• International Journal of Internet, Broadcasting and Communication
• /
• v.6 no.2
• /
• pp.1-9
• /
• 2014

This paper presents a study on nonlinear time varying systems based on differential geometry. A brief introduction about controllability and involutivity will be presented. As an example, the exact feedback linearization and the approximate feedback linearization are used in order to show some application examples.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.631-635
• /
• 2008

In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.1228-1233
• /
• 2005

In this paper, we present a new guidance law for a reusable launch vehicle (RLV) that lands vertically after reentry. In our past studies, a guidance law was developed for a vertical/soft landing to a target point. The guidance law, which is analytically obtained, can regenerate a trajectory against disturbances because it is expressed in the form of state feedback. However, the guidance law does not necessarily guarantee a vertical/soft landing when a dynamical system such as an RLV includes a nonlinear phenomenon owing to the atmosphere of the earth. In this study, we introduce a design of the guidance law for a nonlinear system to achieve a vertical/soft landing on the ground using the exact linearization method and solving the two-point boundary-value problem for the derived linear system. Numerical simulation confirmed the validity of the proposed guidance law for an RLV in an atmospheric environment.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.5
• /
• pp.2116-2124
• /
• 2018

Magnetic levitation system with the advantages of non-contact, no friction and no wear can satisfy the requirement of high precision and high speed positioning. In this paper, magnetic levitation positioning stage which mainly consists of planar coil and HALBACH permanent magnet array and its control and driving system are designed. Magnetic levitation system is a highly nonlinear and strongly coupled complex system and its control performance can be influenced by the uncertainty and external disturbance. So exact feedback linearization method is used to realize exact linearization and decoupling, and a strategy of sliding mode control based on disturbance observer is proposed to compensate the uncertainty and external disturbance. Detailed proofs of observer's convergence property and system stability are derived. Both the simulation and experiment results verify the effectiveness of sliding mode control algorithm based on disturbance observer.

• 한국전산유체공학회:학술대회논문집
• /
• 2003.10a
• /
• pp.33-34
• /
• 2003

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.381-391
• /
• 2012

In this paper, the formal linearization method is used to construct multisoliton solutions for three model of shallow water waves equations. The three models are completely integrable. The formal linearization method is an efficient method for obtaining exact multisoliton solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones.

• Proceedings of the IEEK Conference
• /
• 2003.07c
• /
• pp.2863-2866
• /
• 2003

In nonlinear control fields, for irregular nonlinear systems, control form which consists of approximate tracking control law and exact tracking control law and which switches between two laws has been proposed recently. In this thesis, we design new switching control law which connect approximate linearization control law and exact linearization control law by fuzzy rules for irregular nonlinear system, ball and beam system. Fuzzy switching controller designed by fuzzy concept is proved that designed scheme overcomes singularities of irregular system, improves unstability problem of switching procedure, and has more efficient control value through simulation. Stability of fuzzy control system proved by Lyapunov's stability theorems.

• ETRI Journal
• /
• v.28 no.2
• /
• pp.231-234
• /
• 2006

The cancellation performance of a linearization loop is limited by the degree of an amplitude imbalance and a phase imbalance. A delay mismatch causes a phase variation as a function of frequency. Therefore, the cancellation performance and linearization bandwidth are limited by a delay mismatch. The expression for the effects of an amplitude imbalance, a phase imbalance, and a delay mismatch on the characteristics of a linearization loop is derived and analyzed. The simulation results are compared with the results obtained by means of using a commercial simulation tool and the exact agreement is reported. The derived equation could be used in designing a linearization loop and predicting the cancellation performance of the linearization loop usefully. Some useful characteristics, known from the simulation results obtained by using the derived equation, of a linearization loop for designing and implementing feedforward amplifiers are described in detail.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
• /
• 2003.11a
• /
• pp.183-187
• /
• 2003

The expression for the effects of an amplitude imbalance, a phase imbalance and a delay mismatch on the characteristics of a linearization loop in feedforward amplifiers is derived and analyzed. The simulation results are compared with the results obtained by means of using a commercial simulation tool and the exact agreement is reported.

• Structural Engineering and Mechanics
• /
• v.30 no.5
• /
• pp.593-602
• /
• 2008

This paper presents a new linearization algorithm to find the periodic solutions of the Duffing equation, under harmonic loads. Since the Duffing equation models a single degree of freedom system with a cubic nonlinear term in the restoring force, finding its periodic solutions using classical harmonic balance (HB) approach requires numerical integration. The algorithm developed in this paper replaces the integrals appearing in the classical HB method with triangular matrices that are evaluated algebraically. The computational cost of using increased number of frequency components in the matrixbased linearization approach is much smaller than its integration-based counterpart. The algorithm is computationally efficient; it only takes a few iterations within the region of convergence. An example comparing the results of the linearization algorithm with the "exact" solutions from a 4th order Runge- Kutta method are presented. The accuracy and speed of the algorithm is compared to the classical HB method, and the limitations of the algorithm are discussed.