Magnetic bearing is well-known for its advantage of reducing friction in rotary machines and is placing conventional bearings where high-speed operations and cleanliness are essential. It can be shown that the AM is a nonlinear system due to the relation between the magnetic force and current/rotor displacement. In this paper, a mathematical model of a 4-DOF AMB supported by four dual electric magnets is presented. The control objective is placed in a view of control input saturation and output limitation that are meaningful aspect in practical applications. Backstepping algorithm based control strategy is then adopted in order to achieve the high dynamic performance of the bearing. The control is designed in such a way that it takes input and output constraints into account by flexibly using hyperbolic tangent and barrier Lyapunov functions. Informative simulation studies are carried out to understand the operations of the machine and evaluate the controller quality.
This document summarizes a paper presented at the International Conference on Mechatronics in Kumamoto, Japan in May 2007. The paper presents analysis and implementation of exact model knowledge and direct adaptive control schemes for a 4th order ball and beam system. Two controllers are designed - one using the exact model and one using direct adaptive control. Experimental results show that both controllers can track constant and sinusoidal references for the ball position asymptotically on a physical ball and beam system.
PID Controller Design for a Real Time Ball and Beam System – A Double Integra...idescitation
In this paper, the authors have discussed and shown
how to tune the PID controller in closed loop with time-delay
for the double integrator systems for a particular stability
margins. In math model it is assumed that time delay (ô) of
the plant is known. As a case study the authors have consid-
ered the mathematical model of the real-time beam and ball
system and analyzed the simulation and real time response.
Mechatronics design of ball and beam system education and researchAlexander Decker
This document describes the proposed design of a mechatronics ball and beam system for educational and research purposes. The system aims to test and analyze various control strategies by using a servo motor to continuously adjust the angle of a beam to stabilize a rolling ball. It discusses the requirements, conceptual design, and concurrent selection and integration of subsystems including the mechanical design, sensors, actuators, and control algorithm. Preliminary block diagrams and component layouts are presented and the mechanical system parts are listed. The design is intended to help users visualize and experiment with different control methods on a precise and cost-effective experimental unit.
Iaetsd design of a robust fuzzy logic controller for a single-link flexible m...Iaetsd Iaetsd
This document describes the design of a fuzzy logic controller for a single-link flexible manipulator. A fuzzy-PID controller is used to control an uncertain flexible robotic arm and its internal motor dynamics parameters. The controller is tested against conventional integral and PID controllers in simulations. The results show the proposed fuzzy PID controller has better robustness under variations in motor dynamics compared to the other controllers.
The present work deals to investigate the performance of linear switched reluctance motor designed for a sliding door application. The objective of this paper is to develop an analytical model in order to predict the dynamic behaviour of the studied motor. Firstly, the characteristics of the proposed motor in open loop operation was computed.Secondly, the effect of the load on the response of the motor was investigated. In this context, a two technoque in open loop were adopted to solve the error positioning with load and to damp the oscillation observed in the characteristics of the motor in order to obtain a smooth motion.
Nonlinear Control of an Active Magnetic Bearing with Output ConstraintIJECEIAES
In this paper, an appropriate control strategy is proposed to handle the nonlinear dy- namics of an active magnetic bearing (AMB). The goal of the control design is to drive the AMB rotor to the origin with improved transient response. In order to achieve this task, back stepping control technique with a barrier Lyapunov function are employed to keep the tracking error trajectory inside a predefined zone to avoid possible mechanical contact between rotor and stator. Besides, a speed observer is also used since information about rotor speed is not always available. The stability of the closed-loop system is proven. The effectiveness of the proposed control strategy is verified by numerical simulations.
—This paper presents a new image based visual servoing (IBVS) control scheme for omnidirectional wheeled mobile robots with four swedish wheels. The contribution is the proposal of a scheme that consider the overall dynamic of the system; this means, we put together mechanical and electrical dynamics. The actuators are direct current (DC) motors, which imply that the system input signals are armature voltage applied to DC motors. In our control scheme the PD control law and eye-to-hand camera configuration are used to compute the armature voltages and to measure system states, respectively. Stability proof is performed via Lypunov direct method and LaSalle's invariance principle. Simulation and experimental results were performed in order to validate the theoretical proposal and to show the good performance of the posture errors. Keywords—IBVS, posture control, omnidirectional wheeled mobile robot, dynamic actuator, Lyapunov direct method.
This document discusses modal analysis of rotating structures using active magnetic bearings. It begins by introducing modal analysis and its importance for analyzing high-speed rotating machinery. It then describes the experimental setup which uses active magnetic bearings to both levitate and excite a test rotor. Natural frequencies and mode shapes are identified for the free-free rotor both with and without bearing stiffness. Introducing bearing stiffness is found to increase natural frequencies and introduce additional modes. The document concludes by explaining how the active magnetic bearings can be used to artificially excite the rotor to measure its frequency response functions and identify its dynamic characteristics.
This document summarizes a paper presented at the International Conference on Mechatronics in Kumamoto, Japan in May 2007. The paper presents analysis and implementation of exact model knowledge and direct adaptive control schemes for a 4th order ball and beam system. Two controllers are designed - one using the exact model and one using direct adaptive control. Experimental results show that both controllers can track constant and sinusoidal references for the ball position asymptotically on a physical ball and beam system.
PID Controller Design for a Real Time Ball and Beam System – A Double Integra...idescitation
In this paper, the authors have discussed and shown
how to tune the PID controller in closed loop with time-delay
for the double integrator systems for a particular stability
margins. In math model it is assumed that time delay (ô) of
the plant is known. As a case study the authors have consid-
ered the mathematical model of the real-time beam and ball
system and analyzed the simulation and real time response.
Mechatronics design of ball and beam system education and researchAlexander Decker
This document describes the proposed design of a mechatronics ball and beam system for educational and research purposes. The system aims to test and analyze various control strategies by using a servo motor to continuously adjust the angle of a beam to stabilize a rolling ball. It discusses the requirements, conceptual design, and concurrent selection and integration of subsystems including the mechanical design, sensors, actuators, and control algorithm. Preliminary block diagrams and component layouts are presented and the mechanical system parts are listed. The design is intended to help users visualize and experiment with different control methods on a precise and cost-effective experimental unit.
Iaetsd design of a robust fuzzy logic controller for a single-link flexible m...Iaetsd Iaetsd
This document describes the design of a fuzzy logic controller for a single-link flexible manipulator. A fuzzy-PID controller is used to control an uncertain flexible robotic arm and its internal motor dynamics parameters. The controller is tested against conventional integral and PID controllers in simulations. The results show the proposed fuzzy PID controller has better robustness under variations in motor dynamics compared to the other controllers.
The present work deals to investigate the performance of linear switched reluctance motor designed for a sliding door application. The objective of this paper is to develop an analytical model in order to predict the dynamic behaviour of the studied motor. Firstly, the characteristics of the proposed motor in open loop operation was computed.Secondly, the effect of the load on the response of the motor was investigated. In this context, a two technoque in open loop were adopted to solve the error positioning with load and to damp the oscillation observed in the characteristics of the motor in order to obtain a smooth motion.
Nonlinear Control of an Active Magnetic Bearing with Output ConstraintIJECEIAES
In this paper, an appropriate control strategy is proposed to handle the nonlinear dy- namics of an active magnetic bearing (AMB). The goal of the control design is to drive the AMB rotor to the origin with improved transient response. In order to achieve this task, back stepping control technique with a barrier Lyapunov function are employed to keep the tracking error trajectory inside a predefined zone to avoid possible mechanical contact between rotor and stator. Besides, a speed observer is also used since information about rotor speed is not always available. The stability of the closed-loop system is proven. The effectiveness of the proposed control strategy is verified by numerical simulations.
—This paper presents a new image based visual servoing (IBVS) control scheme for omnidirectional wheeled mobile robots with four swedish wheels. The contribution is the proposal of a scheme that consider the overall dynamic of the system; this means, we put together mechanical and electrical dynamics. The actuators are direct current (DC) motors, which imply that the system input signals are armature voltage applied to DC motors. In our control scheme the PD control law and eye-to-hand camera configuration are used to compute the armature voltages and to measure system states, respectively. Stability proof is performed via Lypunov direct method and LaSalle's invariance principle. Simulation and experimental results were performed in order to validate the theoretical proposal and to show the good performance of the posture errors. Keywords—IBVS, posture control, omnidirectional wheeled mobile robot, dynamic actuator, Lyapunov direct method.
This document discusses modal analysis of rotating structures using active magnetic bearings. It begins by introducing modal analysis and its importance for analyzing high-speed rotating machinery. It then describes the experimental setup which uses active magnetic bearings to both levitate and excite a test rotor. Natural frequencies and mode shapes are identified for the free-free rotor both with and without bearing stiffness. Introducing bearing stiffness is found to increase natural frequencies and introduce additional modes. The document concludes by explaining how the active magnetic bearings can be used to artificially excite the rotor to measure its frequency response functions and identify its dynamic characteristics.
Design of an adaptive state feedback controller for a magnetic levitation sy...IJECEIAES
This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controller in terms of the operating point. The results of the simulation show that the operating point has significant effect on the performance of nonadaptive SFC, and this performance may degrade as the operating point deviates from the equilibrium point, while the ASFC achieves the required design specification for any operating point and outperforms the state feedback controller from this point of view.
