The document presents a study on robust control of linear and nonlinear dynamical systems using an extended state observer. It discusses various plant dynamics including motion control, magnetic levitation, flexible links, and an inverted pendulum. It proposes using an extended state observer to estimate states and uncertainties, combined with feedback linearization control. Several examples are presented to demonstrate the effectiveness of this approach in achieving robust control of nonlinear systems with uncertainties.
Debabrata Pal, Aksum University, College of Engineering and Technology Department of Electrical and Computer Engineering Ethiopia, NE Africa, Email:debuoisi@gmail.com,website:www.ijrd.in
Multi parametric model predictive control based on laguerre model for permane...IJECEIAES
The permanent magnet linear motors are widely used in various industrial applications due to its advantages in comparisons with rotary motors such as mechanical durability and directly creating linear motions without gears or belts. The main difficulties of its control design are that the control performances include the tracking of position and velocity as well as guarantee limitations of the voltage control and its variation. In this work, a cascade control strategy including an inner and an outer loop is applied to synchronous linear motor. Particularly, an offline MPC controller based on MPP method and Laguerre model was proposed for inner loop and the outer controller was designed with the aid of nonlinear damping method. The numerical simulation was implemented to validate performance of the proposed controller under voltage input constraints.
Contenido:
1. Introducción
2. Componentes básicos y circuitos eléctricos
3. Leyes de voltaje y corriente
4. Análisis nodal y de malla básicos;
5. Técnicas de análisis de circuitos útiles
6. El amplificador operacional
7. Capacitores e inductores
8. Circuitos RL y RC básicos;
9. El circuito RLC
10. Análisis de estado permanente senoidal
11. Análisis de circuitos de potencia de CA
12. Circuitos polifásicos
13. Circuitos acoplados magnéticamente
14. Frecuencia compleja y la transformada de Laplace
15. Análisis de circuitos en el dominio de s
16. Respuesta en frecuencia
17. Redes de dos puertos
18. Análisis de circuitos de Fourier Apéndice 1: una introducción a la topología de redes
This paper presents a nonlinear Integral backstepping control approach based on field oriented control technique, applied to a Double Star Induction Machine ‘DSIM’ feed by two power voltage sources. We present this technique of integral backstepping by using reduced and complete Model of DSIM. The objective is to improve the robustness of machine under internal parameter variation with nonlinear Integral backstepping control. The robustness test results obtained by simulation prove the effectiveness of control with using complete model of DSIM.
Debabrata Pal, Aksum University, College of Engineering and Technology Department of Electrical and Computer Engineering Ethiopia, NE Africa, Email:debuoisi@gmail.com,website:www.ijrd.in
Multi parametric model predictive control based on laguerre model for permane...IJECEIAES
The permanent magnet linear motors are widely used in various industrial applications due to its advantages in comparisons with rotary motors such as mechanical durability and directly creating linear motions without gears or belts. The main difficulties of its control design are that the control performances include the tracking of position and velocity as well as guarantee limitations of the voltage control and its variation. In this work, a cascade control strategy including an inner and an outer loop is applied to synchronous linear motor. Particularly, an offline MPC controller based on MPP method and Laguerre model was proposed for inner loop and the outer controller was designed with the aid of nonlinear damping method. The numerical simulation was implemented to validate performance of the proposed controller under voltage input constraints.
Contenido:
1. Introducción
2. Componentes básicos y circuitos eléctricos
3. Leyes de voltaje y corriente
4. Análisis nodal y de malla básicos;
5. Técnicas de análisis de circuitos útiles
6. El amplificador operacional
7. Capacitores e inductores
8. Circuitos RL y RC básicos;
9. El circuito RLC
10. Análisis de estado permanente senoidal
11. Análisis de circuitos de potencia de CA
12. Circuitos polifásicos
13. Circuitos acoplados magnéticamente
14. Frecuencia compleja y la transformada de Laplace
15. Análisis de circuitos en el dominio de s
16. Respuesta en frecuencia
17. Redes de dos puertos
18. Análisis de circuitos de Fourier Apéndice 1: una introducción a la topología de redes
This paper presents a nonlinear Integral backstepping control approach based on field oriented control technique, applied to a Double Star Induction Machine ‘DSIM’ feed by two power voltage sources. We present this technique of integral backstepping by using reduced and complete Model of DSIM. The objective is to improve the robustness of machine under internal parameter variation with nonlinear Integral backstepping control. The robustness test results obtained by simulation prove the effectiveness of control with using complete model of DSIM.
Simultaneous State and Actuator Fault Estimation With Fuzzy Descriptor PMID a...Waqas Tariq
In this paper, Takagi-Sugeno (T-S) fuzzy descriptor proportional multiple-integral derivative (PMID) and Proportional-Derivative (PD) observer methods that can estimate the system states and actuator faults simultaneously are proposed. T-S fuzzy model is obtained by linearsing satellite/spacecraft attitude dynamics at suitable operating points. For fault estimation, actuator fault is introduced as state vector to develop augmented descriptor system and robust fuzzy PMID and PD observers are developed. Stability analysis is performed using Lyapunov direct method. The convergence conditions of state estimation error are formulated in the form of LMI (linear matrix inequality). Derivative gain, obtained using singular value decomposition of descriptor state matrix (E), gives more design degrees of freedom together with proportional and integral gains obtained from LMI. Simulation study is performed for our proposed methods.
