This study has been focused on the linear and nonlinear behavior and investigative in single-ring resonator. Optical fiberring resonators have great interest due to different applications, especially in communication, secured communication, slowlight, fast light and light storage in optical buffers. There are many proposed applications of optical ring resonators. Opticalfiber ring resonators can be readily constructed from standard optical fiber components, which allow their properties to bestudied in a systematic manner. In this paper, we describe our studies of the optical transmission, intensity, shift phase andgroup delay characteristics of a family of such devices. In this case, Gaussian beam has been used as an input pulse insideto microring resonators. In this paper, transmission, intensity, shift phase and group delay characteristics of device havebeen investigated. It has been compared together in different coupling coefficients in frame of linear and nonlinear.

Nonlinear behavior is a common feature of all real-world systems. However, for the sake of simplicity, a linear model is often used in the controller design procedure. Nevertheless, the neglected nonlinear dynamics could degrade the performance of controller drastically. This study presents a new method of designing a model predictive controller (MPC) for a class of nonlinear systems. In the proposed method, an MPC is first designed in state space based on a linear model and then modified by using modal series to compensate for the effect of the neglected nonlinear dynamics in the linear model. Because the proposed controller adjusts a linear controller instead of designing a new one, it can be easily applied in industries to modify controllers that have been designed based on linear models. In addition, its computational burden is much less than that of nonlinear MPC methods. In this study, the proposed technique is used to control two real-world systems, and the results of its application are discussed.

Recently, a large amount of studies have been related to nonlinear systems with multi-degrees of freedom as well as continuous systems. The purpose of this paper is to optimize passive vibration absorbers in linear and nonlinear states for an Euler-Bernoulli beam with a nonlinear vibratory behavior under concentrated moving load. The goal parameter in the optimization is maximum deflection of the beam. The large deformation for beam modeling is considered, i.e. the relation between strains and deflections is nonlinear. The force magnitude and beam length are two effective factors for the beam deflection. Vibration absorber with linear damping and linear or nonlinear stiffness is also considered in this manuscript. The results show that, for normal forces and short beams, linear and nonlinear models have similar behaviors, while surveying nonlinear behavior is necessary by increasing the force and length of the beam, i.e. large deflections. Moreover, the difference between linear and nonlinear beam models for regular force magnitudes and beam lengths is negligible. For higher loads and longer beams, beam model nonlinearity can be important. Results demonstrate that, in the presented numerical values (train bridge application) for cubic nonlinear vibration absorber, there are two optimal locations for vibration absorber installation: one inclined from the middle of the beam to the direction of moving loads and the second which is more interestingly inclined from the middle of the beam to moving loads in the opposite direction. Moreover, depending on the model’s numerical parameters, for short beams, linear vibration absorber is more effective, while for long beams, cubic nonlinear beam behaves better than the linear one.