In this thesis, two novel applications involving embedded sensors arestudied, one dealing with loader crane positioning and the other involving rotorRevolutions Per Minute (RPM) measurement. The thesis presents a generalintroduction to the embedded sensor, its architecture and its use in mechanicalindustry, and provides the reader with an overview of conventional sensortechnologies within the fields of angle sensors and angular speed sensors, coveringtheir working principles, features, advantages and disadvantages and typicalapplications. The particular problems associated with the use of conventionalsensors in both loader crane positioning and rotor RPM measurement aredescribed and these problems provided the motivation for the designs of theembedded sensor systems developed in this thesis.In the case of the loader crane positioning, the origins of the project and thespecial requirements of the application are described in detail. In addition, apreliminary study is conducted in relation to the idea of a contactless joint angularsensor using MEMS inertial sensors in which four different methods, namely, theCommon-Mode-Rejection with Gyro Integration (CMRGI), Common-Mode-Rejection (CMR), Common-Mode-Rejection with Gyro Differentiation (CMRGD)and Distributed Common-Mode-Rejection (DCMR), are conceived, modeled andtested on a custom-designed prototype experimental setup. The results gatheredfrom these four methods are compared and analyzed in order to identify thedifferences in their performances. The methods, which proved to be suitable, arethen further tested using the prototype sensor setup on a loader crane and theperformance results are analyzed in order to make a decision in relation to the twomost suitable methods for the application of the loader crane positioning. Theresults suggested that the two most suitable were the CMRGD and the DCMR. Thepractical design issues relating to this sensor system are highlighted andsuggestions are made in the study. Additionally, possible future work for thisproject is also covered.In the first case for the rotor RPM measurement, the thesis presents themodeling and simulation of the stator-free RPM sensor idea using the Monte Carlomethod, which demonstrated the special features and performance of this sensor.The design aspects of the prototype sensor are described in detail and theprototype is tested on an experimental setup. The conclusions for the stator-freeRPM sensor are then made from the analysis of the experimental results and futurework in relation to this sensor is also proposed.In the second case of the rotor RPM measurement, the thesis presentsanother idea involving the laser mouse RPM sensor and the main focus of thestudy is on the performance characterization of the laser mouse sensor and theverification of the RPM sensor idea. Experiments are conducted using the test setup and results are gathered and analyzed and conclusions are drawn.Possibilities in relation to future work for this laser mouse RPM sensor are alsoprovided.The summary and the conclusion form the final chapter of the thesis andseveral important aspects of the designs relating to both the loader cranepositioning project and the rotor RPM measurement project are discussed.
This paper presents the analysis for joint angle measurement on rigid body that is based on distributed biaxial MEMS accelerometers. It focuses on two methods, one called CMR and another DCMR, and utilizes the property of rigid body kinematics to explain their advantages and weaknesses. Unlike CMR method, DCMR method has no requirement on placing the sensors close to the joint center. This provides greater flexibility for the sensor installation. On the basis of the error model of CMR method, we give an analysis outlining the advantage of theoretically error-free DCMR method. The sensor calibration and alignment is described and both methods are characterized on a rigid body robot arm model. The experiment shows the angular error up to 0.4rad from CMR method whereas just 0.03rad from DCMR method. The noise level from both methods is also compared and analyzed. The result reveals a larger but tunable noise for DCMR method.
The present invention relates to a torque sensor (1) comprising a body (2), at least one airtight chamber (3) provided in the body, a pressure sensor (4) measuring 1 the pressure in said at least one airtight chamber, and a pressure to torque converter (5) connected with the pressure sensor. Each airtight chamber is arranged to change its volume when the body is subjected to a torque, wherein the volume change causes a change of pressure of the enclosed air in the airtight chamber. The change of pressure is detected and converted to the corresponding torque.