This paper presents a developed application for using Fraction Order PID controller (FOPID) in controlling of DC motors installed incelestron telescope, this is done through controlling the angles of two DC motors driven the telescope. The model of celestron telescope is mathematically represented by highly non linear differential equations, this types of nonlinear model is recommended to be controlled using Artificial Intelligent based controller. In this paper, optimal fuzzy FOPID is implemented instead of conventional PID controllers. Genetic Algorithm, fuzzy logic are used for tuning the FOPID parameters.FOPID controller is based on position error and its rate of change as an input vector, the proposed controller set presents a complete precision in forcing the telescope motors to satisfy the predefined position. The simulation results show the dynamic response of the system and the enhancement achieved in rising time and settling time when using FOPID. The response of FOPID is compared with the conventional PID with the same input position reference.
MODELLING ANALYSIS & DESIGN OF DSP BASED NOVEL SPEED SENSORLESS VECTOR CONTRO...IAEME Publication
Unscented Kalman Filter (UKF), which is an update d version of EKF, is proposed as a state estimator for speed sensorless field oriented contr ol of induction motors. UKF state update computations, different from EKF, are derivative fr ee and they do not involve costly calculation of Jacobian matrices. Moreover, variance of each state is not assumed Gaussian, therefore a more realistic approach is provided by UKF. In order to examine the rotor speed (state V) estimation performance of UKF experimentally under varying spe ed conditions, a trapezoidal speed reference command is embedded into the DSP code. EKF rotor speed estimation successfully tracks the trapezoidal path. It has been observed that the est imated states are quite close to the measured ones. The magnitude of the rotor flux justifies that the estimated dq components of the rotor flux are estimated accurately. A number of simulations were carried out to verify the performance of the speed estimation with UKF. These simulated results are confirmed with the experimental results. While obtaining the experimental results, the real time stator voltages and currents are processed in Matlab with the associated EKF and UKF programs.
P-Q theory based design of Unified Power Quality Conditioner for tranquilliza...ijiert bestjournal
This paper presents unified power quality conditioner (UPQC) which is an integration of shunt and series Active Power Filters and aims to compensate for voltage sag,voltage and current unbalance and other power quality problems [1],[5],[6]. The UPQC helps to improve power qualit y at the point of installation on power distribution system or industrial power system. This paper deals w ith design of UPQC by considering a controller based on PQ theory. Reference signal generation for shunt active filter is done by using PQ theory while for series dual PQ theory is used [2],[3]. Reference si gnals are then applied to pulse generators. Pulse generation is carried out by using hysteresis band controller f or each filter. The validation of proposed scheme is carried out by using Matlab/Simulink
A Comparison Study between Inferred State-Space and Neural Network Based Syst...Ahmed Momtaz Hosny, PhD
In this paper, system identifications of an unmanned aerial vehicle (UAV) based on inferred state space and multiple neural networks were presented. In this work an optimization approach was used to conclude an inferred state space and the multiple neural networks system identifications based on the genetic algorithms separately. The UAV is a multi-input multi-output (MIMO) nonlinear system. Models for such MIMO system are expected to be adaptive to dynamic behavior and robust to environment.
Comparative Study of Speed Characteristics of DC Motor with and without Contr...IJMTST Journal
In this paper a dc motor is modeled using transfer function analysis and the speed characteristics are
plotted for dc motor with and without controllers. The difference between load torque and electromagnetic
torque is improved using discrete p, I, d controllers for improving the speed characterics.the best speed
characteristics is obtained using proportional plus derivative controller. These characteristics are obtained by
formulating a relation between speed and torque. The entire simulation is conducted on mat
lab/simulink2013 environment.
Performance Analysis of a DTC and SVM Based Field- Orientation Control Induct...IJPEDS-IAES
This study presents a performance analysis of two most popular control strategies for Induction Motor (IM) drives: direct torque control (DTC) and space vector modulation (SVM) strategies. The performance analysis is done by applying field-orientation control (FOC) technique because of its good dynamic response. The theoretical principle, simulation results are discussed to study the dynamic performances of the drive system for individual control strategies using actual parameters of induction motor. A closed loop PI controller scheme has been used. The main purpose of this study is to minimize ripple in torque response curve and to achieve quick speed response as well as to investigate the condition for optimum performance of induction motor drive. Depending on the simulation results this study also presents a detailed comparison between direct torque control and space vector modulation based field-orientation control method for the induction motor drive.
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.
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
The stabilization of forced inverted pendulum via fuzzy controllereSAT Journals
Abstract
In the field of nonlinear control engineering, the inverted pendulum can be considered as a bench mark problem. For an inverted
pendulum, there are mainly two types of equilibrium which are categorized as stable equilibrium and unstable equilibrium. The
stable equilibrium is the one in which the pendulum is in normal pendent position and not requires any control force since
because it is naturally stable. Under the influence of an external force, the stable equilibrium loses its stability and there comes
the need of a stabilizing controller. Therefore unstable equilibrium refers to the pendulum in upright position strictly under the
influence of a stabilizing controller. The inverted pendulum is strictly nonlinear, under actuated system; challenging task comes
with the stability analysis. A forced inverted pendulum is considered which has been modeled with respect to the cart motion. To
improve the performance and stabilize the system, a fuzzy controller is designed for the respective system. Simulation results
validate the fact that the stabilization is achieved through out and the perfect result is obtained for the system.