Transient stability enhancement by ann basediaemedu
This document discusses using an artificial neural network (ANN) to perform adaptive load shedding to improve transient stability. It summarizes:
1) Conventional load shedding schemes are not efficient for all disturbances as they do not consider system dynamics. ANN can calculate the minimum load to shed based on contingencies.
2) The IEEE 9-bus system is simulated in ETAP to analyze transient stability under various contingencies like generator outages and faults. ANN is implemented in MATLAB.
3) ANN is trained using input-output datasets of disturbances and required load shedding. It can then quickly calculate the optimal load to shed to maintain stability for new disturbances.
Iaetsd estimation of frequency for a single link-flexibleIaetsd Iaetsd
This document proposes an adaptive control method for an uncertain flexible robotic arm. It uses a fast online closed-loop identification method combined with an output feedback controller called a Generalized Proportional Integral (GPI) controller. An algebraic identification method is used to identify unknown system parameters and update the GPI controller in real-time. Simulations show the robustness of the adaptive controller. The document describes the flexible manipulator model, GPI controller design, algebraic estimator development, adaptive control procedure, and simulation results showing the effectiveness of the adaptive control system.
Analysis of the Effect of Electric and Magnetic Loadings on the Design Parame...IJERA Editor
This paper looks at the effect of magnetic loading and electric loading on the design parameters of an induction motor and its performance. The study involves the use of MATLAB to simulate 50kW, 3-phase, 415V, 50Hz, 6 poles induction machine. Based on the variation of the magnetic and electric loading of the machine, the various design values of the rotor and stator of the machine are specified. The performance index which includes stator loss, rotor loss, cost, power factor, efficiency, and torque are also specified for squirrel cage induction motor (SCIM)
Iaetsd modelling and controller design of cart inverted pendulum system using...Iaetsd Iaetsd
This document presents a model reference adaptive control (MRAC) scheme for stabilizing a cart-inverted pendulum system. The cart-inverted pendulum is a highly nonlinear and unstable system that is challenging to control. The proposed controller uses Lyapunov stability theory to design an MRAC controller. Simulation results show the controller is able to balance the inverted pendulum in the unstable upright position and regulate the cart position, demonstrating the effectiveness of the proposed MRAC control approach.
Vibration attenuation control of ocean marine risers with axial-transverse co...TELKOMNIKA JOURNAL
The target of this paper is designing a boundary controller for vibration suppression of marine risers with coupling mechanisms under environmental loads. Based on energy approach and the equations of axial and transverse motions of the risers are derived. The Lyapunov direct method is employed to formulated the control placed at the riser top-end. Proof of existence and uniqueness of the solutions of the closed-loop system is provided. Stability analysis of the closed-loop system is also included.
Simulation of inverted pendulum presentationPourya Parsa
This document presents a simulation of controlling an inverted pendulum. It includes equations of motion to model the system state based on the pendulum angle and position over time. A sliding control method is used to control the pendulum angle and ride height, choosing control inputs to minimize errors between the actual and desired states. Simulation results are shown controlling the pendulum velocity and angle to stabilize the system. An animation demonstrates the full simulated control of the inverted pendulum.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
In this paper, the tracking control scheme is presented using the framework of finite-time sliding mode control (SMC) law and high-gain observer for disturbed/uncertain multi-motor driving systems under the consideration multi-output systems. The convergence time of sliding mode control is estimated in connection with linear matrix inequalities (LMIs). The input state stability (ISS) of proposed controller was analyzed by Lyapunov stability theory. Finally, the extensive simulation results are given to validate the advantages of proposed control design.
1) The document provides an overview of inverted pendulum control, focusing on mobile inverted pendulums.
2) It describes the structure of a mobile inverted pendulum system with a cart and mounted pendulum. Equations of motion are provided.
3) Two common control strategies for inverted pendulums are discussed: PID control and fuzzy logic control. Performance comparisons using simulations show fuzzy logic control provides better response.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Neural Network Control Based on Adaptive Observer for Quadrotor HelicopterIJITCA Journal
A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional high gain observer by introducing some changes in observer’s original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme
Comparative analysis of observer-based LQR and LMI controllers of an inverted...journalBEEI
An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.
Solar Panel Control System using an Intelligent Control: T2FSMC and Firefly A...TELKOMNIKA JOURNAL
Solar panel is a solar energy converter to electrical energy. On solar tracker, there is a controller which sets the movement of solar panel such that it is perpendicular with solar rays. Previous research had designed Type 2 Fuzzy Sliding Mode Control (T2FSMC) controller to control the position of solar panel. However, there was trial and error process to determine gain scale factor so the development of optimization method is needed. This paper aims to modify gain scale factor using Firefly algorithm to increase performance of system. The simulation shows that T2FSMC Firefly has better performance than T2FSMC. T2FSMC Firefly shows the increase of performance on rise time, settling time, and integral time absolute error.
OPTIMAL TRAJECTORY OF ROBOT MANIPULATOR FOR ENERGY MINIMIZATION WITH QUARTIC ...cscpconf
In this paper, a different way to find the trajectory of the robot manipulators for energyoptimization is presented. In our method, the joint angles of the manipulator are set as quadratic polynomial functions. Then, with them taken into the variational function of energy consumption, Finite Element Modelling is employed to optimize the unknown parameters of the fourth order joint angles
This document proposes a novel method for calculating and optimizing the electromechanical characteristics of switched reluctance motors (SRMs). The method combines electric circuit theory and electromagnetic field theory approaches. It establishes a relationship between stator coil inductance and rotor angle that is incorporated into differential equations describing the electromechanical process in SRMs. Simulation results using MATLAB/Simulink software validate the accuracy of the proposed model for an 8/6 SRM. The method provides a way to simultaneously calculate varying magnetic field characteristics and electrical circuit properties during simulation, overcoming a key challenge for SRM modeling.
Comparison of a triple inverted pendulum stabilization using optimal control ...Mustefa Jibril
In this paper, modelling design and analysis of a triple inverted pendulum have been done using
Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable
without using feedback control system. In this paper an optimal control method means a linear
quadratic regulator and pole placement controllers are used to stabilize the triple inverted
pendulum upside. The impulse response simulation of the open loop system shows us that the
pendulum is unstable. The comparison of the closed loop impulse response simulation of the
pendulum with LQR and pole placement controllers results that both controllers have stabilized
the system but the pendulum with LQR controllers have a high overshoot with long settling time
than the pendulum with pole placement controller. Finally the comparison results prove that the
pendulum with pole placement controller improve the stability of the system.
The Neural Network-Combined Optimal Control System of Induction MotorIJECEIAES
This research aims to propose the optimal control method combined with the neuron network for an induction motor. In the proposed system, the induction motor is a nonlinear object which is controlled at each working point. At these working-points, the state equation of the induction motor is linear, so it is possible to apply the linear quadratic regular algorithm for the induction motor. Therefore, the parameters of the state feedback controller are the functions. The output-input relationships of these functions are set through the neural network. The numerical simulation results show that the quality of the control system of the induction motor is very high: The response speed always follows the desired speed with the short transition time and the small overshoot. Furthermore, the system is robust in the case of changing the load torque, and the parameters of the induction motor are incorrectly defined
Fuzzy Gain-Scheduling Proportional–Integral Control for Improving the Speed B...IJPEDS-IAES
In this article, we have set up a vector control law of induction machine
where we tried different type of speed controllers. Our control strategy is of
type Field Orientated Control (FOC). In this structure we designed a Fuzzy
Gain-Scheduling Proportional–Integral (Pi) controller to obtain best result
regarding the speed of induction machine. At the beginning we designed a Pi
controller with fixed parameters. We came up to these parameters by
identifying the transfer function of this controller to that of Broïda (second
order transfer function). Then we designed a fuzzy logic (FL) controller.
Based on simulation results, we highlight the performances of each
controller. To improve the speed behaviour of the induction machine, we
have designend a controller called “Fuzzy Gain-Scheduling Proportional–
Integral controller” (FGS-PI controller) which inherited the pros of the
aforementioned controllers. The simulation result of this controller will
strengthen its performances.
Wind turbine doubly-fed induction generator defects diagnosis under voltage dipsTELKOMNIKA JOURNAL
Voltage dips are brief but frequent disturbances that can be defined as the most important problem affecting all electrical grids, it cannot be completely avoided and represent the main priority for the industry. This study remains part of monitoring the quality of electrical energy’s field. Its aim is to apply two approaches signals for improving the failure recognition in wind turbine conversion chain. One is based on the combination of spectral analysis of stator current by fast Fourier transform and Lissajous curves technique of grid currents. The second approach is based on the stator current analysis by discrete wavelet transform which is considered an ideal tool for this purpose due to its time-frequency localization. These defects diagnosis methods have shown their efficiency in detection, visualization and analysis of voltage dips in order to develop a control strategy for a wind turbine requiring continuity of its service despite the presence of voltage dips.
