For the encoders, especially the sine-cosine magnetic ones, a new method to measure absolute angular position is proposed in the paper. In the method, the code disc of the encoder has only two circle tracks and each one was divided into
Absolute angular position measurement is very important in industrial applications and robotic systems [
For the optical encoders, based on the arrangement forms of the photodetectors, the methods can be divided into two types. In the first type of the encoding method, the photodetectors are arranged along the radial direction. One method of this type is the natural binary encoding method which makes it easy for the encoders to obtain the absolute rotating angle. However, the encoders are prone to reading errors, especially the cross errors, since more bits may change between adjacent scale sectors [
Based on the analysis of the methods used in the optical encoders, developing an absolute angular position measurement method which can decrease dimensions of the encoders and the numbers of the reading heads is necessary. Moreover, if the method can be used not only in optical encoders but also in the magnetic or the electromagnetic encoders, it is much better. Based on this, a novel absolute angular position measurement method which can be widely used in different types of encoders is proposed in the paper. Without loss of generality in the paper, the attention will only focus on the electromagnetic angular encoders in the validation section. The structure of the paper is organized as follows: for a proper analysis of the method, physical modeling and mathematical validation process are required. Therefore, the paper starts with derivation process of the method in Section
According to the measurement method applied in the optical encoders, the method proposed in the paper to measure absolute rotating angle needs the code disc of the encoder to have two tracks. Unlike other methods mentioned above, the two tracks of the encoder can be divided into
As shown in Figure
Two circles rotating around the same axis.
Therefore, the positions of any points
Based on the model, if
According to the physical model above, if
Then
Taking (
As known from the physical model established in the first part, there are When When
If
The form of (
According to the physical model, there are two circles which have
From (
Therefore, the conclusion about the common condition which is similar to (
From (
As
If
It is known from the physical model that the numerical relationships between
If
Therefore,
Therefore, from (
Summarizing all the mathematical validation process of the method above, (
The validation system will be expatiated in two aspects: working principle of the sensor and the validation system including the encoder system and the experimental platform.
Working principle of the encoder system is the law of electromagnetic induction which means the mutual inductance voltage can be generated under the effect of the changing magnetic field [
Working principle of the sensor.
Five copper windings integrated into the sensor are shown in the middle part of the figure. The larger one shown in the figure is injected by high frequency signals from outside and a time-varying magnetic field can be generated. Therefore, the other four small helices located under the larger winding will generate voltage signals. The amplitudes of the voltage signals induced by the four small coils are equal to each other as they have the same dimension and all the distances between central positions of the small coils and the larger one are equal to each other. Two of them with the opposite rotation directions are connected into a group to magnify amplitudes of the signals. Phase difference between voltage signals generated by each group is 90 degrees as there is a radius position difference between the corresponding coils in each group. As one of the copper sheets marked on the code disc moving under the four helices, the high frequency voltage signals will be generated. As copper sheets are with a certain dimension and are laid out with regulated positions relative to the sensor, the regular signals which are sine and cosine signals can be generated if the maximum and minimum values of the signals are selected as shown in the right part of Figure
All the components of the validation system can be seen from Figure
Validation system.
The encoder system is mainly composed of two sensors, the signal processing electrical circuit board and the code disc. Working principle of the encoder system has been illustrated in the section above. The other parts including the signal processing electrical circuit board and the code disc will be described in detail. The part of the system labeled ① in the figure is the electrical circuit board used to process signals and communicate with the CPU (central processing unit). Each sensor will produce two groups of difference signals which are
Look-up table of
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0 | 0.1736 | 0.3420 | ⋯⋯ | −0.1736 | 1 |
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1 | 0.9848 | 0.9396 | ⋯⋯ | 0.9848 | 0 |
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0 | 10 | 20 | ⋯⋯ | 350 | 360 |
The code disc, another part of the encoder system, is labeled ② in Figure
Part ③ of the system is the driven system. As shown in the figure, the three main parts of the driven system including the controller board, the driver board, and the motor are numbered sequentially from 1 to 3 in the figure. The driven system can realize the purpose of position control, speed control, and current control. The code disc of the encoder system is fixed on the driven system through the other connection components to have the relative rotation with the electrical circuit board.
In fact, part ④, a relative magnetic sensor used to calibrate the absolute electromagnetic position sensor system, has been fixed into the driven system for the purpose of reducing dimensions of the system. The resolution of the magnetic sensor is 14 bits and measuring precision is 0.0001 degrees which can satisfy requirements of calibrating the electromagnetic sensor system.
To regulate the relative positions between the code disc and the sensors, the electrical circuit board has been fixed on a three-dimensional platform labeled ⑤ in the figure. It can move along
Based on the system established above, the experiment has been done. All the original signals of these two sensors monitored by oscillograph can be seen in Figure
Testing results monitored by oscillograph.
There are 90 degrees of phase differences between the signals generated by the same sensor such as
Figure
Testing results.
From Figure
According to the inverse trigonometric function,
Therefore, the absolute angular position value can be easily obtained using the four groups of the original signals.
There is no error caused by the method if
The first one is the approximation of the
The second one is the changes of all the signals including the amplitudes and phases. Amplitude changes can be easily observed from Figure
In the equation above,
Consequently, the errors of the encoder system can be shown in the following equation:
In the equation above, the amplitudes of
The changes of amplitudes and phases are caused by different reasons such as the distance differences between the encoder and two sensors, the sensors not perpendicular to the encoder, and the errors of the input voltage. Therefore, in the near future, the manufacturing and assembly precisions of the sensor system and the experimental platform should be improved. All in all, correctness of the method has been validated by the experiment.
To measure the absolute angular position, a method including physical modeling and mathematical analysis has been proposed in the paper. Besides, to validate the method, an electromagnetic encoder system and the testing platform have been established. Comparing the experimental results of the electromagnetic encoder with position information obtained from a magnetic sensor, the conclusion that the method can be used to measure absolute angular position is obtained. Some prominent characteristics of the method can be listed as follows: Using this method, the structure of the encoder is simple and easy to be designed. Besides, the size of the encoder can largely be compacted. For example, the encoder system designed in the paper is based on an application in a robot arm. The inner diameter is required to be 45 mm. Based on the method, the outer diameter of the code disc is 70 mm and the width of the encoder system is just 5.9 mm (sensor width: 0.9 mm, encoder disc width: 1.5 mm, the electrical circuit board: 1.5 mm, the highest component: 1 mm, and distance between the code disc and the sensors: 0.2 mm). It is more compact than the other absolute sensors on the market such as the magnetic encoders. Algorithm of the method is simple and easy to be realized. The calculation algorithm can be decreased as there is no need to change analog signals to digital ones. It is friendly to customers. As the exporting signals are analog ones, the suitable interpolation ratio can be set by the customers as they are willing to. The method is suitable to be used in the encoders especially when their output signals are sine-cosine analog signals. It is because the code angle value, which is defined as changing from 0° to 360°, can be easily obtained if full circles of sine and cosine signals can be generated within a code cell.
Although the purpose of validating the correctness of the method has been achieved, there are many limitations in the paper and some further works should be done. First, measurement precision of the sensor system is about ±0.5 degrees which is low compared with other sensors such as the optical sensors whose resolution can reach up to
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work was sponsored by the National Key Basic Research and Development Program (973 Program) and National High Technology Research and Development Program of China (State 863 project), 2011AA7045041.