This paper proposes a torque sensor based on the differential air pressure measurement method using the volumetric strain of a mechanical sensing structure. A model of the measurement system based on the differential air pressure from the volumetric strain of the mechanical sensing structure is proposed and theoretically discussed. The error sources are identified and an error propagation model is presented for the proposed torque measurement method. Considering these error sources, a prototype torque sensor is presented as a case study for the method verification. Both the mechanical and readout electronics designs are discussed and analyzed. The mechanical sensitivity, resolution, and maximum stresses are analyzed using finite-element modeling. Based on the results from the simulation, a prototype torque sensor is manufactured and experimentally verified using a readout electronics design. For verification, the sensor prototype is measured under static torque to have a sensitivity of 0.04272V/N. m and a range of +/- 117N . m. Compared with the nominal mechanical sensitivity result from the FEM simulation, this measured sensitivity has a difference less than 6%. The noise analysis of the designed readout electronics shows that the resolution of 0.006% can be achieved with this design. Furthermore, hysteresis analysis shows an error of 0.012% of full scale. From these results, it is also shown that the actual performance of the sensor is mainly limited by the differential pressure sensor and the readout electronics design and is not by the mechanical design of the sensor.
This paper presents an analysis of rigid-body joint-angle measurement based on microelectromechanical-system (MEMS) biaxial accelerometers and uniaxial gyroscopes. In comparison to conventional magnetic and optical joint angular sensors, this new inertial sensing principle has the advantages of flexible installation and true contactless sensing. This paper focuses on the comparison of four different inertial-sensor combination methods that are reported in reference papers and utilizes the theory of rigid-body kinematics to explain and analyze their advantages and weaknesses. Experiments have also been conducted to further verify and strengthen the arguments put forward in the analysis. All experiments in this paper took place on a custom-built rigid-body robot arm model that can be manipulated by hand. Sensor calibration and accelerometer alignment issues are also described, and their details are discussed. The experiment results presented in this paper show significant differences with reference to the achieved angular accuracy for various situations when using the four different sensor combination methods. In some cases, the angular error based on one method is more than 0.04 rad, while that from another method is within +/-0.005 rad. The noise levels of angular readings from different methods are also experimentally compared and analyzed. The conclusion drawn serves to guide readers toward a suitable method for their particular application.
This paper presents a feasibility study that deals with a local positioning system for a loader crane based on battery-powered wireless sensors and consists of two joint angular sensors and one telescopic boom length ranger. The practical challenges associated with using conventional sensors are described in order to provide the motivation behind the choice to use the sensing methods proposed in this paper. A novel method is tested using microelectromechanical system inertial sensors mounted around the crane joints to indirectly measure the joint angles, as well as an ultrasound time-of-flight ranging method to measure the telescopic boom length. The local positioning system's wireless sensor prototype designs are described in detail. Data from the angular sensor experiments conducted on a loader crane and the ultrasound ranging experiments conducted both in the laboratory and on the loader crane are presented and analyzed. The preliminary results from these experiments show that the performance of the new sensors is promising. The conclusion is drawn from the experimental results, and future work for this local positioning system is also described.
This paper presents an experimental study using laser mouse sensors for the contactless revolutions per minute (RPM) measurement of a rotating shaft. The sensor performance characterization experiment is firstly conducted under different parameter setups. After the optimal parameter value has been found, the rotor RPM experiment is then conducted with a speed sweep from 500 to 3800 rpm, and data are gathered at 30 different speeds and processed using two different methods to convert the sensor readings into the RPM of the rotating shaft; the results are then displayed. The performance differences between the two methods are compared, and the observation is that both the linearity and the signal-to-noise ratio of the frequency correlation method are several times better than those for the amplitude correlation method. The conclusion summarizes the experimental results and the advantage associated with this new RPM sensing method and provides the motivation for its potential applications and its future works.
Paper presents new idea of modelling the magnetic hysteresis in the Jiles-Atherton model. Presented approach considers physical principles of magnetisation process and main assumptions of Jiles-Atherton model. As a result modified differential equation stating the model was proposed. This equation was verified on the base of magnetic hysteresis loops of non grain oriented electrical steel. Presented results indicate, that proposed approach to modelling the magnetic hysteresis loops well correspond with results of experimental measurements.
This paper presents the design and implementation of a prototype of a stator-free revolutions-per-minute (RPM) sensor based on two microelectromechanical-system uniaxial accelerometers. This paper first introduces the operating principle of the stator-free RPM sensor. It then discusses the associated architecture and design issues of this new sensing method. It then describes the detail of the prototype sensor hardware and software design of the common-mode rejection method and its signal processing. Experiments using the prototype sensor have been also conducted to further verify and strengthen the arguments put forward in the previous discussion. All experiments in this paper took place on a lathe machine in a laboratory. Sensor calibration under a MATLAB environment is also described. Experimental results confirm the interesting property of this sensor, namely, that it provides higher precision at higher RPM. The conclusion summarizes the design considerations, the experimental results, and the motivation in relation to future works for this stator-free RPM sensing method.