Bank of Extended Kalman Filters for Faults Diagnosis in Wind Turbine Doubly F...TELKOMNIKA JOURNAL
This document presents a model-based fault diagnosis approach using a bank of extended Kalman filters to detect and isolate faults in the current sensors and stator and rotor windings of a doubly fed induction generator (DFIG) used in variable speed wind turbines. A nonlinear state space model of the DFIG is developed and discretized. An extended Kalman filter is used to estimate states including currents and resistances to generate residuals for fault detection. A bank of extended Kalman filters is proposed to handle multiple simultaneous faults according to a dedicated observer scheme. Simulation results demonstrate the effectiveness of the approach in diagnosing and quantifying sensor and winding faults.
Design of an adaptive state feedback controller for a magnetic levitation sy...IJECEIAES
This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controller in terms of the operating point. The results of the simulation show that the operating point has significant effect on the performance of nonadaptive SFC, and this performance may degrade as the operating point deviates from the equilibrium point, while the ASFC achieves the required design specification for any operating point and outperforms the state feedback controller from this point of view.
Transient stability enhancement by ann basediaemedu
This document discusses using an artificial neural network (ANN) to perform adaptive load shedding to improve transient stability. It summarizes:
1) Conventional load shedding schemes are not efficient for all disturbances as they do not consider system dynamics. ANN can calculate the minimum load to shed based on contingencies.
2) The IEEE 9-bus system is simulated in ETAP to analyze transient stability under various contingencies like generator outages and faults. ANN is implemented in MATLAB.
3) ANN is trained using input-output datasets of disturbances and required load shedding. It can then quickly calculate the optimal load to shed to maintain stability for new disturbances.
Iaetsd estimation of frequency for a single link-flexibleIaetsd Iaetsd
This document proposes an adaptive control method for an uncertain flexible robotic arm. It uses a fast online closed-loop identification method combined with an output feedback controller called a Generalized Proportional Integral (GPI) controller. An algebraic identification method is used to identify unknown system parameters and update the GPI controller in real-time. Simulations show the robustness of the adaptive controller. The document describes the flexible manipulator model, GPI controller design, algebraic estimator development, adaptive control procedure, and simulation results showing the effectiveness of the adaptive control system.
Analysis of the Effect of Electric and Magnetic Loadings on the Design Parame...IJERA Editor
This paper looks at the effect of magnetic loading and electric loading on the design parameters of an induction motor and its performance. The study involves the use of MATLAB to simulate 50kW, 3-phase, 415V, 50Hz, 6 poles induction machine. Based on the variation of the magnetic and electric loading of the machine, the various design values of the rotor and stator of the machine are specified. The performance index which includes stator loss, rotor loss, cost, power factor, efficiency, and torque are also specified for squirrel cage induction motor (SCIM)
Iaetsd modelling and controller design of cart inverted pendulum system using...Iaetsd Iaetsd
This document presents a model reference adaptive control (MRAC) scheme for stabilizing a cart-inverted pendulum system. The cart-inverted pendulum is a highly nonlinear and unstable system that is challenging to control. The proposed controller uses Lyapunov stability theory to design an MRAC controller. Simulation results show the controller is able to balance the inverted pendulum in the unstable upright position and regulate the cart position, demonstrating the effectiveness of the proposed MRAC control approach.
Vibration attenuation control of ocean marine risers with axial-transverse co...TELKOMNIKA JOURNAL
The target of this paper is designing a boundary controller for vibration suppression of marine risers with coupling mechanisms under environmental loads. Based on energy approach and the equations of axial and transverse motions of the risers are derived. The Lyapunov direct method is employed to formulated the control placed at the riser top-end. Proof of existence and uniqueness of the solutions of the closed-loop system is provided. Stability analysis of the closed-loop system is also included.
Simulation of inverted pendulum presentationPourya Parsa
This document presents a simulation of controlling an inverted pendulum. It includes equations of motion to model the system state based on the pendulum angle and position over time. A sliding control method is used to control the pendulum angle and ride height, choosing control inputs to minimize errors between the actual and desired states. Simulation results are shown controlling the pendulum velocity and angle to stabilize the system. An animation demonstrates the full simulated control of the inverted pendulum.
Controller design of inverted pendulum using pole placement and lqreSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
In this paper, the tracking control scheme is presented using the framework of finite-time sliding mode control (SMC) law and high-gain observer for disturbed/uncertain multi-motor driving systems under the consideration multi-output systems. The convergence time of sliding mode control is estimated in connection with linear matrix inequalities (LMIs). The input state stability (ISS) of proposed controller was analyzed by Lyapunov stability theory. Finally, the extensive simulation results are given to validate the advantages of proposed control design.
1) The document provides an overview of inverted pendulum control, focusing on mobile inverted pendulums.
2) It describes the structure of a mobile inverted pendulum system with a cart and mounted pendulum. Equations of motion are provided.
3) Two common control strategies for inverted pendulums are discussed: PID control and fuzzy logic control. Performance comparisons using simulations show fuzzy logic control provides better response.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Neural Network Control Based on Adaptive Observer for Quadrotor HelicopterIJITCA Journal
A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional high gain observer by introducing some changes in observer’s original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme
Comparative analysis of observer-based LQR and LMI controllers of an inverted...journalBEEI
An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.
Solar Panel Control System using an Intelligent Control: T2FSMC and Firefly A...TELKOMNIKA JOURNAL
Solar panel is a solar energy converter to electrical energy. On solar tracker, there is a controller which sets the movement of solar panel such that it is perpendicular with solar rays. Previous research had designed Type 2 Fuzzy Sliding Mode Control (T2FSMC) controller to control the position of solar panel. However, there was trial and error process to determine gain scale factor so the development of optimization method is needed. This paper aims to modify gain scale factor using Firefly algorithm to increase performance of system. The simulation shows that T2FSMC Firefly has better performance than T2FSMC. T2FSMC Firefly shows the increase of performance on rise time, settling time, and integral time absolute error.
OPTIMAL TRAJECTORY OF ROBOT MANIPULATOR FOR ENERGY MINIMIZATION WITH QUARTIC ...cscpconf
In this paper, a different way to find the trajectory of the robot manipulators for energyoptimization is presented. In our method, the joint angles of the manipulator are set as quadratic polynomial functions. Then, with them taken into the variational function of energy consumption, Finite Element Modelling is employed to optimize the unknown parameters of the fourth order joint angles
This document proposes a novel method for calculating and optimizing the electromechanical characteristics of switched reluctance motors (SRMs). The method combines electric circuit theory and electromagnetic field theory approaches. It establishes a relationship between stator coil inductance and rotor angle that is incorporated into differential equations describing the electromechanical process in SRMs. Simulation results using MATLAB/Simulink software validate the accuracy of the proposed model for an 8/6 SRM. The method provides a way to simultaneously calculate varying magnetic field characteristics and electrical circuit properties during simulation, overcoming a key challenge for SRM modeling.
Comparison of a triple inverted pendulum stabilization using optimal control ...Mustefa Jibril
In this paper, modelling design and analysis of a triple inverted pendulum have been done using
Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable
without using feedback control system. In this paper an optimal control method means a linear
quadratic regulator and pole placement controllers are used to stabilize the triple inverted
pendulum upside. The impulse response simulation of the open loop system shows us that the
pendulum is unstable. The comparison of the closed loop impulse response simulation of the
pendulum with LQR and pole placement controllers results that both controllers have stabilized
the system but the pendulum with LQR controllers have a high overshoot with long settling time
than the pendulum with pole placement controller. Finally the comparison results prove that the
pendulum with pole placement controller improve the stability of the system.
The Neural Network-Combined Optimal Control System of Induction MotorIJECEIAES
This research aims to propose the optimal control method combined with the neuron network for an induction motor. In the proposed system, the induction motor is a nonlinear object which is controlled at each working point. At these working-points, the state equation of the induction motor is linear, so it is possible to apply the linear quadratic regular algorithm for the induction motor. Therefore, the parameters of the state feedback controller are the functions. The output-input relationships of these functions are set through the neural network. The numerical simulation results show that the quality of the control system of the induction motor is very high: The response speed always follows the desired speed with the short transition time and the small overshoot. Furthermore, the system is robust in the case of changing the load torque, and the parameters of the induction motor are incorrectly defined
Fuzzy Gain-Scheduling Proportional–Integral Control for Improving the Speed B...IJPEDS-IAES
In this article, we have set up a vector control law of induction machine
where we tried different type of speed controllers. Our control strategy is of
type Field Orientated Control (FOC). In this structure we designed a Fuzzy
Gain-Scheduling Proportional–Integral (Pi) controller to obtain best result
regarding the speed of induction machine. At the beginning we designed a Pi
controller with fixed parameters. We came up to these parameters by
identifying the transfer function of this controller to that of Broïda (second
order transfer function). Then we designed a fuzzy logic (FL) controller.
Based on simulation results, we highlight the performances of each
controller. To improve the speed behaviour of the induction machine, we
have designend a controller called “Fuzzy Gain-Scheduling Proportional–
Integral controller” (FGS-PI controller) which inherited the pros of the
aforementioned controllers. The simulation result of this controller will
strengthen its performances.
Wind turbine doubly-fed induction generator defects diagnosis under voltage dipsTELKOMNIKA JOURNAL
Voltage dips are brief but frequent disturbances that can be defined as the most important problem affecting all electrical grids, it cannot be completely avoided and represent the main priority for the industry. This study remains part of monitoring the quality of electrical energy’s field. Its aim is to apply two approaches signals for improving the failure recognition in wind turbine conversion chain. One is based on the combination of spectral analysis of stator current by fast Fourier transform and Lissajous curves technique of grid currents. The second approach is based on the stator current analysis by discrete wavelet transform which is considered an ideal tool for this purpose due to its time-frequency localization. These defects diagnosis methods have shown their efficiency in detection, visualization and analysis of voltage dips in order to develop a control strategy for a wind turbine requiring continuity of its service despite the presence of voltage dips.
