DE102021113633A1 - Method for determining the angle of rotation and speed of one or more rotors - Google Patents

Abstract

Method for determining the angle of rotation (cp) and speed (ω) of one or more rotors (2, 3), each of which is rotated by a drive (15) about a rotor axis (6) relative to a stator (10), with a reference rotational position (φref) of each rotor (2, 3) is detected by at least one sensor (9) and the time of this detection is recorded as the detection time of the respective rotor (2, 3), a system-theoretical model (Σd) of each drive (15) and each rotor (2, 3) comprehensive system (13) based estimator (14) is provided, to which the detection time of each rotor (2, 3) or a variable derived therefrom is made available as a measured variable (y) of the respective rotor Estimator (14) is executed one or more times and with each execution of the estimator (14) estimated values for the angle of rotation (φ) and the speed (ω) of each rotor (2, 3) are predicted.

Description

The invention relates to a method for determining the angle of rotation and speed of one or more rotors, which are each rotated by a drive about a rotor axis relative to a stator, with a reference rotational position of each rotor being detected by at least one sensor and the time of this detection as the detection time of the respective Rotor is detected.

Imbalance exciters are used in machines in order to generate vibrations and/or to eliminate or at least reduce disturbing vibrations, for example by means of destructive interference. In order to control or regulate an imbalance exciter, it is usually necessary to know the angle of rotation and the speed of the rotating imbalance. It is known from the prior art to measure the angle of rotation and speed of rotating parts by means of resolvers, absolute encoders or incremental encoders, which include encoder wheels, for example. However, the known options are expensive, which makes their use in the automotive industry difficult.

Proceeding from this, the object of the invention is in particular to create a cost-effective possibility for determining current values for the speed and the angle of rotation of a rotor.

According to the invention, this object is achieved by a method according to claim 1 . Preferred developments of the invention are given in the dependent claims in the following description.

• - eine Referenzdrehlage jedes Rotors durch wenigstens einen Sensor erkannt und der Zeitpunkt dieses Erkennens als Erkennungszeitpunkt des jeweiligen Rotors erfasst wird,

wird erfindungsgemäß insbesondere dadurch weitergebildet, dass

• - ein auf einem systemtheoretischen Modell eines jeden Antrieb und jeden Rotor umfassenden Systems basierender Schätzer bereitgestellt wird, dem der Erkennungszeitpunkt jedes Rotors und/oder eine davon abgeleitete Größe als Messgröße des jeweiligen Rotors zur Verfügung gestellt wird,
• - der Schätzer ein- oder mehrmals ausgeführt wird,
• - bei jeder Ausführung des Schätzers Schätzwerte für den Drehwinkel und die Drehzahl jedes Rotors prädiziert werden.

A method for determining the angle of rotation and speed of one or more rotors, which are each rotated by a drive about a rotor axis relative to a stator, wherein

• - a reference rotational position of each rotor is detected by at least one sensor and the time of this detection is recorded as the detection time of the respective rotor,

is developed according to the invention in particular in that

• - an estimator based on a system-theoretical model of each drive and each rotor-encompassing system is provided, to which the detection time of each rotor and/or a variable derived therefrom is made available as a measured variable of the respective rotor,
• - the estimator is executed one or more times,
• - With each execution of the estimator, estimated values for the angle of rotation and the speed of each rotor are predicted.

With the method according to the invention, it is sufficient to record only one measured value per revolution of each rotor. A simple and therefore cost-effective sensor can thus be used to detect the rotational movement of the rotor.

In each execution of the estimator, the estimated values for the angle of rotation and the rotational speed of each rotor are preferably predicted by the estimator. Preferably, the estimated values for the angle of rotation and the speed of each rotor are estimates for the current angle of rotation and the current speed of the respective or each rotor. The expression "at least one" includes in particular the meaning of "one" or "exactly one".

The rotors are preferably rotated about the same rotor axis. In particular, the rotor axis forms a common rotor axis. Preferably the rotors are rotated relative to the same stator. In particular, the stator forms a common stator. The reference rotational position of each rotor is detected, for example, by at least one sensor per rotor. However, the reference rotational position of each rotor is preferably detected by a maximum of one sensor per rotor. Preferably, the reference rotational positions of the rotors are detected by the same at least one sensor. The at least one sensor forms in particular a sensor and/or a common sensor. The at least one sensor is preferably stationary relative to the stator. In particular, the at least one sensor is firmly and/or rigidly connected to the stator. Each rotor is preferably mounted on the stator so that it can rotate, in particular about the rotor axis.

The stator is preferably coupled to a carrier, in particular by one or more coupling elements which, for example, comprise at least one fastening means and/or at least one spring and/or at least one damper. The at least one spring and/or the at least one damper must be but are not explicitly present as components, but can also result, for example, from the manner in which the stator is coupled to the carrier and/or from the nature of the one or more coupling elements. For example, the at least one fastener includes the at least one spring and/or the at least one damper. The stator and/or the support and/or the one or more coupling elements is or are referred to in particular as a support system.

The system preferably includes, in particular additionally, the stator and/or the at least one sensor. The system preferably comprises, in particular additionally, the carrier and/or the one or more coupling elements and/or the carrying system. The system-theoretical model of the drive is advantageously created, in particular before it is made available.

Preferably, each rotor is or will be assigned the or a reference rotational position. Each rotor is or will preferably be assigned only a single reference rotational position, in particular in this case. Advantageously, the reference rotational position of each rotor is recognized by the at least one sensor after this assignment. By detecting the reference rotational position of each rotor, one revolution of the respective rotor is preferably detected. The detection of the reference rotational position of each rotor thus corresponds in particular to the detection or detection of a revolution of the respective rotor. A revolution of each rotor is preferably detected by detecting the reference rotational position of the respective rotor.

The reference rotational position of each rotor is detected in particular when a reference location of the respective rotor assumes a reference position in relation to a, preferably common, reference location of the stator, which is given, for example, by the fact that the reference location of the respective rotor is at a maximum or a minimum distance from the reference location of the stator having. The reference location of the stator is preferably defined by the location of the at least one sensor. In particular, the reference location of the stator corresponds to the location of the at least one sensor.

The angle of rotation of each rotor is preferably greater than or equal to 0 and less than 360°, in particular by definition. Thus, e.g. every possible rotational position of each rotor can be described. The angle of rotation of each rotor in the reference rotational position is preferably equal to zero. The angle of rotation or the estimated value for the angle of rotation of each rotor is determined, for example, by integration, in particular numerical, preferably from the speed or the estimated value for the speed of the respective rotor.

A flag is preferably assigned to each rotor. The flag of each rotor is preferably set when the reference rotational position of the respective rotor has been detected, in particular by the at least one sensor. Each flag is preferably not set at the beginning of the method.

The estimator is preferably executed periodically. The estimator is preferably executed with an execution rate, in particular a predetermined one. For example, the execution rate of the estimator is 100 Hz. The maximum speed of each rotor is advantageously less than or equal to the execution rate. The estimator is preferably executed several times for each or during one or each revolution of each rotor and/or between two consecutive detection times of each rotor. It is thus possible, in particular, to predict a plurality of estimated values for the angle of rotation and the rotational speed of each or the respective rotor during the or one or each revolution of each rotor. The reference rotational position of the respective rotor is preferably detected once or exactly once during one or each revolution of each rotor, in particular by the at least one sensor.

Preferably, before or during or at each execution of the estimator, the or an, in particular current, execution time of the estimator is recorded. Advantageously, the variable derived from the detection time of each rotor forms or includes a value, preferably linear, extrapolated for the angle of rotation of this or the respective rotor or each rotor. For example, the expression "a quantity derived therefrom" can be replaced by the expression "an extrapolated value for the angle of rotation derived therefrom".

