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

Two-dimensional differential transform for partial differential equations

On solving the initial-value problems using the differential transformation method

The demand for high-precision stages has received great attention due to the progress of nano-technology in recent years. Systems to provide long-range and high-precision performance for positioning, tracking and contouring actions have become stringent issues. Among these systems, the ball-screw-driven systems have been widely used in industrial applications and academic researches. In such systems, the friction behavior dominates the resulting performance and is usually known as the stick-slip phenomenon. The friction dynamics can be divided into the static and the dynamic regimes according to the conventional usage. In this paper, friction models are introduced to describe the dynamic behavior of a conventional ball-screw-driven x – y stage. The coherence between the theoretical and experimental data supports the validity of these models. Two sets of controllers corresponding to the static and the dynamic friction models are proposed based on the integral type sliding mode control (SMC) law. Experimental results demonstrate that the system achieves high-precision (10 nm) and long-range (10 cm) positioning performance with repeatability and robustness by the proposed control approaches.

Modeling and high-precision control of a ball-screw-driven stage

In this paper, a sliding mode controller is applied to control the cubic Chua’s circuit system. The sliding surface of this paper used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specication and use less control energy by comparing with the result in the current existing literature. The results show that the proposed controller can steer Chua’s circuit system to the desired state without the chattering phenomenon and abrupt state change.

Sliding mode control of chaos in the cubic chua's circuit system

This paper presents the analysis and control of active magnetic bearing (AMB) systems with a flexible rotor. A sliding mode controller design scheme is proposed to compensate for the nonlinear effects of the AMB system. A nonlinear model of the AMB system with an electromagnetic actuator and a flexible rotor is proposed to facilitate the present system analysis and controller design. This nonlinear model takes into account the dynamics of the flexible rotor, the characteristics of the nonlinear electromagnetic suspended system, and the contact force between the auxiliary bearing and the shaft. This study also considers the auto-centering control of the AMB system when subjected to disturbances and variations in the system parameters. The numerical results show that the system exhibits a periodic motion and demonstrates high accuracy and robustness when operating under sliding mode control.

Ming-Jyi Jang

Papers

Two-dimensional differential transform for partial differential equations

On solving the initial-value problems using the differential transformation method

Modeling and high-precision control of a ball-screw-driven stage

Sliding mode control of chaos in the cubic chua's circuit system

Sliding mode control for active magnetic bearing system with flexible rotor