Bank of Extended Kalman Filters for Faults Diagnosis in Wind Turbine Doubly F...TELKOMNIKA JOURNAL
This document presents a model-based fault diagnosis approach using a bank of extended Kalman filters to detect and isolate faults in the current sensors and stator and rotor windings of a doubly fed induction generator (DFIG) used in variable speed wind turbines. A nonlinear state space model of the DFIG is developed and discretized. An extended Kalman filter is used to estimate states including currents and resistances to generate residuals for fault detection. A bank of extended Kalman filters is proposed to handle multiple simultaneous faults according to a dedicated observer scheme. Simulation results demonstrate the effectiveness of the approach in diagnosing and quantifying sensor and winding faults.
Direct torque control and dynamic performance of induction motor using fract...IJECEIAES
Conventional direct torque control (DTC) is one of the best control systems for regulating the torque of an induction motor (IM). However, the DTC’s enormous waves in flux and torque cause acoustic noise that degrades control performance, especially at low speeds due to the DTC’s low switching frequency. Direct torque control systems, which focus just on torque and flux, have been proposed as a solution to these problems. In order to improve DTC control performance, this work introduces a fractionalorder fuzzy logic controller method. The objective is to analyze this technique critically with regard to its efficacy in reducing ripple, its tracking speed, its switching loss, its algorithm complexity, and its sensitivity to its parameters. Simulation in MATLAB/Simulink verifies the anticipated control approach’s performance.
Mobile robot turned on by sound and directionally controlled by an external l...IJECEIAES
This paper presents theoretical, numerical, and experimental tests of a mobile robot, which starts on the emission of a strong sound, like an applause, and the direction and speed of the vehicle is controlled by an external pulsed light source (PWM signal). The simulation is performed in MATLAB-Simulink; electrical circuits and the experiment are shown in detail. The results show that the vehicle speed can be controlled with a PWM signal from an external light falling on the LDR sensors. Besides, the circuit was designed to consume less than 1 ampere with the four motors moving at full speed, which can easily be powered by lithium battery.
NEW SYSTEM OF CHAOTIC SIGNAL GENERATION BASED ON COUPLING COEFFICIENTS APPLI...University of Malaya (UM)
The nonlinear behavior (chaotic) of light traveling in an optical fiber ring resonator such as an add/drop system
is presented. The chaotic behavior is considered to be a beneficial effect that can be used in the communication
system. Such a system can be used to secure the information signals, therefore, the ability of chaotic carriers to synchronize in a communication system is performed. The used optical material is InGaAsP/InP regarding to suitable parameters of the system. The nonlinear refractive index is fixed to n2 = 3.8 × 10−20 m2
/W, and the 20,000 iterations of round-trip within the system is simulated. The input powers are selected at 1 W, where the coupling coefficient of the system varies according to two critical cases, where 0 0.1
and 0.1 1. As a results, larger coupler coefficient corresponds to lower input power for the case of
0 0.1 and smaller coupling coefficient of the system is corresponds to lower input power when
0.1 1. To optimize the microring systems, Lower input power is recommended in many applications in optical optical communication systems.
Robots play important roles in day to day
activities of human endeavour and can perform
complex tasks speedily and accurately. Robots are
employed to imitate human behaviours and then
apply these behaviours to the skills that lead to
achieving a certain task in solving the challenges
faced by impaired people in society. This robotic arm
was achieved using light-weight steel iron for the
frames, a moderate torque MG995 Towerpro, and
servo motor. Two Atmega328 Arduino
microcontroller was employed to control the motors
through the use of pulse width modulation
technique. Mathematical models were developed for
the mechanism to represent the kinematics involved
at each joint with mathematical variables. Then, the
stability of the system was carried out using a step
input signal being a type zero system.
Comparison of Estimated Torques Using Low Pass Filter and Extended Kalman Fil...IAES-IJPEDS
Torque calculation process is one of the major concerns for controlling induction motors in industry, which requires very accurate state estimation of unmeasurable variables of nonlinear models. This can be solved if the variables used for torque calculation is accurately estimated. This paper presents a torque calculation based on a voltage model represented with a low-pass filter (LPF), and an extended Kalman filter (EKF). The experimental results showed that the estimated torque at low speed based on EKF is more accurate in the expense of more complicated and larger computational time.
In this article, we are interested in the improvement of the performances of Doubly Fed Induction Machine (DFIM) operating in motor mode by the use of the direct torque control (DTC). Firstly, we focused on the modeling of the DFIM and the study of the principle of functioning of the DTC control. Then, we implement this control on the Matlab/Simulink environment. Secondly, we present the simulation results of the proposed control. The analysis of these results shows clearly that the system based on the DFIM studied follows perfectly the set points, what allowed us to justify the efficiency of the elaborate control.
This paper focuses on the modeling and control of a wind energy conversion chain using a permanent magnet synchronous machine. This system behaves a turbine, a generator, DC/DC and DC/AC power converters. These are connected on both sides to the DC bus, where the inverter is followed by a filter which is connected to the grid. In this paper, we have been used two types of controllers. For the stator side converter, we consider the Takagi-Sugeno approach where the parameters of controller have been computed by the theory of linear matrix inequalities. The stability synthesis has been checked using the Lyapunov theory. According to the grid side converter, the proportional integral controller is exploited to keep a constant voltage on the DC bus and control both types of powers. The simulation results demonstrate the robustness of the approach used.
IRJET - Optimizing a High Lateral Misalignment Tolerance of the Short-Ra...IRJET Journal
This document analyzes different capacitive compensation topologies for optimizing lateral misalignment tolerance in inductive wireless power transfer systems. It compares the series-series, parallel-series, series-parallel, and parallel-parallel topologies through analytical and experimental methods. The results show that the series-series topology provides the best optimization as it has independence of resonance frequency from misalignment, high voltage and current gains, and zero phase shift at any misalignment, leading to lower switching losses.
17.pmsm speed sensor less direct torque control based on ekfMouli Reddy
This document presents a speed sensorless direct torque control method for permanent magnet synchronous motors (PMSM) using an Extended Kalman Filter (EKF). The EKF is used to estimate the stator flux linkage and rotor speed without needing a mechanical speed sensor. This overcomes issues with traditional direct torque control methods like large current and flux ripples. Simulation results show the EKF method maintains the fast torque response of direct torque control while improving dynamic and static performance and robustness to parameter and load variations compared to traditional methods.
This document summarizes a research article that addresses controlling a wind energy conversion system (WECS) consisting of a wind turbine connected to the grid via a doubly fed induction generator (DFIG) and an AC/DC/AC converter. The control objectives are to: 1) control the generator speed to track an optimal reference, 2) control the stator reactive power to be null, 3) regulate the DC-link voltage to a constant value, and 4) ensure a unitary power factor. A high gain observer is designed to estimate unmeasurable mechanical variables. A sliding mode controller is developed using the observer to achieve the control objectives. Simulation results using MATLAB/SIMULINK evaluate the performance of the proposed controller under a
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Fuzzy optimization strategy of the maximum power point tracking for a variab...IJECEIAES
Wind power systems are gaining more and more interests; in order to diminish dependence on fossil fuels. In this paper, we present a variable speed-wind energy global system based on a synchronous generator with permanent magnetic (PMSG). The major goal of this study is to track the maximum power that is present in the turbine. An examination of control methods to extract the MPPT point, from a wind energy conversion system (WECS) under variable speed situations is presented. An intelligent controller based on the fuzzy logic control (FLC) is proposed for regulating permanent magnetic synchronous generator (PMSG) output power, in order to improve tracking performance. The principle of this maximum power point tracking (MPPT) algorithm consists in looking for an optimal operating relation of the maximum power, then tracking this last. We simulated our system with MATLAB-Simulink software. The found results will be debated to elucidate performance of the global system.
Numerical Deterministic Method of Including Saturation Effect in the Performa...IJERD Editor
This document describes a numerical method for including the effect of magnetic saturation in the performance analysis of a single-phase induction motor. The author computes the magnetic saturation factor (Ksat) of the motor to be 1.18 by determining the magnetomotive force (mmf) in different parts of the magnetic circuit through numerical calculations. Using the saturation factor, the saturated values of the motor reactances are obtained. Performance parameters like efficiency, torque, current, losses are then computed using the saturated reactances. The efficiency decreases by 2.92% and starting torque increases by 17.1% with saturation included in the analysis.
Modeling & Simulation of PMSM Drives with Fuzzy Logic ControllerIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Analytical Model of Cage Induction Machine Dedicated to the Study of the Inne...IJECEIAES
This paper presents a new analytical model for inner bearing raceway defect. The model is based on the presentation of different machine inductances as Fourier series without any kind of reference frame transformation. The proposed approach shows that this model is able to give important features on the state of the motor. Simulation based on spectral analysis of stator current signal using Fast Fourier Transform (FFT) and experimental results are given to shed light on the usefulness of the proposed model.