Before or during or for each execution of the estimator, it is preferably checked for each rotor whether the reference rotational position of the respective rotor has been recognized since the estimator was last executed.

Preferably, especially if the reference rotational position of the respective rotor has been detected since the estimator was last executed, based on the last predicted estimated value for the speed of the respective rotor and a time difference between the, in particular current, execution time of the estimator and the detection time of the respective rotor or a, preferably linear, extrapo calculated value for the angle of rotation of the respective rotor is determined and preferably made available to the estimator as, in particular, the measured variable of the respective rotor. The extrapolated value for the angle of rotation of the respective or each rotor advantageously forms the variable derived from the time of detection of the respective or each rotor. The extrapolated value for the angle of rotation of the respective rotor or each rotor results in particular from the product of the last predicted estimated value for the rotational speed of the respective rotor and the time difference between the, in particular current, execution time of the estimator and the detection time of the respective rotor.

According to one embodiment, the estimator is or will be modeled in the state space. The angle of rotation and the rotational speed of each rotor preferably form state variables of the estimator. With each execution of the estimator, values for the state variables are preferably predicted, preferably by the estimator. Advantageously, the values of or for the state variables include or form the, in particular predicted, estimated values for the angle of rotation and the speed of each rotor. For example, an angular acceleration of each rotor forms, in particular additionally or also, a state variable of the estimator.

If it is assumed, in particular at least approximately, that the dynamic behavior of the system is described exactly with the system-theoretical model and the sensor measures correctly, the estimator can be formed by an observer, for example. For example, the estimator includes or forms an observer. In this case, instead of "predicate", the term "reconstruct" is used in particular. The meaning of the word predict preferably also includes this meaning of reconstruct. The observer is e.g. a Luenberger observer.

In reality, however, random system disturbances that cannot be described deterministically occur regularly. For example, the estimator takes into account, in particular only, the angle of rotation and/or the speed and/or the detection times as state variables and/or as input variables and/or as measured variables. In practice, however, acceleration of each rotor can also occur, for example. Furthermore, the detection of the reference rotational position of each rotor by means of the at least one sensor is usually not error-free.

The estimator preferably takes into account random system disturbances that cannot be described deterministically in the form of system noise. The estimator preferably takes into account accelerations of the rotor as, in particular additive, disturbances in the form of the system noise or noise. The system noise is advantageously zero-mean and/or additive and/or white and/or Gaussian noise.

The estimator preferably takes into account a measurement inaccuracy of the sensor as, in particular additive, interference in the form of measurement noise. The measurement noise is preferably a mean value-free and/or additive and/or white and/or Gaussian noise. The variance of the measurement noise is advantageously determined and/or estimated and/or determined on the basis of an in particular given and/or determined angle measurement inaccuracy of the sensor, for example with the aid of the three sigma rule. For example, the amount of angular measurement uncertainty of the sensor is set equal to three times the standard deviation of the measurement noise.

The noise processes, i.e. in particular the system noise and the measurement noise, are preferably uncorrelated.

The system noise and/or the measurement noise are preferably modeled as random processes. As a rule, however, the state variables and/or output variables of the estimator also become random processes. An estimator with which such random processes can be handled is e.g. the Kalman filter. The estimator preferably comprises or forms a Kalman filter. Good results have been obtained in experiments using a Kalman filter as an estimator.

According to a development, the estimator carries out a prediction step for each rotor in each execution, in which in particular the estimated values for the angle of rotation and the rotational speed of each or the respective rotor are predicted.

For example, whenever the estimator is executed, preferably if the reference rotational position of the respective rotor has not been detected since the estimator was last executed, in particular in the or a prediction step, the estimated values for the angle of rotation and the speed of the respective rotor, in particular on the basis of the last predicted or the last predicted estimated values for the angle of rotation and the speed of the respective rotor, preferably by the estimator.

Advantageously, for example each time the estimator is executed, particularly if the reference rotational position of the respective rotor has been recognized since the estimator was last executed, preferably before the prediction step or a prediction step, particularly in a correction step, the last predicted or the last predicted estimated values for the angle of rotation and the The rotational speed of the respective rotor is corrected, in particular on the basis of the detection time of the respective rotor or the variable derived therefrom and/or on the basis of the measured variable of the respective rotor, preferably by the estimator, after which, in particular in the or a prediction step, the estimated values for the angle of rotation and the speed of the respective rotor is predicted based on the corrected estimated values for the angle of rotation and the speed of the respective rotor, preferably by the estimator. Preferably, for example each time the estimator is executed, if the reference rotational position of the respective rotor has been detected since the estimator was last executed, the flag of the respective rotor is preferably additionally deleted or reset. Advantageously, for example each time the estimator is executed, the flag of each rotor is deleted or reset if the reference rotational position has been recognized and/or a correction step has been carried out for the respective rotor since the estimator was last executed.

Preferably, for example each time the estimator is executed, the check is carried out as to whether the reference rotational position of the respective rotor has been recognized since the estimator was last executed, by checking the flag of the respective rotor. If the flag is set, e.g. the reference rotational position of the respective rotor has been recognized since the estimator was last executed. If the flag is not set, the reference rotational position of the respective rotor has not been recognized since the estimator was last run.

Preferably, for example with each execution of the estimator, preferably if the reference rotational position of the respective rotor has not been recognized since the last execution of the estimator, in particular before the or a prediction step, the elements of the Kalman amplification and/or feedback matrix relevant to the respective rotor , preferably set to zero before or in the or a correction step. This applies in particular if the estimator comprises or forms a Kalman filter. It can thus be ensured, for example, that the estimated values for the angle of rotation and the speed of the respective rotor are predicted on the basis of the last predicted estimated values for the angle of rotation and the speed of the respective rotor.

Preferably, for example in each execution of the estimator, advantageously in the prediction step, the estimated values for the angle of rotation and the speed of each or the respective rotor are predicted, in particular additionally or also, on the basis and/or taking into account the or a system noise.

Preferably, for example each time the estimator is executed, in particular if the reference rotational position of the respective rotor has been detected since the last execution of the estimator, advantageously in the correction step, the last predicted estimated values for the angle of rotation and the speed of the respective rotor are, in particular additionally or also, on Corrected on the basis and/or taking into account the or a measurement noise.

According to one embodiment, the drive of each rotor is a speed-controlled drive, by means of which in particular the speed of the respective rotor is controlled, preferably as a function of a target value for the speed of the respective rotor. The speed-controlled drive of each rotor preferably comprises a speed controller and a motor. The motor of the speed-controlled drive of each rotor preferably comprises a motor shaft, for example designed as a hollow shaft. The motor shaft of the motor of the speed-controlled drive of each rotor is advantageously connected to the respective rotor, in particular in a torsionally rigid manner. Additionally or alternatively, the motor shaft of the motor of the speed-controlled drive of each rotor is formed, for example, by the respective rotor and/or is formed integrally with it. The estimated value for the speed of the respective rotor is preferably controlled by means of the speed controller of the speed-controlled drive of each rotor as a function of the or a desired value for the speed of the respective rotor. The speed controller of the speed-controlled drive of each rotor is preferably a PI controller. The desired value for the rotational speed of each rotor is advantageously made available to the estimator as an input variable, in particular for the respective rotor.

For example, in each execution of the estimator, advantageously in the prediction step, the estimated values for the angle of rotation and the speed of each or the respective rotor are preferred, in particular additionally or also, on the basis and/or taking into account the, in particular respective, input size and/or the target value for the speed of the respective rotor. Preferably, for example each time the estimator is executed, in particular if the reference rotational position of the respective rotor has been detected since the last execution of the estimator, advantageously in the correction step, the last predicted estimated values for the angle of rotation and the speed of the respective rotor are, in particular additionally or also, on Corrected on the basis and/or taking into account the, in particular respective, input variable and/or the target value for the rotational speed of the respective rotor.

