• Journal of Institute of Control, Robotics and Systems
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• v.16 no.12
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• pp.1197-1200
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• 2010

The problem of designing a nonlinear sliding surface for an uncertain system is considered. The proposed sliding surface comprises a linear time invariant term and an additional time varying nonlinear term. It is assumed that a linear sliding surface parameter matrix guaranteeing the asymptotic stability of the sliding mode dynamics is given. The linear sliding surface parameter matrix is used for the linear term of the proposed sliding surface. The additional nonlinear term is designed so that a Lyapunov function decreases more rapidly. By including the additional nonlinear term to the linear sliding surface parameter matrix we obtain a nonlinear sliding surface such that the speed of responses is improved. We also give a switching feedback control law inducing a stable sliding motion in finite time. Finally, we give an LMI-based design algorithm, together with a design example.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.4
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• pp.379-384
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• 1999

In this paper, we present a new time-varying sliding surface to achieve fast and robust tracking of higher-order uncertain systems. The surface passes through an initial error, and afterwards, it moves towards a predetermined target surface by means of a variable named by sliding surface gain and its intercept. Specifically, the sliding surface gain is determined so that its initial value can minimize a shifting distance of the surface and that the system roots in sliding mode can follow certain stable trajectories. The designed sliding mode control forces the system errors to stay always on the proposed surface from the beginning. By this means, the system remains insensitive to system uncertainties and disturbances for the whole time. To illustrate the effectiveness of the proposed method, the comparative study with conventional time-invariant sliding mode control is performed.

• Geomechanics and Engineering
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• v.16 no.4
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• pp.415-421
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• 2018

A location determining method is proposed for critical sliding surface in the stability analysis of the filling materials in karst caves. First, a preliminary location of the sliding surface is determined based on simulation results which includes displacement contour and plastic zone. The sliding surface will locate on the bottom contact interface when the friction angle is relative small. However, a weakened contact interface always becomes the critical sliding surface no matter what the friction angle is. Then when the friction angle becomes larger, the critical sliding surface inside fillings can be determined by a parabola, the coefficient of which increases linearly with the friction angle under the same cohesion. Finally, the critical sliding surface approximately remains unchanged with friction angle. The influence of cohesion is similar to that of friction angle. Although affected by shape, size or position of the karst cave, the critical sliding surface mainly depends on both friction angle and cohesion. Thus, this method is always useful in determining the critical sliding surface.

• Journal of the Korean GEO-environmental Society
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• v.17 no.7
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• pp.27-33
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• 2016

This study expanded Terzaghi arching formula, which assumed a vertical surface as a sliding surface, to consider an arbitrarily inclined surface as a sliding surface and examined the effect of a sliding surface. This study firstly developed a formula to expand the existing Terzaghi arching formula to consider an inclined surface as well as a vertical surface as a sliding surface under the downward movement of a trap door. Using the expanded formula, the effect of excavation, ground, and surcharge conditions on a vertical stress was examined and the results were compared with them from Terzaghi arching formula. The comparison indicated that the induced vertical stress was highly affected by the angle of an inclined sliding surface and the degree of influence depended on the excavation, ground, and surcharge conditions. It is expected that the results from this study would provide a better understanding of various arching phenomenon in the future.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.1
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• pp.39-46
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• 1991

In the VSS control, the trajectories with a conventional sliding surface have a reaching phase which is an interval from the initial state to the first touching of the sliding surface. Since the sliding mode control can not be realized in a reaching phase, the trajectories may be sensitive to the disturbances and parameter variations. A simple nonlinear sliding surface is proposed to improve the robustness in a reaching phase. The position control of a PM DC servo motor using a new sliding surface is carried out and is compared to the one using the conventional surface. The sliding mode occurs in entire trajectories with the proposed new sliding surface and the improved robustness is obtained.

• Journal of IKEEE
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• v.11 no.1 s.20
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• pp.1-14
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• 2007

In this paper, a design of an integral augmented nonlinear optimal variable structure system(INOVSS) is presented for the prescribed output control of uncertain MIMO systems under persistent disturbances. This algorithm basically concerns removing the problems of the reaching phase and combining with the nonlinear optimal control theory. By means of an integral nonlinear sliding surface, the reaching phase is completely removed. The ideal sliding dynamics of the integral nonlinear sliding surface is obtained in the form of the nonlinear state equation and is designed by using the nonlinear optimal control theory, which means the design of the integral nonlinear sliding surface and equivalent control input. The homogeneous $2{\upsilon}(\kappa)$ form is defined in order to easily select the $2{\upsilon}$ or even $(\kappa)-form$ higher order nonlinear terms in the suggested sliding surface. The corresponding nonlinear control input is designed in order to generate the sliding mode on the predetermined transformed new surface by means of diagonalization method. As a result, the whole sliding output from a given initial state to origin is completely guaranteed against persistent disturbances. The prediction/predetermination of output is enable. Moreover, the better performance by the nonlinear sliding surface than that of the linear sliding surface can be obtained. Through an illustrative example, the usefulness of the algorithm is shown.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.359-361
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• 1993

In this paper, a variable structure controller with time-varying sliding surface is proposed for robot manipulators. The proposed time-varying sliding surface ensures the existence of sliding mode from an initial state, while the contentional sliding surface cannot achieve the robust performance against parameter variations and disturbances before the sliding mode occurs. Therefore, error transient can be fully prescribed in advance for all time. Furthermore, it is shown that the overall system is globally exponetially stable. The efficiency of the proposed method for the trajectory tracking has been demonstrated by simulations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.3
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• pp.623-629
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• 2010

In this paper, a new robust variable structure controller based on a nonlinear integral type sliding surface is presented for the control of uncertain systems with mismatched uncertainties and disturbance. A nonlinear integral type sliding surface is suggested for removing the reaching phase. After its ideal sliding dynamics is obtained, the two design methods are presented. A corresponding control input is proposed to satisfy the closed loop stability in the sense of Lyapunov and the existence condition of the sliding mode on the nonlinear integral type sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1997.04a
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• pp.80-88
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• 1997

Repeated sliding contact wear test was performed with copper specimens to obtain the relationship between wear and surface hardening. Wear surface and wear track section were observed by optical microscopy. Wear volume and micro-vikers hardness of sublayer below wear surface were obtained. These results suggested that wear mechanism depended on contact load than sliding velocity. Therefore wear mechanism was abrasive wear within critical contact load and adhesive wear over critical contact load. Wear rate increased with contact load, sliding distance but decreased with sliding velocity. Surface hardening increased with sliding velocity and sliding distance but decreased with contact load.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.8
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• pp.467-472
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• 2000

A three-level decoupled sliding mode controller is developed to achieve asymptotic stability for a class of sixth-order nonlinear systems. The sixth-order system is decoupled into three subsystems according to the structure of the whole system. Each subsystem has a separate control target in the form of a sliding surface. The information of the third sliding surface is transferred to the second one through an intermediate variable and the information of the second sliding surface is transferred to the first one through another intermediate variable. Consequently, the controller designed on the basis of the first sliding surface can make three subsystems move toward their sliding surfaces, respectively. The three-level decoupled sliding mode controller is applied to the double-inverted pendulum problem where the zero stable states are required.