Keyword: Fuzzy, Heuristic, Forced Inverted Pendulum
Simultaneous State and Actuator Fault Estimation With Fuzzy Descriptor PMID a...Waqas Tariq
In this paper, Takagi-Sugeno (T-S) fuzzy descriptor proportional multiple-integral derivative (PMID) and Proportional-Derivative (PD) observer methods that can estimate the system states and actuator faults simultaneously are proposed. T-S fuzzy model is obtained by linearsing satellite/spacecraft attitude dynamics at suitable operating points. For fault estimation, actuator fault is introduced as state vector to develop augmented descriptor system and robust fuzzy PMID and PD observers are developed. Stability analysis is performed using Lyapunov direct method. The convergence conditions of state estimation error are formulated in the form of LMI (linear matrix inequality). Derivative gain, obtained using singular value decomposition of descriptor state matrix (E), gives more design degrees of freedom together with proportional and integral gains obtained from LMI. Simulation study is performed for our proposed methods.
This paper presents a developed application for using Fraction Order PID controller (FOPID) in controlling of DC motors installed incelestron telescope, this is done through controlling the angles of two DC motors driven the telescope. The model of celestron telescope is mathematically represented by highly non linear differential equations, this types of nonlinear model is recommended to be controlled using Artificial Intelligent based controller. In this paper, optimal fuzzy FOPID is implemented instead of conventional PID controllers. Genetic Algorithm, fuzzy logic are used for tuning the FOPID parameters.FOPID controller is based on position error and its rate of change as an input vector, the proposed controller set presents a complete precision in forcing the telescope motors to satisfy the predefined position. The simulation results show the dynamic response of the system and the enhancement achieved in rising time and settling time when using FOPID. The response of FOPID is compared with the conventional PID with the same input position reference.
MODELLING ANALYSIS & DESIGN OF DSP BASED NOVEL SPEED SENSORLESS VECTOR CONTRO...IAEME Publication
Unscented Kalman Filter (UKF), which is an update d version of EKF, is proposed as a state estimator for speed sensorless field oriented contr ol of induction motors. UKF state update computations, different from EKF, are derivative fr ee and they do not involve costly calculation of Jacobian matrices. Moreover, variance of each state is not assumed Gaussian, therefore a more realistic approach is provided by UKF. In order to examine the rotor speed (state V) estimation performance of UKF experimentally under varying spe ed conditions, a trapezoidal speed reference command is embedded into the DSP code. EKF rotor speed estimation successfully tracks the trapezoidal path. It has been observed that the est imated states are quite close to the measured ones. The magnitude of the rotor flux justifies that the estimated dq components of the rotor flux are estimated accurately. A number of simulations were carried out to verify the performance of the speed estimation with UKF. These simulated results are confirmed with the experimental results. While obtaining the experimental results, the real time stator voltages and currents are processed in Matlab with the associated EKF and UKF programs.
P-Q theory based design of Unified Power Quality Conditioner for tranquilliza...ijiert bestjournal
This paper presents unified power quality conditioner (UPQC) which is an integration of shunt and series Active Power Filters and aims to compensate for voltage sag,voltage and current unbalance and other power quality problems [1],[5],[6]. The UPQC helps to improve power qualit y at the point of installation on power distribution system or industrial power system. This paper deals w ith design of UPQC by considering a controller based on PQ theory. Reference signal generation for shunt active filter is done by using PQ theory while for series dual PQ theory is used [2],[3]. Reference si gnals are then applied to pulse generators. Pulse generation is carried out by using hysteresis band controller f or each filter. The validation of proposed scheme is carried out by using Matlab/Simulink
A Comparison Study between Inferred State-Space and Neural Network Based Syst...Ahmed Momtaz Hosny, PhD
In this paper, system identifications of an unmanned aerial vehicle (UAV) based on inferred state space and multiple neural networks were presented. In this work an optimization approach was used to conclude an inferred state space and the multiple neural networks system identifications based on the genetic algorithms separately. The UAV is a multi-input multi-output (MIMO) nonlinear system. Models for such MIMO system are expected to be adaptive to dynamic behavior and robust to environment.
Comparative Study of Speed Characteristics of DC Motor with and without Contr...IJMTST Journal
In this paper a dc motor is modeled using transfer function analysis and the speed characteristics are
plotted for dc motor with and without controllers. The difference between load torque and electromagnetic
torque is improved using discrete p, I, d controllers for improving the speed characterics.the best speed
characteristics is obtained using proportional plus derivative controller. These characteristics are obtained by
formulating a relation between speed and torque. The entire simulation is conducted on mat
lab/simulink2013 environment.
