, for example to control the generation of the input signal 1.

Furthermore, the control device 40 is designed to convert the detected input signal 1 and the detected output signal 2 from the time domain to the frequency domain and, based on the converted signals 1, 2, to generate a Bode diagram B with an amplitude response A and a phase response P. For this purpose, as explained above, the control device can generate a positive input signal vector and a positive output signal vector, the entries of which are assigned to complex numbers and frequencies greater than zero.

The arrangement 100 is thus designed to carry out a method according to an embodiment described in this disclosure.

2 shows an embodiment of a method for generating a Bode diagram B for a dynamic system 10 (cf. 1 ).

In a step S1, the dynamic system 10 is excited by means of an input signal 1. The input signal 1 is designed as a jump signal and is generated, for example, by means of a device 20 designed as a signal generator for excitation (cf. 1 ). The input signal 1 can stimulate all frequencies of the dynamic system 10 simultaneously.

In a step S2, the input signal 1 and an output signal 2 of the dynamic system 10 are detected, for example by means of detection devices 30, 31, and transmitted to a control device 40 for further processing (cf. 1 ).

In a step S3, the detected input signal 1 and the detected output signal 2 are converted from the time domain to the frequency domain, for example by means of a fast Fourier transformation. By the By converting the captured signals 1, 2 into the frequency domain, the information contained in the captured signals 1, 2 can be displayed in a frequency-dependent manner.

In a step S4, a transfer function is determined based on the converted input signal and the converted output signal. This can be done, for example, by means of the control device 40 (cf. 1 ). The transfer function indicates, for example, a ratio of the converted output signal to the converted input signal, in particular a ratio of entries in a positive signal input vector and a positive signal output vector, which are assigned with the same index.

In a step S5, an amplitude response A and a phase response P are determined. This is done based on the determined transfer function and can be carried out, for example, by the control device 40 (cf. 1 ).

In a step S6, the Bode diagram B is generated based on the specific amplitude response A and the specific phase response P. To generate the Bode diagram B, it is therefore sufficient to record only an input signal 1 and an output signal 2 (cf. 1 ). The captured signals 1, 2 contain all the information required to generate the Bode diagram B. This significantly reduces the time to capture the relevant signals.

3-A shows a Bode diagram B, which was determined using a method explained below according to the prior art. The Bode diagram B includes a diagram which represents the phase response P for a dynamic system 10 over logarithmically plotted frequency values f. The Bode diagram B can be generated, for example, by excitation using a large number of sinusoidal excitation signals. Since the input and output signals must be recorded individually for each excited frequency, a corresponding amount of time is required to record the signals. In addition, a considerable amount of data is created, which also makes further processing of the signals more difficult. A further disadvantage of this approach according to the prior art is that the resolution of the generated Bode diagram B decreases with increasing frequency. This is in 3-A For example, this can be seen from the fact that the signal values W _A and W _P of the amplitude response A and the phase response P are further apart from one another as the frequency f increases.

3-B On the other hand, shows a Bode diagram B, which according to the in 2 The method shown was determined, whereby it can be seen that the Bode diagram B has a uniform resolution of the signal values W _A and W _P of the amplitude response A and the phase response P. The resolution of the Bode diagram B is therefore improved compared to the prior art (cf. 3-A ). This is due in particular to the fact that all frequencies of the dynamic system 10 are excited simultaneously by means of the jump-like input signal 1, which enables the Bode diagram B to be determined more quickly in time. With a correspondingly high sampling rate of the detected input signal 1 and the detected output signal 2, higher frequencies in the Bode diagram B can also be determined in a simple manner with high resolution.

Reference symbol list

1

Input signal

2

Output signal

10

dynamic system

20

Facility for stimulation

30

Detection device for detecting the input signal

31

Detection device for detecting the output signal

40

Control device

100

arrangement

A

Amplitude response

b

Bode diagram

E

Entrance

f

frequency

G

Exit

P

Phase response

S

Control voltage

S1

Stimulating step

S2

Step of capturing

S3

Converting step

S4

Step of determining

S5

Step of determining

S6

Step of creation

WA

Value of the amplitude response

WP

Value of the phase response

Claims (10)

Method for generating a Bode diagram (B) for a dynamic system (10), comprising the steps: - Exciting (S1) the dynamic system (10) by means of at least one input signal (1), the at least one input signal (1) being designed as a jump signal, - Detecting (S2) the at least one input signal (1) and at least one output signal (2), - converting (S3) the at least one input signal (1) and the at least one output signal (2) from the time domain to the frequency domain, - determining (S4) at least one transfer function based on the converted input signal and the converted output signal, - determining (S5) at least one amplitude response (A) and at least one phase response (P) using the determined at least one transfer function, - Generate (S6) the Bode diagram (B) based on the determined at least one amplitude response (A) and the determined at least one phase response (P). Procedure according to Claim 1 , characterized in that the detection (S2) of the at least one input signal (1) and the at least one output signal (2) takes place in a period of less than one second. Method according to one of the preceding claims, characterized in that a time interval between excitation (S1) of the dynamic system (10) and detection of the at least one output signal (2) has a value of 1 millisecond to 1000 milliseconds. Method according to one of the preceding claims, characterized in that an offset is further removed from the detected at least one input signal (1) and/or from the detected at least one output signal (2). Method according to one of the preceding claims, characterized in that the detected, at least one output signal (2) is differentiated in time at least once. Method according to one of the preceding claims, characterized in that the detected at least one input signal (1) and/or the detected at least one output signal (2) is smoothed by means of filtering. Method according to one of the preceding claims, characterized in that the method further comprises the steps: - determining an averaged input signal from at least two converted input signals, - determining an averaged output signal from at least two converted output signals, - determining the transfer function using the averaged input signal and the averaged output signal. Method according to one of the preceding claims, characterized in that at least a first portion of the specific phase response (P) and/or at least a first portion of the specific amplitude response (A) is smoothed by means of a first filtering and at least a further portion of the specific phase response (P ) and/or at least a further portion of the specific amplitude response (A) is smoothed by means of further filtering. Method according to one of the preceding claims, characterized in that signal values (W _P ) of the phase response (P) are corrected using a moving average method. Arrangement (100) for generating a Bode diagram (B) for a dynamic system (10), comprising: - at least one device (20) for exciting the at least one dynamic system (10), - at least one detection device (30, 31) for detecting at least one input signal (1) and at least one output signal (2), - at least one control device (40) for processing the detected signals (1, 2), the arrangement (100) being designed to implement a method according to one of Claims 1 until 9 to carry out.

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