Resolver Outputs Research Articles

New RDC Method Using Trapezoidal Excitation Signal Considering Resolver Nonlinearity

The resolver is a kind of transformer that requires one excitation signal. Among numerous resolver-to-digital conversion (RDC) methods, the square wave excitation method has the advantage of being easy to demodulate and implement, but nonlinear problems may arise due to the high-frequency components in the square wave. These nonlinear problems distort the resolver output signals and make demodulation difficult. To minimize these nonlinear problems while maintaining the advantages of the square-wave excitation method, a new RDC method using a trapezoidal excitation signal is proposed in this article. The trapezoidal excitation signal is expressed through a Fourier series expansion to find the optimal point at which the total harmonic distortion (THD) along the length of the flat region is minimized. Additionally, a simple circuit for implementing trapezoidal excitation signals is also introduced. The effectiveness of the proposed method is verified through experiments.

Presentation of a Novel Variable Reluctance Tubular Resolver

Encoders and resolvers are the most common position sensors in controlling electrical machines. However, due to their ability to work under harsh conditions, resolvers are more preferred. In linear position detection, the transversal edge effects and the longitudinal end-effects adversely affect the accuracy of conventional linear resolvers. On the contrary, due to the cylindrical symmetry of tubular machines, they are not subject to the edge effects. With this idea, this article presents a novel linear VR resolver with a tubular structure to achieve higher accuracy than the existing linear resolvers. A magnetic equivalent circuit model is then developed to prove the correct performance of the proposed resolver. It is discussed that the proposed resolver is tolerant of mechanical eccentricities. Different configurations are studied, and finite-element analysis is conducted to analyze the resolver's outputs considering longitudinal end-effects and under mechanical eccentricities. The results show the proposed configuration has a robust performance under eccentricities while its accuracy sharply deteriorates due to the longitudinal end effect. Therefore, an effective method is proposed for compensating the longitudinal end effect. Finally, the compensated resolver is experimentally built and tested to verify the success of the developed sensor.

Type-III resolver-to-digital converter using synchronous demodulation / Tipo-III conversor resolver-para-digital utilizando a desmodulação síncrona

Resolver is an angular position sensor widely used in applications such as electric/hybrid vehicles, CNCs, antennas and robotics. However, the estimation of the angular position from resolver outputs is more difficult than the analysis of encoder signals, and it is still an open question. Most algorithms proposed in literature are based on type-I or type-II angle tracking ob- servers. Some type-III observers were proposed, but they require a high sampling frequency. This paper explores the use of synchronous demodulation of the resolver outputs to simplify the implementation of a type-III angle tracking observer. The resolver outputs are sampled at the peaks and valleys of the excitation resolver signal, being easy to get sine and cosine of the angular position. The proposed approach reduces the computational cost and the required sampling frequency to implement the type-III observer. Simulation and experimental results prove the accuracy of the proposed approach.

Image Registration Technique to Improve a Self-Sensing Estimation for Model Predictive Controlled Interior PMSM Drives

Current responses based self-sensing control estimates rotor position by detecting magnetic saliency of a machine. However, the estimation error can be resulted from several nonideal factors, especially magnetic cross-saturation, as effects of these factors show up in current responses. This article applies image registration technique to improve the accuracy of a self-sensing estimation for model predictive control (MPC) interior permanent magnet synchronous machines (IPMSM) drives by minimizing impacts of nonideal factors on measured current responses. In commissioning process, two images are generated. The inverter voltage vectors in MPC excite current responses, represented by a set of vectors that generate a response image. Nonideal factors that result in estimation errors also deform the response image. A primitive image based on resolver output can be considered as a template. An image registration technique is investigated to register deformed images with corresponding primitive images, and transformations contain operations of rotation, scale, translation, and shear can be derived. During the drive, the deformed pixel points are online mapped to new pixel points by applying these operations. The current responses after transformation are less subject to nonideal factors. As a result, impacts of these deformation factors that contribute to estimation errors can be reduced. Finally, the application of image registration technique to the self-sensing estimation is verified on a 3.7-kW IPMSM drive.

Improved Acquisition System for Sensored Vector Control Through Frequency-Domain Multiplexing, Synchronous Sampling, and Differential Evolution

Frequency domain multiplexing (FDM) allows simplifying the data acquisition in vector control when the resolver is used as a position sensor. However, the crosstalk reduction in the demultiplexing process is still a difficult task. This article proposes an improvement of the FDM-based acquisition system through synchronous sampling and Differential Evolution (DE). The resolver signals and the PWM carrier are synchronized so that the resolver outputs are zero when the PWM carrier reaches its valleys. Thus, the fundamental component of the stator currents can be easily estimated from the signals sent to the acquisition system. These estimated current signals and an angle tracking observer (ATO) are used to estimate the angular position. DE and a discretized model of the ATO are applied in order to improve the angle estimation transient response and to reduce crosstalk. Conditions to apply the proposed multiplexing approach will be defined. Simulation and experimental results show that the proposed approach allows an accurate estimation of the current fundamental components and the angular position when FDM is used, with better performance respect to other approaches in the literature. This is the first time that a DE is used to tune an ATO.