Performance Analysis of a DTC and SVM Based Field- Orientation Control Induct...IJPEDS-IAES
This study presents a performance analysis of two most popular control strategies for Induction Motor (IM) drives: direct torque control (DTC) and space vector modulation (SVM) strategies. The performance analysis is done by applying field-orientation control (FOC) technique because of its good dynamic response. The theoretical principle, simulation results are discussed to study the dynamic performances of the drive system for individual control strategies using actual parameters of induction motor. A closed loop PI controller scheme has been used. The main purpose of this study is to minimize ripple in torque response curve and to achieve quick speed response as well as to investigate the condition for optimum performance of induction motor drive. Depending on the simulation results this study also presents a detailed comparison between direct torque control and space vector modulation based field-orientation control method for the induction motor drive.
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.
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
The stabilization of forced inverted pendulum via fuzzy controllereSAT Journals
Abstract
In the field of nonlinear control engineering, the inverted pendulum can be considered as a bench mark problem. For an inverted
pendulum, there are mainly two types of equilibrium which are categorized as stable equilibrium and unstable equilibrium. The
stable equilibrium is the one in which the pendulum is in normal pendent position and not requires any control force since
because it is naturally stable. Under the influence of an external force, the stable equilibrium loses its stability and there comes
the need of a stabilizing controller. Therefore unstable equilibrium refers to the pendulum in upright position strictly under the
influence of a stabilizing controller. The inverted pendulum is strictly nonlinear, under actuated system; challenging task comes
with the stability analysis. A forced inverted pendulum is considered which has been modeled with respect to the cart motion. To
improve the performance and stabilize the system, a fuzzy controller is designed for the respective system. Simulation results
validate the fact that the stabilization is achieved through out and the perfect result is obtained for the system.
Keyword: Fuzzy, Heuristic, Forced Inverted Pendulum
Controller design of inverted pendulum using pole placement and lqreSAT Journals
Abstract In this paper modeling of an inverted pendulum is done using Euler – Lagrange energy equation for stabilization of the pendulum. The controller gain is evaluated through state feedback and Linear Quadratic optimal regulator controller techniques and also the results for both the controller are compared. The SFB controller is designed by Pole-Placement technique. An advantage of Quadratic Control method over the pole-placement techniques is that the former provides a systematic way of computing the state feedback control gain matrix.LQR controller is designed by the selection on choosing. The proposed system extends classical inverted pendulum by incorporating two moving masses. The motion of two masses that slide along the horizontal plane is controllable .The results of computer simulation for the system with Linear Quardatic Regulator (LQR) & State Feedback Controllers are shown in section 6. Keyword-Inverted pendulum, Mathematical modeling Linear-quadratic regulator, Response, State Feedback controller, gain formulae.
MODELLING AND SIMULATION OF INVERTED PENDULUM USING INTERNAL MODEL CONTROLJournal For Research
The internal model control (IMC) philosophy relies on the internal model principle, which states that control can be achieved only if the control system encapsulates, either implicitly or explicitly, some representation of the process to be controlled. In particular, if the control scheme is developed based on an exact model of the process, then perfect control is theoretically possible. Transfer function of Inverted Pendulum is selected as the base of design, which examines IMC controller. Matlab/simulink is used to simulate the procedures and validate the performance. The results shows robustness of the IMC and got graded responses when compared with PID. Furthermore, a comparison between the PID and IMC was shows that IMC gives better response specifications.
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.
Design of observers for nonlinear systems using the Frobenius theorem. Presentation for the defense of my MSc Thesis at the School of Applied Mathematics, NTU Athens.
Locational marginal pricing framework in secured dispatch scheduling under co...eSAT 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.
Hardware-in-the-loop based comparative analysis of speed controllers for a tw...journalBEEI
A comparative study of speed control performance of an induction motor drive system connecting to a load via a non-rigid shaft. The nonrigidity of the coupling is represented by stiffness and damping coefficients deteriorating speed regulating operations of the system and can be regarded as a two-mass system. In the paper, the ability of flatness based and backstepping controls in control the two-mass system is verified through comprehensive hardware-in-the-loop experiments and with the assumption of ideal stator current loop performance. Step-by-step control design procedures are given, in addition, system responses with classical PID control are also provided for parallel comparisons.
Extraction of photovoltaic generator parameters through combination of an an...IJECEIAES
In the present work, we propose an improved method based on a combination of an analytical and iterative approach to extract the photovoltaic (PV) module parameters using the measured current-voltage characteristics and the simple diode model. First, we calculate the series resistance using a set of analytical formulas for the base values of the three current-voltage curves. Then, the three other parameters are analytically expressed as functions of serial resistance and ideality factor based on the linear least-squares method. Finally, the ideality factor is calculated applying an iterative algorithm to minimize the normalized root mean square error (NRMSE) value. The proposed method was validated with a real experimental set of two PV generators, which showed the best fit to the I-V curve. Moreover, the proposed method needs only the initial value of the ideality factor.
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.
