Mathematical Model Of Induction Motor Research Articles

Sliding Mode with Equivalent Control for Induction Motor Drive Based on Multi-Pulse VSC

In this work, the application of a sliding mode equivalent control for an induction motor drive based on a multi-pulse Voltage Source Converter is proposed. This is accomplished by transforming the squirrel-cage induction motor mathematical model into a block control form. The equivalent control method is applied to the sliding manifold, where the voltages are obtained in the stationary reference frame to control the angular velocity of the motor. In addition, a proportional-integral control is designed and applied to the motor represented in this form in order to make performance comparisons with the equivalent control method. Multi-pulse converters of 6, 12, and 84 pulses are used directly to feed the plant that is being controlled. The outcomes of using these power electronics devices are used to perform comparisons among the velocity tracking performance, control voltages in stationary reference frame, tracking errors, and rejection of external disturbances. Furthermore a dynamic and steady-state analysis of the velocity tracking performance is executed. The energy profiles for the startup, torque variations, and steady-state are also obtained. Additionally, total harmonic distortion values are added. All comparisons are carried out using the established plan for the motor, both with and without the use of power electronics converters, and with both control algorithms. The obtained results demonstrate that the use of a high-quality voltage source converter, along with a good control strategy, allows for a general improvement in the overall system and a significant reduction in energy usage, whilst also reducing controller complexity.

Reducing torque ripple of induction motor control via direct torque control

<span lang="EN-US">The induction motor is extremely well known and used as an alternating current (AC) machine. Therefore, torque and speed regulations are very essential for this type of machine. This paper presents direct torque control (DTC) based on induction motors (IM). The mathematical model of IM is reported, and the machine is modeled in a synchronous coordinate farm. Classic DTC is applied to IM with two bandwidths of hysteresis controller for electromagnetic torque and stator flux. The system is simulated and investigated via MATLAB/Simulink and the results carry out a high ripple on the torque. There are numerous of improving torque response, one of them is adding a new loop for speed with proportional, integral, and derivative (PID) controllers. IM model with PID based on DTC is simulated through MATLAB. A contrast performance of IM is presented between traditional DTC and DTC with PID. As result, the new DTC with PID carries out improvement in the speed response as well reduces the ripples of torque.</span>

Influence of Parameter Uncertainty to Stator Current Reconstruction Using Modified Luenberger Observer for Current Sensor Fault-Tolerant Induction Motor Drive.

In modern systems with induction motors (IM), in addition to precision, it is also very important to ensure the highest possible reliability and safety. To ensure the above, information about the stator current value is required. If the current sensor (CS) fails, a redundant sensor or an algorithmic solution can be used. The Luenberger observer (LO) can be used to estimate the lost stator current without increasing the cost of the drive system. However, this solution is based on the mathematical model of IM, which is sensitive to its parameters. Therefore, this paper presents a modified LO (MLO) and investigates the effect of a coefficient in the error gain matrix on improving robustness to changes in the IM parameters. As shown by extensive studies, the proposed solution has significantly reduced the influence of the IM parameters on the accuracy of the stator current estimation, which has not been previously reported in the known literature.

Model-Based Design of Induction Motor Control System in MATLAB

A mathematical model of induction motor (IM) based on the second Kirchhoff’s law with Maxwell’s equation taken into account has been developed. A mathematical model of a three-phase induction motor with a short-circuited rotor in phase axes without taking into account the saturation of the magnetic circuit and the losses in steel has been elaborated. A nonlinear model of asynchronous motor in the state space in the rotating system (d-q) of coordinates synchronized with the stator flux and a simulation model of IM in MatLab/Simulink software, with the possibility of setting angular velocity of rotation and resistance torque, have also been developed. The model-oriented design of the control program is performed on the example of digital signal processors from Texas Instruments on the LAUNCHXL-F28379D board. This description of the dynamics provides a direct insight into the physical processes in IMs. The advantage of the considered mathematical description of electromechanical energy conversion processes in three-phase IM is that it uses instantaneous values of currents and voltages of stator and rotor winding phases as variables.

