Model-based calibration of sine-cosine angle sensors

Abstract

In a method for calibrating an angle sensor (4), a mathematical model (30) is created for a curve (22) of generated value pairs (14) in a plane (16), real value pairs (14) are recorded as training data (32) for a plurality of different angles of rotation (w), the model (30) is approximated to the actual curve (22) with the aid of an error minimization method (34) by iteratively minimizing an error sum of the deviations between training data (32) and model (30), the modified model (30) is used as a model (30) for the real curve (22), so that measured angles of rotation (w) can be determined from measured value pairs (14) using the error-minimized model (30). A sensor arrangement (2) contains the angle sensor (4), a calibration module (6) for carrying out the method and an evaluation module (8) with the error-minimized model (30) in order to determine and provide measured angles of rotation (w) from measured value pairs (14) using the error-minimized model (30).

Description

The invention relates to a sine-cosine angle sensor.A sine-cosine angle sensor known from practice outputs two values (e.g. voltages) corresponding to a sine and a cosine function for each rotation angle. This means that in an imaginary value (e.g. x-y) plane, the two values describe coordinates of a point in each case in the plane. Points that are established over the possible rotational angles are located on a course line. The location on the extension line represents the associated angle of rotation. Ideally, a unit circle (circle segment with less than 360° angular coverage) is obtained as the extension line. Real sensors have errors, which does not result in an ideal circuit. Angle sensors of this type must be calibrated, i.e. the course line of the points in the plane for the possible rotational angles must be determined.In practice, the sensors are calibrated by traversing one or more full revolutions (0° to 360°) of the sensor. Typically, for the calibration of a sine-cosine-based angle sensor, the two signals are thus recorded for a plurality of revolutions.Alternatively, constructions with reference measurement (e.g. second external angle sensor in the end-of-line test / calibration) are also possible. However, these are complicated and, depending on the design, are not always possible.It is an object of the invention to provide improvements in such calibration.The object is achieved by a method according to claim 1. preferred or advantageous embodiments of the invention and other categories of invention are evident from the further claims, the following description and the attached figures.The method serves or is configured to calibrate a sine-cosine angle sensor. The following angle sensor is assumed here: the angle sensor assigns a respective sine-cosine value pair in a value plane to a respective angle of rotation, as explained above. The value pairs are ideally located on or along the unit circle in the plane depending on the angle of rotation. In real terms, however, the values lie in the region of an initially unknown curve in the plane. In the detection of the value pairs, it is particularly good if the respective sine and cosine values of a value pair are detected as simultaneously as possible, in order not to create any correlation problems here.The pair of values thus represents a measured value which is mapped onto a (measured) angle of rotation via the curve.Precisely because of the fact that the course curve is initially unknown, the angle sensor requires calibration, i.e. the course curve is to be determined in the plane. Otherwise, no meaningful / correct angle of rotation can be assigned to the measured value.Merely by way of example, the relationships are explained as follows: the x-y plane is assumed as the plane. For a specific angle of rotation w, the sensor then delivers a value pair consisting of x=sin w and y=cos w. All value pairs are thus located on the unit circle, for w=0° the starting value is obtained as a value pair (x=0, y=1). The passage through the unit circle for increasing angles w is clockwise. For w=360 °, the starting point (0, 1) is reached again.In the region of the curve it is certain that the values do not lie exactly on the curve, but--for example, due to inaccuracies in the generation of values--statistically distributed in a strip surrounding the curve, the region around the curve, i.e., in the vicinity thereof.In the method, a mathematical model for the curve in the plane is first created. The model is in particular an ellipse model, i.e. models a curve in the form of an ellipse. Initially, a potential curve, initially presumed or estimated in this way, is initially assumed. The model thus represents a corresponding curve. Within the framework of the actual calibration, this initially estimated initial "start" curve is now to be approximated as well as possible to the actual, real curve.This is done as follows: The angle sensor is now rotated in real fashion and the assigned real value pairs are acquired as training data for a plurality of different rotation angles.Subsequently, with the aid of an error minimization method, the model (and thus the initially suspected profile curve, which is mapped by the model or represented by it) is approximated in the plane of the actual profile curve. This is in turn effected in that an error sum of the deviations of the real value