DE10163504B4 - Method for iterative error compensation of sin / cos position measuring systems for offset, amplitude and phase errors - Google Patents

Abstract

Method for evaluating sin / cos position measuring systems with iterative error compensation with the following method steps:
- Determining measured values of the cosine track (x) and the sine track (y) per signal period, wherein a number of n = 2 ^Z measured values per signal period is determined and wherein a number of equidistant as possible measured values per signal period is determined,
- Estimation of offset error (x ₀ , y ₀ ) and / or amplitude error (a / b) and / or phase error (Δφ) or of proportional magnitudes from the measured values obtained with a Fourier analysis, wherein
- Fourier coefficients for the fundamental and the first harmonic are determined and
Offset errors (x ₀ , y ₀ ) are essentially determined from the Fourier coefficients of the fundamental oscillation and
Amplitude error (a / b) and / or phase error (Δφ) are essentially determined from the Fourier coefficients of the first harmonic, wherein
- respective estimated error parameters are refined by iterative application of the Fourier analysis to approximately exact correction values, and wherein
The compensation of the determined error parameters (x ₀ , y ₀ , a / b, ...

Description

The The invention relates to a method for evaluating sin / cos position measuring systems with iterative error compensation based on the determination of Measurements of the cosine track and the sine track.

Position measuring systems are used, for example, as rotor position encoder systems used. Here one differentiates between the types coder (Encoder) and resolver. Both systems fulfill the task of an angular size in one usually to transfer digital output size, e.g. a digital position signal for controlling an inverter. In addition to the so-called absolute position measuring systems today are the Incremental position measuring systems in use, which often have a sine / cosine output.

there becomes the location information about the signal periods counted (hereinafter referred to as coarse layer). You can also evaluate by the sine and cosine trace the location within a signal period (hereinafter referred to as fine layer) determine even more accurately. To There are already a number of known methods. This procedure can the more precise work, such as the errors of the sine and cosine track in terms of Offset, amplitude and phase errors are corrected. For the correction Various methods are known.

From the German patent application DE 101 12 772 A1 For example, a method of compensating for periodic signals at a sensor output is known. The method includes determining a sum signal from sensor outputs of M sensor elements, determining amplitude and phase of N frequency components in the sum signal, and calculating a sensor output signal gain adjustment coefficient for each sensor output.

From the German patent application DE 199 14 447 A1 A self-calibrating position transducer system and method is known. The position transducer system, or method, uses the position transducer itself as a position reference during calibration, thereby eliminating the use of an external reference during calibration.

Out the publication "iee Automation Proceedings " SPS / IPC / DRIVES, Electrical Automation Systems and Systems Components, Trade Fair & Congress, 23-25th November 1999 Nuremberg, Pages 617-626, is a method for increasing accuracy in position measuring systems known by self-learning compensation systematic errors. In the process are over a model of the Weggebers all deterministic errors recorded, stored in a suitable form and then to Correction of further measured values used.

So far There are analog or quasi-analogue regulators that measure the amplitudes and Determine offset offset and compensate. The phase error is so far from the user over adjusted a configurable fixed value. The adjustment takes place but not exactly, but it will be a signal with the double Frequency of the sine / cosine track subtracted in the correct phase. Besides There are two other methods: one proposed by the Applicant and not yet published Method is that in a complex calculation the offset, Amplitude and phase errors from any number not necessarily equidistant Measured values are calculated. Another already known method is that the errors by means of a Fourier transform from a number of 2 ^ n as equidistant as possible Values estimated become and the angle over a table is corrected. The Fourier analysis returns the errors but only approximately, which is disadvantageous and therefore undesirable is.

task The present invention is therefore a method for error compensation to suggest with the in a Fourier analysis a near exact result for Correction values can be achieved.

• – Ermitteln von Messwerten der Cosinus-Spur und der Sinus-Spur pro Signalperiode, wobei eine Anzahl von n=2^Z Messwerten pro Signalperiode ermittelt wird und wobei eine Anzahl von möglichst äquidistanten Messwerten pro Signalperiode ermittelt wird,
• – Schätzen von Offsetfehler und/oder Amplitudenfehler und/oder Phasenfehler oder von dazu proportionalen Größen aus den ermittelten Messwerten mit einer Fourieranalyse, wobei
• – Fourierkoeffizienten für die Grundschwingung und für die erste Oberschwingung ermittelt werden und
• – Offsetfehler im wesentlichen aus den Fourierkoeffizienten der Grundschwingung bestimmt werden und,
• – Amplitudenfehler und/oder Phasenfehler im Wesentlichen aus den Fourierkoeffizienten der ersten Oberschwingung bestimmt werden, wobei
• – jeweilige geschätzte Fehlerparameter durch iterative Anwendung der Fourieranalyse zu annähernd exakten Korrekturwerten verfeinert werden und wobei
• – die Kompensation der bestimmten Fehlerparameter für eine Auswertung der Feinlage des Lagemesssystems nach
  
  erfolgt.

