• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1960-1965
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• 2005

This paper presents theory for stability analysis and design of a servo system for a MIMO Wiener system with nonlinear uncertainty. The Wiener system consists of a linear time-invariant system(LTI) in cascade with a static nonlinear part ${\psi}$(y) at the output. We assume that the uncertain static nonlinear part is sector bounded and decoupled. In this research, we treat the static nonlinear part as multiplicative uncertainty by dividing the nonlinear part ${\psi}$(y) into ${\phi}$(y) := ${\psi}$(y)-y and y, and then we reduce this stabilizing problem to a Lur'e problem. As a result, we show that the servo system with no steady state error for step references can be constructed for the Wiener system.

• East Asian mathematical journal
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• v.24 no.2
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• pp.191-199
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• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.141-144
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• 1999

The authors have recently developed a new method for identification of Volterra kernels of nonlinear systems by use of pseudorandom M-sequence and correlation technique. And it is shown that nonlinear systems which can be expressed by Volterra series expansion are well identified by use of this method. However, there exist many nonlinear systems which can not be expressed by Volterra series mathematically. A nonlinear system having backlash type nonliear element is one of those systems, since backlash type nonlinear element has multi-valued function between its input and output. Since Volterra kernel expression of nonlinear system is one of the most useful representations of non-linear dynamical systems, it is of interest how the method of Volterra kernel identification can be ar plied to such backlash type nonlinear system. The authors have investigated the effect of application of Volterra kernel identification to those non-linear systems which, accurately speaking, is difficult to express by use of Volterra kernel expression. A pseudorandom M-sequence is applied to a nonlinear backlash-type system, and the crosscorrelation function is measured and Volterra kernels are obtained. The comparison of actual output and the estimated output by use of measured Volterra kernels show that we can still use Volterra kernel representation for those backlash-type nonlinear systems.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.272-275
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• 1989

In this paper feedback linearization of valve-controlled nonlinear hydraulic velocity control system is studied. The $C^{\infty}$ nonlinear transformation T is obtained, and it is shown that this transformation is global one. Linear equivalence of nonlinear hydraulic velocity control system is obtained by this global nonlinear transformation, and linear state feedback control law is applied to this linear model. It is shown that this transformation method is to the linear approximation by simulation study..

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.259-270
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• 2017

The stochastic vibration response of the sandwich beam with the nonlinear adjustable visco-elastomer core and supported mass under stochastic support motion excitations is studied. The nonlinear dynamic properties of the visco-elastomer core are considered. The nonlinear partial differential equations for the horizontal and vertical coupling motions of the sandwich beam are derived. An analytical solution method for the stochastic vibration response of the nonlinear sandwich beam is developed. The nonlinear partial differential equations are converted into the nonlinear ordinary differential equations representing the nonlinear stochastic multi-degree-of-freedom system by using the Galerkin method. The nonlinear stochastic system is converted further into the equivalent quasi-linear system by using the statistic linearization method. The frequency-response function, response spectral density and mean square response expressions of the nonlinear sandwich beam are obtained. Numerical results are given to illustrate new stochastic vibration response characteristics and response reduction capability of the sandwich beam with the nonlinear visco-elastomer core and supported mass under stochastic support motion excitations. The influences of geometric and physical parameters on the stochastic response of the nonlinear sandwich beam are discussed, and the numerical results of the nonlinear sandwich beam are compared with those of the sandwich beam with linear visco-elastomer core.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.6
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• pp.1173-1178
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• 2010

In this note, a systematic design of a new robust nonlinear integral variable structure controller based on state dependent nonlinear form is presented for the control of uncertain more affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear integral variable structure controller is presented. To be linear in the closed loop resultant dynamics and remove the reaching phase problems, the linear integral sliding surface is suggested. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear integral sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1754-1760
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• 2011

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.945-949
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• 2010

In this paper, a systematic design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.931-933
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• 1989

If the nonlinear term in a nonlinear control system equation can be deleted by state feedback control, the original system becomes a linear system. For this linear control system, many well known methods may be used to handle it, and then reverse it back to nonlinear form. Many problems of nonlinear control systems can be solved in this way. In this paper, this method will be used to transfer the identification problem of nonlinear systems into a linear control problem. The nonlinear observer is established by constructing linear observer. Then the state control of nonlinear systems is realized. Finally, the technique of the PID controller obtained by using bang-bang tracker as a differentiator provides a stronger robust controller. Even though the method in this paper may not theoretically perfect, many numerical simulations show that it is applicable.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1150-1158
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• 2004

In this paper, we present an adaptive observer for nonlinear systems that include unknown constant parameters and are not necessarily observable. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into an adaptive observer canonical form. Once a nonlinear system is transformed into the proposed adaptive observer canonical form, an adaptive observer can be designed under the assumption that a certain system is strictly positive real. An illustrative example is included to show the effectiveness of the proposed method.