Similar to A non-linear control method for active magnetic bearings with bounded input and output (20)
The aim of this research is the speed tracking of the permanent magnet synchronous motor (PMSM) using an intelligent Neural-Network based adapative backstepping control. First, the model of PMSM in the Park synchronous frame is derived. Then, the PMSM speed regulation is investigated using the classical method utilizing the field oriented control theory. Thereafter, a robust nonlinear controller employing an adaptive backstepping strategy is investigated in order to achieve a good performance tracking objective under motor parameters changing and external load torque application. In the final step, a neural network estimator is integrated with the adaptive controller to estimate the motor parameters values and the load disturbance value for enhancing the effectiveness of the adaptive backstepping controller. The robsutness of the presented control algorithm is demonstrated using simulation tests. The obtained results clearly demonstrate that the presented NN-adaptive control algorithm can provide good trackingperformances for the speed trackingin the presence of motor parameter variation and load application.
The document presents a new method for fault classification and direction discrimination in transmission lines using 1D convolutional neural networks (1D-CNNs). A 132kV transmission line model is simulated to generate training and testing data for the 1D-CNN algorithm. The proposed 1D-CNN approach directly uses the voltage and current signals from one end as input, merging feature extraction and classification into a single learning process. Testing shows the 1D-CNN method accurately classifies and discriminates fault direction with higher accuracy than conventional neural network and fuzzy neural network methods under different fault conditions.
Among the most widespread renewable energy sources is solar energy; Solar panels offer a green, clean, and environmentally friendly source of energy. In the presence of several advantages of the use of photovoltaic systems, the random operation of the photovoltaic generator presents a great challenge, in the presence of a critical load. Among the most used solutions to overcome this problem is the combination of solar panels with generators or with the public grid or both. In this paper, an energy management strategy is proposed with a safety aspect by using artificial neural networks (ANNs), in order to ensure a continuous supply of electricity to consumers with a maximum solicitation of renewable energy.
In this paper, the artificial neural network (ANN) has been utilized for rotating machinery faults detection and classification. First, experiments were performed to measure the lateral vibration signals of laboratory test rigs for rotor-disk-blade when the blades are defective. A rotor-disk-blade system with 6 regular blades and 5 blades with various defects was constructed. Second, the ANN was applied to classify the different x- and y-axis lateral vibrations due to different blade faults. The results based on training and testing with different data samples of the fault types indicate that the ANN is robust and can effectively identify and distinguish different blade faults caused by lateral vibrations in a rotor. As compared to the literature, the present paper presents a novel work of identifying and classifying various rotating blade faults commonly encountered in rotating machines using ANN. Experimental data of lateral vibrations of the rotor-disk-blade system in both x- and y-directions are used for the training and testing of the network.
This paper focuses on the artificial bee colony (ABC) algorithm, which is a nonlinear optimization problem. is proposed to find the optimal power flow (OPF). To solve this problem, we will apply the ABC algorithm to a power system incorporating wind power. The proposed approach is applied on a standard IEEE-30 system with wind farms located on different buses and with different penetration levels to show the impact of wind farms on the system in order to obtain the optimal settings of control variables of the OPF problem. Based on technical results obtained, the ABC algorithm is shown to achieve a lower cost and losses than the other methods applied, while incorporating wind power into the system, high performance would be gained.
The significance of the solar energy is to intensify the effectiveness of the Solar Panel with the use of a primordial solar tracking system. Here we propounded a solar positioning system with the use of the global positioning system (GPS) , artificial neural network (ANN) and image processing (IP) . The azimuth angle of the sun is evaluated using GPS which provide latitude, date, longitude and time. The image processing used to find sun image through which centroid of sun is calculated and finally by comparing the centroid of sun with GPS quadrate to achieve optimum tracking point. Weather conditions and situation observed through AI decision making with the help of IP algorithms. The presented advance adaptation is analyzed and established via experimental effects which might be made available on the memory of the cloud carrier for systematization. The proposed system improve power gain by 59.21% and 10.32% compare to stable system (SS) and two-axis solar following system (TASF) respectively. The reduced tracking error of IoT based Two-axis solar following system (IoT-TASF) reduces their azimuth angle error by 0.20 degree.
Kosovo has limited renewable energy resources and its power generation sector is based on fossil fuels. Such a situation emphasizes the importance of active research and efficient use of renewable energy potential. According to the analysis of meteorological data for Kosovo, it can be concluded that among the most attractive potential wind power sites are the locations known as Kitka (42° 29' 41" N and 21° 36' 45" E) and Koznica (42° 39′ 32″ N, 21° 22′30″E). The two terrains in which the analysis was carried out are mountain areas, with altitudes of 1142 m (Kitka) and 1230 m (Koznica). the same measuring height, about 84 m above the ground, is obtained for these average wind speeds: Kitka 6,667 m/s and Koznica 6,16 m/s. Since the difference in wind speed is quite large versus a difference in altitude that is not being very large, analyses are made regarding the terrain characteristics including the terrain relief features. In this paper it will be studied how much the roughness of the terrain influences the output energy. Also, that the assumption to be taken the same as to how much they will affect the annual energy produced.
The document summarizes a research paper that proposes using a battery energy storage system (BESS) with droop control to reduce frequency fluctuations in a multi-machine power system connected to a large-scale photovoltaic (PV) plant. The paper develops a droop control strategy for the BESS that incorporates a frequency error signal and dead-band. Simulation results using PSCAD/EMTDC software show that the proposed droop control-based BESS can efficiently curtail frequency oscillations caused by fluctuations in PV power injection due to changing solar irradiance.
This study investigates experimentally the performance of two-dimensional solar tracking systems with reflector using commercial silicon based photovoltaic module, with open and closed loop control systems. Different reflector materials were also investigated. The experiments were performed at the Hashemite University campus in Zarqa at a latitude of 32⁰, in February and March. Photovoltaic output power and performance were analyzed. It was found that the modified photovoltaic module with mirror reflector generated the highest value of power, while the temperature reached a maximum value of 53 ̊ C. The modified module suggested in this study produced 5% more PV power than the two-dimensional solar tracking systems without reflector and produced 12.5% more PV power than the fixed PV module with 26⁰ tilt angle.
The development of modeling wind speed plays a very important in helping to obtain the actual wind speed data for the benefit of the power plant planning in the future. The wind speed in this paper is obtained from a PCE-FWS 20 type measuring instrument with a duration of 30 minutes which is accumulated into monthly data for one year (2019). Despite the many wind speed modeling that has been done by researchers. Modeling wind speeds proposed in this study were obtained from the modified Rayleigh distribution. In this study, the Rayleigh scale factor (Cr) and modified Rayleigh scale factor (Cm) were calculated. The observed wind speed is compared with the predicted wind characteristics. The data fit test used correlation coefficient (R2), root means square error (RMSE), and mean absolute percentage error (MAPE). The results of the proposed modified Rayleigh model provide very good results for users.
This paper deals with an advanced design for a pump powered by solar energyto supply agricultural lands with water and also the maximum power point is used to extract the maximum value of the energy available inside the solar panels and comparing between techniques MPPT such as Incremental conductance, perturb & observe, fractional short current circuit, and fractional open voltage circuit to find the best technique among these. The solar system is designed with main parts: photovoltaic (PV) panel, direct current/direct current (DC/DC) converter, inverter, filter, and in addition, the battery is used to save energy in the event that there is an increased demand for energy and not to provide solar radiation, as well as saving energy in the case of generation more than demand. This work was done using the matrix laboratory (MATLAB) simulink program.
The objective of this paper is to provide an overview of the current state of renewable energy resources in Bangladesh, as well as to examine various forms of renewable energies in order to gain a comprehensive understanding of how to address Bangladesh's power crisis issues in a sustainable manner. Electricity is currently the most useful kind of energy in Bangladesh. It has a substantial influence on a country's socioeconomic standing and living standards. Maintaining a stable source of energy at a cost that is affordable to everyone has been a constant battle for decades. Bangladesh is blessed with a wealth of natural resources. Bangladesh has a huge opportunity to accelerate its economic development while increasing energy access, livelihoods, and health for millions of people in a sustainable way due to the renewable energy system.
When the irradiance distribution over the photovoltaic panels is uniform, the pursuit of the maximum power point is not reached, which has allowed several researchers to use traditional MPPT techniques to solve this problem Among these techniques a PSO algorithm is used to have the maximum global power point (GMPPT) under partial shading. On the other hand, this one is not reliable vis-à-vis the pursuit of the MPPT. Therefore, in this paper we have treated another technique based on a new modified PSO algorithm so that the power can reach its maximum point. The PSO algorithm is based on the heuristic method which guarantees not only the obtaining of MPPT but also the simplicity of control and less expensive of the system. The results are obtained using MATLAB show that the proposed modified PSO algorithm performs better than conventional PSO and is robust to different partial shading models.
