Modern automation robotics have replaced many human workers in industrial factories around the globe. The robotic arms are used for several manufacturing applications, and their responses required optimal control. In this paper, a robust approach of optimal position control for a DC motor in the robotic arm system is proposed. The general component of the automation system is first introduced. The mathematical model and the corresponding transfer functions of a DC motor in the robotic arm system are presented.  The investigations of using DC motor in the robotic arm system without controller lead to poor system performance. Therefore, the analysis and design of a Proportional plus Integration plus Divertive (PID) controller is illustrated.

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

Research Hypothesis from the fact that kicks off the effect that agricultural production in Iraq plays an important role in overcoming the food problem and achieving food security, but he became far far away from the provision of sufficient quantities of food products and then securing the Iraqi consumer food basket by the challenges faced by the agricultural sector.
To prove the hypothesis research in its structure in three axes came, the first axis eating historical significance to the subject of food over time periods as well as to clarify the concept of food security, and the second axis touched on the most important challenges facing the agricultural sector in Iraq and prevent the achievement of food requirements for members of

This article presents a new cascaded extended state observer (CESO)-based sliding-mode control (SMC) for an underactuated flexible joint robot (FJR). The control of the FJR has many challenges, including coupling, underactuation, nonlinearity, uncertainties and external disturbances, and the noise amplification especially in the high-order systems. The proposed control integrates the CESO and SMC, in which the CESO estimates the states and disturbances, and the SMC provides the system robustness to the uncertainty and disturbance estimation errors. First, a dynamic model of the FJR is derived and converted from an underactuated form to a canonical form via the Olfati transformation and a flatness approach, which reduces the complexity of th