Resolvers are widely used in electric vehicles, trains, and other harsh fields because of their robustness. However, the resolver outputs two orthogonal analog signals, which make the resolver decoding either high hardware cost or poor decoding accuracy. A noise robust resolver decoding method using Hilbert transform and angle-tracking observer (ATO) is proposed in this paper. Firstly, Hilbert transform is employed to obtain the modular envelopes of resolver signals. Next, the modular envelopes are filtered, and their quadrants are recognized by the polarity relation of the resolver signals and the modular envelope extreme point. Then, the ideal demodulating signals are gained through the linearization of the envelope zero point. Finally, the improved ATO is used to obtain the rotor angle by iteratively calculating the demodulating signal. The effectiveness of the proposed method is verified by experiments under various rotor speed conditions and compared with other methods in noise immunity. The results show that the proposed method can control the decoding error within 0.5° when the SNR is 30 dB, which provides a high-precision and low-cost decoding scheme for practical applications.

Resolver, a type of position sensor, has the advantages of durability and adaptability to harsh environments and is widely used in rail transit, new energy vehicles, aerospace, and other industrial fields [

Existing methods of resolver decoding can be divided into two categories: hardware-based and software-based [

The software-based method usually takes two steps to decode resolver signals, and obtaining the demodulation signal is the first step. As a time-frequency analysis tool, S-transform is used to extract the resolver signal envelope in [

The second step of the software-based method is to calculate the rotor angle according to the demodulation signal. The commonly used angle calculation methods include arc-tangent method and ATO [

The software-based decoding method has become a better choice for many applications due to its low cost and flexibility. However, the accuracy and noise robustness of the existing software-based methods need to be further improved [

In this paper, combining the advantages of Hilbert transform in envelope extraction and ATO in angle calculation, a new resolver decoding method is proposed for various conditions. Firstly, Hilbert transform is used to transform the resolver signals into an analytic signal and extract their modular envelope. Then, after filtering the modular envelope, the perfect demodulation signal is formed by using the polarity rule and zero-crossing linearization. Finally, the improved ATO is used to decode the demodulated signal to obtain the rotation angle. Through the simulations under various conditions, it is verified that the decoding error of the proposed method is less than 0.5° when the SNR is 30 dB. Compared with other methods such as the peak detection method and multiplying excitation technique, the proposed method has better antinoise performance.

The working principle of the resolver is shown in Figure

Schematic diagram of the resolver.

It can be seen from (

The Hilbert transform

An analytic signal

The modular envelope of the resolver signal can be directly obtained by Hilbert transform, and the envelope

The complete demodulation signal can be obtained by imposing quadrant interpretation to the modular envelope. And the complete demodulation signal will be employed to solve rotor angle

The principle of the ATO is to track the angle error through the trigonometric function of the angle difference by using the detected demodulation signal. As shown in Figure

ATO schematic diagram.

Therefore, the value of

The resolver decoding method proposed in this paper is shown in Figure

Decoding process diagram.

As shown in Figure

A multiplication rule is adopted to obtain the demodulation signals

As mentioned above, the rotor angle _{1} = 1 is adopted in this paper to avoid the result oscillation caused by the excessive value.

The iterative termination condition of (

To sum up, the proposed resolver decoding method is implemented in the following steps:

Step 1: formulas (

Step 2: the amplitudes of

Step 3: a FIR filter is used to smooth the modular envelopes to get

Step 4: formula (

Step 5: formulas (

According to the above algorithm steps, the calculation of this algorithm is mainly in three aspects, that is, (1) using Hilbert transform to form the analytic signal, (2) using FIR to filter the demodulation signal, and (3) using the ATO to decode the angle. If the processed data are

In order to verify the feasibility of the proposed method for resolver decoding, experiments were carried out through MATLAB simulation. The initial angle is set as 30°, the excitation frequency _{s} = 160 kHz, the excitation amplitude

Original signals.

Take the medium speed working condition (2000 r/min) as an example, and noise is superimposed on the original signal, and the SNR is set to 30 dB. The simulation results are shown in Figure

Simulation results without the filter. (a) Demodulation signals. (b) Rotor angle. (c) Angle error.

Simulation results using the filter. (a) Demodulation signals. (b) Rotor angle. (c) Angle error.

As shown in Figure _{l} from the polar conversion point as two endpoints, and then update the data between the two ends through the linear equation. In this way, the zero-crossing signal distortion caused by the weakening of the extreme point can be eliminated. Generally, _{l} can be 5∼20. The simulation results after linearization are shown in Figure

Simulation results using the filter and zero-crossing linearization. (a) Demodulation signals. (b) Angle error.

As shown in Figure

In order to verify the effectiveness of the proposed method under various working conditions, four working conditions, namely, the ultralow rotation speed (100 rpm), low rotation speed (1000 rpm), medium rotation speed (2000 rpm), and high rotation speed (8000 rpm), are set up for the adaptability experiment, and the noise level is 30 dB. A large number of experiments have been performed under various working conditions, and a section of signals (2500 samples) and their decoded results are randomly selected for statistical analysis. Figure

Simulation results under various working conditions. (a) Demodulation signals. (b) Rotor angle. (c) Angle error.

Angle error statistics under various working conditions.

Working condition (rpm) | Error (degree) | ||
---|---|---|---|

Maximum | Mean | Standard deviation | |

100 | 0.406 | 0.028 | 0.167 |

1000 | 0.452 | −0.021 | 0.180 |

2000 | 0.445 | −0.020 | 0.175 |

8000 | 0.492 | −0.117 | 0.152 |

It can be seen from Table

In order to compare the antinoise performance of the proposed method with other methods, a comparative experiment was conducted with the peak detection method [

Decoding errors of various decoding methods for noise-containing signals.

SNR (dB) | Maximum error (degree) | ||
---|---|---|---|

Hilbert + ATO | Multiplied excitation signal | Peak detection | |

40 | 0.162 | 0.501 | 2.067 |

30 | 0.445 | 1.850 | 5.617 |

The difficulty of resolver decoding is to achieve the best balance between cost and availability. If the software-based decoding technology can meet the actual requirements, the decoding system will have cost advantage. In this paper, a new method for calculating rotation angle is proposed by using Hilbert transform and improved ATO, which can adapt to various working conditions of the resolver and meet the requirements of precision and real time. The analytic signal formed by Hilbert transform can extract the signal envelope effectively; the zero-crossing linearization can eliminate the error caused by the filter on the minimum point of the module envelope. The decoding error of the proposed method is less than 0.5° when the SNR is 30 dB, and the algorithm time is less than 0.3 ms when the data length is 256 points, which can meet the accuracy and real-time requirements of practical applications. Compared with other methods, it also has advantages in noise immunity. Therefore, as a low-cost software decoding method, this method has a good application prospect. It is true that in order to make the proposed method run in the actual system, the software and hardware design based on the DSP chip need to be further studied.

No data were used to support this study.

The authors declare that they have no conflicts of interest.

This work was supported by the Scientific Research Fund of Hunan Education Department of China (18A272).