The target value for the rotational speed of each rotor is preferably specified and/or provided, in particular by means of a control unit. In particular, the preferably predicted and/or corrected estimated values for the angle of rotation and/or the speed of each or the respective rotor are made available to the control unit and/or the speed-controlled drive of the respective rotor and/or the speed controller of the speed-controlled drive of the respective rotor .

The motor of the speed-controlled drive of each rotor is preferably an electric motor, for example a brushless DC motor. The speed-controlled drive of each rotor preferably includes a current controller. Advantageously, at least one electric motor current fed to the electric motor of the speed-controlled drive of the respective rotor is regulated by means of the current controller of the speed-controlled drive of each rotor, preferably as a function of at least one setpoint value for the motor current of the electric motor of the speed-controlled drive of the respective rotor. Preferably, the at least one setpoint for the at least one motor current of the electric motor of the speed-controlled drive of each or the respective rotor is provided or made available, in particular by the speed controller of the speed-controlled drive of the respective rotor.

The current controller of the speed-controlled drive of each rotor is preferably subordinate to the speed controller of the speed-controlled drive of the respective rotor and/or connected between the speed controller and the electric motor of the speed-controlled drive of the respective rotor. The speed control of the electric motor of the speed-controlled drive of each rotor and a speed control with subordinate current control are advantageously involved. The current controller of the speed-controlled drive of each rotor is preferably a PI controller.

A control device is preferably provided, which in particular includes the estimator and/or the observer and/or the Kalman filter and/or the speed controller of the drive of each rotor and/or the current controller of the drive of each rotor and/or the control unit. The control device preferably comprises the at least one sensor and/or is connected to it. The control device advantageously includes at least one digital computer. For example, the control device includes at least one digital signal processor and/or microcontroller. The estimator is preferably in the form of a program which is executed by the control device and/or by the digital computer and/or by the digital signal processor and/or by the microcontroller.

The target value for the rotational speed of each rotor is preferably specified and/or provided, in particular by means of the control device. In particular, the preferably predicted and/or corrected estimated values for the angle of rotation and/or the speed of each rotor are made available to the control device and/or the speed-controlled drive of the respective rotor and/or the speed controller of the speed-controlled drive of the respective rotor.

A time recording device is preferably provided. The recognition times and/or each recognition time is preferably recorded by the or a time recording device. The control device advantageously includes the time recording device.

According to a development, each rotor has a main axis of inertia that is offset relative to the rotor axis. In particular, the rotation of each rotor results in an imbalance. The system and/or each drive and/or each rotor and/or the stator and/or the at least one sensor preferably forms an imbalance exciter. The imbalances are preferably superimposed, in particular resulting in an imbalance. Each rotor preferably has an unbalanced mass, in particular eccentric with respect to the rotor axis, which is preferably arranged at a distance, in particular radial, from the rotor axis. For example, each imbalance mass is or will be mounted on the respective rotor. Each unbalanced mass preferably forms a projection, in particular a radial projection, of the respective rotor. The unbalanced masses preferably extend, in particular in each case, in the direction of the rotor axis. The imbalance exciter is advantageous for compensating for and/or reducing vibrations, in particular those that are disruptive deployed. For example, the imbalance exciter is used in a vehicle, which is in particular a motor vehicle.

According to one embodiment, the at least one sensor is used, preferably for each rotor, to detect changes in distance between the respective rotor or each rotor and the at least one sensor, in particular changes caused by eccentricity. The reference rotational position of the respective or each rotor is preferably recognized, in particular as a result. Advantageously, preferably for each rotor, the reference rotational position of the respective or each rotor is recognized by the at least one sensor in that changes in distance, in particular those caused by eccentricity, between the at least one sensor and the respective or each rotor are detected by means of the at least one sensor. Preferably, the at least one sensor is a proximity sensor. For example, the reference position and/or reference rotational position is or will be defined, preferably for each or the respective rotor, by a minimum or by a maximum distance between the respective or each rotor and the at least one sensor. The reference position corresponds, for example, to the reference rotation position. The reference rotational position of each rotor is recognized in particular when the distance between the reference location of the respective rotor and the reference location of the stator assumes a minimum or a maximum.

A sensor signal is preferably made available by the at least one sensor, which in particular characterizes the or a distance between the reference location of each rotor and the reference location of the stator. For example, the sensor signal characterizes the distance between the imbalance mass of the respective rotor or each rotor and the sensor. Preferably, the sensor is or will be combined with a threshold switch. The reference rotational position of each rotor is thus advantageously detected, in particular, in that the or a sensor signal made available by the sensor reaches or exceeds or falls below a threshold value, in particular a predetermined one.

Each rotor and/or the unbalanced mass of each rotor preferably consists, in particular at least partially, of a magnetic material, advantageously of a ferromagnetic material. The at least one sensor preferably forms or comprises one or at least one magnetic field sensor. For example, the at least one sensor forms or includes one or at least one Hall sensor. At least one magnet is advantageously provided together with the at least one sensor, which magnet preferably generates a measuring magnetic field to which the at least one sensor is exposed. The measuring magnetic field can preferably be influenced and/or changed by the rotor and/or by the imbalance mass, which can be detected in particular by means of the at least one sensor. The at least one magnet is preferably a permanent magnet.

The rotors preferably rotate in the same direction and/or the rotors have in particular the same direction of rotation. For example, the rotors are mechanically decoupled from one another. In this case, the estimated values for the angle of rotation and the speed of the rotors can, for example, be predicted independently of one another. In particular, however, the rotors are mechanically coupled to one another, for example via the stator and/or the support system.

According to a development, the number of rotors is two. For example, one of the rotors forms a first rotor and another of the rotors forms a second rotor. The rotors are preferably constructed identically. The unbalanced mass of the first rotor preferably projects in the direction of the second rotor and/or the unbalanced mass of the second rotor preferably projects in the direction of the first rotor. Advantageously, a plane arranged centrally between the rotors and running perpendicularly to the rotor axis intersects both unbalanced masses.

According to a development, a maximum of one sensor is used per rotor, which detects the imbalance mass mounted on the rotor. With the help of one sensor it is normally only possible to determine the speed averaged over complete rotations. However, the use of the system-theoretical model (system model), which is calculated on a control microcontroller in particular, opens up new possibilities for estimating the angle of rotation and speed. Thus, more expensive rotation angle sensors for determining the speed and rotation angle of the rotors can be saved. A typical sensor for determining the angle of rotation is, for example, an incremental angle sensor, which includes a sensor wheel, for example. However, due to the high accuracy requirements, such sensor wheels cause high production costs and also require a high-frequency evaluation of the tooth flanks. The system model is simplified especially for use with variable speed motors. Furthermore, only relevant variables are considered. The setpoint values for the speeds of the rotors and/or motors are therefore preferably used as input variables. The estimated values for the speeds and Angle of rotation, in particular in a half-open interval [0 °, 360 °) output. For the subsystem of a motor, the transfer function of the controlled system is advantageously formed with the desired speed as the input variable and the resulting speed as the output variable. A tenth-order transfer function resulting therefrom is preferably approximated to form a first-order delay element. In particular, the angle of rotation of the system can be determined numerically in a stable manner by means of integration. For this purpose, a known start position is assumed, which is not available in the application. To solve this problem, the model is preferably continuously corrected during operation, as a result of which the absolute angle of rotation of the rotor and/or motor can be determined. The continuous correction of the system model takes place in particular with the aid of a suitable estimator or filter (here preferably a Kalman filter). This filter is able to estimate states of the system as long as the necessary conditions for use are met. The good resilience of the filter in the case of fluctuating measured variables, which occur, for example, due to superimposed noise, is advantageous. The filter preferably has two, particularly essential, steps that are run through during execution, namely correction and prediction. In the correction step, the prediction of the last cycle is in particular combined with the current measurement in order to determine the estimated state vector of the current cycle. For this purpose, in particular the predicted output variable of the previous cycle is determined and compared with the current measured variable. If there is good agreement, there will only be a small difference. In particular, the Kalman gain for correction is determined on the basis of the covariance of the estimation errors and the covariance of the measured variables. The correction not only adjusts the states of the system, but also reduces the covariance of the estimation errors. In the prediction step, the state for the next cycle is predicted in particular with the generated system model on the basis of the current states and the known input variables. Since the uncertainty of the state vector increases as a result of the prediction, the covariance of the estimation errors is preferably increased.

