Response Time Domain of Fractional Water Tank Problem

Authors

In this work, linear differential equations for dynamic systems of integer orders

were studied by solving them and studying the stability of the system. Stability

was studied through the mathematical tool, the transfer function, which

represents the relationship between inputs and outputs, and extracting the roots

of the denominator that determine the stability of dynamic systems for two types

of inputs (unit step function-Dirac function ) and programming them, as it was

shown that the systems are stable. The work has been developed of study and

solution of linear differential equations of fractional orders, where the stability

of dynamic systems of fractional orders was studied through the fractional

transfer function and for two types of inputs and extracting the roots of the

denominator using De movers and other algebraic methods and programming

them and comparing them with the correct differential equations, where it was

noted through the work that the fractal differential equations and the Dirac input

give the system more stability. the response of the water tank problem was

studied and modified to (Fractional Order System). to improve the accuracy of

stability of the water level. The research focused on stability the response time

in the time domain of the water level in the tank when changes in inputs occur.

The study showed that the problem system is characterized by higher flexibility

and a greater ability to represent the dynamic behavior of the tank. This

contributes to improving the control efficiency of hydraulic and industrial

systems and reduces operational errors Through comparison, it is shown that

fractal differential equations are better at stabilizing dynamic systems, giving a

more stable system at a lower cost.