A stable operation of wind turbines connected to the grid is an essential requirement to ensure the reliability and stability of the power system. To achieve such operational objective, installing static synchronous compensator static synchronous compensator (STATCOM) as a main compensation device guarantees the voltage stability enhancement of the wind farm connected to distribution network at different operating scenarios. STATCOM either supplies or absorbs reactive power in order to ensure the voltage profile within the standard-margins and to avoid turbine tripping, accordingly. This paper present new study that investigates the most suitable-location to install STATCOM in a distribution system connected wind farm to maintain the voltage-levels within the stability margins. For a large-scale squirrel cage induction generator squirrel-cage induction generator (SCIG-based) wind turbine system, the impact of STATCOM installation was tested in different places and voltage-levels in the distribution system. The proposed method effectiveness in enhancing the voltage profile and balancing the reactive power is validated, the results were repeated for different scenarios of expected contingencies. The voltage profile, power flow, and reactive power balance of the distribution system are observed using MATLAB/Simulink software.
The electrical and environmental parameters of polymer solar cells (PSC) provide important information on their performance. In the present article we study the influence of temperature on the voltage-current (I-V) characteristic at different temperatures from 10 °C to 90 °C, and important parameters like bandgap energy Eg, and the energy conversion efficiency η. The one-diode electrical model, normally used for semiconductor cells, has been tested and validated for the polemeral junction. The PSC used in our study are formed by the poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester (PCBM). Our technique is based on the combination of two steps; the first use the Least Mean Squares (LMS) method while the second use the Newton-Raphson algorithm. The found results are compared to other recently published works, they show that the developed approach is very accurate. This precision is proved by the minimal values of statistical errors (RMSE) and the good agreement between both the experimental data and the I-V simulated curves. The obtained results show a clear and a monotonic dependence of the cell efficiency on the studied parameters.
The inverter is the principal part of the photovoltaic (PV) systems that assures the direct current/alternating current (DC/AC) conversion (PV array is connected directly to an inverter that converts the DC energy produced by the PV array into AC energy that is directly connected to the electric utility). In this paper, we present a simple method for detecting faults that occurred during the operation of the inverter. These types of faults or faults affect the efficiency and cost-effectiveness of the photovoltaic system, especially the inverter, which is the main component responsible for the conversion. Hence, we have shown first the faults obtained in the case of the short circuit. Second, the open circuit failure is studied. The results demonstrate the efficacy of the proposed method. Good monitoring and detection of faults in the inverter can increase the system's reliability and decrease the undesirable faults that appeared in the PV system. The system behavior is tested under variable parameters and conditions using MATLAB/Simulink.
The document describes a proposed modified bridge-type nonsuperconducting fault current limiter (NSFCL) for distribution networks. The NSFCL consists of a bridge rectifier, two DC reactors (one small in series and one large in parallel), and an IGBT semiconductor switch controlled by a command circuit. During normal operation, the IGBT is on and the parallel reactor is bypassed, making the NSFCL invisible. During a fault, the IGBT turns off, inserting the parallel reactor to limit fault current. Simulation results showed the design effectively limits fault current while minimally affecting normal operation.
This paper provides a new approach to reducing high-order harmonics in 400 Hz inverter using a three-level neutral-point clamped (NPC) converter. A voltage control loop using the harmonic compensation combined with NPC clamping diode control technology. The capacitor voltage imbalance also causes harmonics in the output voltage. For 400 Hz inverter, maintain a balanced voltage between the two input (direct current) (DC) capacitors is difficult because the pulse width modulation (PWM) modulation frequency ratio is low compared to the frequency of the output voltage. A method of determining the current flowing into the capacitor to control the voltage on the two balanced capacitors to ensure fast response reversal is also given in this paper. The combination of a high-harmonic resonator controller and a neutral-point voltage controller working together on the 400 Hz NPC inverter structure is given in this paper.
Direct current (DC) electronic load is a useful equipment for testing the electrical system. It can emulate various load at a high rating. The electronic load requires a power converter to operate and a linear regulator is a common option. Nonetheless, it is hard to control due to the temperature variation. This paper proposed a DC electronic load using the boost converter. The proposed electronic load operates in the continuous current mode and control using the integral controller. The electronic load using the boost converter is compared with the electronic load using the linear regulator. The results show that the boost converter able to operate as an electronic load with an error lower than 0.5% and response time lower than 13 ms.
This paper presents a new simplified cascade multiphase DC-DC buck power converter suitable for low voltage and large current applications. Cascade connection enables very low voltage ratio without using very small duty cycles nor transformers. Large current with very low ripple content is achieved by using the multiphase technique. The proposed converter needs smaller number of components compared to conventional cascade multiphase DC-DC buck power converters. This paper also presents useful analysis of the proposed DC-DC buck power converter with a method to optimize the phase and cascade number. Simulation and experimental results are included to verify the basic performance of the proposed DC-DC buck power converter.
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A non-linear control method for active magnetic bearings with bounded input and output
1. International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 11, No. 4, December 2020, pp. 2154∼2163
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v11.i4.pp2154-2163 r 2154
A non-linear control method for active magnetic bearings
with bounded input and output
Danh Huy Nguyen, Tung Lam Nguyen, Duc Chinh Hoang
School of Electrical Engineering, Hanoi University of Science and Technology, Vietnam
Article Info
Article history:
Received Apr 24, 2020
Revised Jun 10, 2020
Accepted Jul 28, 2020
Keywords:
Active magnetic bearing
Backstepping control
Barrier Lyapunov function
Input saturation
ABSTRACT
Magnetic bearing is well-known for its advantage of reducing friction in rotary ma-
chines and is placing conventional bearings where high-speed operations and clean-
liness are essential. It can be shown that the AM is a nonlinear system due to the
relation between the magnetic force and current/rotor displacement. In this paper,
a mathematical model of a 4-DOF AMB supported by four dual electric magnets is
presented. The control objective is placed in a view of control input saturation and
output limitation that are meaningful aspect in practical applications. Backstepping
algorithm based control strategy is then adopted in order to achieve the high dynamic
performance of the bearing. The control is designed in such a way that it takes input
and output constraints into account by flexibly using hyperbolic tangent and barrier
Lyapunov functions. Informative simulation studies are carried out to understand the
operations of the machine and evaluate the controller quality.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Tung Lam Nguyen,
School of Electrical Engineering,
Hanoi University of Science and Technology, Vietnam.
Email: lam.nguyentung@hust.edu.vn
1. INTRODUCTION
AMB is one of the magnetic suspension methods which enables rotor shaft in rotary machines to be
lifted off without mechanical support by actively controlling the electromagnet [1]. Absence of mechanical
contact results in friction reduction. Thus, speed or acceleration of supported components can be increased
significantly when comparing with conventional bearing in use. Authors in [2] has listed many advantages of
AMB such as the absence of lubrication and contaminating wear, high speed rotation, low bearing losses, etc.
These benefits allow AMB to be integrated into electrical motor which can rotate upto 200000 rpm [3] and
be applicable as ultra-high speed spindle in machine tools [4, 5]. AMB can also be adopted in vacuum and
cleanroom systems [6] or equipment with harsh working condition like turbo machinery [7, 8]. Design and
different structures of magnetic bearings have been presented in [2, 9]. It can be seen that the system is highly
non-linear, and can become very complex. Thus the challenge lies in developing control scheme of bearing
so that it assures high performance features, especially nanometer accuracy [10] since the gap between rotor
shaft and bearings can be extremely tiny. Poor design of controller may result in rotor unbalances and internal
damping which in turns create vibration in machines, crack in motor shaft and failure at the end [11, 12]. The
classical PID algorithm have been widely used to control AMB system due to its simplicity, adaptability and
maturity [13, 14]. As AMB is a non-linear system, other methods like feedback linearisation or sliding mode
control can also be applied [10, 15]. With an effort to eliminate uncertainties in plant modelling, Bonffito et al
propose an offset free control for AMB based on classical model predictive control [16].
Journal homepage: http://ijpeds.iaescore.com
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It is evident that in previously mentioned research, hard limitation on control input and output is
omitted [17-20]. Control saturation might result in control degradation and violation of output constraint leads
to system mechanical failure. In this paper, we have adopted backstepping control algorithm to regulate and
stabilize the operation of AMB. The backstepping method há been employed in robotics [21], process control
[22], space applications [23, 24], and in AMB systems [25]. It is proven to be suitable with strict-feedback
system and to have the flexibility of removing instability while avoiding cancellation of potentially useful
nonlinearities [21]. The contribution of the paper can be named is the consideration of bounded system input
and output in control design. This paper is organized as the following. The mathematical model of AMB is
first developed in Section 2. Controller design process is presented in Section 3. In Section 4. simulation results
are provided together with the discussions. Finally, Section 5. concludes this paper.
2. MATHEMATICAL MODEL OF A DUEL COILS MAGNETIC ACTUATOR
It is fundamental that the magnetic force is proportional to the current square. Thus, regulating the
current can result in the force change. It is assumed that the rotor shaft has already been elevated along z axis
in vertical direction by another system. The system includes 2 pairs of the same electromagnets along x and y
axes in horizontal directions, ones of each pair are placed in the opposite position as illustrated in Figure 1.
Figure 1. Four electromagnet system
Each pair, then produce the forces of attraction F1&F2 and F3&F4 which are adjusted by regulating
the currents i1, i2, i3 and i4 respectively so that the shaft can be kept balance in the space within those magnets.