• 1) Für keinen Rotor wurde die Referenzdrehlage erkannt: Es kann für keinen Rotor eine Korrektur ausgeführt werden. Das Filter führt lediglich einen zusätzlichen Prädiktionsschritt aus.
• 2) Es wird nur für den ersten Rotor die Referenzdrehlage erkannt: Anhand der vorliegenden Informationen lässt sich der Zustandsvektor des Modells nur für den ersten Rotor betreffende Größen korrigieren.
• 3) Es wird nur für den zweiten Rotor die Referenzdrehlage erkannt: Anhand der vorliegenden Informationen lässt sich der Zustandsvektor des Modells nur für den zweiten Rotor betreffende Größen korrigieren.
• 4) Es werden für beide Rotoren die Referenzdrehlagen erkannt: Es liegen alle benötigten Informationen vor, um den vollständigen Zustandsvektor zu korrigieren.

In particular, it is not possible with the target system to record new measured values for each iteration step of the filter. The sequence of the filter thus preferably changes, so that a correction only takes place after new measured values are available and only those states are corrected for which there are related measured values. A modified flow plan thus preferably takes into account the fact that new information for correction is not available for each filter call. Since the measured values for the rotors and/or motors do not occur at the same time as the execution due to the preferably fixed execution time of the filter, it can only be recognized whether the reference rotational positions for the rotors and/or motors were recorded between two calls. In particular, a distinction is made between the following four options.

• 1) The reference rotational position was not recognized for any rotor: A correction cannot be carried out for any rotor. The filter only performs an additional prediction step.
• 2) The reference rotational position is only recognized for the first rotor: Based on the information available, the state vector of the model can only be corrected for variables relating to the first rotor.
• 3) The reference rotational position is only recognized for the second rotor: Based on the information available, the state vector of the model can only be corrected for variables relating to the second rotor.
• 4) The reference rotational positions are recognized for both rotors: all the information required to correct the complete state vector is available.

For meaningful correction of the states, it is advantageous that the angles of rotation serve as measured variables for comparing the model and reality. With the at least one sensor, however, the angles of rotation cannot in particular be measured, but times can be recorded.

The values for the angles of rotation can be extrapolated with the known location of the sensor and/or with the known reference rotational position, the last predicted rotational speeds and the elapsed time from the detection of the reference rotational position to the filter call. There are good values for the angle of rotation if the speeds are predicted with good accuracy. In particular, the measured time can never be greater than the execution rate of the filter. The system model for the Kalman filter can be set up with the output variables. Since this is preferably a non-jumpable system, a direct path with a throughput matrix is not required.

The method was implemented on an imbalance exciter prototype and showed good agreement with reference measurements that were made with sensor wheels. The deviations of the predicted angles of rotation were consistently less than 2.5°. Furthermore, the deviations in the speed were less than 1%, largely even less than 0.5%.

• 1 eine schematische Ansicht eines Unwuchterregers mit zwei Rotoren,
• 2 eine Schnittansicht des Unwuchterregers entlang der in 1 ersichtlichen Schnittlinie A-A,
• 3 eine schematische Darstellung eines durch den Unwuchterreger gebildeten Systems und eines Schätzers,
• 4 eine schematische Darstellung eines drehzahlgeregelten Antriebs des Unwuchterregers,
• 5 ein Ersatzschaltbild für den Ankerkreis eines Elektromotors des drehzahlgeregelten Antriebs,
• 6 ein Flussdiagramm zur Veranschaulichung von Korrektur und Prädiktion von Drehwinkel und Drehzahl für einen der Rotoren des Unwuchterregers und
• 7 ein Flussdiagramm zur Veranschaulichung von Korrektur und Prädiktion von Drehwinkel und Drehzahl für beide Rotoren des Unwuchterregers.

The invention is described below using a preferred embodiment with reference to the drawing. Show in the drawing:

• 1 a schematic view of an unbalance exciter with two rotors,
• 2 a sectional view of the unbalance exciter along the in 1 apparent cutting line AA,
• 3 a schematic representation of a system formed by the imbalance exciter and an estimator,
• 4 a schematic representation of a speed-controlled drive of the imbalance exciter,
• 5 an equivalent circuit diagram for the armature circuit of an electric motor of the speed-controlled drive,
• 6 a flowchart to illustrate the correction and prediction of the angle of rotation and speed for one of the rotors of the imbalance exciter and
• 7 a flowchart to illustrate the correction and prediction of the angle of rotation and speed for both rotors of the unbalance exciter.

1 1 shows a schematic view of an imbalance exciter 1, which has two rotors 2 and 3, which are each rotated about a rotor axis 6 by an electric motor 4 and 5, respectively. The rotor 2 , which is also referred to as the first rotor, is rotated by the electric motor 4 and the rotor 3 , which is also referred to as the second rotor, is rotated by the electric motor 5 . The rotors 2 and 3 are preferably constructed identically and, in particular, rotate in the same direction. The electric motors 4 and 5 are preferably each formed by a brushless DC motor. The motor 4 is referred to in particular as the first motor and the motor 5 in particular as the second motor.

Each rotor has an unbalanced mass which is arranged at a radial distance from the rotor axis 6 . The rotor 2 has the unbalanced mass 7 and the rotor 3 has the unbalanced mass 8 . Due to the imbalance masses 7 and 8, the main axes of inertia of the rotors 2 and 3 are offset relative to the rotor axis 6, so that the rotation of the rotors 2 and 3 about the rotor axis 6 results in an imbalance. this is in 2 for the rotor 2, where an offset a between the rotor axis 6 and the main axis of inertia 23 of the rotor 2 is illustrated. The imbalances are superimposed to form an imbalance, the frequency and phase of which can be adjusted in particular by the angle of rotation and the speed of the rotors 2 and 3 . The revolutions of the rotors 2 and 3 are detected by a sensor 9 .

The imbalance exciter 1 has a stator 10 to which the electric motors 4 and 5 and the sensor 9 are firmly connected. The stator 10 is shown only schematically and is formed, for example, by at least one holder and/or by at least one housing. The electric motors 4 and 5 each comprise a motor shaft 11 designed as a hollow shaft, to which the respective rotor is rigidly or torsionally rigidly connected. Also provided is an axis 12 which is rigidly connected to the stator 10 and on which the rotors 2 and 4 are mounted so as to be rotatable about the rotor axis 6 . The rotors 2 and 3 are thus mounted on the stator 10 such that they can rotate at least indirectly about the rotor axis 6 . The stator 10 is coupled to a carrier 22, for example by one or more coupling elements 21, with the carrier 22 and the coupling elements 21 forming in particular a carrying system.