This paper presents an statistical performance simulation for rigid-body revolutions per minute (RPM) measurement based on two uni-axial accelerometers mounted on rotor. In comparison with other existing sensing methods that are based on two coupled parts, namely stator and rotor and which include conventional electro-magnetic RPM sensors and photo-electric RPM sensors, this new stator-free inertial sensing principle has the advantage of high bandwidth at low RPM, true contact-free sensing and flexible installation. The paper first focuses on the description of the operating principle and the common mode rejection (CMR) method of the stator-free RPM sensor, and then its error model is developed and the error sources are statistically simulated based on Monte Carlo method. The simulation result presents a most interesting property of this sensor, that is, it gives lower precision at lower RPM and higher precision at higher RPM. The conclusion summarizes the modeling analysis result and motivates potential application for this new RPM sensing method.
This paper presents an experimental investigation on switching transients in a submodule of a cascaded H-bridge converter with the aim of investigating effects of direct integration of supercapacitor modules in switching converters. Departing from simulation studies focusing on overvoltage transients and effects from the Equivalent Series Inductance of the supercapacitor module. A passive absorption circuit is introduced to mitigate the transients on supercapacitor and switching components. The simulations are compared to experimental results on a submodule prototype. An operating point of the submodule corresponding to an output power of 6.2kW is investigated in a double pulse test. The experimental results show that effects of the series inductance across the switches are mitigated. The relationship between the equivalent series inductance of the supercapacitor and the rate of change of current is identified as causing overvoltages across the supercapacitor. Methods to handle the rate of change of current and high frequency voltage ripple across switches are suggested.
A high copper fill factor allows reducing the resistive losses responsible for more than 50 % of the losses in today's most commonly used electrical motors. Single-turn windings achieve a copper fill factor close to one. Furthermore, they do not suffer from turn to turn faults and provide a low thermal resistance between winding and stator. The reduced EMF of single-turn winding configurations promotes the use of extra-low voltage high current MOSFETs. Rapid development of these MOSFETs allows reversing common design principles to explore new applications, such as battery electric traction drives. This paper presents a 2.5 V 1 kW MOSFET driven 13-phase permanent magnet DC motor with a single-turn winding configuration. The motor prototype with a copper fill factor of 0.84 was tested with continuous drive currents up to 600 A. The measured torque-efficiency map shows that such a high-current concept with voltages below 60 V is feasible using today's extremely low-voltage high current semiconductors. Due to the rapid development of such switches, there is great potential in this concept for further improvements. This work presents a small-scale version of the high-current drive, which is part of the development of an extra-low voltage traction drive concept.
To verify the FEM simulation of the air-gap flux density, it is necessary to measure the flux density distribution as function of the angular machine position. This paper presents a scalable 3-D direct air-gap flux density magnitude measurement system for rotating electrical machines. A combination of eight linear Hall effect flux sensors and a rotary encoder is used to measure the flux density magnitude as function of the angular machine position. The system is designed for permanent magnet motors with an air gap of at least 1 mm, but can also be used for other types of machines. The miniaturized sensor array with the flux sensors is 0.7 mm thick, and measures the distribution of the air-gap flux density magnitude in a range of ±2 T along the rotor axis. The design of the measurement system is described and tested on a prototype of an electronically commutated permanent magnet DC motor. The obtained measurement results are compared with the FEM simulation results of the prototype motor. A good match between the simulated and measured flux density magnitude is shown. The conclusions presented in this study, are used to further optimize the simulation model and the prototype motor.
Rapid development of extremely-low voltage high current MOSFETs allows reversing common design principles to explore new applications, such as battery powered traction drives. This enables the usage of multi-phase single-turn stator windings which can achieve a copper fill factor close to one. This paper briefly describes the proposed 2V, 1.1kW MOSFET commutated 13-phase permanent magnet DC motor and presents the efficiency and resistive loss measurements of the first prototype. The motor was successfully run with drive currents up to 520 A. Most of the obtained losses were resistive contact losses due to the flexible winding connections, less than 6% are dedicated to the MOSFETs. The results show that such a high current drive system is feasible and has great potential for further improvements, which is supported by the rapid development of extremely-low voltage high current semiconductors.
