Sinusoidal Encoder Research Articles

Linearization interpolation method with high robustness and high accuracy for sinusoidal encoders

This paper presents a linearization interpolation method with high robustness and high accuracy for sinusoidal encoders. Based on the pseudo-linearized signal constructed by the ratio of absolute values difference and absolute values sum of the sine and cosine signals, a compensation coefficient is designed to amplify pseudo-linearized signal to approximate ideal linearized signal for improving the linearity. The linearity is improved from 9.05% to 0.015%, which means that the linearized signal can be used to accurately determine the phase angle. This method is easy to implement, has high accuracy, and does not require the lookup tables (LUTs) or processors. The theoretical phase error is less than 0.007° over 0° ∼ 360°, corresponding to about 15-bit accuracy per signal period. In addition, the proposed method is implemented on the hardware platform with a field-programmable gate array (FPGA). Finally, the effectiveness of proposed method is demonstrated by experiments using simulated sinusoidal encoder.

Encoder Calibration Method for High Precision Servo Systems With a Sinusoidal Encoder

The sinusoidal encoder is used as an absolute position (velocity) transducer to implement the position (velocity) of actuators in many industrial applications. However, the performance of the position (velocity) can be degraded due to nonideal factors such as differential amplitudes of the encoder signals, offset, and phase shift. To analyze this problem, we formulate the relationship between the coefficients of ideal signals and the nonideal signals characteristic, which is an ellipse formed by plotting the encoder signals versus each other. In this article, we propose a nonideal signal calibration for the imperfect components of existing sinusoidal signals to improve position (velocity) regulation performance. The fictitious cosine function is used to detect the phase shift between the sine and cosine signals, and it can be designed by using the frequency of sinusoidal signals. The proposed method is validated by simulation and experimental implementation, showing noticeable improvement in estimating nonideal signal components, Lissajous error curve, phase distribution, and the position (velocity) error signal. Experimental results show that the proposed method is able to obtain the components of the nonideal signals and the accurate position (velocity) with a small error in real time, while other calibration methods are difficult to apply to fast motion.

A Linear Direct-Digital Converter for Sinusoidal Encoders

This paper proposes a novel linear direct-digital converter for sinusoidal encoders (LDCS) to measure the angular position of a rotating shaft. The outputs of a sinusoidal encoder vary as sine and cosine functions of the shaft angle. The proposed LDCS, which has a low component count, processes these outputs and renders a linear accurate direct-digital output for full-circle range. The LDCS is suitable for both static and dynamic measurements of the shaft angular position. The working principle of the LDCS is mathematically derived and explained in this paper. An elaborate evaluation of non-ideal parameters affecting the LDCS operation is carried out and reported. Furthermore, the static and dynamic performances of the LDCS are verified using simulation and emulation studies. The output nonlinearity obtained during emulation studies, for static measurement, is 0.027 %. A close agreement between simulation and emulation results is observed during these studies. Later, a tunneling magnetoresistance (TMR) angle sensing unit which acts as a representative sinusoidal encoder is fabricated. The LDCS is interfaced with the sensing unit, and several experimental tests are carried out. The worst-case nonlinearity in the static measurement of shaft angle is 0.29 %. Additional tests which study the dynamic performance and effect of mechanical misalignments of the combined TMR-LDCS system is also revealed in this paper.

Development of a digital interpolation module for high-resolution sinusoidal encoders

This paper presents a digital interpolation module for high-resolution sinusoidal encoders. The proposed strategy performs phase-shifting manipulation on the sinusoidal encoder signals, and takes advantage of the linear sections of the absolute values of the phase-shifted sinusoidal signals. Thus, an approximately linear signal is obtained, from which the displacement can be linearly determined. Simulation result shows that the theoretical error of the proposed interpolate strategy is within 0.072° over the 360° signal period. Furthermore, a digital interpolation module is developed by implementing the interpolate strategy in a field-programmable gate array (FPGA), and performance evaluation experiments are carried out by applying it to a linear optical encoder with a pitch of 20 μm. The effectiveness of the digital interpolation module has been validated by both simulation results and experimental results.