Nonlinear time-varying sliding mode synchronous control of double-lift overhead cranes under unknown disturbances

During the synchronous operation of the double-container, the double-lift overhead cranes suffer from the perturbation of system internal parameters, friction and external unknown disturbances. To address the impact of the above-mentioned negative factors, based on the mathematical model of induction motor and the coupled dynamics model of double-container, this paper proposes a synchronous control method combining variable gain extended state observer and nonlinear time-varying sliding mode surface for the synchronous coordination control of double-lift overhead cranes system. The load dynamics model of the double-container interlocking mode is established. Then, a nonlinear time-varying sliding mode surface is designed by means of nonlinear function and dynamic exponential term, which effectively speeds up the convergence of the system state and enhances the robustness of the system. Furthermore, the design adaptive reaching law is used to weaken the unwanted chattering and improve the performance of the controller. At the same time, the designed variable gain extended state observer estimates the aggregated disturbances in the system and then compensates them into the controller. The Lyapunov stability theory is used to prove the stability of the control system. The simulation experiments illustrate the effectiveness of the proposed synchronization control scheme.

Influence of Selected Non-Ideal Aspects on Active and Reactive Power MRAS for Stator and Rotor Resistance Estimation

Mathematical models of induction motor (IM) used in direct field-oriented control (DFOC) strategies are characterized by parametrization resulting from the IM equivalent circuit and model-type selection. The parameter inaccuracy causes DFOC detuning, which deteriorates the drive performance. Therefore, many methods for parameter adaptation were developed in the literature. One class of algorithms, popular due to their simplicity, includes estimators based on the model reference adaptive system (MRAS). Their main disadvantage is the dependence on other machines’ parameters. However, although typically not considered in the respective literature, there are other aspects that impair the performance of the MRAS estimators. These include, but are not limited to, the nonlinear phenomenon of iron losses, the effect of necessary discretization of the algorithms and selection of the sampling time, and the influence of the supply inverter nonlinear behavior. Therefore, this paper aims to study the effect of the above-mentioned negative aspects on the performance of selected MRAS estimators: active and reactive power MRAS for the stator and rotor resistance estimation. Furthermore, improved reduced-order models and MRAS estimators that consider the iron loss phenomenon are also presented to examine the iron loss influence. Another merit of this paper is that it shows clearly and in one place how DFOC, with the included effect of iron losses and inverter nonlinearities, can be modeled using simulation tools. The modeling of the IM and DFOC takes place in MATLAB/Simulink environment.

Offline Measurement of Induction Motor Rotor Time Constant Based on Least Squares Algorithm

In order to solve the problems of disturbance and error accumulation in the traditional off-line strategy of rotor time constant, this paper optimizes the off-line measurement method of rotor time constant of induction motor. The off-line measurement method of rotor time constant based on recursive least squares (RLS) algorithm is analyzed in detail. Through the static characteristics of induction motor, the mathematical model of induction motor is simplified, and then the linear model of RLS algorithm is derived. The simulation results show that the rotor time constant measured by the least square method is more stable than that measured by the conventional method, which proves the practicability of the off-line measurement method. Finally, the error analysis of the main factors affecting the off-line measurement results of the rotor time constant based on the least square algorithm is given.

A Mathematical Model of a Three-Phase Induction Motor with a Phase Rotor

A mathematical model of an induction motor (IM) with a phase rotor is developed on the basis of the usual assumptions that does not use the supposition that there is an annular rotating field in its air gap and various transformations of coordinates. The model is valid for both transient and steady-state modes and with various ways of control by changing the parameters of the three-phase feeding voltage system of the IM stator coil. It is shown that the desired stationary operation mode that exists in the developed nonlinear IM model at a constant feeding voltage of the stator and load torque corresponds to the constant electromagnetic torque and spinning frequency of the rotor at sine-wave rotor and stator currents. A digital IM model is developed in the MATLAB system. An analytical solution is derived for the system of linear differential equations that describes the IM with a retarded rotor and allows evaluating the nonlinear digital model for correctness. Examples of applying the IM model in analyzing transient and steady-state operation modes of this motor are provided.