According to the present invention, this object is achieved by a method for evaluating sin / cos position measurement systems with iterative error compensation with the following method steps:

• - Determining measured values of the cosine track and the sine track per signal period, wherein a number of n = 2 ^Z measured values per signal period is determined and wherein a number of equidistant as possible measured values per signal period is determined,
• - Estimation of offset error and / or amplitude error and / or phase error or proportional thereto magnitudes from the measured values obtained with a Fourier analysis, wherein
• - Fourier coefficients for the fundamental and the first harmonic are determined and
• Offset errors are essentially determined from the Fourier coefficients of the fundamental oscillation and
• Amplitude error and / or phase error are essentially determined from the Fourier coefficients of the first harmonic, wherein
• - respective estimated error parameters are refined by iterative application of the Fourier analysis to approximately exact correction values, and wherein
• - The compensation of certain error parameters for an evaluation of the fine position of the position measuring system after
  
  he follows.

It is recommended that a number of n = 2 ^Z measured values per signal period is determined. In addition, a number of as equidistant measured values per signal period should be determined.

erfolgt.Furthermore, it has proved to be advantageous if a compensation of the specific error parameters x ₀ , y ₀ , a / b, Δφ for an evaluation of the fine layer φ of the position measuring system

he follows.

angenommenen und

• – aus den Messwerten damit ein Winkel φ für die Feinlage errechnet, wobei
• – eine Periode der Feinlage in n=2^Z gleichgroße Winkelbereiche aufgeteilt wird, wobei
• – zu jedem Winkelbereich ein Messwert r gemäß

abgespeichert wird.According to a further advantageous embodiment of the invention, a fault-free signal according to

accepted and

• - Calculated from the measured values so that an angle φ for the fine layer, wherein
• - A period of the fine layer is divided into n = 2 ^Z equal-sized angular ranges, wherein
• - For each angular range a measured value r according to

is stored.

there can possible angle ranges, for which no measured value is present, by interpolation of adjacent measured values be provided with an associated measured value.

mit k=1 für die Grundschwingung und K=2 für die erste Oberschwingung.Furthermore, it has proved to be favorable if the Fourier coefficients are determined separately according to real part and imaginary part as follows:

with k = 1 for the fundamental and K = 2 for the first harmonic.

The error parameters from the calculated Fourier coefficients are then determined according to the invention preferably as follows:

ermittelt.According to a further advantageous embodiment of the method according to the present invention, refined error parameters are determined in the context of an iteration according to

determined.

A particularly effective evaluation of the fine layer φ of the position measuring system is obtained by:

In the method according to the invention, therefore, a closed loop is constructed, the after egg niger iterations of a Fourier analysis provides an approximately exact result for the desired correction values.

One decisive advantage of the invention is that the little expensive estimation by finally a Fourier analysis but to a complete Correction of errors leads.

Further Advantages and details, especially with regard to the mathematical backgrounds The calculations are based on the following statements and in conjunction with the figures. These show in schematic representation:

1 to 20 a graphical overview of determined real and imaginary parts according to the invention for the individual error parameters or disturbance variables in the operating point of an error-free signal.

Based on the above-mentioned known method of approximate determination of correction values by means of a Fourier analysis, the offset, amplitude and phase errors are first estimated from a number of 2 ^Z as equidistant measured values per signal period as possible with a Fourier analysis.

In the method according to the invention will now be complementary built a closed loop, which is an iterative process to determine a nearly exact result for the desired Correction values provides, which will be explained in more detail below.

To further illustrate the invention, the following signal model of the position measuring system is initially used: x = a · cos (φ + Δφ) + x 0 y = b · sin (φ) + y 0

Where x is the cosine track, y is the sinusoidal track. The designations a and b are the respective amplitudes of the tracks, x ₀ and y ₀ is the respective signal offset and Δφ is the phase error, φ corresponds to the fine position.

Ideally, a = b should be. The deviation a / b is called the amplitude error. If the errors parameter a / b, x _0, y ₀ and Δφ known, one can determine the required fine position using the following formula:

The Error parameters are to be determined from the corrected measured values x ^ and y ^ become.

angenommenen.Initially, the start condition is an error-free signal

adopted.

abgespeichert.The angle φ is calculated from the measured values x and y. One period of the fine layer (φ = 0..360 °) is divided into n = 2 ^Z equal-sized angular ranges. For each of these angular ranges, hereinafter referred to as "angle fan" 0..n-1, a measured value r is determined according to

stored.

If the angle fan largely filled with measured values are, can any gaps also be interpolated from the measured values of the neighboring angle fan.

For the collected data, Fourier coefficients for the fundamental and the first harmonic (k = 1 and k = 2, respectively) are calculated separately for the real and imaginary parts as follows:

The offset errors x ₀ and y ₀ are formed essentially in the coefficients of the fundamental mode (re ₁ and in FIG. ₁ ). The amplitude and phase error appears essentially in the coefficients of the first harmonic (re ₂ and in _FIG . ₂ ).

