• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.649-672
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• 2024

This paper explores the significance and implications of fixed point results related to orbital contraction as a novel form of contraction in various fields. Theoretical developments and theorems provide a solid foundation for understanding and utilizing the properties of orbital contraction, showcasing its efficacy through numerous examples and establishing stability and convergence properties. The application of orbital contraction in control systems proves valuable in designing resilient and robust control strategies, ensuring reliable performance even in the presence of disturbances and uncertainties. In the realm of financial modeling, the application of fixed point results offers valuable insights into market dynamics, enabling accurate price predictions and facilitating informed investment decisions. The practical implications of fixed point results related to orbital contraction are substantiated through empirical evidence, numerical simulations, and real-world data analysis. The ability to identify and leverage fixed points grants stability, convergence, and optimal system performance across diverse applications.

• Journal of the Korean Society of Marine Environment & Safety
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• v.26 no.5
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• pp.437-444
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• 2020

This study was focused on the stabilization of surge motions of a moored vessel under irregular head seas. A two-point moored vessel shows strong non-linearity even in regular sea, owing to its inherent non-linear restoring force. A long-crested irregular wave is subjected to the vessel system, resulting in more complex nonlinear behavior of the displacement and velocities than in the case of regular waves. Sliding mode control (SMC) is implemented in the moored vessel to control both surge displacement and surge velocity. The SMC can provide a closed-loop system with performance and robustness against parameter uncertainties and disturbances; however, chattering is the main drawback for implementing SMC. The goal of minimizing the chattering and state convergence with accuracy is achieved using a quasi-sliding mode that approximates the discontinuous function via a continuous sigmoid function. Numerical simulations were conducted to validate the effectiveness of the proposed control algorithm.

• Journal of Mechanical Science and Technology
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• v.19 no.3
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• pp.778-791
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• 2005

A novel pneumatic artificial muscle actuator (PAM actuator), which has achieved increased popularity to provide the advantages such as high strength and high power/weight ratio, low cost, compactness, ease of maintenance, cleanliness, readily available and cheap power source, inherent safety and mobility assistance to humans performing tasks, has been regarded during the recent decades as an interesting alternative to hydraulic and electric actuators. However, some limitations still exist, such as the air compressibility and the lack of damping ability of the actuator bring the dynamic delay of the pressure response and cause the oscillatory motion. Then it is not easy to realize the performance of transient response of pneumatic artificial muscle manipulator (PAM manipulator) due to the changes in the external inertia load with high speed. In order to realize satisfactory control performance, a variable damper-Magneto­Rheological Brake (MRB), is equipped to the joint of the manipulator. Superb mixture of conventional PID controller and a phase plane switching control method brings us a novel controller. This proposed controller is appropriate for a kind of plants with nonlinearity, uncertainties and disturbances. The experiments were carried out in practical PAM manipulator and the effectiveness of the proposed control algorithm was demonstrated through experiments, which had proved that the stability of the manipulator can be improved greatly in a high gain control by using MRB with phase plane switching control method and without regard for the changes of external inertia loads.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1983-1989
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• 2005

Industrial robots are powerful, extremely accurate multi-jointed systems, but they are heavy and highly rigid because of their mechanical structure and motorization. Therefore, sharing the robot working space with its environment is problematic. A novel pneumatic artificial muscle actuator (PAM actuator) has been regarded during the recent decades as an interesting alternative to hydraulic and electric actuators. Its main advantages are high strength and high power/weight ratio, low cost, compactness, ease of maintenance, cleanliness, readily available and cheap power source, inherent safety and mobility assistance to humans performing tasks. The PAM is undoubtedly the most promising artificial muscle for the actuation of new types of industrial robots such as Rubber Actuator and PAM manipulators. However, some limitations still exist, such as the air compressibility and the lack of damping ability of the actuator bring the dynamic delay of the pressure response and cause the oscillatory motion. In addition, the nonlinearities in the PAM manipulator still limit the controllability. Therefore, it is not easy to realize motion with high accuracy and high speed and with respect to various external inertia loads in order to realize a human-friendly therapy robot To overcome these problems a novel controller, which harmonizes a phase plane switching control method with conventional PID controller and the adaptabilities of neural network, is newly proposed. In order to realize satisfactory control performance a variable damper - Magneto-Rheological Brake (MRB) is equipped to the joint of the manipulator. Superb mixture of conventional PID controller and a phase plane switching control using neural network brings us a novel controller. This proposed controller is appropriate for a kind of plants with nonlinearity uncertainties and disturbances. The experiments were carried out in practical PAM manipulator and the effectiveness of the proposed control algorithm was demonstrated through experiments, which had proved that the stability of the manipulator can be improved greatly in a high gain control by using MRB with phase plane switching control using neural network and without regard for the changes of external inertia loads.