A Normalized Frequency-Domain Energy Operator for Broken Rotor Bar Fault Diagnosis

In the motor current signal, the characteristic frequency of broken rotor bar (BRB) fault is modulated by the supply frequency and it decreases with the decrease of the load, resulting it to be easily buried under light load conditions. Teager–Kaiser energy operator (TKEO) has shown better performance to detect the BRB faults than classical methods, such as envelope analysis and spectral analysis. However, the original definition of TKEO leads to its result lack of physical meanings and the causal processing in TKEO can lead to phase distortion and nonideal filter characteristics. Therefore, this article proposes a normalized frequency-domain energy operator (FDEO) for the BRB fault diagnosis, which does not require causal processing and calculates multiple differentiations in the frequency domain with equal accuracy in one operation. Furthermore, the normalized FDEO removes the influence of the supply frequency followed by the spectral analysis to extract fault features. The mathematical model of induction motor (IM) under healthy and faulty condition is studied in this article. Then, the proposed approach is experimentally validated with seeded one and two BRB faults operating under various load conditions. To verify the effectiveness, the results are compared with the TKEO, envelope analysis, and spectral analysis. It was found that the proposed method provides slightly obvious fault features with respect to the TKEO, especially when the IMs run under light load conditions with two BRB faults.

Linear and Nonlinear Controllers of a Solar Photovoltaic Water Pumping System

This paper provided a comparative study between linear and nonlinear controllers of a solar photovoltaic (PV) water pumping system using an induction motor and a centrifugal pump. For linear controller, classical Perturb and Observe was selected to ensure the operation of the PV system at the maximum power point (MPP) and is combined with Indirect Rotor Field Oriented Control (IRFOC) based on a conventional proportional integral speed regulator chosen to control and to optimize the rotor speed. In second and third controllers, Backstepping and first order sliding mode controls were proposed for controlling the whole system. To regulate and optimize rotor speed in the nonlinear controller, all considered control techniques were combined with IRFOC in order to establish easy control laws. In addition, MPP was tracked by acting on the DC-DC converter and using its mathematical model for developing control laws. Maximum delivered power was used as reference signal for optimizing actual rotor speed. The controlled system is operated without mechanical sensors. Estimators of rotor speed and load torque disturbances were proposed based on the mathematical model of induction motor and centrifugal pump and using only available output measurements. Induction motor was supplied by a voltage source inverter controlled using a PWM technique. Stability based on Lyapunov functions of the closed-loop system was evaluated. Simulation results were investigated and reveal some very interesting features and the effectiveness of the nonlinear proposed strategies.

Linear and nonlinear controllers of a solar photovoltaic water pumping system

This paper provided a comparative study between linear and nonlinear controllers of a solar photovoltaic (PV) water pumping system using an induction motor and a centrifugal pump. For linear controller, classical Perturb and Observe was selected to ensure the operation of the PV system at the maximum power point (MPP) and is combined with Indirect Rotor Field Oriented Control (IRFOC) based on a conventional proportional integral speed regulator chosen to control and to optimize the rotor speed. In second and third controllers, Backstepping and first order sliding mode controls were proposed for controlling the whole system. To regulate and optimize rotor speed in the nonlinear controller, all considered control techniques were combined with IRFOC in order to establish easy control laws. In addition, MPP was tracked by acting on the DC-DC converter and using its mathematical model for developing control laws. Maximum delivered power was used as reference signal for optimizing actual rotor speed. The controlled system is operated without mechanical sensors. Estimators of rotor speed and load torque were proposed based on the mathematical model of induction motor and centrifugal pump and using only available output measurements.. Simulation results were investigated and the effectiveness of the nonlinear proposed strategies.