Assuming that (x1, i1), (x2, i2), (x3, i3), (x4, i4) are the positions and currents of electromagnets 1, 2, 3, and 4
respectively. The expression of the magnetic forces is given as
F1 =
µgN2
i1
2
Ag
4x1
2
=
K
4
i1
x1
2
, F2 =
µgN2
i2
2
Ag
4x2
2
=
K
4
i2
x2
2
F3 =
µgN2
i3
2
Ag
4x3
2
=
K
4
i3
x3
2
, F4 =
µgN2
i4
2
Ag
4x4
2
=
K
4
i4
x4
2
(1)
where K is a coefficient and calculated as K = µgN2
Ag, where µg is the permeability of air, N is
the number of turns in each coil, and Ag is the cross-section area of the electromagnet. It is assumed that the
inertia and geometric rotating axes of the rigid rotor coincide to each other, hence, the central point G is the
mass center of the rotor and m as its mass. its mass. The x axis direction forces (1) exerted on rotor result in
translational and rotational motions such that x and θy DOF’s force and torque equations are given as (2) and
(3) respectively:
m(ẍg) = (F1 − F2) + (F3 − F4) (2)
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Ir.θ̈y = −Ia.ω.θ̇x + (F1 − F2).Du − (F3 − F4).Dl (3)
Where Ia and Ir are the total moments of inertia about axial and radial direction axes z, x and y
through the rotor’s mass centre or center of weigth, respectively, θy is the rotor angle over y axis, Du is the
distance form the top electromagnets to rotor central G, Dl is the distance form the bottom electromagnets
to rotor central G, −Ia.ω.θ̇x is the reinforced torque of rotor, as shown in Figure 1. If the distance between
rotor and the magnet at stable position is x0, movement of rotor within the top two magnets is xu and that
within the bottom two magnets is xl, the distances x1, x2, x3, x4 between rotor and each magnet can be calcu-
lated as with respect to the top two magnets:
x1 = x0 − xu
x2 = x0 + xu
and with respect to the bottom two magnets:
x3 = x0 − xl
x4 = x0 + xl
. It is found that the AMB 4th order system with two pairs of electromagnets arranged as in
Figure 1 can be separated into two magnet systems, or simplified to two 2nd order systems. In that case, with
an assumption of very small θy, the movement of rotor is represented as, wrt. the two upper magnets:
xu = xg + Duθy (4)
and for the two lower magnets:
xl = xg − Dlθy (5)
Taking 2nd order derivatives of (4), and combining with (2) and (3), we have
ẍu = ẍg + Duθ̈y
=
1
m
F1 −
1
m
F2 + Du
1
Ir
F1Du −
1
Ir
F2Du
= au
i2
1
(x0 − xu)2
−
i2
2
(x0 + xu)2
(6)
where au = Ku
4
1
m +
D2
u
Ir
. It is noted that the coupling term related to θx and θy is omitted.
The coupling effects is considered as system disturbances. Applying the same procedure, from (5):
ẍl = ẍg − Dlθ̈y
= al
i2
3
(x0 − xl)
2 −
i2
4
(x0 + xl)
2
#
(7)
where al = Kl
4
1
m +
D2
l
Ir
. On the other hand, applying Kirchhoff’s voltage law for each coil, we
have the following equations:
u1 = Ri1 + Ls
di1
dt
+
K
2
d
dt
i1
x1
, u2 = Ri2 + Ls
di2
dt
+
K
2
d
dt
i2
x2
(8)
u3 = Ri3 + Ls
di3
dt
+
K
2
d
dt
i3
x3
, u4 = Ri4 + Ls
di4
dt
+
K
2
d
dt
i4
x4
(9)
Deriving form (8) and (9), the currents are represented as:
i̇1=
2(x0 − xu)
2Ls(x0 −xu)+K
(u1 −Ri1 −
K.vui1
2(x0 −xu)
2 ), i̇2=
2(x0 + xu)
2Ls(x0 + xu) + K
(u2 − Ri2 +
K.vui2
2(x0 + xu)
2 ), (10)
i̇3=
2(x0 − xl)
2Ls(x0 − xl) + K
(u3 − Ri3 −
K.vli3
2(x0 − xl)
2 ), i̇4=
2(x0 + xl)
2Ls(x0 + xl) + K
(u4 − Ri4 +
K.vli4
2(x0 + xl)
2 ), (11)
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4. Int J Pow Elec Dri Syst ISSN: 2088-8694 r 2157
In (4), (10), together presents the mathematical model of the two upper magnets as below:
ẋu = vu
v̇u = au
i1
x0 − xu
2
− au
i2
x0 + xu
2
i̇1=
2(x0 − xu)
2Ls(x0 − xu) + K
(u1−Ri1−
Kvui1
2(x0 − xu)
2 )
i̇2=
2.(x0 + xu)
2Ls(x0 + xu) + K
(u2−Ri2 +
Kvui2
2.(x0 + xu)
2 )
(12)
Similarly, (5), (11) provides the mathematical model of the two lower magnets:
ẋl = vl
v̇l = al
i3
x0 − xl
2
− al
i4
x0 + xl
2
i̇3=
2(x0 − xl)
2Ls(x0 − xl) + K
(u3−Ri3−
Kvli3
2(x0 − xl)
2 )
i̇4=
2(x0 + xl)
2Ls(x0 + xl) + K
(u4−Ri4+
Kvli4
2(x0 + xl)
2 )
(13)
In summary, the system model of AMB studied in this work consists of (12) and (13) and will be used
in the subsequent sections to design controller and investigate the operation.
3. CONTROLLER DESIGN
It is assumed that the speed can be estimated as derivative of position, the effect of rotor speed on
system operation is negligible, and magnetizing currents are taken as control input.
3.1. Control law of the two upper electromagnets
Step 1: Find the controller to enable the position xu of the rotor track desired set point at the stable
value which is 0 (along 0x axis). If z1 is the difference between the rotor position and the stable one: z1 = xu,
and its derivative is ż1 = ẋu = vu. Considering the following barrier Lyapunov candidate function:
V1 =
1
2
ln
k2
b
k2
b − z2
1
(14)
where kb is the limit of z1. It is clear that V1(z1) is radially unbounded as z1 approaches kb or −kb.
The Barrier Lyapunov function is used to reduce the error in rotor shaft position when comparing with the
desired value, so as it would prevent the rotor shaft move too far away with a large distance which is greater
than the air gap. This would lead to the collision between the rotor and the magnets, then damage the system.
The derivative of (14) is
V̇1 =
z1.ż1
k2
b − z2
1
(15)
Based on Lyapunov stability, it is required that V̇1 ≤ 0, thus virtual control function can be selected as
vudk = − k2
b − z2
1
k1z1 (16)
where k1 is a positive constant. Then, V̇1 = z1vudk
k2
b −z2
1
= −k1z2
1 ≤ 0 satisfies the stable condition.
Let vudk = α1, we have:
v̇udk = α̇1 =
∂α1
∂z1
ż1 = −k1k2
b + 3k1z2
1
ż1 (17)
A non-linear control method for active magnetic bearings with ... (Danh Huy Nguyen)
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Thus, vu is the virtual control which facilitates xu reach the set points.
Step 2: Identify virtual control to regulate vu to match vudk. If deviation of vu from vudk is z2:
z2 = vu − vudk = vu − α1 (18)
Or it can be represented as vu = vudk + z2. Derivative of (18) results in:
ż2 = v̇u − α̇1 = v̇u −
∂α1
∂z1
ẋu (19)
The Lyapunov candidae function in this step is chosen as: V2 = V1 + 1
2 z2
2, we then differentiate both
side to get:
V̇2 = −k1z2
1 +
z1z2
k2
b − z2
1
+ z2(v̇u − α̇1) (20)
In order to have V̇2 ≤ 0, the virtual control function is selected as v̇udk = α2 = −k2z2 + α̇1 − z1
k2
b −z2
1
,
where k2 is a positive constant. Substitute v̇udk in (3.1.) for v̇u in (20) , we have:
V̇2 = −k1z2
1 +
z1z2
k2
b − z2
1
+ z2(−k2z2 + α̇1 −
z1
k2
b − z2
1
− α̇1)
= −k1z2
1 − k2z2
2
(21)
In (21) shows that V̇2 ≤ 0 as required for stability. Therefore, v̇u as virtual control law is identified.
It is a function of i1 and i2 based on (12):
v̇u = au.
i1
x0 − xu
2
− au.
i2
x0 + xu
2
(22)
Let αu = α2/au, from the above equation, it can be shown that α̇u = ∂αu
∂z1
ż1 + ∂αu
∂vu
v̇u
Step 3: Design the current control law such that current i would match the set point id. As presented
in Step 2, the virtual control law v̇u is a function of 2 currents i1 and i2, which are equivalent to electromagnetic
forces of the two magnets. The fact that these two magnets operate simultaneously to maintain electromagnetic
forces leads to higher energy consumption. Thus, a control scheme of switching on and off the two currents
sequentially is employed to achieve energy savings as the following:
Case 1: xu 0 and i2 = 0, it is shown that
i1d = (x0 − xu)
√
αu (23)
On the other hand: i̇1d = ∂i1d
∂z1
ż1 + ∂i1d
∂vu
v̇u, where v̇u = au.
i1
x0−xu
2
. Call zv1 is the deviation
between i1 and set point i1d, i.e.: zv1 = i1 − i̇1d. Differentiating both side of Equation 3.1., we get: żv1 =
i̇1 − i̇1d. In order to limit the input signal, i.e. current, within a bounded range, the current variable is provided
as (
i̇1 = I1
i1 = im tanh
v
im
(24)
where im is the magnitude of current range, and v is the coefficient of tanh(). Consider the Lyapunov
candidate function in this step as: V3 = V2 + 1
2 z2
v1, the derivative of this Equation is:
V̇3 = V̇2 + zv1
I1 −
∂i1d
∂z1
ż1 −
∂i1d
∂vu
v̇u
(25)
Based on (25) and the condition that V̇3 ≤ 0, the control law I1 is selected as
I1 = −kv1zv1 +
∂i1d
∂z1
ż1 +
∂i1d
∂vu
v̇u (26)
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6. Int J Pow Elec Dri Syst ISSN: 2088-8694 r 2159
where kv1 is a positive constant. Substitute this I1 in (25), we have
V̇3 =V̇2 + zv1
−kv1zv1 +
∂i1d
∂z1
ż1 +
∂i1d
∂vu
v̇u
−
∂i1d
∂z1
ż1 −
∂i1d
∂vu
v̇u
=V̇2 − kv1z2
v1
(27)
It can be seen from (27) that V̇3 ≤ 0 which satisfies stable condition. Thus, with xu 0, I1 as in (26)
is the control law to stabilize the upper part of the rotor.
