The key element of an automatized positioning system is an encoder; a device which measures the linear movement or angular rotation of the moving parts. The demands for accuracy, repeatability and robustness increase rapidly as the technology is progressing. Encoders with embedded anisotropic magnetoresistive sensors are a well-established solution for harsh industrial environments. However, magnetic hysteresis remains one of their main drawbacks.
The purpose of this work is to analyze the hysteresis phenomena and its effects on the measurement, the construction of a mathematical model for simulations of the error due to hysteresis on the encoder level, and the integration of presented model in an algorithm for real-time compensation of the measurement error. Then we propose a calibration routine for model parameters and experimentally verify the overall algorithm. The hysteresis phenomenon is observed on a chosen type of an anisotropic magnetoresistive sensor (AMR) for linear measurement of a displacement along an interchangeably magnetized scale. The measuring principle is explained, firstly on a sensor level and secondly how the produced signals are used on the higher level, level of the encoder. AMR effect is explained through the spin-orbit interaction of the valence electrons in nickel and iron, main two ingredients in sensing material permalloy. The latter is usually deposited on a silicon wafer thorough photolithographic technique. Its thin-film structure allows us to approximate its magnetic properties with a single magnetic domain. The Stoner-Wohlfarth model was used to describe the orientation of magnetization of the material in dependence of external magnetic field strength and the anisotropy along the easy axis of the domain. After modeling a small piece of permalloy, the model was extended to a whole sensor area where parts of the material are exposed to different external fields according to their spatial position. Thus, we have shown that hysteresis behavior of AMR can be explained through the energy equilibrium of each magnetic domain. Furthermore, we present the field of mathematical hysteresis modeling. Along with the physical understanding of the phenomena we were able to construct a new model, based on »domain« operator from the family of mathematical operators play. Hysteresis effect is calculated as a weighted sum of states of domains. Some adaptations must be introduced due to the periodic nature of the input and output quantity as we are measuring the position within a magnetic period. The results of the simulation were qualitatively compared to the measurements. The model was thus verified for the chosen set of parameters.
We have proposed a routine, through which one is able to measure the parameters of the hysteresis of a sensor under given circumstances (ride height, temperature, the strength of the actuator…). The measured parameters are then transformed into input parameters for the model. Thus, one can adjust the lagging domain model (MZD) to their system in a stable and robust way.
In order to quantitatively describe the effectiveness of the model and later the compensating algorithm, a criterion function was proposed which calculates the value of an indicator NMH (ang. HME, the error of encoder due to hysteresis). The MZD model was finally implemented into firmware of an encoder and used for hysteresis error compensation. The algorithm was tested on a group of magnetoresistive sensor samples of various types. The error due to hysteresis has decreased for up to 90% when the compensation was properly applied. The duty-cycle of the encoder was not significantly prolonged. Thus, we have proven the usability of the proposed algorithm for compensation of the hysteresis error, based on the lagging-domain model. The algorithm was presented to the scientific community in [1].
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