Out of 2 is a sectional view of the imbalance exciter 1 along the in 1 visible section line AA. Furthermore, the sensor 9 is shown schematically in order to illustrate its position relative to the rotor 2 . The location of the sensor 9 defines a reference location of the stator 10. Furthermore, each unbalanced mass defines a reference location of the respective rotor. The unbalanced mass 7 defines a reference location of the rotor 2 and the unbalanced mass 8 a reference location of the rotor 3. Thus, a rotation angle φ can be defined for each rotor rotating at a speed ω, which defines a rotational position of the reference location of the respective rotor in relation to the reference location of the stator 10 characterizes what is made for the first rotor 2 2 is evident. The rotational position of the reference location of each rotor preferably forms a rotational position of the respective rotor. A revolution of each rotor is detected in particular when it assumes or passes through a reference rotational position φ _ref , which is preferably defined in that the distance d between the reference location of the respective rotor and the reference location of the stator 10 assumes a minimum. The sensor 9 is preferably a Hall sensor, and the imbalance masses 7 and 8 are preferably made of a ferromagnetic material. Furthermore, in particular a magnet 37 is provided for generating a measuring magnetic field (see FIG 1 ). A rotation of the rotor 2 is detected, for example, each time it assumes or passes through the reference rotational position φ _ref in which its unbalanced mass 7 is at the smallest distance d from the sensor 9 . The same applies to the second rotor 3.

In order to control the angle of rotation and the speed of the rotors, it is desirable to be able to measure values for the angle of rotation and the speed of each rotor as continuously or quasi-continuously as possible. With the sensor 9, however, only a single angle of rotation per revolution can be measured for each rotor. Furthermore, the speed can only be measured averaged over one revolution with the sensor 9 for each rotor. In order to increase the resolution for the values of the angle of rotation and the speed of each rotor, a Kalman filter estimator is used.

Out of 3 a schematic representation of a system 13 with an estimator 14 can be seen, which is formed here in particular by a Kalman filter. The physical system 13 corresponds to the imbalance exciter 1, which is represented as a system-theoretical, time-continuous model Σ in the state space as follows: $$\mathrm{\Sigma }:\{\begin{array}{cc}\underset{\_}{\dot{x}}\left(t\right)=\underset{\_}{A}\cdot \underset{\_}{x}\left(t\right)+\underset{\_}{B}\cdot \underset{\_}{\mathrm{and}}\left(t\right),& x\left(0\right)={\underset{\_}{x}}_0\\ y\left(t\right)=\underset{\_}{C}\cdot \underset{\_}{x}\left(t\right)+\underset{\_}{D}\cdot \underset{\_}{\mathrm{and}}\left(t\right)& \end{array}$$

The quantity x (t) is the state vector, the quantity ẋ(t) the time derivative of the state vector, the quantity u(t) the input vector, the quantity y(t) the output vector, the quantity t the time, the quantity A the system matrix, size B the control matrix, size C the observation matrix and size D the transit matrix. Since the estimator 14 is preferably in the form of a program which is executed on a digital computer, the following results for the system-theoretical, time-discrete model Σ _d in the state space: $${\mathrm{\Sigma }}_{\mathrm{i.e}}:\{\begin{array}{ll}\underset{\_}{x}\left(k+1\right)={\underset{\_}{A}}_{\mathrm{i.e}}\cdot \underset{\_}{x}\left(k\right)+{\underset{\_}{B}}_{\mathrm{i.e}}\cdot \underset{\_}{\mathrm{and}}\left(t\right),\hfill & x\left(0\right)={\underset{\_}{x}}_0\hfill \\ \underset{\_}{y}\left(k\right)=\underset{\_}{C}\cdot \underset{\_}{x}\left(k\right)+\underset{\_}{D}\cdot \underset{\_}{\mathrm{and}}\left(t\right)\hfill & \hfill \end{array}$$

$${\underset{\_}{B}}_d={\displaystyle {\int }_0^{T_S}{e}^{\underset{\_}{A}\cdot \tau }\cdot d\tau }$$

The discrete system matrix A _d and the discrete observer matrix B _d result with the sampling time T _s as follows: $${\underset{\_}{A}}_{\mathrm{i.e}}=e^{\underset{\_}{A}\cdot T_S}$$

$${\underset{\_}{B}}_{\mathrm{i.e}}={\displaystyle {\int }_0^{T_S}{e}^{\underset{\_}{A}\cdot \tau }\cdot \mathrm{i.e}\tau }$$

The Kalman filter 14 results with the aid of the system-theoretical, time-discrete model Σ _d in the state space and the Kalman gain K(k). The output vector y(k), in particular time-discrete, of the system preferably represents a measured variable for the estimator 14. The block z ^-1 describes in particular a delay element and/or a memory.

In order to determine the system-theoretical, time-continuous model Σ in the state space, the following prerequisites apply. Each electric motor is part of a speed-controlled drive 15, which includes a speed controller 16 and a current controller 17 in addition to the respective electric motor. The drive 15 comprising the electric motor 4 is shown schematically in 4 shown. The electric motor 4 is logically divided into an electrical block 18 and a mechanical block 19 . Furthermore, the rotor 2 is added to the electric motor 4 as a mechanical load. The speed controller 16 has the transfer functions G _R,ω and is designed as a PI controller. How out 4 As can be seen, a target value for the speed is made available and is denoted by ω _target . The actual value for the speed, on the other hand, is denoted by ω here. The current controller 17 has the transfer functions G _R,i and is designed as a PI controller. How out 4 As can be seen, the speed controller 16 provides a desired value for the motor current, which is denoted by I _desired . The actual value for the motor current, on the other hand, is denoted by /.

mit $$e_A\left(t\right)=c_E\cdot \omega \left(t\right)$$

$$M\left(t\right)=c_M\cdot I_A\left(t\right)$$

$$M\left(t\right)=J\cdot \dot{\omega }\left(t\right)$$

According to an equivalent circuit diagram, which consists of 5 can be seen, the armature circuit of the electric motor 4 can be represented as follows: $$u_A\left(t\right)=R\cdot I_A\left(t\right)+L\cdot i_A\left(t\right)+e_A\left(t\right)$$

With $$e_A\left(t\right)=c_E\cdot \omega \left(t\right)$$

$$M\left(t\right)=c_M\cdot I_A\left(t\right)$$

$$M\left(t\right)=J\cdot \dot{\omega }\left(t\right)$$

Variable U _A is the electrical voltage applied to the armature circuit, variable I _A is the electrical current flowing through the armature circuit, which in particular forms the motor current, variable L is the armature inductance, variable R is the armature resistance, variable e _A is the induced voltage, variable M is the effective torque, variable J is the moment of inertia of the armature, variable ω is the angular velocity of the armature and variables c _E and c _M are machine constants of the electric motor 4.

Thus, for block 18, the Lapalce transform of the transfer function G _I results in: $$G_I=\frac{J_{Ges}\cdot s}{L\cdot J_{Ges}\cdot s^2+R\cdot J_{Ges}\cdot s+c_M\cdot c_E}$$

Furthermore, for block 19, the Laplace transform of the transfer function G _ω results in: $$G_{\omega }=\frac{c_M}{J_{Ges}\cdot s}$$

The variable J _tot results from the resulting mass moment of inertia of the armature and rotor 2.

The drive comprising the electric motor 5 is designed accordingly, although the rotor 3 is added to the electric motor 5 as a mechanical load.

How out 1 As can be seen, the imbalance exciter 1 includes a control device 20, which includes the speed controller and the current controller for both electric motors 4 and 5 and is connected to these by electrical lines 38, which are shown in dashed lines. Furthermore, the sensor 9 is electrically connected to the control device 20, which is indicated by the dashed line 39 with an arrowhead. In particular, the control device 20 also specifies the setpoint values for the speed, the setpoint value for the speed of the first rotor 2 also being designated ω _1,soll and the setpoint value for the speed of the second rotor 3 with ω _2,soll .

A transfer function of a higher order, in particular of the tenth order, results for the overall system. For simplification, this transfer function is approximated by a first-order system, resulting in the following differential equation: $$\dot{y}=\frac{-1}{T_I}y+\frac{1}{T_I}\mathrm{and}$$

To increase the accuracy, the transfer function for the overall system can also be approximated by a system of the second or higher order. In the following, however, the first-order system is assumed, since good results have already been achieved with this.