pairs of the training data from the model / the profile curve is iteratively minimized. This takes place until the minimization method is concluded, in particular until an end criterion of the corresponding minimization method is reached. The error minimization method is carried out in a manner customary in the art; for this purpose, a series of possible methods are available to the person skilled in the art, which should not be enumerated and explained in more detail here.Now, therefore, an error-minimized model which has meanwhile been modified is available, which thus also represents a modified (in comparison to its initial profile) profile curve. The error-minimized model / curve can now be expected to come as close as possible to the actual curve within the scope of the minimization method or to model it sufficiently accurately.The model, which has meanwhile been iteratively modified, is used for the (i.e. as a replacement / model / simulation / approximation of) curve.As a result, a respective measurement angle (measured or determined angle of rotation) can now be determined from a respectively measured value pair on the basis of the error-minimized model. In particular, the inverse model is used here, namely to map a pair of values to a determined angle of rotation (measurement angle). Each point of the curve is now assigned to a specific angle of rotation via the error-minimized model.A real value pair which lies in the region next to the course curve can be projected in particular perpendicular or perpendicular to the course curve. The corresponding projection point on the curve then delivers the angle of rotation to the measured value pair.The invention is based on the idea that real angle sensors have errors, e.g. offset, gain and phase offset, as a result of which the ideal profile curve (unit circle, circle) changes, e.g. towards a twisted ellipse. In order for the angle sensor to be able to be used in a system (finally installed in an object to be used), these errors usually have to be measured and corrected at least once.According to the invention, a particularly simple method results, since constructions with reference measurement (for example second external angle sensor) can be dispensed with. In addition, the method is simple and robust with respect to outliers (value pairs which are far away from the actual course curve) and is also possible if no complete sensor revolution (i.e. less than 360°) can be carried out within the scope of the calibration (for example because of installation in the insert object and rotational angle limitation).In a preferred embodiment, the model is created on the basis of a previously known specification. The previously known specification is therefore present before the model creation or has been determined in advance. The specification consists, for example, in that the curve is initially assumed to be the unit circle. A typical profile curve for the relevant sensor or a specific sensor type can also be known, which usually results or has already been historically obtained, for example, in the corresponding application or installation situation of a sensor. The specifications can be determined theoretically or empirically and can be based in particular on the previous calibration of other, for example, sensors of the same type or similar type, etc. By means of a good specification, a corresponding error minimization method can be carried out particularly quickly and lead to particularly good results, since the "real" profile curve is then already very well approximated.In a preferred embodiment, at least six value pairs are acquired as training data. Particularly in the case of a uniform distribution of the six value pairs over the entire possible rotational or angular range of the sensor, good results can already be achieved thanks to the method.In a preferred embodiment, the sensor is rotated within an angle range of less than 360°, in particular of less than 330 or 300 or 280°, in order to generate the training data. The method can thus also be used for already installed angle sensors which, due to the installation, can no longer execute a full revolution of 360°, but only within a smaller angle range.In a preferred embodiment, the training data is generated such that they are distributed uniformly over the angular range. For example, value pairs are detected in a specific angle range at most at the distance of 1°, 0.1°, 0.01 °, etc. In particular, one or more values / measurements or acquisitions for the training data are carried out at each rotation angle, in particular at each rotation angle the same number. This results in particularly good results for the error minimization methods.In a preferred variant of this embodiment, the training data is generated uniformly distributed over the angular range in that the sensor is rotated uniformly, in particular at a constant angular speed, over the angular range and, in the process, value pairs are interrogated at an equally uniform, in particular constant, clock rate. An equal distribution of the value pairs over the angle range can thus be achieved particularly easily.In a preferred embodiment, a gradient descent method is used as the error minimization method. Such processes provide particularly good results within the scope of the invention. This applies in particular to the adaptation of a vector of parameters for the progression curve, see below.In a