A Novel Method for Eliminating Residual Voltage in a Resolver With Signal Fitting Implementation

This paper presents a compensation algorithm with software implementation for eliminating the residual voltage in a resolver. The algorithm provides lower-cost implementation and more significant effects than the existing adopted compensation coils. The paper studies the characteristics of the resolver output signals, which mainly consist of the ideal induced signal, the odd-order harmonic components and the residual voltage. First, the resolver output parameters-amplitude, phase and DC component-are estimated by signal fitting methods when the shaft stops at a certain position. Then, the three parameters are again obtained after the driving shaft rotates 180 degrees with respect to the initial position. Because the induced voltage varies with the shaft rotational angle but the residual voltage does not, the amplitude of the residual voltage is obtained by employing the trigonometric identity of the rotational angles to eliminate the amplitude of the induced signal. The experimental results indicate that the proposed compensation method can effectively eliminate the residual voltage in the induced signal and improve the measurement accuracy of the resolver sensors.

Angle Tracking Observer with Improved Accuracy for Resolver-to-Digital Conversion

A resolver is an absolute shaft sensor which outputs pair signals with ortho-symmetric amplitudes. Ideally, they are sinusoidal and cosinusoidal functions of the shaft angle. In order to demodulate angular position and velocity from resolver signals, resolver-to-digital conversion (RDC) is necessary. In software-based RDC, most algorithms mainly employ a phase-locked loop (PLL)-based angle tracking observer (ATO) to form a type-II system. PLL can track the detected angle by regulating the phase error from the phase detector which depends on the feature of orthogonal symmetry in the resolver outputs. However, a type-II system will result in either steady-state errors or cumulative errors in the estimation of angular position with constant accelerations. Although type-III ATOs can suppress these errors, they are still vulnerable to high-order acceleration signals. In this paper, an improved PLL-based ATO with a compensation model is proposed. By using dynamic compensation, the proposed ATO becomes a type-IV system and can reduce position estimation errors for high-order acceleration signals. In addition, the parameters of ATO can be tuned according to the bandwidth, noise level and capability of error suppression. Simulation and experimental results demonstrate the effectiveness of the proposed method.

High-Accuracy Automatic Calibration of Resolver Signals via Two-Step Gradient Estimators

In the software-based resolver-digital converters, angular position and speed are often demodulated from resolver signals after envelope detection. The accuracy of demodulation depends on the degree of perfectness of two envelope signals of the resolver. However, the envelope signals cannot be derived perfectly from the resolver outputs and they are often disturbed by amplitude deviations, DC offsets, and nonorthogonal phase shifts. In order to attenuate the effects of the unexpected factors on the accuracy of demodulation, an offline automatic calibration strategy is proposed for the two envelope signals of the resolver based on two-step gradient estimators. The first-step estimator is designed to obtain the estimate of only one parameter, i.e., angular frequency. At the second step, another gradient estimator is designed to estimate amplitudes, DC offsets, and phases of the two envelope signals. Since the angular frequency is estimated by an individual estimator which is independent from the other parameters, its estimation accuracy can be improved effectively. By using the estimate of the angular frequency with higher accuracy, the accuracy of the second-step estimator also can be improved. The effectiveness of the proposed method is verified by simulation and experimental results.

Improved Demultiplexing Algorithm for Hardware Simplification of Sensored Vector Control Through Frequency-Domain Multiplexing

Frequency-domain multiplexing was proposed to reduce the number of signals to be digitized in vector control using a resolver as position sensor. Signals from resolver and current sensors can be multiplexed through analog adders. This approach has many advantages over using analog switches. On the other hand, the conventional demultiplexing system involves filtering and delay compensation, while the rotor angle is obtained after the signal demultiplexing. However, this conventional approach is difficult to implement because the required filters must have good stopband rejection, without adding a significant phase delay. This paper proposes an improved demultiplexing system whose structure is simpler than the conventional approach. A type-III angle tracking observer estimates the rotor angle and the resolver outputs directly from the multiplexed signals. The estimated resolver outputs and stopband filters are used to get the current signals. Thus, the demultiplexing of resolver signals and the delay compensators used in the conventional approach were eliminated. Experimental results prove that the proposed approach gives accurate estimations of the rotor angle and current signals. Besides, conditions for the resolver excitation frequency, the inverter switching frequency, and for current synchronous sampling were defined for the application of frequency-domain multiplexing.