On-Line Parameter Identification of a Squirrel Cage Induction Motor

Based on the principle of coordinate transformation, a mathematical model of induction motors in the three-phase stationary coordinate system was transformed to that in the synchronous rotating coordinate system. For motors with low-speed rotors, the multi-variable, high-order, strong-coupling and nonlinear equation of motors was further transformed to a linear equation. However, it was found difficult to solve the deduced linear equation through the method of least squares due to its high singularity. The steady-state stator resistance could be predetermined by temperature revision on the stator resistant in the motor nameplate. Identification of four motor parameters (Ls,M, Rr, Lr) was followed by the recursive least-squares method. Simulations of motor parameter estimation were carried out in Simulink of Matlab. The recursive least-squares method was used to deal with the measured data. The results demonstrate that the real-time electrical parameters (Ls, σ, Tr) can be accurately predicted. Given the assumption of Ls = Lr in the classical motor theory, the other three electrical parameters (M, Rr, Lr) can also be identified. The identification of these parameters is of great importance for the analysis, control and fault diagnosis of induction motors.

Modelling of soft starters for automated electric drive

In this paper we investigated the conditions of favorable start-up of fixed-speed induction motors in order to increase the functional reliability of the engines. The methods of controlled soft start of induction electric motors with a squirrel-cage rotors are investigated. The study of the mathematical model of induction motors for determining the dependencies of reducing the dynamic component of the transient electromagnetic moment and the magnitude of the starting current. A computer simulation to identify the effectiveness of different methods of controlled start-up of induction motor was carried out. To generate the starters’ models, the MatLab modelling application, Simulink and SimPowerSystems block libraries were used. Based on the results of transient processes simulation in MatLab, the comparative characteristics for different methods of starting an induction motor were given.

The Novel Rotor Flux Estimation Scheme Based on the Induction Motor Mathematical Model Including Rotor Deep-Bar Effect

During torque transients, rotor electromagnetic parameters of an induction motor (IM) vary due to the rotor deep-bar effect. The accurate representation of rotor electromagnetic parameter variability by an adopted IM mathematical model is crucial for a precise estimation of the rotor flux space vector. An imprecise estimation of the rotor flux phase angle leads to incorrect decoupling of electromagnetic torque control and rotor flux amplitude regulation which in turn, causes deterioration in field-oriented control of IM drives. Variability of rotor electromagnetic parameters resulting from the rotor deep-bar effect can be modeled by the IM mathematical model with rotor multi-loop representation. This paper presents a study leading to define the unique rotor flux space vector on the basis of the IM mathematical model with rotor two-terminal network representation. The novel rotor flux estimation scheme was validated with the laboratory test bench employing the IM of type Sg 132S-4 with two variants of rotor construction: a squirrel-cage rotor and a solid rotor manufactured from magnetic material S235JR. The accuracy verification of the rotor flux estimation was performed in a slip frequency range corresponding to the IM load adjustment range up to 1.30 of the stator rated current. This study proved the correct operation of the developed rotor flux estimation scheme and its robustness against electromagnetic parameter variability resulting from the rotor deep-bar effect in the considered slip frequency range.

Substantiation of the parameters of short-circuited rings for integrated design of an asynchronous motor using quasi-three-dimensional field analysis and modeling

Purpose. To justify and apply an improved mathematical model of induction motors for solving problems of increasing their energy efficiency as part of electromechanical systems. To investigate the effect of increasing the cross-sectional area of the short-circuited rotor rings on the efficiency in the operating mode of the electromechanical system of the engine-mechanism, the multiplicity of starting current and torque. Methodology. The use of a refined mathematical model of the engine when integrating it into a simulation model of an electromechanical system that takes into account the nonlinear dependencies of the parameters of the equivalent circuit calculated from the results of a quasi-three-dimensional field analysis. Results. Originality. With reduced requirements for starting torque, it is reasonable to use an improved mathematical model of the engine when determining the parameters of the rings of a short-circuited rotor. Practical value. The effect of increasing the cross-sectional area of the short-circuited rotor rings on the engine operating and starting characteristics is investigated. The approximation dependences of the electromagnetic parameters as a function of the magnitude of the design parameters are substantiated.