preferred embodiment, it is assumed that the curve has an elliptical shape or can be approximated sufficiently well by such a curve. The model is then an ellipse model. The modeled ellipse is described by a vector of parameters. The vector contains as parameters: the center of an ellipse, in particular 2 parameters in the form of x- and y-coordinates. The size of the main and secondary axes thereof, in particular the two radii or diameters of the axes). The angular offset of the ellipse to the unit circle or its zero angle in the form of a parameter. "angular offset" therefore means the angle between the respective 0° rotation angles on the unit circle and the profile curve. In particular, this results in a vector having a total of 5 entries / parameters / scalars.In other words, a curve in the form of an ellipse is assumed which lies in the plane but is displaced and rotated with respect to the zero point.The model or the assumed course curve is then iteratively changed and the actual course curve is approximated as well as possible by the vector being changed. In particular, the gradient descent method is applied to the vector. This results in a particularly simple and fundamentally conventional gradient descent method, which can therefore be used particularly effectively.In a preferred embodiment, the calibration or the present method is carried out without using a further angle sensor. Thus, the method becomes particularly inexpensive.In a preferred embodiment, the calibration is carried out on an angle sensor which is already finally installed on an insert object (in an installation state / installation position). As explained above, sensors can also be calibrated here which can be rotated less than 360° in the installation position, but which can nevertheless be calibrated with high quality. This is done without additional expense, such as external angle sensors, measuring assemblies, etc.The object of the invention is also achieved by a sensor arrangement according to claim 11, which contains the angle sensor explained above, which thus assigns a respective sine-cosine value pair in a value plane to a respective angle of rotation, wherein the value pairs lie in the region of a course curve in the plane depending on the angle of rotation. The sensor arrangement contains a calibration module which is configured to carry out the method according to the invention as described above. The sensor arrangement contains an evaluation module. This contains the error-minimized model (representing the error-minimized profile curve that approximates the real profile curve sufficiently exactly) for the angle sensor (i.e., the "result" of the method according to the invention). The evaluation module is configured to determine and provide the respective determined angle of rotation (measurement angle) from the respectively measured value pair on the basis of the error-minimized model / the approximated profile curve. As explained, in more detail, the inverse model / the inverse error-minimized curve is used here.The sensor arrangement and at least a part of its possible embodiments and the respective advantages have already been explained accordingly in connection with the method according to the invention.In a preferred embodiment, the angle sensor and the evaluation module form an operational, in particular structural unit. The calibration module is configured separately for this purpose, in particular structurally separated. The calibration module is generally to be used only once or at least only at relatively large intervals, namely in order to determine the error-minimized profile curve / model or to re-improve / re-calibrate it again over time. Thanks to the separation from the unit, it can be removed from the unit after completion of a task. This is because the task is accomplished when the error-minimized model / curve curve is present with sufficient accuracy. Then, in real measuring operation, only the operational unit consisting of angle sensor and evaluation module is still required. The operational unit is in particular a structural unit in the form of a sensor module, which then provides a determined angle of rotation for each measured value pair.The invention is based on the following findings, observations or considerations and still has the following preferred embodiments. These embodiments are also sometimes referred to simply as "the invention". The embodiments can also contain parts or combinations of the above-mentioned embodiments or correspond to these and / or optionally also include embodiments not mentioned up to now.According to the invention, in particular a numerical (iteration method) parameter determination for calibrating sine-cosine angle or rotation sensors is obtained. In particular, there results an iterative parameterization or calibration of sine-cosine-based angle sensors in the construction (finally in the object to be used) with a restricted displacement range (possible angle of rotation range less than 360°) and without a reference angle sensor.The invention is suitable in particular for use in the field of e-mobility, for example for a parking lock actuator or a disconnect actuator for decoupling an electric motor from a drive train.The invention is based inter alia on the following finding, which also forms an assumption for the present invention: the curve has the shape of an ellipse. Thanks to the invention, what is usual in