This paper reports on the design and implementation in DSP as hardware in the loop of a nonlinear control strategy for a grid-connected variable speed wind turbine using a doubly fed induction generator (DFIG). The objective of this work is to build a real-time nonlinear hybrid approach combining Backstepping control and sliding mode control strategies for DFIG used in wind energy conversion systems (WECS). The results of the DSP implementation are discussed and qualitative and quantitative performance evaluations are performed under various disturbed conditions. The implementation is performed using the TMS320F28335 DSP combined with the MATLAB/Simulink (2016a) environment. The experimental results have been satisfactorily achieved, which implies that the proposed strategy is an efficient and robust approach to monitor the WECS.
OPTIMAL PID CONTROLLER DESIGN FOR SPEED CONTROL OF A SEPARATELY EXCITED DC MO...ijscmcjournal
This paper presents a new approach to determine the optimal proportional-integral-derivative controller
parameters for the speed control of a separately excited DC motor using firefly optimization technique.
Firefly algorithm is one of the recent evolutionary methods which are inspired by the Firefly’s behavior in
nature. The firefly optimization technique is successfully implemented using MATLAB software. A
comparison is drawn from the results obtained between the linear quadratic regulator and firefly
optimization techniques. Simulation results are presented to illustrate the performance and validity of the
design method.
Optimal PID Controller Design for Speed Control of a Separately Excited DC Mo...ijscmcj
This paper presents a new approach to determine the optimal proportional-integral-derivative controller parameters for the speed control of a separately excited DC motor using firefly optimization technique. Firefly algorithm is one of the recent evolutionary methods which are inspired by the Firefly’s behavior in nature. The firefly optimization technique is successfully implemented using MATLAB software. A comparison is drawn from the results obtained between the linear quadratic regulator and firefly optimization techniques. Simulation results are presented to illustrate the performance and validity of the design method.
This paper proposed a nonlinear robust control for spacecraft attitude based on passivity and
disturbance suppression vector. The spacecraft model was described using quaternion. The control law
introduced the suppression vector of external disturbances and had no information related to the system
parameters. The desired performance of spacecraft attitude control could be achieved using the designed
control law. And stability conditions of the nonlinear robust control for spacecraft attitude were given. The
stability could be proved by applying Lyapunov approach. The verification of the proposed attitude control
method was performed through a series of simulations. The numerical results showed the effectiveness of
the proposed control method in controlling the spacecraft attitude in the presence of external disturbances.
The main benefit of the proposed attitude control method does not need angular velocity measurement
and has its robustness against model uncertainties and external disturbances.
A New Approach to Design a Reduced Order ObserverIJERD Editor
In this paper, a new method for designing a reduced order observer for linear time-invariant system is
proposed. The approach is based on matrix inversion with proper dimension. The arbitrariness associated with
the method proposed by O’Reilly is presented here and has been reduced with the help of pole-placement
technique. It also helps reducing the computations regarding the observer design parameters. Illustrative
numerical examples with simulation results are also included.
Development of deep reinforcement learning for inverted pendulumIJECEIAES
This paper presents a modification of the deep Q-network (DQN) in deep reinforcement learning to control the angle of the inverted pendulum (IP). The original DQN method often uses two actions related to two force states like constant negative and positive force values which apply to the cart of IP to maintain the angle between the pendulum and the Y-axis. Due to the changing of too much value of force, the IP may make some oscillation which makes the performance system could be declined. Thus, a modified DQN algorithm is developed based on neural network structure to make a range of force selections for IP to improve the performance of IP. To prove our algorithm, the OpenAI/Gym and Keras libraries are used to develop DQN. All results showed that our proposed controller has higher performance than the original DQN and could be applied to a nonlinear system.
STABILIZATION AT UPRIGHT EQUILIBRIUM POSITION OF A DOUBLE INVERTED PENDULUM W...ijcsa
A double inverted pendulum plant has been in the domain of control researchers as an established model for studies on stability. The stability of such as a system taking the linearized plant dynamics has yielded satisfactory results by many researchers using classical control techniques. The established model that is analyzed as part of this work was tested under the influence of time delay, where the controller was fine tuned using a BAT algorithm taking into considering the fitness function of square of error. This proposed
method gave results which were better when compared without time delay wherein the calculated values
indicated the issues when incorporating time delay
OPTIMAL PID CONTROLLER DESIGN FOR SPEED CONTROL OF A SEPARATELY EXCITED DC MO...ijscmcj
This paper presents a new approach to determine the optimal proportional-integral-derivative controller
parameters for the speed control of a separately excited DC motor using firefly optimization technique.
Firefly algorithm is one of the recent evolutionary methods which are inspired by the Firefly’s behavior in
nature. The firefly optimization technique is successfully implemented using MATLAB software. A
comparison is drawn from the results obtained between the linear quadratic regulator and firefly
optimization techniques. Simulation results are presented to illustrate the performance and validity of the
design method.
Robust Adaptive Controller for Uncertain Nonlinear SystemsIJITCA Journal
Control robustness is study for uncertain nonlinear systems transformed in semi strict feedback systems. An adaptive backstepping sliding mode control and an adaptive backstepping control robustness is considered. Robustness is studied when the unknown parameter are constants and varied. The simulation results prove that the sliding mode control is more robust than the backstepping control to tracking trajectory and to estimate the unknown parameter in two cases.