This paper proposes an extremely-low voltage high current MOSFET-based drive architecture. A single-turn multiphase winding design allows a copper fill factor approaching one. The single-turn coil design leads to a low EMF voltage and high current design which requires a matched drive system. To identify the technical design obstacles and verify the feasibility of the proposed architecture, a small scale prototype is built and successfully tested. The described prototype consists of an extremely-low voltage 13-phase single-turn coil permanent magnet DC motor and MOSFET-based commutator. The prototype's locked rotor-torque and no-load power consumption, as well as the EMF voltage measurements are presented and the DC motor constants are extracted. The experimental results from the prototype measurements indicate a promising potential for cost-effective extremely-low voltage high current MOSFET-based drive systems.
Traction drive applications demand high power density motors with a good stator cooling design. We propose a novel multi-phase winding for a 48 V traction drive design having identical preformed hollow copper conductors with in-conductor direct cooling capability. This paper studies the cooling performance of an individual conductor phase using either EGW50/50 or water as coolant. Analytical calculations and experiments are conducted on a straight conductor of the same length using 20°C water as coolant. The results are then cross verified with those from the FEM simulations to validate the simulation setup. Then a final simulation is conducted at a current of 700A and a current density of 49.5 A/mm 2 on the preformed conductor using 65 CEGW50/50 as coolant at a pressure of 140kPa. The results highlight the exceptional performance of the cooling design which enables a power dissipation of 71OW at a maximum conductor temperature rise of only 56. 9 C.
This paper will discuss a wireless control system for a loader crane, where the focus lies on the wireless communication protocol supporting the implementation of the real-time system. To aid the discussion, a system model is included, which together with the control strategy will allow low power consumption for the energy constraint sensor devices. A simple and power aware medium access control protocol is proposed. The protocol together with the specific loader crane requirements make it possible to save valuable sensor resources. Simulations on real world loader crane data show a simplified view of the power requirements for the control model, and the importance of utilizing correct system parameters to achieve low power consumption.
In this paper the use of the IIEEE 802.15.4 standard in a wireless control system is analyzed and discussed. The standard is described and applied on a heavy duty crane application and the discussion focuses on the possibilities and limitations of the standard in the application. A formula is presented which can be used to calculate maximum sample rate according to the number of sensor nodes and the payload the nodes may carry. The discussion reveals that the standard may be utilized in the crane application but that it is not a good solution. Several limitations within the standard, such as network size and system sample rate, will put a stop to future extensions of the wireless control system. As a result, the 802.15.4 standard protocol shall not be employed in the heavy duty crane application.
A wireless sensor network is always an integrated part of a system. The physical and logical structure of the system, where the sensor network is integrated, are together with other environmental requirements the constraints for the design of the network and the wireless sensor devices. These requirements are very different for different applications and even for one specific system the requirements may be very different on the sensor devices. When developing efficient wireless sensor devices these constraints must be taken into consideration. The diverse constraints we are facing when developing wireless sensor networks and devices for various applications makes it necessary to have a platform-based development approach where as much of the components can be re-used. For the communication, the standard IEEE 802.15.4 provides an excellent platform for developing short range power aware sensor networks. In this paper a hardware platform is presented with its modular structure it provides a highly flexible solution suitable for rapid prototyping of wireless sensors. This platform is a tool for developers of wireless sensor devices as well as system integrators that need to explore different system solutions experimentally
This paper demonstrates the implementation and tests the performance of a low angular speed sensor for rotary machinery based on a microelectromechanical system gyroscope. First, an experimental test setup is presented that features a top-of-the-line optical absolute angle encoder as a reference for characterizing the proposed sensor in a controlled environment chamber. A prototype of the proposed sensor has been designed and implemented with its architecture and hardware design described in detail. For the experimental purposes, a wireless synchronization scheme between the reference and the gyroscopic sensor is also discussed. The experimental measurement has taken place to benchmark the performance of the realized sensor. The experimental data have been processed and analyzed, and the results have been presented. The gyroscopic sensor has shown satisfactory results. The sensor has an accuracy of 0.06 degrees/s, standard deviation of 0.45 degrees/s, and hysteresis of 0.08 degrees/s.