High-Precision Resolver-to-Velocity Converter

Accurate velocity estimation for rotary control over a large velocity range has been a challenge. In this paper, we propose a virtually analog resolver-to-velocity converter that applies trigonometric transformations to the resolver outputs. We also present hardware that extends the output range of a previously proposed resolver-to-position circuit from 90° to 360°. The position and velocity outputs of the two circuits are evaluated against the position and velocity obtained from an optical encoder using the backward difference differentiation technique. Recommendations for tuning and improvements in the circuitry are also provided.

Classification and Compensation of DC Offset Error and Scale Error in Resolver Signals

This study proposes a classification and compensation algorithm of two non-ideal output signals of a resolver to reduce position errors. Practically, a resolver generates position errors because of amplitude imbalance and quadrature imperfection between the two output signals of the resolver. In this study, a digital signal processor system based on a resolver-to-digital converter is used to reconstruct the two output signals of the resolver. The two output signals, "sin" and "cos," can be represented by a unit circle on the xy-plot. The classification and compensation of the errors can be obtained by using the radius and area of the circle made by the resolver signals. The method computes the integration of the areas made by the two resolver output signals to classify and compensate the error. This system cannot be applied during transient response given that the area integration during the transient state causes an error in the proposed method. The proposed method does not need any additional hardware. The experimental results verify the effectiveness of the proposed algorithm.

Design of a MGy radiation tolerant resolver-to-digital convertor IC for remotely operated maintenance in harsh environments

During future ITER maintenance operations, sensors and their embarked electronics will be exposed to a hostile and radioactive environment. This paper presents the design of a MGy radiation tolerant 16 bit resolver-to-digital converter (RDC) in 130nm CMOS technology. The RDC features a Type II digital tracking loop, able to track resolvers with speeds up to 300rps, and excitation frequencies up to 4kHz. The RDC uses two integrated ΔΣ-analog-to-digital converters (ADCs) to digitize the resolver outputs. The 16 bit, 10kHz ADCs utilize a correlated double sampling technique to remove radiation induced offset and 1/f-noise. The front-end features a static angular resolution of 16 bits (4.2arcsecrms) and a resolution of 10 bits (6arcminrms) at a rotor speed of 100rps. The circuit has a simulated radiation tolerance exceeding 1MGy. It has the ability to operate under temperatures up to 125°C, and to allow multiplexing with signals from other conventional sensors for compact, robust read-out architectures.

A Novel Design Method for Resolver-to-Digital Conversion

A simple and novel design method for resolver-to-digital conversion is presented. The proposed method takes advantage of the auxiliary sinusoidal signals generated by addition and subtraction operations of the demodulated signals of the resolver's outputs. A pseudolinear signal is obtained through appropriate mathematical manipulation between the auxiliary sinusoidal signals and the demodulated ones. A calibration strategy is then provided to achieve the highest possible precision. It is shown that the error between the calibrated angular and the true angular position is less than 0.00235° over 0° ~ 360°. The proposed method enables the determination of the angular position without utilizing a lookup table or additional reference signals. Furthermore, the presented strategy is implemented using a field-programmable gate array. Finally, our method is tested on a tracking radar antenna servo system where resolvers are installed on it. Several experiments under different conditions are performed to further verify the effectiveness of the proposed method.

Software Resolver-to-Digital Converter for Compensation of Amplitude Imbalances using D-Q Transformation

Resolvers are transducers that are used to sense the angular position of rotational machines. The analog resolver is necessary to use resolver to digital converter. Among the RDC software method, angle tracking observer (ATO) is the most popular method. In an actual resolver-based position sensing system, amplitude imbalance dominantly distorts the estimate position information of ATO. Minority papers have reported position error compensation of resolver's output signal with amplitude imbalance. This paper proposes new ATO algorithm in order to compensate position errors caused by the amplitude imbalance. There is no need premeasured off line data. This is easy, simple, cost-effective, and able to work on line compensation. To verify feasibility of the proposed algorithm, simulation and experiments are carried out.

A Method of Producing Z-Pulse Output From Thin Axial Resolver

A thin axial resolver with the Z-pulse output coexisting with a resolver operation is presented. The method of producing the Z-pulse utilizes an additional primary square coil, a figure-eight-shaped secondary coil, and a rotor made from grain-oriented silicon steel with a slit made parallel to the easy axis of the rotor material. When the slit passes over the figure-eight coil, the coil detects magnetic field distribution from the slit and produces the Z-pulse output. Furthermore, the nonlinearity error of the resolver output is almost the same as that of the resolver whose rotor has no slit.