Thus the systems-theoretical, time-continuous model Σ in the state space follows: $$\mathrm{\Sigma }:\{\begin{array}{l}\begin{array}{lllllll}\left(\begin{array}{c}{\dot{\phi }}_1\\ {\dot{\phi }}_2\\ {\dot{\omega }}_1\\ {\omega }_2\end{array}\right)=\hfill & \left(\begin{array}{cccc}0& 0& 6& 0\\ 0& 0& 0& 6\\ 0& 0& \mathrm{i.e}& q\\ 0& 0& q& \mathrm{i.e}\end{array}\right)\cdot \left(\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="\phi "\; filenames="DE102021113633A1\_0022.png,DE102021113633A1\_0023.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_1\\ {\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="DE102021113633A1\_0022.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_2\\ {\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021113633A1\_0022.png,DE102021113633A1\_0023.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1\\ {\omega }_2\end{array}\right)+\left(\begin{array}{ll}0\hfill & 0\hfill \\ 0\hfill & 0\hfill \\ v\hfill & 0\hfill \\ 0\hfill & v\hfill \end{array}\right)\cdot \left(\begin{array}{c}{\mathrm{and}}_1\\ {\mathrm{and}}_2\end{array}\right)+\left(\begin{array}{ll}0\hfill & 0\hfill \\ 0\hfill & 0\hfill \\ 1\hfill & 0\hfill \\ 0\hfill & 1\hfill \end{array}\right)\cdot \left(\begin{array}{c}{\mathrm{e.g}}_1\\ {\mathrm{e.g}}_2\end{array}\right)\hfill & \hfill & \hfill & \hfill & \hfill & \hfill \end{array}\\ \left(\begin{array}{c}{y}_1\\ y_1\end{array}\right)=\left(\begin{array}{llll}1\hfill & 0\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 0\hfill & 0\hfill \end{array}\right)\cdot \left(\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="\phi "\; filenames="DE102021113633A1\_0022.png,DE102021113633A1\_0023.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_1\\ {\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="DE102021113633A1\_0022.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_2\\ {\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021113633A1\_0022.png,DE102021113633A1\_0023.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1\\ {\omega }_2\end{array}\right)\end{array}$$

The size φ ₁ is the rotation angle of the first rotor 2, the size ω ₁ is the speed of the first rotor 2, the size φ ₂ is the rotation angle of the second rotor 3, the size ω ₂ is the speed of the second rotor 3, the size u ₁ is the first component of the input vector u(t), the quantity u ₂ is the second component of the input vector u(t), quantity y ₁ is the first component of the output vector y(t), quantity y ₂ is the second component of the output vector y(t), quantity z ₁ is the first component of a disturbance vector z(t) and the quantity z ₂ is the second component of the disturbance vector z(t). Acceleration of the masses of the imbalance exciter is taken into account in particular by the disturbance vector z(t). Such an acceleration can occur, for example, due to additional vibrations of the support system. In a second-order system, for example, the angular acceleration of each rotor can also be taken into account in the state vector.

The speeds ω ₁ and ω ₂ are specified in particular in revolutions per minute (rpm). Furthermore, the components of the input vector u(t) representing the input variable are preferably formed by the desired values for the speeds, with u ₁ =ω _1,soll and u ₂ =ω _2,soll .

The three variables d, q and v particularly characterize the reaction of the system. For example, the variable v determines the system dynamics. In particular, for example, the reaction speed to changes in the input variable is described. Preferably: v=1/T _I . In particular, the variables d and q indicate the extent to which the rotors influence each other during operation. The greater q is compared to d, the greater the mutual influence, for example. This decreases in particular with increasing mass of the support system. The relationship: d+q+v=0 preferably applies, particularly in the event that there is no steady-state control deviation. This means that only two variables are preferably required for a complete description, since the third one results from the aforementioned relationship. The three variables d, q and v are particularly suitable to choose.

des Messrauschens lässt sich insbesondere aus der Winkelmessungenauigkeit ±Δφ des Sensors 9 bestimmen, indem z.B. der Betrag der Winkelmessungenauigkeit Δφ mit 3σ_sens gleichgesetzt wird. Die Kovarianzen des Messrauschens werden insbesondere zu Null angenommen, da der Sensor 9 für beide Rotoren verwendet wird. Somit lässt sich die Kovarianzmatrix des Messrauschens R aufstellen zu: $$\underset{\_}{R}=\left(\begin{array}{cc}{\sigma }_{sens}^2& 0\\ 0& {\sigma }_{sens}^2\end{array}\right)$$

In order to be able to implement the Kalman filter, a measurement noise and a system noise still have to be determined. The variance ${\sigma }_{sens}^2$

of the measurement noise can be determined in particular from the angle measurement inaccuracy ±Δφ of the sensor 9, for example by equating the magnitude of the angle measurement inaccuracy Δφ to 3σ _sens . In particular, the covariances of the measurement noise are assumed to be zero since the sensor 9 is used for both rotors. The covariance matrix of the measurement noise R can thus be set up as follows: $$\underset{\_}{R}=\left(\begin{array}{cc}{\sigma }_{sens}^2& 0\\ 0& {\sigma }_{sens}^2\end{array}\right)$$

The disturbance z(t) or time-discrete z(k) is preferably taken into account as system noise. In order to determine the covariance matrix of the system noise Q, the associated power density spectrum q(k) is to be determined in particular, which is preferably assumed to be constant here. Using several criteria, the power density spectrum can now be determined and the covariance matrix of the system noise Q can be determined. One of these criteria states, for example, that the variance of the system noise should be selected to be greater than the variance of the measurement noise, in particular by a certain factor. Another of these criteria says, for example, that a scalar should be used as the power density spectrum. Those skilled in the art are now able to determine appropriate values for the system noise Q covariance matrix. Finally, suitable starting values for the state vector and the covariance of the estimation error still have to be determined.

In operation, the Kalman filter specifically performs two steps, namely a prediction step (prediction) and a correction step (correction).

$$\widehat{\underset{\_}{P}}\left(k+1\right)={\underset{\_}{A}}_d\cdot \underset{\_}{\overline{P}}\left(k\right)\cdot {\underset{\_}{A}}_d^T+{\underset{\_}{G}}_d\cdot \underset{\_}{Q}\left(k\right)\cdot {\underset{\_}{G}}_d^T,mit\underset{\_}{Q}\left(k\right)=Vart\left(\underset{\_}{z}\left(k\right)\right)$$

prediction: $$\widehat{\underset{\_}{x}}\left(k+1\right)={\underset{\_}{A}}_{\mathrm{i.e}}\cdot \widetilde{\underset{\_}{x}}\left(k\right)+{\underset{\_}{B}}_{\mathrm{i.e}}\cdot \underset{\_}{\mathrm{and}}\left(k\right)$$

$$\widehat{\underset{\_}{P}}\left(k+1\right)={\underset{\_}{A}}_{\mathrm{i.e}}\cdot \underset{\_}{\overline{P}}\left(k\right)\cdot {\underset{\_}{A}}_{\mathrm{i.e}}^T+{\underset{\_}{G}}_{\mathrm{i.e}}\cdot \underset{\_}{Q}\left(k\right)\cdot {\underset{\_}{G}}_{\mathrm{i.e}}^T,mit\underset{\_}{Q}\left(k\right)=Va\mathrm{right}t\left(\underset{\_}{\mathrm{e.g}}\left(k\right)\right)$$

$$\underset{\_}{\tilde{x}}=\underset{\_}{\widehat{x}}\left(k\right)+\underset{\_}{K}\left(k\right)\cdot (\underset{\_}{y}\left(k\right)-\underset{\_}{C}\left(k\right)\cdot \widehat{\underset{\_}{x}}\left(k\right)-\underset{\_}{D}\cdot \underset{\_}{u}\left(k\right)$$

$$\widetilde{\underset{\_}{P}}\left(k\right)=\left(\underset{\_}{I}-\underset{\_}{K}\left(k\right)\cdot \underset{\_}{C}\right)\cdot \widehat{\underset{\_}{P}}\left(k\right)$$