practice can be avoided: For there, the two signals are typically recorded for a plurality of revolutions for calibrating a sine-cosine-based angle sensor. The minimums and maximums are used to determine the offsets of the signals first, then the gain and then the phase offset with respect to one another.The method, on the other hand, enables the learning of a sine-cosine angle sensor in the construction (finally in the object to be used) without reference measurement and with a limited range of angles of rotation.The following applies in particular to the assumption of an ellipse shape for the curve: The ellipse is to be described for these purposes by means of the following parameters:Center points of the ellipse (offset)Radius of the ellipse per axis (gain)φ: Angle of rotation of the ellipse about its center (phase)The parameter vector thus results:For this purpose, the following equation is used:For the correction or as a calibration method, the following method is now proposed in particular: 1. the angle sensor, for example the axis of the actuator to be measured (on which the angle sensor is finally installed as an object to be used), is moved over the available angle range at the most constant angular speed possible. 2. the sine and cosine values are recorded as value pairs as simultaneously as possible and at constant time intervals (the method already works starting from six measured values (value pairs), but more measured values increase the accuracy considerably). The set of (here number n) value pairs form the training data. 3. The algorithm for parameter determination (iterative adaptation of the vector), as below, is applied to the recorded value pairs / training data. This can also be carried out in an external computing unit (e.g. EOL computer) for a more rapid learning process 4. the determined parameters (iteratively adapted vector, i.e. model / profile curve) are stored in the microcomputer (evaluation module) of the actuator (sensor arrangement) and can be used in inverted form for correcting the angle sensor system (angle sensor).For the iterative determination of the parameters, the error square sum of the measured values / value pairs (training data) is minimized. The residue of an individual measured value / value pair for a specific parameter set (model of a respective interpolation stage) is obtained as follows:The square error sum over n measured values / value pairs (i.e. the training data) corresponds to:The aim is now to iteratively find a parameter set (iteratively modified model) which describes the properties of the installed sensor (the real profile curve) as well as possible. For a first estimation (creation of the ellipse model), parameters are selected according to the specification, which correspond as far as possible to the typical values of the sensor in the construction. In order to be able to optimize these subsequently in a targeted manner, the square residual E is partially derived once for each parameter. The resulting gradient describes how, for any point and parameter set, the five parameters can be adjusted (gradient descent) to achieve as high a change as possible in the least squares sum:The gradient can be determined analytically relatively without problems, but on the basis of its length it is not described here.With each iteration k, each value pair of the n training data is thus calculated for each recorded measured value, the gradient is calculated with the current parameter set and the mean value is then formed over all gradients:The new parameter set is then obtained as follows: L denotes the learning rate and can be executed either as a scalar or 5x5 matrix. By means of the parameter L / the matrix, it is possible to control how quickly the algorithm learns with respect to a specific parameter (of the parameter vector).The learning processes can be aborted as soon as a residual residue sufficient for the application has been reached.Further features, effects and advantages of the invention will become apparent from the following description of a preferred exemplary embodiment of the invention and from the attached figures. In each case, a schematic schematic diagram shows: FIG. 1 shows an angle sensor installed in an insert object, FIG. 2 shows curves in the x-y plane for value pairs of the angle sensor from FIG. 1FIG. 1 shows a sensor arrangement 2, which contains an angle sensor 4, a calibration module 6 and an evaluation module 8, angle sensor 4 and evaluation module 8 form an operational, here also structural unit 10; calibration module 6 is designed separately from unit 10, here structurally separately as an independent device, since it is only required for calibrating angle sensor 4 or unit 10, but not for its / its regular measurement operation.The angle sensor 4 is finally installed on an insert object 12, here a shaft of an electric motor (not shown). The angle sensor is fixed in terms of rotation on the shaft, that is to say detects a current angle of rotation w of the shaft. In the corresponding installation or installation situation, the rotational capability of the insert object 12 and thus of the angle sensor 4 is limited to an angle range BW of less than 360°, namely here starting from a neutral angle 0° to -80° to +190°, that is to say BW=27°. Thus, the angle sensor 4 can be rotated only within the angle range BW. In the example, the angle of rotation w can therefore assume only values