This paper focuses on the thermal stability of a high performance, low-range calibration setup for differential airpressure sensors. The setup is a dual parallel chamber design with the full range of ±320 Pa, which can be translated to a temperature mismatch of only about 0.93oC between the chambers. Due to the limitations of existing temperature measurement technology, we propose a finite element model(FEM) analysis to study the effect of thermal gradient on the calibration setup. The model setup includes the dual parallel chamber design inside a conventional climate chamber. From the conducted analysis we observe that, due to the non-ideal heat distribution inside the climate chamber, the calibration setup can experience an error of more than 20 % of full range.To minimize this error, we propose an optimized dual cascaded chamber calibration setup design and verify its thermal performance under the same environmental setup. The results show that the proposed design reduces the error, due to thermal gradient, down to 1.8 % of full range. In conclusion it is also discussed that the proposed design reduces error sources related to its mechanical complexity. Future work is proposed on the design and implementation of the optimized design.
This paper presents an experimental comparative analysis of a torque measurement method based on volumetric strain, utilizing a prototype torque sensor design is compared to a reference high performance torque sensor. A brief description of the background work of the numerical analysis of the method is also discussed as well as the readout electronics design. Based on the simulations and readout electronics analysis it is concluded that the sensor has a mechanical range of ±300 N·m. The manufacturing details of the prototype torque sensor are also discussed. A test setup is used to place the two torque sensors in line, to allow comparison for which a high performance conventional off-the-shelf torque sensor is selected. The experiments show that the proposed method of torque measurement can be fully implemented and used to measure torque with higher response time, resolution and wider range. Furthermore, future work is proposed to fully characterize the sensor over the full range using a reference setup rather than a torque sensor, as the available conventional sensors cannot be used to characterize the prototype torque sensor in full range with higher performance than the sensor itself.
The calibration of sensors is one of the most frequently carried out maintenance operations on sensor networks. This paper presents the design of a reference instrument for the static calibration of low-range (up to ±320 Pa) differential pressure sensors. A method is proposed for the calibration setup and the design issues are discussed in addition to a complete error analysis. An experimental setup is also proposed. From the conducted experiments, it is verified that the sensitivity of the reference setup is at least 0.032 Pa with the achievable resolution of 0.001% of full scale. This paper also presents an embedded electronics design for both the calibration and the characterization profile handling. A full performance characterization of a sample differential pressure sensor is also presented in terms of sensitivity, linearity, hysteresis, and temperature dependency. A comprehensive discussion involving the design parameters analysis and the worst case performance is also included. In conclusion, it is summarized that the proposed design out performs the conventional reference instruments, so that it can be used for the calibration and characterization of a wide variety of low-range differential pressure sensors.
This paper proposes a torque measurement method based on volumetric strain. A model of the measurement system based on the differential pressure monitoring is proposed and theoretically discussed. The error sources are identified and an error propagation model is presented for the proposed torque measurement method. Considering these error sources, a prototype torque sensor is presented as a case study for the method verification. Both the mechanical and readout electronics design are discussed and analyzed. The mechanical sensitivity and maximum stresses are analyzed using Finite Element Method. Whereas, the readout electronics is experimentally verified using an off-the-shelf high performance differential pressure sensor. The results from the conducted analysis show that the presented design of torque sensor can be used to measure torque in the range of ±300 N·m with the resolution of 0.006 % of full scale. The maximum observed stress on the proposed structure is 220 MPa. The experiments conducted on the readout electronics show that the differential pressure sensor is the limiting factor in the design when it comes to the resolution. In conclusion it is summarized that the presented torque sensor can be used in industrial applications requiring both high resolution and wide range. Moreover, the method is fully adaptable to various performance requirements in terms of range and resolution. The future work is also discussed to implement the presented design and characterize it using reference instruments.
This paper presents a torque sensor design based on a differential pressure measurement, focusing on thermal stability. The sensor utilizes the principle of measuring the differential volumetric strain due to the applied torque. The proposed design of the sensor is an improvement to the previous design of the sensor. Both the previous design and the improved design are discussed in terms of thermal stability. Comprehensive thermal simulations are conducted on the design in order to compare the thermal stability and performance of the sensors. Based on the presented results it is shown that prosed design of the sensor can achieve at least 99.61% better stability then the previous design. The range of the sensor is +/- 150N.m. Furthermore, it is also concluded that the new design also improves on the manufacturability, ease of integration and overall size of the sensor.
