• International Journal of Control, Automation, and Systems
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• v.4 no.3
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• pp.293-301
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• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• Structural Engineering and Mechanics
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• v.87 no.5
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• pp.461-473
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• 2023

This study aims to solve for nonlinear cylindrical shell systems with a semi-analytical and numerical approach implementing the P-T method. The procedures and conditions for such a study are presented in practically solving and analyzing the cylindrical shell systems. An analytical model for a nonlinear thick cylindrical shell (TCS) is established on the basis of the stress function and Reddy's higher-order shear deformation theory (HSDT). According to Reddy's HSDT, Hooke's law in three dimensions, and the von-Kármán equation, the stress-strain relations are developed for the thick cylindrical shell systems, and the three coupled nonlinear governing equations are thus established and discretized as per the Galerkin method, for implementing the P-T method. The solution generated with the approach is continuous everywhere in the entire time domain considered. The approach proposed can also be used to numerically solve and analyze the nonlinear shell systems. The procedures and recurrence relations for numerical solutions of shell systems are presented. To demonstrate the application of the approach in numerically solving for nonlinear cylindrical shell systems, a specific nonlinear cylindrical shell system subjected to an external excitation is solved numerically. In numerically solving for the system, the present approach shows higher efficiency, accuracy, and reliability in comparison with that of the Runge-Kutta method. The approach with the P-T method presented is practically sound especially when continuous and high-quality numerical solutions for the shell systems are considered.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.2
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• pp.138-143
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• 2006

This paper presents intelligent digital redesign method for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an . example to guarantee the stability and effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2286-2288
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• 2003

In this paper, a novel and efficient discretization method of a continuous-time Takagi-Sugeno (TS) fuzzy system is proposed. Because of the highly complex and nonlinear interaction among the subsystems, it is very difficult to develop the discretized version of continuous-tine TS fuzzy system. More precisely, to obtain the suitable discretized version, it is necessary to solve two main problems: to discretize global state equations of the continuous-tine TS fuzzy system and to hold the polytopic structure after the discretization. This paper will show the solution to above two problems. Main key idea is to transforme the sampling period into the intersampling period. Finally, To show the feasibility and the validity of the proposed method, a computer simulation is provided.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.641-658
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• 2012

The goal of this paper is to develop a nonlinear observer-based control strategy for a multi-variables continuous stirred tank reactor (CSTR). A new robust nonlinear observer is constructed to estimate the whole process state variables. The observer is coupled with a nonlinear controller, designed based on the input-output linearization for controlling the concentration and reactor temperature. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Finally, computer simulations are developed for showing the performance of the proposed controller.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.368-373
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• 1998

This paper presents a GA-based fuzzy modelling scheme of nonlinear systems. The fuzzy model is a type of the Sugeno-Tagaki's fuzzy model whose consequence parts are described by a linear continuous dynamic equation as subsystem of a nonlinear system. The centers and width of the membership functions of the fuzzy sets defined over the input space and the orders and parameters of subsystems in the consequence parts are adjusted by a genetic algorithm. The effectiveness of the proposed method is verified

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.385-388
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• 2006

The purpose of this study is to offer an appropriate method of the degree of the flexural moment redistribution for continuous reinforced concrete beams. Twenty-four two-span continuous beams were selected to determine the manner and degree of moment redistribution. The concept of ductility is linked to the moment redistribution capacity and, consequently, the safety of the structure. Knowledge of the plastic rotation capacity of plastic regions of the structure is important for a plastic analysis or a linear analysis with moment redistribution. A nonlinear finite element analysis program named RCAHEST (Reinforced Concrete Analysis in Higher Evaluation System Technology) was used to evaluate the ultimate strength and degree of moment redistribution. The nonlinear material model for the reinforced concrete is composed of models for characterizing the behavior of the concrete, in addition to a model for characterizing the reinforcing bars.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.181-184
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• 1997

This paper propose the systematic procedure of the fuzzy model based controller for the continuous nonlinear system. Fuzzy controller have been successfully applied to many uncertain and complex industrial plants. The design of the fuzzy controller mainly depends on the knowledge from the expert who are familiar with the plant by trial and error. Therefore we need more systematic approach to the design of the fuzzy controller. In this paper, we design fuzzy model based controller applied to the nonlinear system. Unlike the design procedures reported in[8] and[9], we use the nonlinear process directly in designing the controller. This controller has been successfully applied to an inverted pendulum.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.172.1-172
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• 2001

In this paper we show the stability analysis of the discrete nonlinear system with average bounded variation of the input. This is the discrete counterpart of that continuous one. We use the Lyapunov stability to prove the boundedness of the steady-state error. Also the allowable maximum variation bounds and the region of attraction are given as the function of the system parameters. Moreover, we prove the uniform convergence for the constant input.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.581-584
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• 1998

This paper presents a scheme for fuzzy modelling and control of continuous-time nonlinear systems using a genetic algorithm. A fuzzy model is characterized by fuzzy "if-then" rules whose consequence part has a linear dynamic equation as subsystem of the system. The parameters of the fuzzy model are adjusted by a genetic algorithm. Then a tracking controller which guarantees stability of the overall system is designed. The simulation result demonstrates the effectiveness of the proposed method.