This essential insight of the inventors can be seen with reference to the figures 1 to 20 understand well. Here, the course of the coefficients of the fundamental oscillation (re ₁ and in _{FIG. 1} ) and the coefficients of the first harmonic (re ₂ and in _{FIG. 2} ) are in one for each disturbance variable
Operating point: x ₀ = 0 y ₀ = 0 a = 1 b = 1 Δφ = 0
plotted graphically.

The Designations are as follows:

x ₀ , y ₀

Disturbance offset error

from

Disturbance amplitude error

Δφ

Disturbance phase error

re ₁

Real part of the fundamental

in the ₁

Imaginary part of fundamental

re ₂

Real part of the first harmonic

in the _2nd

Imaginary part of first harmonic

The individual diagrams show the relationships for a calculation with n = 64 angular compartments and a variation of the respective disturbance by -0.2 .. + 0.2 from the undisturbed operating point (x ₀ = 0, y ₀ = 0, Δφ = 0; a = 1, b = 1). It can be seen from the diagrams that approximately the following dependencies apply in this operating point:

Since these dependencies only apply approximately and are also dependent on the selected operating point, an iterative calculation is required to exactly correct the errors. Since only the ratio of a / b is required for the calculation of the correct angle φ, it does not interfere with the fact that in re ₂ one can not distinguish which of the two quantities is disturbed.

The correction values for the next iteration are thus:

There for the Determining the new correction values always the already corrected Measured values x ^ and y ^ are used, the method is already approaching after a few iterations of the exact solution.

If one considers the argument of the arctangent, then one can also resort directly to the following formula in the calculation of y ^ / x ^:

In other words, you get this:

A new set of correction coefficients x ₀ , y ₀ , d, q can be determined by the microprocessor in a slow task (time slice). When using the correction coefficients in the fast task (time slice) then only multiplications and additions / subtractions are required, which can be performed quickly by a microprocessor. In this way one thus obtains a particularly effective realization of the invention.

One Encoder system often owns several signal periods. The errors in the individual signal periods can become more or less different. After a favorable Development of the invention, the signal periods of a Coarse position counter counted. With the meter reading of the Groblage counter can one therefore identifies individual signal periods.

This makes it possible to carry out the determination of correction coefficients selectively for individual signal periods or even for groups of signal periods. In each case, sets of correction coefficients x ₀ , y ₀ , d, q are produced, which are stored in the microprocessor. In the fast task (time slice) it can be decided on the basis of the coarse count counter which set of correction coefficients is currently being used must become.

Claims (7)

Method for evaluating sin / cos position measuring systems with iterative error compensation with the following method steps: - Determining measured values of the cosine track (x) and the sine track (y) per signal period, wherein a number of n = 2 ^Z measured values per signal period is determined and wherein a number of equidistant as possible measured values per signal period is determined, - Estimation of offset error (x ₀ , y ₀ ) and / or amplitude error (a / b) and / or phase error (Δφ) or of proportional to the determined variables Measured values with a Fourier analysis, wherein - Fourier coefficients for the fundamental and for the first harmonic are determined and - Offset errors (x ₀ , y ₀ ) are essentially determined from the Fourier coefficients of the fundamental and - Amplitude errors (a / b) and / or phase errors (Δφ) are essentially determined from the Fourier coefficients of the first harmonic, wherein - respective estimated error par ameter by iterative application of the Fourier analysis to approximately exact correction values are refined and wherein - the compensation of the specific error parameters (x ₀ , y ₀ , a / b, Δφ) for an evaluation of the fine position (φ) of the position measuring system after

he follows. Method for evaluating sin / cos position measuring systems with iterative error compensation according to claim 1, wherein - as a start condition, a fault-free signal according to

and - from the measured values (x, y) an angle φ is calculated for the fine layer, wherein - a period of the fine layer is divided into n = 2 ^Z equal-sized angular ranges, whereby -for each angular range a measured value r according to

is stored. Method for evaluating sin / cos position measurement systems with iterative error compensation according to claim 2, wherein - the Fourier coefficients separated by real part and imaginary part are determined as follows:

with k = 1 for the fundamental and K = 2 for the first harmonic. Method for evaluating sin / cos position measurement systems with iterative error compensation according to claim 3, wherein - the error parameters are determined from the determined Fourier coefficients as follows:

Method for evaluating sin / cos position measuring systems with iterative error compensation according to claim 3 or 4, wherein - refined error parameters in the context of an iteration according to

be determined. Method for evaluating sin / cos position measuring systems with iterative error compensation according to one of claims 2 to 5, where - eventual Angular ranges, for which no measured value (r) is present, by interpolation of adjacent Measured values are to be provided with an assigned measured value. Method for error-compensated evaluation of sin / cos position measuring systems according to claim 5, wherein an evaluation of the fine position (φ) of the position measuring system according to

he follows.