Case 2: xu 0 with respect to i1 = 0. The condition implies that: i2d = (x0 + xu)
√
−αu where
v̇u = −au.
i2
x0+xu
2
. Call zv2 is the deviation between i2 and set point i2d: zv2 = i2 − i̇2d. Differentiating
both side of (3.1.), we get żv2 = i̇2 − i̇2d. Similar to case 1:
(
i̇2 = I2
i2 = im tanh
v
im
(28)
The Lyapunov candidate function in this case is V4 = V2 + 1
2 z2
v2. The derivative of this Lyapunov
function is:
V̇4 = V̇2 + zv2
I2 −
∂i2d
∂z1
ż1 −
∂i2d
∂vu
v̇u
(29)
With the condition of V̇4 ≤ 0, the control function I2 is selected as:
I2 = −kv2zv2 +
∂i2d
∂z1
ż1 +
∂i2d
∂vu
v̇u (30)
where kv2 is a positive constant. Substitute the selected I2 in (29), we have:
V̇4 =V̇2 + zv2
−kv2zv2 +
∂i2d
∂z1
ż1 +
∂i2d
∂vu
v̇u
−
∂i2d
∂z1
ż1 −
∂i2d
∂vu
v̇u
=V̇2 − kv2z2
v2
(31)
In (31) shows obviously that V̇4 ≤ 0 which satisfies stable condition, and the control law I2 selected
can stabilize the upper part of the rotor.
3.2. Control law of the two lower electromagnets
The design procedure is similar to that of two upper electromagnets as presented in a). It also includes
3 steps as the following:
Step 1: Identify position control xl to reach the stable position, which is 0 (along 0x axis). Let z3 be
the deviation between rotor shaft and the stable position, i.e.: z3 = x1 ⇒ ˙
z3 = ẋl = vl The barrier Lyapunov
candidate function is V5 = 1
2 ln
k2
b
k2
b −z2
3
. The virtual control is chosen as vldk = − k2
b − z2
3
k3z3 where k3 is a
positive constant. Similarly, it can be proven that this control law renders ˙
V5 ≤ 0. Let vldk = α3, and compute
its time derivative
v̇ldk = α̇3 =
∂α3
∂z3
ż3 = −k3k2
b + 3k3z2
3
ż3 (32)
Step 2: Select virtual control so that vl would be able to reach vldk. Let the difference between vl and
vldk be z4: z4 = vl − vldk = vl − α3. Or vl = vldk + z3 In this step, the Lyapunov candidate function is
V6 = V5 + 1
2 z2
4. We pick the virtual control to satisfy that V̇6 ≤ 0 as:
v̇ldk = α4 = −k4z4 + α̇3 −
z3
k2
b − z2
3
(33)
A non-linear control method for active magnetic bearings with ... (Danh Huy Nguyen)
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where k is a positive constant. In (13) provides the calculation of v̇l from i3 and i4 as:
v̇l = al.
i3
x0 − xl
2
− al.
i4
x0 + xl
2
(34)
Let αl = α3/al, we have α̇l = ∂αl
∂z3
ż3 + ∂αl
∂vl
v̇l
Step 3: The switching scheme of currents supplied to lower magnets are
Case 1: xl 0 and i4 = 0 implies that: i3d = (x0 − xl)
√
αl And thus, i̇3d = ∂i3d
∂z3
ż3 + ∂i3d
∂vl
v̇l. Let zv3 is the
deviation of i3 from set point i3d, we have: zv3 = i3 − i̇3d. Using tanh to limit i3 in the required range:
(
i̇3 = I3
i3 = im tanh
v
im
(35)
Barrier Lyapunov function in this step is V7 = V6 + 1
2 z2
v3. In order to render V̇7 ≤ 0, virtual control I3 is
selected as
I3 = −kv3zv3 +
∂i3d
∂z3
ż3 +
∂i3d
∂vl
v̇l (36)
where kv3 is a positive constant.
Case 2: xl 0 and i3 = 0 yields i4d = (x0 + xl)
√
−αl and its derivatives is i̇4d = ∂i4d
∂z3
ż3 + ∂i4d
∂vl
v̇l,
where v̇l = −al.
i4
x0+xl
2
. Applying the analogous design. then selecting virtual control I4 is shown as below
I4 = −kv4zv4 +
∂i4d
∂z3
ż3 +
∂i4d
∂vl
v̇l (37)
where kv4 is a positive constant.
4. SIMULATION AND DISCUSSION
Numerical simulation parameters used in the study are presented as: Rotor mass m=5kg; number of
coil turns N=400 turns; nominal air gap x0=0.001m; maximum position error kb=0.001m; initial position of
upper rotor shaft xu=0.0001m; initial position of lower rotor shaft xl=0.0001m; self inductance Ls is 0.001H;
cross section area of iron core Ag is 0.001m2
; permeability of air gap µg=1.256×10−6
H/m; moment of inertia
Ir=2.900 × 10−2
kg · m2
; distance from rotor central to upper magnets Du=4.166 × 10−2
m; distance from
rotor central to lower magnets Dl=7.602 × 10−2
m. Controller’s coefficients are of k1 = 11; k2 = 1700; kv1 =
700; kv2 = 10000; k3 = 10; k4 = 1600; kv3 = 700; kv4 = 10000. In the paper, to emphasize the ability of
handling input and output constraints of the proposed controller, the rotor shaft is driven to equilibrium position
and accelerating to 1000rpm. This simulation procedure implies the effects of coupling term related to θx and
θy can be eliminated.
Case study 1: current limit is im = 3A. As shown in Figure 2a and 2b, the upper and lower body of
the AMB can be regulated from its deviation to the stable position within 0.01 second. Duration to reach the
zero displacement lower body is also around 0.01 second, however the overshoot is a little bit more, i.e. around
5µm, it is clear that the value is well below the threshold define by kb. Meanwhile the duration of central
displacement is corrected within the same interval and the overshoot is slightly smaller than that of lower body.
Case study 2: current limit is im = 2A. The current limit is reduced to 2A in this case, but the initial
displacement of the rotor shaft is kept the same. It is clearly observed that the settling times of the upper
body and lower body in Figure 2a and Figure 2b are slightly longer that those in case one in Figure 3a, 3b
respectively. It is due to the fact that controllers need to take more effort to stabilise the system with smaller
current fed thanks to the use of the hyperbolic tangent function in the design. The peak currents supplied to the
AMB electromagnetics are all less than the provided limit as shown in both two cases as illustrated in Figure 4
and Figure 5. These peak values for lower magnets are also less than those of the upper ones. When the current
limit is decreased, it is observed that there is more oscillation of current response. The cause can be explained
as less magnetic forces provided to the system.
Int J Pow Elec Dri Syst, Vol. 11, No. 4, December 2020 : 2154 – 2163
8. Int J Pow Elec Dri Syst ISSN: 2088-8694 r 2161
(a) (b)
Figure 2. Rotor displacement, (a) Upper body displacement, and (b) Lower body displacement
(a) (b)
Figure 3. Rotor displacement, (a) Upper body displacement, and (b) Lower body displacement
(a) (b)
Figure 4. Current responses, (a) Upper magnets, and (b) Lower magnets
(a) (b)
Figure 5. Current responses, (a) Upper magnets, and (b) Lower magnets
A non-linear control method for active magnetic bearings with ... (Danh Huy Nguyen)
9. 2162 r ISSN: 2088-8694
5. CONCLUSIONS
In this paper, a 4th order AMB has been modeled as two 2nd order subsystem with magnetizing cur-
rent is treated as control input. The backstepping method is adopted in control design for the obtained model.
The controllers have been built and validated via simulation in different case studies in a view of input satu-
ration and bounded output . It is shown that our proposed approach is able to facilitate the AMB regulate gap
deviations as desire and thus stabilizes the system. Future work include practical implementation of the whole
system, it would enable further investigation of the proposed works thoroughly for real-life applications.
ACKNOWLEDGEMENTS
This research was funded by Hanoi University of Science and Technology grant number T2018-PC-
057.
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A non-linear control method for active magnetic bearings with ... (Danh Huy Nguyen)