Software-Based Resolver-to-Digital Converter for DSP-Based Drives Using an Improved Angle-Tracking Observer

In this paper, a new resolver-to-digital conversion method is presented. This method is based on synchronous demodulation of resolver's output signals. A modified angle-tracking observer is proposed to extract the rotor angle in high speeds as well as in low speeds. An estimation algorithm, which is based on the sign and absolute values of sine and cosine of the rotor angle, is introduced to find an appropriate initial value for this observer. This method can be incorporated in a DSP-based motor drive system. The proposed method is simple and cost effective when an appropriate microcontroller is selected for motor control. This method has been successfully implemented in a DSP board. Several tests at different speeds and initial positions have been performed to evaluate the proposed method.

High-Accuracy All-Digital Resolver-to-Digital Conversion

In this paper, a high-accuracy all-digital resolverto-digital (R/D) converter is presented. The two basic components of a conventional tracking R/D converter, the phase detector and the loop filter, are software implemented by frequency-shifting techniques and a decoupled double synchronous reference frame-based phase-locked loop (DSRF-PLL). This PLL allows the simultaneous extraction of the angular position and speed of the rotatory resolver, even in the presence of gain and phase errors in the resolver. In order to increase accuracy and to minimize the time lag of the whole system, oversampling methods and downsampling finite-impulse response digital filters are introduced. Finally, DSP implementation issues, like the use of techniques to synchronize the resolver output signals with the excitation one, are discussed. Using these combined techniques and a standard DSP with a 12-bit analog-to-digital converter, resolutions of up to 14 bits can be achieved with a computation cost of about 13% of the total (100 MIPs). The paper presents the main techniques, simulation, and experimental results.

Systematic error cancellations and fault detection of resolver angular sensors using a DSP based system

Resolver sensor based angular position and speed sensing are extensively used in safety critical servo applications that demands accurate as well as high-resolution position and speed information for feedback control. In this paper, a novel scheme for position and speed sensing along with fault detection and identifications of a resolver sensor with systematic errors like magnitude imbalance, imperfect quadrature, and inductive harmonics is presented. The proposed scheme of resolver-to-digital (R/D) conversion mitigates the errors in position and speed estimate due to these common resolver imperfections and provides fault indicators such as good resolver signal, degradation of signal, and loss of signal for fault tolerant operation and diagnosis of malfunctions in the sensor system for safety critical systems. The proposed method incorporates software generation of the resolver carrier using a digital filter for synchronous demodulation without unintended time delay of the processed outputs, in such a way that there is substantial saving in hardware, for instance, carrier oscillator and associated digital and analog circuits for amplitude demodulators. The R/D converter incorporates an adaptive phase-locked loop (APLL) that accurately estimates the angular position and speed for a large range of operation along with superior tracking performance under dynamic conditions. Also, it provides the estimate of the magnitudes of the resolver outputs, estimate of the imperfect quadrature, and indication of harmonic distortion in the sensing angle, which can be used to directly access the quality of the resolver sensor system. Computer simulations and experimental results demonstrate an accurate R/D converter with adaptive capabilities to mitigate all the major systematic disturbances with reduced hardware complexity.

Software-Based Resolver-to-Digital Conversion Using a DSP

A simple and cost-effective software-based resolver-to-digital converter using a digital signal processor is presented. The proposed method incorporates software generation of the resolver carrier using a digital filter for synchronous demodulation of the resolver outputs in such a way that there is a substantial savings on hardware like the costly carrier oscillator and associated digital and analog circuits for amplitude demodulators. In addition, because the method does not cause any time delay, the dynamics of the servo control using the scheme are not affected. Furthermore, the method enables the determination of the angle for a complete 360deg shaft rotation with reasonable accuracy using a lookup table that contains entries of only up to 45deg. Computer simulations and experimental results demonstrate the effectiveness and applicability of the proposed scheme.

Instantaneous angular position and speed measurement using a DSP based resolver-to-digital converter

High performance servo control systems require the measurement of angular position and speed for improved accuracy, tracking, and feedback control. Resolvers are extensively used in such applications that demand instantaneous, accurate, and high-resolution information of these parameters for feedback control. In this paper, a scheme is presented for position and speed sensing using a resolver-to-digital (R/D) converter that is completely software implementable. The technique incorporates software generation of the resolver carrier using a digital filter and synchronous demodulation of the resolver outputs using the same. This allows saving of the costly carrier oscillator and associated digital and analog hardware for amplitude demodulation of the resolver outputs. Also, as the amplitude demodulation as well as the measurement of position and speed does not cause any time delay, the dynamics of the servo control that uses the scheme is not affected. Computer simulations and experimental results show outstanding performance at considerably attractive computational cost and hardware, demonstrating the effectiveness and applicability of the proposed scheme.