Correction: $$K\left(k\right)=\underset{\_}{\widehat{P}}\left(k\right)\cdot {\underset{\_}{C}}^T\cdot {\left(\underset{\_}{C}\cdot \widehat{\underset{\_}{P}}\left(k\right)\cdot {\underset{\_}{C}}^T+\underset{\_}{R}\left(k\right)\right)}^{-1}$$

$$\underset{\_}{\tilde{x}}=\underset{\_}{\widehat{x}}\left(k\right)+\underset{\_}{K}\left(k\right)\cdot (\underset{\_}{y}\left(k\right)-\underset{\_}{C}\left(k\right)\cdot \widehat{\underset{\_}{x}}\left(k\right)-\underset{\_}{D}\cdot \underset{\_}{\mathrm{and}}\left(k\right)$$

$$\widetilde{\underset{\_}{P}}\left(k\right)=\left(\underset{\_}{I}-\underset{\_}{K}\left(k\right)\cdot \underset{\_}{C}\right)\cdot \widehat{\underset{\_}{P}}\left(k\right)$$

The quantity x̂(k) is the predicted state vector, the quantity x̃(k) is the corrected state vector, the quantity P(k) is the predicted covariance matrix of the estimation error, the quantity P̃(k) is the corrected covariance matrix of the estimation error, the quantity G _d is a matrix for the system noise, the quantity Q(k) is the variance of the system noise z(k), the quantity R(k) is the variance of the measurement noise and the quantity I is the identity matrix. The superscript T means it is the transpose of that matrix. For example, CT denotes the transpose of the matrix C.

In the correction step, the last predicted state vector x̂(k) is corrected on the basis of a deviation Δy(k) between measured output values y(k) and predicted output values ỹ(k), resulting in a corrected state vector x̃(k). For example: Δy(k) = y(k) - ỹ(k) or Δy(k) = ŷ(k) - y(k). Furthermore, the corrected covariance matrix of the estimation error P̂(k) results, which is reduced in particular compared to P̂(k). In the prediction step, a new state vector x-(k+1) is predicted on the basis of the corrected state vector x-(k). Furthermore, a newly predicted covariance matrix of the estimation error P(k+1) results, which is increased compared to P(k), in particular.

The state vector x̂(k) preferably includes the last predicted estimated values for the angle of rotation and the speed. The state vector x̃(k) preferably includes the corrected, last predicted estimated values for the angle of rotation and the speed. The state vector x̂(k+1) advantageously includes the newly predicted estimated values for the angle of rotation and the speed.

$${\phi }_{2e}=\left(t_A-t_{\mathrm{2,}m}\right)\cdot {\omega }_2$$

In the case of the imbalance exciter 1, each revolution of each rotor is detected by the sensor 9 at a detection time t _M . The recognition times are recorded and form measured values on which the correction step is to be based. Furthermore, the execution time t _A of the estimator 14 is recorded. Now, by multiplying the last predicted estimated value for the rotational speed ω of each rotor by the time difference Δt = t _A - t _M between the execution time of the estimator 14 and the last recorded detection time of the respective rotor, an extrapolated value for the rotation angle φ _e = Δt ω of the respective rotor is calculated. The extrapolated values for the angle of rotation of each or the respective rotor are made available to the estimator 14 in particular as a measured value y(k) of the respective rotor. If a rotation is detected for the first rotor 2 at a detection time t _1,M and a rotation for the second rotor 3 at a detection time t _2,M , the extrapolated values for the angles of rotation of the rotors 2 and 3 result in particular as follows: $${\phi }_{1e}=\left(t_A-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="DE102021113633A1\_0022.png,DE102021113633A1\_0023.png"\; state="\{\{state\}\}">t</figure-callout>}}_{\mathrm{1,}m}\right)\cdot {\mathrm{<figure-callout\; id="1"\; label="\omega "\; filenames="DE102021113633A1\_0022.png,DE102021113633A1\_0023.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_1$$

$${\phi }_{2e}=\left(t_A-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="DE102021113633A1\_0022.png"\; state="\{\{state\}\}">t</figure-callout>}}_{\mathrm{2,}m}\right)\cdot {\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="DE102021113633A1\_0022.png"\; state="\{\{state\}\}">\omega </figure-callout>}}_2$$

Here, φ _1e designates the extrapolated value for the angle of rotation of the first rotor 2 and φ _2e the extrapolated value for the angle of rotation of the second rotor 3.

Each prediction is usually made on the basis of corrected variables. In this case, however, the estimator 14 could only be executed once per revolution of each rotor. However, the estimator 14 is preferably executed more frequently, so that a new detection time t _M and/or a new extrapolated value for the angle of rotation φ _e is not available as a measured value each time the estimator 14 is executed.

Therefore, before or during each execution of the estimator 14, a check is made for each rotor as to whether the reference rotational position of the respective rotor has been recognized since the estimator 14 was last executed. No correction is made for each rotor for which the reference rotational position was not recognized when the estimator 14 was executed since the estimator 14 was last executed, ie no measured value is available. Instead, for each rotor for which no measured value is available when the estimator is executed, the estimated values for the angle of rotation and the speed are predicted on the basis of the previously predicted estimated values for the angle of rotation and the speed. This can be taken into account in the program for the estimator 14, for example, by assigning the previously predicted estimated values for the angle of rotation and the speed to the estimated values for the angle of rotation and the speed for the respective rotor in the corrected state vector and/or by assigning the respective rotor relevant elements of the feedback matrix or Kalman gain are set to zero in the correction step. Thus, the corrected state vector x̃ (k) can be used formally in the prediction step, although this does not include corrected values for the respective rotor, but rather the last predicted estimated values for the angle of rotation and the speed. For each rotor for which the reference rotational position was recognized when estimator 14 was executed since the last execution of estimator 14, i.e. a measured value is available, the extrapolated value for the angle of rotation φ _e is determined and sent to estimator 14 as a measured value for the respective rotor provided.

6 shows a flowchart to illustrate correction and prediction for the rotor 2. The same applies in particular to the rotor 3. In the following it is assumed that a rotation of the rotor 2 is considered to be recognized when the reference rotational position φ _ref for the rotor 2 is recognized was and / or a revolution is considered not recognized if the reference rotational position φ _ref for the rotor 2 was not recognized. In a test step 24, it is checked whether a revolution has been recognized for the rotor 2 since the estimator 14 was last executed. If this is the case, in a subsequent extrapolation step 25, the extrapolated value for the angle of rotation φ _e is determined from the detection time t _m , the execution time t _A of the estimator 14 and the last predicted estimated value for the speed ω, which the estimator 14 uses as a measured variable is provided, with φ _e = (t _A - t _m ) · ω. In a subsequent correction step 26, the last predicted estimated values for the angle of rotation and the speed of the rotor 2 are corrected, after which in a prediction step 28 the estimated values for the angle of rotation and the speed of the rotor 2 are based on the corrected estimated values for the angle of rotation and the speed of the rotor 2 are repredicated. An optional step 27 is provided between the correction step 26 and the prediction step 28, in which a task can be completed with the currently available estimated values for the angle of rotation and the speed of the rotor 2, such as a speed control of the rotor 2. If no revolution is detected, the last predicted estimated values for the angle of rotation and the speed of the rotor 2 are accepted as current or corrected estimated values for the angle of rotation and the speed of the rotor 2 in a transfer step 29, after which in the prediction step 28 the estimated values for the angle of rotation and the speed of the rotor 2 can be re-predicted on the basis of the last predicted estimated values for the angle of rotation and the speed of the rotor 2. Here, too, the optional step 27 can be carried out between the correction step 26 and the prediction step 28 .