Low range differential air pressure sensors are used widely in various applications. In this paper the effects of temperature change on transient behavior of the calibration setup for differential air pressure sensors, due to temperature gradient are analyzed. A high performance reference setup utilizing ideal gas law, for differential air pressure sensors, is selected for experimental analysis. The range of the setup is ±320 Pa with the achievable resolution down to 0.001% of the full scale. Due to the nature of ideal gas law, the experimental setup should also exhibit a high sensitivity to the temperature gradient on mechanical structure. In order to characterize the effects of this temperature gradient on the transient state of the setup, a two stage comparative experimental study is proposed. In stage one a thermal buffer is introduced surrounding the mechanical structure of the setup and the experiments are conducted by changing the temperature to the system. In stage two the temperature is changed in the same manner, but the experiments are conducted with the original experimental setup. From the results obtained by the experiments using the thermal buffer, it is observed that the temperature change of 5°C, can cause the system to stay in transient state for up to 32 hours with an error of up to 10% of full scale. Whereas, the results from the original calibration setup show that the system stays in transient state for more than 96 hours with a monotonic drift. From the comparative analysis of the experimental results we conclude that the high sensitivity calibration setup for differential air pressure sensors also have a high sensitivity to the temperature gradient. Although the thermal buffer can minimize the effects of the temperature gradient on the transient behavior of the calibration setup, the modification to the existing mechanical design is considered as more practical. Future work is proposed in order to study the thermal gradient on the mechanical structure and design a setup that is less vulnerable to it. © 2015 IEEE.
Vibration based condition monitoring is considered to be the most effective method for analyzing the performance of rotating machinery and for early fault detection. Traditional vibration analyzers used for this purpose provide wired interface(s) to connect sensors with the system that analyzes the vibration data. A wireless vibration analyzer can be useful to monitor and analyze the vibration of rotating as well as inaccessible parts of the machinery. However, for a wireless vibration analyzer, both the performance and power consumption are of major concern, especially for real-time tri-axes (horizontal, vertical, and axial) vibration data processing and analyses at a high sampling rate. To evaluate the performance of such an analyzer, we explore different architectures in order to realize a high-performance and low-power wireless vibration analyzer that can be used in addition to traditional analyzers. For this purpose, four different architectures have been implemented in order to evaluate them in terms of performance, power consumption, cost, and design complexity.
Vibration based condition monitoring is the most widely accepted method for determining the defects and the performance degradation of rotating machinery. Common practices for monitoring vibration involve employing a displacement transducer for the rotor and an accelerometer for the stator. This paper presents a novel architecture for on-rotor vibration measurement based on accelerometers, and a high sampling rate vibration monitoring sensor node with analysis capability. A detailed analysis of the technological challenges and bottlenecks including bandwidth, wireless communication, processing capabilities and energy consumption of the proposed architecture are discussed. The experimental results of the rotor and the stator vibration are compared and are presented.
Traditional wireless sensor nodes are designed with low-power modules that offer limited computational performance and communication bandwidth and therefore, are generally applicable to low-sample rate intermittent monitoring applications. Nevertheless, high-sample rate monitoring applications can be realized by designing sensor nodes that can perform high-throughput in-sensor processing, while maintaining low-power characteristics. In this paper, a high-performance and low-power wireless hardware platform is presented. With its compact size and modular structure enabling there to be an integrated customized sensor layer, it can be used for a wide variety of applications. In addition, the flexibility provided through dynamically configurable interfaces and power management, helps optimizing performance and power consumption for different applications.
Jiles-Atherton model is one of the most advanced and most popular models of magnetic hysteresis loop. However, this model is considering different physical phenomena and computational issues. As a result, cross-validation of the results of modelling performed by different authors became difficult. For this reason, the open-source MATLAB/OCTAVE based implementation of Jiles-Atherton model was developed. Proposed implementation covers isotropic model of magnetic hysteresis loops as well as uniaxial and grain oriented electrical steel anisotropy. Moreover, the corrections proposed by Venkataraman together with different approaches to derivative of the anhysteretic magnetization are considered. Developed library is freely available together with the examples of magnetic hysteresis loops. As a result, it can be the base for further development of Jiles-Atherton model for better understanding of magnetization process as well as modelling the inductive components.