• Journal of Ocean Engineering and Technology
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• v.19 no.3
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• pp.66-73
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• 2005

The sway motion control problem of a container hanging on the trolley is considered in this paper. In the container crane control problem, the main issue involves suppressing the residual swing motion of the container at the end of acceleration, during deceleration, or for an unexpected disturbance input. For this problem, in general, many trolley motion control strategies are introduced and applied. In this paper, we introduce and synthesize a swing motion control system, in which a small auxiliary mass is installed on the spreader. In this control system, the actuator reacting against the auxiliary mass applies inertial control forces to the container to reduce the swing motion in the desired manner. In many studies, the controllers used to suppress the vibration have been synthesized for the given mathematical model of plants. In many cases, the designers have not been able to utilize the degree of freedom to adjust the structural parameters for the control object. To overcome this problem, so called "Structure/Control Simultaneous Method" is used. From this, in this paper the simultaneous design method is used to achieve optimal system performance. And the experimental result shows that the proposed control strategy is useful, to the case of that the controlled system is exposed to the uncertainties and, robust to disturbances like wind.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.36S no.6
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• pp.37-44
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• 1999

In this paper, we present a new sliding surface with a time-varying repeated root for fast and robust tracking of higher-order uncertain systems. The repeated root is moved to target one with stabilizing the closed-loop time-varying system in sliding mode. This initial root is obtained so that shifting distance of the surface may be minimized with respect to an initial error, and the intercept is produced so that the surface may pass the initial error. Under the allowable input, fast shifting of the surface and movement of the repeated root enable the error convergence rate to be increased. The proposed sliding mode control makes the error always remain on the surface from the beginning, and therefore, the system is more insensitive to parameter uncertainties and external disturbances. In simulation, the effectiveness of the proposed method is proved by comparison with the conventional one.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.3
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• pp.32-41
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• 2008

In this paper, we describe the synthesis of robust and non-fragile $H^{\infty}$ state feedback controllers for linear systems with affine parameter uncertain tracking servo system of blu-ray disc drive, as well as static state feedback controller with polytopic uncertainty Similarity any other control system, the objective of the track-following system design for optical disc drives is to construct the system with better performance and robustness against modeling uncertainties and various disturbances. Also, the obtained condition can be rewritten as parameterized linear matrix inequalities(PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a resulted polytopic region.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.12
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• pp.1152-1160
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• 2007

In this paper we deal with a design of integral sliding mode controller to reject the disturbance force acting on the suspension system in the magnetically levitated system which is propelled by the linear induction motor. The control scheme comprises an integral controller which is designed for achieving zero steady-state error under step disturbances, and a sliding mode controller which is designed for enhancing robustness under plant uncertainties. A proper continuous design signal is introduced to overcome the chattering problem. The disturbance force produced by the linear motor is formularized by using a curve fitting of the experimental raw data. Computer simulations show the effectiveness of the designed integral sliding mode controller to reject the disturbance force.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.40 no.2
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• pp.13-21
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• 2017

Airline schedules are highly dependent on various factors of uncertainties such as unfavorable weather conditions, mechanical problems, natural disaster, airport congestion, and strikes. If the schedules are not properly managed to cope with such disturbances, the operational cost and performance are severely affected by the delays, cancelations, and so forth. This is described as a disruption. When the disruption occurs, the airline requires the feasible recovery plan returning to the normal operations in a timely manner so as to minimize the cost and impact of disruptions. In this research, an Ant Colony Optimization (ACO) algorithm with re-timing strategy is developed to solve the recovery problem for both aircraft and passenger. The problem consists of creating new aircraft routes and passenger itineraries to produce a feasible schedule during a recovery period. The suggested algorithm is based on an existing ACO algorithm that aims to reflect all the downstream effects by considering the passenger recovery cost as a part of the objective function value. This algorithm is complemented by re-timing strategy to effectively manage the disrupted passengers by allowing delays even on some of undisrupted flights. The delays no more than 15 minutes are accepted, which does not influence on the on-time performance of the airlines. The suggested method is tested on the real data sets from 2009 ROADEF Challenge, and the computational results are compared with the existing ones on the same data sets. The method generates the solution for most of problem set in 10 minutes, and the result generated by re-timing strategy is discussed for its impact.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.3
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• pp.369-374
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• 2010

Linear motors are easily affected by load disturbances, force ripples, friction, and parameter variations because there are no mechanical transmissions that can reduce the effects of model uncertainties and external disturbance. In this study, a nonlinear adaptive controller to achieve high-speed/high-accuracy position control of a two-axis linear motor is designed. The operation of this controller is based on a cross-coupling algorithm. Nonlinear effects such as friction and force ripples are estimated and compensated for. An enhanced cross-coupling algorithm is proposed for effectively improving the biaxial contour accuracy while achieving closed-loop stability. The proposed controller is evaluated by performing computer simulations.