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
A sensorless approach for tracking control problem of tubular linear synchron...IJECEIAES
As well-known, linear motors are widely applied to various industrial applications due to their abilities in providing directly straight movement without auxiliary mechanical transmissions. This paper addresses the sensorless control problem of tubular linear synchronous motors, which belong to a family of permanent magnet linear motor. To be specific, a novel velocity observer is proposed to deal with an unmeasurable velocity problem, and asymptotic convergence of the observer error is ensured. Unlike other studies on sensorless control methods for linear motors, our proposed observer is designed by regrading unknown disturbance load in the tracking control problem whereas considering theoretical demonstrations. By adjusting controller parameters properly, the position and velocity tracking error converge in arbitrary small values. Finally, the effectiveness of the proposed method is verified in two illustrative examples.
A sensorless approach for tracking control problem of tubular linear synchron...
presentation_VIT_final
1. Robust Control of Linear and Non-Linear Dynamical
System by using Extended State Observer
Presented by: Kaliprasad Mahapatro Advisor: Prof Milind E. Rane
Department of Electronics & Telecommunication Engg.
Vishwakarma Institute of Technology, Pune
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 1 / 48
2. Contents I
1 Robust Control
2 Extended State Observer
3 Plant Dynamics
4 Linear and Nonlinear Plants
5 Motion Control
6 Magnetic Levitation
7 Flexible Link
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 2 / 48
3. Contents II
8 Inverted Pendulum
9 Applications
10 Conclusion
11 State of Art
12 Acknowledge
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 3 / 48
4. Robust Control Expectation and Problem
1 Expectation
High Precision Control
with Minimum Convergence Time
2 Problem
Uncertainty due to some unknown dynamics, parameter variations,
external disturbances are prime parameters present in engineering
systems.
Due to their non-linear characteristic it becomes very difficult to
control this unknown parameter.
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 4 / 48
5. Robust Control Solution
The key solution to achieve robust control is to first estimate the
uncertainty and then implement the appropriate control law
based on estimation.
Estimation of state along with uncertainties will serve better
solution for implementing control signal as dependency on
practical plant reduces
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 5 / 48
6. Extended State Observer Innovation
Extended State Observer(ESO)
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 6 / 48
7. Extended State Observer Innovation
1 Owing to the great advances in non-linear control theory, the
observer-based controller has become one of the most commonly
used schemes in industrial applications [WG03] [ARD08].
2 The extended state observer (ESO) has high efficiency in
accomplishing the non-linear dynamic estimation.
3 ESO serves the best estimation by extending the internal and
external disturbance to a rank new state and then apply a special
non-smooth nonlinear error feedback to achieve state
tracking [ZGG12].
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 7 / 48
8. Extended State Observer Innovation
1 Owing to the great advances in non-linear control theory, the
observer-based controller has become one of the most commonly
used schemes in industrial applications [WG03] [ARD08].
2 The extended state observer (ESO) has high efficiency in
accomplishing the non-linear dynamic estimation.
3 ESO serves the best estimation by extending the internal and
external disturbance to a rank new state and then apply a special
non-smooth nonlinear error feedback to achieve state
tracking [ZGG12].
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 7 / 48
9. Extended State Observer Innovation
1 Owing to the great advances in non-linear control theory, the
observer-based controller has become one of the most commonly
used schemes in industrial applications [WG03] [ARD08].
2 The extended state observer (ESO) has high efficiency in
accomplishing the non-linear dynamic estimation.
3 ESO serves the best estimation by extending the internal and
external disturbance to a rank new state and then apply a special
non-smooth nonlinear error feedback to achieve state
tracking [ZGG12].
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 7 / 48
10. Plant Dynamics
Linear and Nonlinear Plants
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 8 / 48
11. Linear and Nonlinear Plants Miscellaneous Plants
Table: Dissertation Flow Structure
Plant Dynamics Application Description
Motion control setup Robotics vehicle Plant dynamics
(2nd order system)
Magnetic levitation Bullet train Design of ESO
(3rd order system) (n+1)th order
Flexible Joint system Robotics arm
(4th order system) Controller Design
Flexible Link system Space robots
(4th order system) Application
Inverted Pendulum Humanoid Robot Classical
(4th order system) launch pad of missile Control
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 9 / 48
13. Motion Control Mathematical Model
˙z1 = z2
˙z2 =
−c∗
d
J∗
d
z2 +
TD
J∗
d
α(x)
+
1
J∗
d
β(x)
u (1)
J∗
d = combined inertia c∗
d = shaft friction coefficient
TD = Torque disturbance u = control voltage
Figure: Plant dynamic model ECP220
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 11 / 48
14. Motion Control Feedback Linearization control law
[SL91] feedback control law can be designed as υ = α(x)+β(x)u
u =
υ −α(x)
β(x)
(2)
υ = ¨υc +k1(υc −z1)+k2( ˙υc −z2) (3)
Figure: Feedback Linearization
u =
υ −a0
b0
where a0 = α(x)+d b0 = β(x)+d (4)
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 12 / 48
15. Motion Control Extended State Observer (ESO)
Extended State Observer(ESO) for ECP-220
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 13 / 48
16. Motion Control Innovation
Figure: Block diagram for FL+ESO
u =
(
υ
k1(υc − ˆz1)−k2 ˆz2 − ˆz3 −a0)
b0
(5)
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 14 / 48
17. Motion Control Mathematical Interpretation of ESO
˙ˆz1 = ˆz2 +β1g1(e)
˙ˆz2 = ˆz3 +β2g2(e)+b0u
˙ˆz3 = β3g3(e)−→ Lumped disturbances
y = z1
e = y− ˆz1−→ error
(6)
βi is the observer gain
where gi is
gi(e,αi,δ) =
| e |αi ,| e |> δ
e
δ1−αi
,| e |≤ δ
(7)
for
Nonlinear ESO α = [1 0.5 0.25]
Linear ESO α = [1 1 1]
δ is a small number used to limit the gain
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 15 / 48
18. Motion Control Result Analysis of NESO and LESO
TD = 10% and b0 = 38 but actually it is b0 = 23.2/Kg−m2
Figure: Tracking for Step input
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 16 / 48
20. Magnetic Levitation Problem Statement
Problem?