Bifurcation diagrams in estimated parameter space using a pruned extreme learning machine

We propose an algorithm to estimate parameter spaces by using a pruned extreme learning machine, but without using principal component analysis, and we plot bifurcation diagrams in the estimated parameter spaces to visualize changes in system patterns. The estimation of parameter spaces can predict changes in the behavior of a system when its parameters are changed. It can be very helpful to adjust the optimal parameters of unknown systems. In this paper, we estimate the dimension of parameter spaces using the singular values of trained synaptic weights and the parameter spaces based on the method proposed by Bagarinao etal., using a pruned extreme learning machine. We motivate this use of a pruned extreme learning machine through numerical experiments, with the estimation of the dimension of parameter spaces for various systems, and we show that the proposed method can successfully plot bifurcation diagrams in the estimated parameter spaces. In addition, we show the results of a bifurcation diagram in the estimated parameter space for maps that are nonlinear-in-parameters, since Bagarinao etal. limited their method to linear-in-parameters maps. In particular, we estimate the parameter spaces for a mathematical model of induction motor drives and for a model of vegetation biomass in ecosystems, which are both nonlinear-in-parameter maps corresponding to real-world systems.

Ограничение колебаний электромагнитного момента асинхронного двигателя при скалярном частотном управлении

The paper presents mathematical models of induction motor as a system of equations and a structure. It also suggests the correction methods of induction motor with scalar control, which decrease fluctuations of electromagnetic torque. The graphs of the transients of the frequency-controlled electric drive with scalar control, obtained based on the mathematical model with and without additional correction device, are given. The presented scalar control system for induction motor allows starting the electric drive and regula­ting the speed with the stabilization of the electromagnetic torque of induction motor with a maximum deviation from the mean value under 5 %, as well as suppressing the engine speed fluctuations in transient modes. The frequency-controlled electric drives with induction motor and scalar control with improved dynamic properties can be applied in metallurgical mechanisms.

Математическая модель асинхронного двигателя с учетом пазовых гармоник в индукции магнитного поля и неисправностей различного типа

Математическая модель асинхронного двигателя с учетом пазовых гармоник в индукции магнитного поля и неисправностей различного типа

Neural network-based discrete-time command filtered adaptive position tracking control for induction motors via backstepping

Considering the problems of parameter uncertainties and load disturbance appeared in induction motor drive systems, a discrete-time command filtered adaptive position tracking control method based on neural networks is proposed in this paper. First, Euler method is used to describe the discrete-time dynamic mathematical model of induction motors (IMs). Next, the neural networks technique is employed to approximate the unknown nonlinear functions. Furthermore, the “explosion of complexity” problem and noncausal problem, which emerged in traditional backstepping design, are eliminated by command filtered control technique. Simulation results prove that tracking error converges to a small neighborhood of the origin and the effectiveness of the proposed approach is illustrated.

Математическая модель асинхронного двигателя с последовательно соединенными обмотками статора и ротора

To provide for the cost-effective use of resources and energy conservation it is vital to enhance unregulated electric drives of copious working mechanisms. The technical process of these mechanisms requires relatively longstanding speed reduction under low static loads. Moreover, another relevant issue is choosing control systems of electric drives in the mentioned systems in accordance with the economic and maintenance aspects. The authors suggest using the systems of impulse-vector control system with wound rotor induction motor that have one essential drawback – the shaft encoder installation. The replacement of the shaft encoder with sensorless impulse-vector control system is complicated due to the lack of proper mathematical description of the electromagnetic processes in schemes with non-traditional windings stator and rotor connection . To solve this problem the authors have developed a mathematical description of impulse-vector control system with wound rotor induction motor supposed to be multiphase and asymmetrical. Angular dependencies of inductances, flux linkages, voltages of engine windings, circuit current and electromagnetic torque relatively to rotor location are derived. In addition to that, the mathematical modeling and research of induction motor configuration with a series connected windings fed by AC voltage source are presented. Equating rotor position in impulse-vector control system with wound rotor induction motor is considered possible through angular dependencies of drop voltages on stator and rotor windings.