between -80° and +190°.FIG. 2 illustrates the following: In operation, the angle sensor assigns a respective sine-cosine value pair 14 to each or a respective current rotation angle w. The value pair 14 consists of the values x and y, which indicate respective x and y coordinates in an x-y plane 16 or a rectangular x-y coordinate system and thus represent a respective measured value 18 in the form of a value pair 14 and thus a point in the x-y plane 16.FIG. 2 shows the x-y plane 16 and a plurality of measurement values 18 or value pairs 14 in the form of crosses. The angle sensor 4 is also called a sine-cosine sensor: Because in the ideal case (ideal angle sensor 4) all value pairs 14 should lie on the unit circle 20 of the plane 16, wherein the x value should specify the respective sine value sin(w) of the relevant angle of rotation w and the y value should specify the cosine value cos(w) of the angle of rotation w.As can be seen in FIG. 2, however, the angle sensor 4 delivers values which are distributed differently in the plane 16, namely along an actual course curve 22.In the present case, it is assumed that the course curve 22 has an ellipse shape which can be mathematically described by its center point 24 with the center point coordinates (xc,yc) and by its main axis 26 awith axis radius xrand secondary axis 26 bwith axis radius yrand a tilt angle φ. The angle of inclination φ describes the angle by which (starting from the center 24) the 0° angle of the ellipse is tilted with respect to the y axis of the x-y plane 16. Depending on the current angle of rotation w, the value pairs are located in the corresponding angular range BW on the course curve 22, which (likewise because of practical deficiencies of the sensor 4) are distributed over a region 28 (only symbolically indicated by dashed lines) which surrounds the course curve 22 on both sides in the form of a tolerance band. The width of the region 28 depends on the accuracy requirements of the angle sensor 4, ambient conditions, etc.It is problematic that the course, position, size, etc. of the course curve 22, in other words the parameters (xc,yc,xr,yr,φ) for the angle sensor 4, are unknown in the corresponding installation situation on the application object 12. Within the scope of a calibration method, the curve 22, i.e. the mentioned parameters, is to be determined as follows:This is also illustrated with reference to FIG. 1 :The following processes take place in the calibration module 6. First, a mathematical model 30 of the curve 22, here an ellipse, is created on the basis of a specification 36, so to speak as a starting value or assumption for the curve for 22, in the plane 16. For this purpose, specific center point coordinates xc,yc, axis radii xr,yr, and tilt angle φ are predefined, assumed or selected. In the simplest case, the specification 36 could consist in the unit circle 20 being represented with the starting parameters. In the present case, however, the ellipse model 30 is selected as specification 36 in such a way as was historically determined for other identically constructed angle sensors 4 on identically constructed insert objects 12 in comparable assembly situations. In other words, the initial model 30 or the initial course curve 22 atherefore originates from the specification 36 (unit circle or here ellipse determined historically for a comparable situation).In the present case, the model 30 is thus an ellipse model and is therefore described by the vector. In other words, the model 30 represents a potential progression curve 22 ain the plane 16.The angle sensor 4 is now rotated, i.e. different rotation angles w are set on the insert object 12 and the assigned real value pairs 14 or real value pairs output or provided by the angle sensor 4 are acquired as training data 32 for a plurality of different rotation angles w. In FIG. 2, the training data 32 is shown as a plurality of crosses in the plane 16, which are drawn around the (currently unknown) curve 22 within the region 28.To generate the training data 32, the angle sensor 4 is thus rotated (on account of the structural limitations) within the angle range BW of only 270° (-80° to + 190°). The angle sensor w is rotated uniformly here or value pairs 14 are generated uniformly, so that they are evenly distributed over the angle range BW. In other words, for each subsection of the angular range BW of equal size, approximately the same number of value pairs 14 are generated. In the present case, this is achieved in that the sensor 4 is rotated uniformly, i.e. at a constant angular speed, and the value pairs 14 are determined at fixed time intervals.With the aid of an error minimization method 34 shown here only symbolically by an arrow, the initially selected model 30 or the progression curve 22 arepresented thereby is now iteratively approximated in the plane 16 of the actual progression curve 22. This is achieved in that iteratively (for the equations see above, not repeated again here) a square error sum SQR of the deviations ε of the real value pairs 14 (x, y) of the training data 32 from the model 30 or the respective course curve for 22 a(current vector) is formed and this square error sum SQR is minimized with the aid of a gradient descent method until an end criterion not explained in more detail here is reached. In other words, the model 30 as well as the curve 22a is changed.In FIG. 2, this is indicated in a very