Use a voltage control electromagnet to suspend a ferromagnetic ball in
air at an height of 3mm and maintain the desired trajectory in-spite of
uncertainty and disturbances by using Feedback Linearization and
Extended State Observer.
Figure: MagLev model
Quanser- Canada
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 18 / 48
21. Magnetic Levitation Problem Statement
˙x1
˙x2
˙x3
=
−(R
L )x1
x3
g− 1
m
x2
1
b0+b1y+b2y2+b3y3
+
1
L
0
0
u
Considering another space coordination zi as stated in [SL91]
˙z =
˙x2
˙x3
d
dt (g− 1
m
x2
1
b0+b1y+b2y2+b3y3 )
[z]T
=
˙x2
˙x3
L3
f h(x)
α(x)
+Lg(L2
f h(x))
β(x)
u
[z]T
Now as stated [SL91] considering a non linear feedback control law
υ = α(x)+β(x)u such that z = φ(x) and the new input υ satisfy a linear
time invariant relation
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 19 / 48
22. Magnetic Levitation Problem Statement
Figure: Block Diagram
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 20 / 48
23. Magnetic Levitation Problem Statement
Due to uncertainty and disturbances
uFL =
k1(υc −z1)−k2z2 −k3z3 −a0 −d
b0
(8)
uESO =
1
b0
(−a0 +k1(υc − ˆz1)−k2 ˆz2 −k3 ˆz3 − ˆz4) (9)
(a) FL (b) ESO+FL
Figure: Estimation of states with 80% uncertainty
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 21 / 48
25. Flexible Link Distinguish between Flexible Joint and Link
Flexible Joint Flexible Link
Bulky Light weight manipulators
Spring Tension No Spring
Less Complex Lightweight slender manipulators,
increasing the complexity
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 23 / 48
26. Flexible Link Distinguish between Flexible Joint and Link
˙θ
˙α
¨θ
¨α
=
0 0 1 0
0 0 0 1
0
Kstif f
Jeq
−A1 0
0 −
Kstif f+Jarm
JeqJarm
A1 0
θ
α
˙θ
˙α
+
0
0
B1
−B1
Vm (10)
where A1
ηmηgKt KmK2
g +BeqRm
JeqRm
and B1
ηmηgKt Kg
JeqRm
.
State space represented in (10) can be simplified in z domain as
˙z1 = z2
˙z2 = z3
˙z3 = z4
˙z4 = −
Kstif f A1
Jeq
z2 −
Kstif f (Jeq +Jarm)
JarmJeq
z3 −A1z4
α
+
Kstif f B1
Jarm
β
Vm
y = z1 (11)
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 24 / 48
27. Flexible Link Distinguish between Flexible Joint and Link
Table: Numerical values of parameters of flexible link system
Symbols Meaning Value
Kstif f modeled stiffness 0.7883 N.m/rad
Jeq gear inertia 0.000931 kg.m2
Jarm link inertia 0.0026 kg.m2
Beq viscous damping coeff 0.0015
ηm motor efficiency 0.69
ηg gearbox efficiency 0.9
Kt torque constant 0.00767 N.m
Kg motor gear ratio 70
Km back-EMF constant 0.00767 V/rpm
Rm armature resistance 2.6 Ω
ωc natural frequency 20.1 rad/s
m mass of link 0.065 kg
l length of link 0.3 m
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 25 / 48
28. Flexible Link Distinguish between Flexible Joint and Link
Figure: Basic Feedback Linearization block
u =
1
β
[
....
υ c +k1(υc −z1)+k2( ˙υc −z2)
+ k3( ¨υc −z3)+k4(
...
υ c −z4)−α] (12)
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 26 / 48
29. Flexible Link Distinguish between Flexible Joint and Link
Figure: ESO and FL block for estimating states and uncertainty
u =
1
b0
[
....
υ c +k1(υc − ˆz1)+k2( ˙υc − ˆz2)
+ k3( ¨υc − ˆz3)+k4(
...