Ratiometric-Linearization-Based High-Precision Electronic Interpolator for Sinusoidal Optical Encoders

Electronic interpolation is the key technology for further improving the measurement resolution of optical encoders. In this paper, an electronic interpolator based on the ratiometric linearization conversion method is presented. The proposed method converts the sinusoidal encoder signals into a nearly perfectly linear output signal through mathematical manipulation that only involves basic operations of addition, subtraction, multiplication, and division. Thus, the displacement can be precisely determined using a simple linear equation. Furthermore, quadrature interpolation pulses are also generated from the linear output signal by using the amplitude subdivision method. Since the linearization procedure is based on the ratiometric operation, interpolation accuracy is independent of amplitude fluctuation of the encoder signals. Theoretical analysis shows that the nonlinear error of the proposed interpolator is below ±0.0034 rad over a signal period of 2 π rad, which corresponds to an interpolation error of ±0.0108 μ m for a linear optical encoder with a pitch of 20 μ m. In the experiment, the proposed strategy is successfully implemented within a field programmable gate array, and applied to a 20 μ m-pitch optical encoder. Experiments are performed to demonstrate the effectiveness of the proposed method.

A Sinusoidal Encoder-to-Digital Converter Based on an Improved Tangent Method

Sinusoidal encoders are used for the measurement of angular position and linear displacement. These provide electrical signals dependent on the sine and cosine of the position $\theta $ of their moving part relative to the stationary one. Conventional tangent/cotangent converters for determining $\theta $ from the encoder signals produce alternating highly non-linear segments of tangent and cotangent. Lookup tables are used for determining $\theta $ . This paper presents a novel converter for estimating $\theta $ without the lookup table. The method is based on dividing the circle angular interval into $N$ sections. A crude or coarse measure $\theta _{C}$ of the unknown angle $\theta $ is first determined by identifying the section in which $\theta $ is located. This is followed by the determination of a fine measure $\theta _{F}$ . These measures are combined to yield a precise measure of $\theta $ ; the maximum error of the method depends on $N$ . The converter has been implemented on a dSPACE set and has been successfully tested both with a sensor emulator and a real Hall-Effect sinusoidal encoder. This paper describes full details of the theory, simulation, and experimental results. The experimental results demonstrate excellent agreement with theory and simulation.

Phase Shift Calibration Method in Optical Sinusoidal Encoder Signals Applied to Servo Track Writer

Abstract: In this paper, an ultra high precision calibration method of optical sinusoidal encoder signals in spiral servo track writing is proposed to improve position (velocity) regulation in the constant velocity region. The proposed method has been aimed toward non-ideal signal calibration for the imperfect components existing sinusoidal encoders and it applies a digital encoder calibration using a fictitious cosine function. The fictitious cosine function is used for finding phase shift between sine and cosine signals. The proposed method is validated by the experimental implementation, showing noticeable improvement in the position (velocity) error signal. Tracking performance in position error signals is improved up to 40 [%] with a positioner.

A New Approach for Calibration of Sinusoidal Encoder Signals

Against to the multi-roots problem existed in Heydemann method for calibration of sinusoidal signals, a new approach containing two procedures is proposed. Firstly, the dc offsets and amplitude deviations of sinusodial signals were estimated by two observers separately. Then, to accept the non-orthogonal phase shift in the sinusodial signals, a simple Heydemann method with only two variables was adopted. Simulation results show that this method is feasible, and can converge to the origin with high accuracy. This method will show great values in the field of calibration of sinusoidal encoder signals.

Signal Compensation for Analog Rotor Position Errors due to Nonideal Sinusoidal Encoder Signals

This paper proposes a compensation algorithm for the analog rotor position errors caused by nonideal sinusoidal encoder output signals including offset and gain errors. In order to achieve a much higher resolution, position sensors such as resolvers or incremental encoders can be replaced by sinusoidal encoders. In practice, however, the periodic ripples related to the analog rotor position are generated by the offset and gain errors between the sine and cosine output signals of sinusoidal encoders. In this paper, the effects of offset and gain errors are easily analyzed by applying the concept of a rotating coordinate system based on the dq transformation method. The synchronous d-axis signal component is used directly to detect the amplitude of the offset and gain errors for the proposed compensator. As a result, the offset and gain errors can be well corrected by three integrators located on the synchronous d-axis component. In addition, the proposed algorithm does not require any additional hardware and can be easily implemented by a simple integral operation. The effectiveness of the proposed algorithm is verified through several experimental results.

