Solutions of the system of differential equations by differential transform method

Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM

The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations

Magnetic field effect on unsteady nanofluid flow and heat transfer using Buongiorno model

Recently differential transform method (DTM) has been used to solve various partial differential equations. In this paper, an alternative approach called the reduced differential transform method (RDTM) is presented to overcome the demerit of complex calculation of differential transform method. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. In addition, three test problems of mathematical physics are discussed to illustrate the effectiveness and the performance of the reduced differential transform method.

Reduced Differential Transform Method for Partial Differential Equations

In this paper, an extended sliding mode controller is applied to control a hyperchaotic motion in Rossler system. The sliding surface of this paper used is one dimension higher than traditional sliding surface and guarantees it passing through the activated initial states of controlled system. Therefore, using the characteristic of this sliding mode to design a controller not only can meet the desired specification but also without chattering phenomenon and abrupt state change. By comparing with the result in the existed literatures, the results show that the proposed controller can steer Rossler system to the desired state accurately. It also provides a good characteristic for disturbance rejection.

Sliding mode control of hyperchaos in Rössler systems

This study describes the high-precision positioning control of a system with asymmetric hysteresis. A switching system concept is adopted to describe the Preisach-type hysteresis, and a systematic modeling procedure is established to obtain the parameters of the system. A piezoelectric actuator system driven by a voltage amplifier is used to verify the modeling accuracy. A control structure, comprising a feedforward controller and a PD-type feedback controller, is used to realize the high-precision positioning control of the piezoelectric actuator driven stage. To enhance tracking control, a high-frequency modified term is incorporated into the hysteresis model. The experimental results confirm that the addition of this modified term reduces the tracking error and prevents the controlling energy from being saturated.

Modeling and control of a piezoelectric actuator driven system with asymmetric hysteresis

This paper studies the bifurcation and nonlinear behaviors of a flexible rotor supported by relative short gas film bearings. A time-dependent mathematical model for gas journal bearings is presented. The finite difference method with successive over relation method is employed to solve the Reynolds’ equation. The system state trajectory, Poincare maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and subharmonic response of the rotor and journal center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

Ming-Jyi Jang

Papers

Sliding mode control of hyperchaos in Rössler systems

Modeling and control of a piezoelectric actuator driven system with asymmetric hysteresis

Bifurcation and nonlinear dynamic analysis of a flexible rotor supported by relative short gas journal bearings

Theoretical analysis of the non-linear behavior of a flexible rotor supported by herringbone grooved gas journal bearings

Analyzing the free vibrations of a plate using finite difference and differential transformation method