υ c − ˆz4)−a0 − ˆz5] (13)
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 27 / 48
30. Flexible Link Distinguish between Flexible Joint and Link
Figure: States and its estimate in flexible link
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 28 / 48
32. Inverted Pendulum Problem Statement
To balance the rod at a 0◦ or at a 7◦
Figure: Inverted Pendulum Apparatus
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 30 / 48
33. Inverted Pendulum Nonlinear & Linear Mathematical Model
d
dt
θ
˙θ
x
˙x
=
z2
2m1z3z4z2−m2lcgsin(z1)−m1gz3cos(z1)−m1l0z3z2
2+F(t)l0
(m1l2
0 −J0)
z4
−J0
m1
F(t)−J0z3z2
2−gJ0sin(z1)−2m1z3l0z4z2+l0(m1l0+m2lc)gsin(z1)+m1gl0z3cos(z1)
m1l2
0 −J0
(14)
By inspection we get
˙z = Az+BF(t);
where z1 = θ, z2 = ˙θ = ˙z1, z3 = x, z4 = ˙x = ˙z3
z =
θ
˙θ
x
˙x
;A =
0 1 0 0
m2lcg
J∗ 0 m1g
J∗ 0
0 0 0 1
(J∗−m2l0lc)g
J∗ 0 −m1l0g
J∗ 0
;B =
1
J∗
0
−l0
0
Joe
m1
;
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 31 / 48
34. Inverted Pendulum Linear-quadratic (LQ) state-feedback regulator
uval = kpf cmdpos −k1enc1pos −k3enc2pos
−k2(enc1pos − pastpos1)−k4(enc2pos − pastpos2) (15)
kpf = hardware gain, k1,2,3,4= lqr constant gains
(a) Simulation (b) Hardware
Figure: Step response of an inverted pendulum by lqr technique
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 32 / 48
36. Applications Plants and its Application
Figure: Flexible Joint
Figure: Flexible Joint Application
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 34 / 48
37. Applications Plants and its Application
Figure: Flexible Link
Figure: Flexible Link Application
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 35 / 48
38. Applications Plants and its Application
Figure: Inverted Pendulum in Military
Figure: Inverted Pendulum in Humanoid
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 36 / 48
40. Conclusion
1 Model dependent trajectory tracking control for linear and
nonlinear plant is possible by using Extended State Observer
(ESO).
2 If we assumed calibration error in position sensor by adjusting
proper observer gains better estimation of position and other
relevant states of plant can be done.
3 Lumped Uncertainty and Disturbances are well estimated by
ESO in model dependent plant
4 All the aforementioned details are proved mathematically and via
simulation to be stable and also validated experimentally on
various plant. Which inherently proves the robustness.
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 38 / 48
42. Conclusion Published Journal
TITLE - A Novel Approach for Internet Congestion Control Using an
Extended State Observer.
JOURNAL - International Journal of Electronics and Communication
Engineering & Technology
TITLE - Comparative Analysis of Linear and Non-linear Extended
State Observer with Application to Motion Control
JOURNAL - IEEE Conference on Convergence of Technology
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 40 / 48
43. Conclusion Communicated Journal
TITLE - Estimating and Compensating Wide Range of Uncertainties in
MagLev by using Extended State Observer.
JOURNAL - Journal of Systems and Control
TITLE - Extended State Observer based Control of Flexible Link
Manipulator in presence of Unknown Payload Dynamics
JOURNAL - Transaction on Institute of Measurement and Control
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 41 / 48
44. State of Art
State of Art
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 42 / 48
45. State of Art
State of Art
1 SAGE Journal of Systems and Control Engineering
2 IEEE Transactions on Industrial Electronics
3 IEEE Transactions on Control Systems Technology
4 IEEE Transactions on Magnetics
5 American Control Conference
6 IEEE/ASME Transaction on Mechatronics
7 Elsevier Automatica
8 International Symposium on Magnetic Bearings
9 ISA Transactions
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 43 / 48
46. State of Art
References I
[ARD08] B. X. S. Alexander, Richard Rarick, and Lili Dong.
A novel application of an extended state observer for high
performance control of nasa’s hss flywheel and fault
detection.
American Control Conference, pages 5216 – 5221, June
2008.
[SL91] Jean Jacques E. Slotine and Weiping Li.
Applied Nonlinear Control.
Prentice Hall, New Jersey, U.S.A, 1st edition, 1991.
[WG03] Weiwen Wang and Zhiqiang Gao.
A comparison study of advanced state observer design
techniques.
In Proceeding of the American Control Conference, pages
4754 – 4759, Denver, Colorado, 2003.
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 44 / 48
47. State of Art
References II
[ZGG12] Qing Zheng, Linda Q. Gao, and Zhiqiang Gao.
On validation of extended state observer through analysis
and experimentation.
Journal of Dynamic Systems, Measurement, and Control,
ASME, 134:024505–1 – 024505–6, March 2012.
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 45 / 48
48. Acknowledge
Profound Thanks
Prof. Milind E. Rane
Prof. S. R. Bandewar
Prof. A. M. Chopde
Staff of Department of E&TC Engg for their kind support.
KALIPRASAD A. MAHAPATRO Vishwakarma Institute of Technology, Pune July 26, 2014 46 / 48