simplified manner in that the original initially selected course curve 22 ais iteratively changed first to a course curve for 22 band then to a course curve 22 cin a total of 2 iteration steps. The end criterion is now reached and the iteration method or error minimization method 34 is ended. The model 30 finally determined therewith, here in the form of the curve 22 c, is used as an error-minimized model / approximation of the real curve 22.The calibration is now complete and the angle sensor 4 can assume its actual calibrated operation. For this purpose, the determined course curve for 22 cis stored in the evaluation module 8 in the form of the error-minimized model 30 and used there. Thus, from each newly real value pair 14, the current angle of rotation w of the angle sensor 4 can be determined on the basis of the (inversely used) curve for 22 cin the form of the model 30. The calibration module 6 is now no longer required. Since this is constructed separately from the unit 10 in terms of construction, it can be removed from the unit 10, so that only this remains on the insert object 12.Reference numerals denote reference numerals2 Sensor arrangement 4 Angle sensor 6 Calibration module 8 Evaluation module 10 Unit (operational) 12 Object to be used 14 Value pair 16 Plane 18 Measured value 20 Unit circle 22, 22 a- c Verlauf curve 24 Center 26 a,b Haupt axis, minor axis 28 Region 30 Model 32 Training data 34 Error minimization method 36 Specification BW Angle range w Angle of rotation x,y Koordinaten xc,yc Center coordinate xr,yr Axis radii φ Angle of inclination Vector

Claims

Method for calibrating a sine-cosine angle sensor (4) which assigns a respective sine-cosine value pair (14) in a value plane (16) to a respective angle of rotation (w), wherein the value pairs (14), depending on the angle of rotation (w), lie in the region (28) of an initially unknown profile curve (22) in the plane (16), in which: - a mathematical model (30) is created for the profile curve (22) in the plane (16), - the angle sensor (4) is rotated and the assigned real value pairs (14) are acquired as training data (32) for a plurality of different angles of rotation (w), - the model (30) in the plane (16) is thereby approximated to the actual profile curve (22) with the aid of an error minimization method (34), iteratively minimizing an error sum of the deviations of the real value pairs (14) of the training data (32) from the model (30), - the iteratively modified model (30) is used as an error-minimized model (30) for the real profile curve (22), - so that a respective measured angle of rotation (w) can be determined from a respectively measured value pair (14) on the basis of the error-minimized model (30).Method according to Claim 1, characterized in that the model (30) is created on the basis of a previously known specification (36).Method according to one of the preceding claims, characterized in that at least six value pairs (14) are acquired as training data (32).Method according to one of the preceding claims, characterized in that the angle sensor (4) is rotated within an angle range (BW) of less than 360° in order to generate the training data (32).Method according to one of the preceding claims, characterized in that the training data (32) are generated in such a way that they are distributed uniformly over the angular range (BW).Method according to Claim 5, characterized in that the training data (32) is generated uniformly distributed over the angular range (BW) by the angle sensor (4) being rotated uniformly over the angular range (BW).Method according to one of the preceding claims, characterized in that a gradient descent method is used as the error minimization method (34).Method according to one of the preceding claims, characterized in that - the model (30) is an ellipse model and is described by a vector ( p → ) which contains the centre point (24) of the ellipse, the size of its principal axis (26a) and secondary axis (26b) and also its angular offset (φ) with respect to the unit circle (20), - the model (30) is approximated to the actual course curve (22) by changing the vector ( p → ) .Method according to one of the preceding claims, characterized in that the calibration is carried out without using a further angle sensor.Method according to one of the preceding claims, characterized in that the calibration is carried out on an angle sensor (4) which is finally installed in an insert object (12).Sensor arrangement (2), - with an angle sensor (4) which assigns a respective sine-cosine value pair (14) in a value plane (16) to a respective angle of rotation (w), wherein the value pairs (14) are in the region (28) of a profile curve (22) of the plane (16) depending on the angle of rotation (w), - with a calibration module (6) which is configured to carry out the method according to one of the preceding claims, - with an evaluation module (8) which contains the error-minimized model (30) for the angle sensor (4) and which is configured to determine and provide the respective measured angle of rotation (w) from the respective measured value pair (14) on the basis of the error-minimized model (30).Sensor arrangement (2) according to Claim 11, characterized in that the angle sensor (4) and the evaluation module (8) form an operational unit (10), and the calibration module (6) is designed separately therefrom.

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