Adaptive digital demodulation of sinusoidal encoder signal for positioning control of spiral servo track writing

An adaptive digital demodulation method for a sinusoidal encoder signal is proposed for fast and accurate analysis of spiral servo track writing (SSTW). The proposed methods combine adaptive signal correction and digital interpolation. In addition, digital phase-shifted sinusoid (PSS) interpolation is proposed in order to acquire precise position information. The adaptive signal correction method compensates for a fast-motion non-ideal encoder signal. The digital PSS can be simply implemented and can resolve the switching noise of conventional analog methods. The proposed adaptive digital demodulation scheme can be simply digitalized and can improve the position control in SSTW. From the simulation and experimental results, we have validated the proposed methods, which show noticeable improvement in terms of the Lissajous error and the position error signal.

A High Speed Calibration Method for Laser Positioner by Constant Velocity Scanning

This paper describes a high speed calibration method for laser positioner by scanning work area under constant velocity. Laser positioner consists of sinusoidal laser encoder, DC motor and the controller. The encoder has diffraction grating scale and laser optics. It generates sine and cosine outputs according to the travel distance. Qualities of the scale and the optics contribute to the fluctuation of output signal amplitude, DC offset and relative phase. First, the controller collects the output data under constant velocity of 4 samples per 1 sine wave length. The parameter can be estimated by simplified discrete Fourier transform method. Calibration data are collected every quarter sine wave length over all positioner work area. The result is stored in the table then referred by the controller in real time operation. Experiment results are also reported for HDD servo track writer application.

An Efficient Approach to Correct the Signals and Generate High-Resolution Quadrature Pulses for Magnetic Encoders

A magnetic encoder (ME) is a kind of sinusoidal encoder using magnetic effects that is currently utilized in many industrial control systems because it has many advantageous characteristics: low cost, simple structure, works in harsh environments, high reliability, and so on. The signals generated by an ME are always disturbed by noises; therefore, these signals are not ideal. The challenge is to achieve the highest resolution and to get the maximum operating speed as well as to use the most cost-effective hardware. To solve this problem, this paper humbly proposes an effective approach, which contains two parts: The main part is “compensating the noisy signals of MEs” by applying a new proposed method called the advanced adaptive digital phase-locked loop (AADPLL), while the second is a pulse interpolator which generates high-resolution quadrature pulses. The AADPLL algorithm provides a robust filtering characteristic to eliminate the noises and improve the accuracy of the ME's input signals. It also takes advantage of tracking high-speed input signals without time lag, unlike the traditional filters. Additionally, the computation burden is significantly reduced in this algorithm to allow it to be easily implemented in a low-cost processor. The pulse interpolator is based on an existing idea that extracts high-order sinusoids from the original ME signals. However, a new scheme is presented to achieve higher resolution per period with smaller noises affecting the output pulses. Both parts are mainly implemented in a unique hardware platform using a low-cost digital signal processor, such as the TMS320F2812, combined with a small-size field-programmable gate array. This method has already been applied to control a linear motor without using an expensive optical linear encoder. Practical results are provided to demonstrate the effectiveness of the proposed method.

Transmission system with improved encoder and decoder that prevents multiple representations of signal components from occurring

In a sinusoidal audio encoder it is known to use different time scales for analyzing different parts of the frequency spectrum. In prior art encoders sub-band filtering is used to split the input signal into a number of sub bands. By splitting the input signal into sub-bands, it can happen that a signal component at the boundary of two sub-bands results in a representation in both sub-band signals. This double representation of signal components can lead to several problems when coding these components. According to the present invention it is proposed to use preventing means (46, 48, 58, 68; 88, 92, 96) to avoid signal components to have multiple representations.

Probabilistic learning technique for improved accuracy of sinusoidal encoders

Sinusoidal-encoder-based digital tachometers are often limited by nonidealities in both encoder construction and interface electronics. A probabilistically based compensation technique is presented which dispenses with the need for specialized calibration equipment. A code-density array, obtained during a learning phase, is utilized to yield a compensation function which approximates to the average relationship over the mechanical cycle between the calculated electrical angle (as determined by an arctangent-based algorithm) and the actual angle. An extended version of this probabilistically compensated sinusoidal encoder technique is used to compensate for variations in the encoder characteristics as it rotates through a mechanical cycle. An analysis of the learning-time requirements of the system is presented. Practical results, utilizing performance measures common in the testing of analog-to-digital converters, confirm the utility of the method. An example of the benefits which accrue from the inclusion of the enhanced sensor in closed-loop systems is also provided.