This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

Research Summary

Praise be to God, and may blessings and peace be upon our master Muhammad al-Mustafa, his family, his companions, and those who follow his gift until the Day of Judgment.

As for the dimension: This is a historical description of my conquest (Al-Khandaq and Ba

The results of the current study showed that the thyroid gland in an adult domestic cat (Felis catus) is located in the neck area on both sides of the trachea at rings 1–5. The gland consists of two lobes (right and left), and it is surrounded by a capsule of connective tissue consisting of two outer and inner layers, and a layer of fatty tissue overlaps with the outer layer of the capsule. In addition, the results of this study found that the histological structure of the thyroid gland is composed of several follicles that appear in different sizes and shapes. The follicles are lined with simple cuboidal epithelial tissue and sometimes appear lined with high and low simple cuboidal epithelial tissue. The gland is histologically c

The results of the current study showed that the thyroid gland in adult domestic cat (Felis catus) is located in the neck area on both sides of the trachea at rings (1-5). The gland consists of two lobes (right and left) and it is surrounded by a capsule of connective tissue consisting of two outer and inner layers, and a layer of fatty tissue overlaps with the outer layer of the capsule. In addition, the results of this study found that the histological structure of the thyroid gland is composed of several follicles that appear in different sizes and shapes; the follicles are lined with simple cuboidal epithelial tissue and sometimes appear lined with high and low simple cuboidal epithelial tissue. The gland is histologically composed of t

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using the Beddington–DeAngelis type of functional response to describe the predation processes. The model’s qualitative features are investigated, including local equilibria stability, permanence, and global stability. Bifurcation analysis is carried out on the temporal model to identify local bifurcations such as transcritical, saddle-node, and Hopf bifurcation. A comprehensive numerical inquiry is carried out using MATLAB to verify the obtained theoretical findings and und

This paper presents a novel idea as it investigates the rescue effect of the prey with fluctuation effect for the first time to propose a modified predator-prey model that forms a non-autonomous model. However, the approximation method is utilized to convert the non-autonomous model to an autonomous one by simplifying the mathematical analysis and following the dynamical behaviors. Some theoretical properties of the proposed autonomous model like the boundedness, stability, and Kolmogorov conditions are studied. This paper's analytical results demonstrate that the dynamic behaviors are globally stable and that the rescue effect improves the likelihood of coexistence compared to when there is no rescue impact. Furthermore, numerical simul

        A newly developed analytical method was conducted for the determination of Ketotifen fumarate (KTF) in pharmaceuticals drugs via quenching of continuous fluorescence of 9(10H)-Acridone (ACD). The method was applied using flow injection system of a new homemade ISNAG fluorimeter with fluorescence measurements at ± 90◦ via 2×4 solar cell. The calibration graph was linear in the range of 1-45 mmol/L, with correlation coefficient r = 0.9762 and the limit of detection 29.785 µg/sample from the stepwise dilution for the minimum concentration in the linear dynamic ranged of the calibration graph. The method was successfully applied to the determination of Ketotifen fumarate in two different pharma