Journal of Sensors

Volume 2015, Article ID 503852, 10 pages

http://dx.doi.org/10.1155/2015/503852

## A Method for Measurement of Absolute Angular Position and Application in a Novel Electromagnetic Encoder System

^{1}School of Software Engineering, East China Normal University and School of Mechatronics Engineering, Harbin Institute of Technology, Heilongjiang 150001, China^{2}School of Mechanical Engineering, Shanghai University of Engineering Science and Shenzhen Graduate School, Harbin Institute of Technology, Heilongjiang 150001, China^{3}State Key Laboratory of Robotics and System, Harbin Institute of Technology (HIT), JQR Building, High Technology Park of HIT, Yikuang Street, Nangang District, Harbin, Heilongjiang 150001, China

Received 14 July 2014; Accepted 4 April 2015

Academic Editor: Aldo Minardo

Copyright © 2015 Zijian Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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 and () equal code cells. The cell angles, changing from 0° to 360° between any two neighboring code cells, are defined to represent any position on the code disc. The position value of the same point can be represented by different cell angle values of different tracks and the absolute angular position of the point can be obtained by the difference value between the cell angle value of the outer track and the inner one. To validate the correctness of the method theoretically, the derivation process of the method was provided. An electromagnetic encoder system was designed and the experimental platform was established to test the method. The experimental results indicate that the electromagnetic encoder can measure the absolute angular position. Besides, it shows that the method is easy to be realized in algorithm and can reduce computational complexity and decrease dimension of the encoder.

#### 1. Introduction

Absolute angular position measurement is very important in industrial applications and robotic systems [1]. There are many different methods for the absolute position sensors especially the encoders.

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 [2]. The gray encoding method, another effective way to measure absolute angular position, is widely used in the optical encoders [3]. This method can eliminate the cross errors introduced by the natural binary encoding method. A shortcoming of this method is that it cannot read the angle value directly as the signals should be translated into the natural binary code. As the higher resolution of the encoder, the more tracks are required in these two methods. Therefore, the encoders using this type of method are relatively large and complex [4]. In the other type of the encoding method, all the photodetectors are arranged along the circumferential direction. The matrix encoding is one method of this type. According to it, the code disc of the encoder is divided into different fan-shaped areas. Besides, many reading heads, lying in the same track but different areas, are used to represent different bits of the position information. The dimension of the encoder can be largely reduced. However, measuring errors caused by installation errors of the encoders will be larger than the other two methods mentioned above [5]. The method of pseudorandom encoding is used in [6] to measure the absolute angular position. In this method, the encoder is composed of the synchronization code track and the index code track which helps to decrease the size of the encoder [7]. However, the numbers of the reading heads and the slits will increase exponentially with improving measuring precision of the encoder. Therefore, the method is rarely used in the high-bit encoders. The vernier-type encoders developed in [4, 8] have two or three tracks on the code disc to measure the absolute rotating position, which are simple in construction and compact with other ones. However, the method for measuring absolute position angle should know the numbers of the slits that the encoder has rotated around which is hardly to be obtained in the real application [9]. The M-code coding method proposed in [10] can avoid gross errors and is useful for minimizing the physical size of encoders. However, to achieve higher resolution, absolute encoders using M-code coding method need to incorporate a small slit pitch, which prevents the encoder’s photodetector from obtaining the fixed signal amplitude [11]. With respect to the quasi-absolute encoding method, the code disc of the encoder is composed of a cyclic code track and an index code track. All the effective coding bits of the position are listed on the index code track. Therefore, there should be many photodetectors along the circumferential direction. The method is useful for minimizing the dimension of the encoder, but it needs a bootstrap process to obtain the first position code [12]. Therefore, in some extent, it does not belong to the absolute position measurement method. Using the second-type method, the dimension of the encoders can be largely reduced compared with the other two methods of the first type. However, there are many photodetectors needed in these methods, which is another limitation to increase the measuring resolution and decrease the dimensions of the encoders. Comparing with the optical encoders, the number of the absolute angular position measurement methods of the magnetic encoders is small. For the magnetic encoders with hollow shaft, the encoder typically supports two output channels (channels A and B) which are dephased by 90 degrees with each other. As the Z phase generated once per circle is used to produce the reference point or the zero point in the magnetic encoders, most types of the magnetic encoders are the relative position sensors. Although the multipole ones were studied in [13], the multipoles ones are difficult to be magnetized [14] and to meet the requirements of small-size, high-resolution, and absolute angle detection [15]. For the type of the magnetic encoders with shaft [16, 17], only one circle of sine and cosine signals will be generated and, therefore, the absolute angular position can be easily obtained by the inverse trigonometric functions. However, this type of sensor cannot be fixed on the devices with hollow shaft such as the robot arms.

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 2. The analytical results have been experimentally verified using a novel electromagnetic sine-cosine encoder system and the implementation details of the validation systems including the sensor system and the experimental platform are discussed in Section 3, whereas the experimental data are presented in Section 4. Final comments and conclusions are stated in Section 5.

#### 2. Derivation Process of the Method

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 and () equal code cells, respectively. Angle values of any point on the disc are represented by the cell angle values which are defined in the paper instead of the unique binary codes used in other encoders. In each code cell, the code angles are defined to change from 0 to 360 degrees and any point within the same code cell can be uniquely represented by this angle value. Therefore, any point can be represented by two different angle values. The absolute angular position can be easily obtained from the difference values between code angle values of the same point on different tracks. If any point is represented by the same angle value of different tracks, it is the absolute zero point. Physical modeling and mathematical validation process are shown as follows.

##### 2.1. Physical Modeling of the Method

As shown in Figure 1, there are two circles, that is, and , rotating around the same axis and they have the same absolute zero point . However, there are relative zero points which are listed uniformly on the circle , while the circle is divided equally into () parts by the relative zero points . and are the angle values of and relative to the nearest relative zero points along the rotating direction. In the model, the cell angle values changing range between any two neighboring relative zero points is defined from 0 to 360 degrees.