Out of 7 a flow chart to illustrate the correction and prediction of the angle of rotation and speed for both rotors 2 and 3 of the imbalance exciter 1 can be seen. In the following it is assumed that a revolution is considered to be recognized for each rotor if the reference rotational position for the respective rotor was recognized and/or a revolution is considered not recognized if the reference rotational position for the respective rotor was not recognized.

A check step 30 checks whether a revolution has been detected for the first rotor 2 since the estimator 14 was last executed. If this is the case, a test step 31 checks whether a revolution has been detected for the second rotor 3 since the estimator 14 was last executed. If this is the case, in a correction step 32 the last predicted estimated values for the angle of rotation and the speed of the rotors are corrected on the basis of the extrapolated values for the angles of rotation of the rotors, after which in a prediction step 33 the estimated values for the angle of rotation and the speed of the rotors are based on of the corrected estimated values for the angle of rotation and the speed of the rotors. In 7 the expression "rev." stands for the word "revolution". Furthermore, the term "R1" stands for the first rotor in particular, and the term "R2" stands for the second rotor in particular.

If no revolution is detected for the second rotor 3 in test step 31 since estimator 14 was last executed, only the most recently predicted estimated values for the angle of rotation and the speed of first rotor 2 are corrected in correction step 34, after which in prediction step 33 the estimated values for the The angle of rotation and the speed of the first rotor 2 are predicted on the basis of the corrected estimated values for the angle of rotation and the speed of the first rotor 2, and the estimated values for the angle of rotation and the speed of the second rotor 3 are predicted on the basis of the previously predicted estimated values for the angle of rotation and the speed of the second rotor 3 can be predicted.

If no revolution has been recognized for the first rotor 2 in test step 30 since estimator 14 was last executed, a check step 35 checks whether a revolution has been recognized for second rotor 3 since estimator 14 was last executed. If this is the case, only the last predicted estimated values for the angle of rotation and the speed of the second rotor 3 are corrected in a correction step 36, after which in the prediction step 33 the estimated values for the angle of rotation and the speed of the second rotor 3 are based on the corrected estimated values for the angle of rotation and the rotational speed of the second rotor 2 is predicted and the estimated values for the rotational angle and the rotational speed of the first rotor 2 are predicted on the basis of the estimated values for the rotational angle and the rotational speed of the first rotor 2 .

If, in test step 35, no revolution has been detected for the second rotor 3 since the estimator 14 was last executed, in the subsequent prediction step 33 the estimated values for the angle of rotation and the speed of the first rotor 2 are calculated on the basis of the previously predicted estimated values for the angle of rotation and the speed of the first rotor 2 is predicted and the estimated values for the angle of rotation and the speed of the second rotor 3 on the basis of the previously predicted estimated values for the angle of rotation and the speed of the second rotor 3 .

Reference List

1

imbalance exciter

2

first rotor

3

second rotor

4

first electric motor

5

second electric motor

6

rotor axis

7

Unbalanced mass of the first rotor

8th

Unbalanced mass of the second rotor

9

sensor

10

stator

11

motor shaft

12

axis

13

system

14

Estimator / Kalman filter

15

drive

16

speed controller

17

current regulator

18

electric block of the electric motor

19

mechanical block of the electric motor

20

control device

21

coupling element

22

carrier

23

main axis of inertia

24

test step

25

extrapolation step

26

correction step

27

optional step

28

prediction step

29

transfer step

30

test step

31

test step

32

correction step

33

prediction step

34

correction step

35

test step

36

correction step

37

magnet

38

electrical line

39

electrical line

a

offset

i.e

Distance

φ

angle of rotation

ω

rotational speed

φe

extrapolated angle of rotation

φref

reference rotation position

Claims (13)

Method for determining the angle of rotation (φ) and speed (ω) of one or more rotors (2, 3), which are each rotated by a drive (15) about a rotor axis (6) relative to a stator (10), wherein - a Reference rotational position (φ _ref ) of each rotor (2, 3) is detected by at least one sensor (9) and the time of this detection is recorded as the detection time of the respective rotor (2, 3), characterized in that - a system-theoretical model (Σ _d ) of each drive (15) and each rotor (2, 3) system (13) based estimator (14) is provided, which the detection time of each rotor (2, 3) or a variable derived therefrom as a measured variable (y) of the respective rotor is made available, - the estimator (14) is executed one or more times, - with each execution of the estimator (14), estimated values for the angle of rotation (φ) and the speed (ω) of each rotor (2, 3) are predicted will. procedure after claim 1 , characterized in that the estimator (14) is executed several times between two consecutive detection times of each rotor (2, 3). procedure after claim 1 or 2 , characterized in that the estimator (14) is modeled in the state space and the angle of rotation (φ) and the speed (ω) of each rotor form state variables of the estimator (14), the values of which are the predicted estimated values for the angle of rotation (φ) and the speed (ω) of each rotor (1, 2). Method according to one of the preceding claims, characterized in that the estimator (14) comprises a Kalman filter. Method according to one of the preceding claims, characterized in that before or during each execution of the estimator (14) for each rotor (2, 3) it is checked whether since the last execution of the estimator (14) the reference rotational position (φ _ref ) of the respective Rotors (2, 3) has been detected. procedure after claim 5 , characterized in that if the reference rotational position (φ _ref ) of the respective rotor has been detected since the estimator was last executed, on the basis of the last predicted estimated value for the speed (ω) of the respective rotor and a time difference between the current execution time (t _A ) of the estimator (14) and the detection time (t _m ) of the respective rotor, an extrapolated value for the angle of rotation (φ _e ) of the respective rotor is determined and made available to the estimator (14) as a measured variable (y) of the respective rotor. procedure after claim 5 or 6 , characterized in that if the reference rotational position (φ _ref ) of the respective rotor has not been recognized since the estimator was last executed, the estimated values for the rotational angle (φ) and the speed (ω) of the respective rotor are based on the last predicted estimated values for the Angle of rotation and the speed of the respective rotor are predicted. Procedure according to one of Claims 5 until 7 , characterized in that if the reference rotational position (φ _ref ) of the respective rotor has been detected since the estimator was last executed, the last predicted estimated values for the angle of rotation (φ) and the speed (ω) of the respective rotor based on the measured variable (y) of the respective rotor are corrected, after which the estimated values for the angle of rotation (φ) and the rotational speed (ω) of the respective rotor is predicted based on the corrected estimated values for the rotational angle (φ) and the rotational speed (ω) of the respective rotor. Method according to one of the preceding claims, characterized in that the drive (15) of each rotor is a speed-controlled drive, by means of which the speed (ω) of the respective rotor is controlled as a function of a target value for the speed (ω _set ) of the respective rotor , whereby the set value for the speed (ω _set ) of each rotor is made available to the estimator as an input variable (u). Method according to one of the preceding claims, characterized in that each rotor has a main axis of inertia (23) which is offset relative to the rotor axis (6). procedure after claim 10 , characterized in that the at least one sensor (9) is used to detect changes in distance between each rotor and the at least one sensor (9), the reference rotational position (φ _ref ) of each rotor being determined by a minimum or maximum distance (d) between the respective rotor and the at least one sensor (9) is defined. procedure after claim 10 or 11 , characterized in that each rotor consists at least partially of a magnetic material and the sensor (9) is a magnetic field sensor. Method according to one of the preceding claims, characterized in that the reference rotational positions (φ _ref ) of the rotors are detected by the same at least one sensor (9).

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