Fractional Calculus

Automatic control is a branch of scientific research that deals, among other things, with automatons. In our daily lives, we keep surrounded by automated systems, such as battery chargers, cruise control mechanisms in cars, automatic pilots for aircrafts and rockets, and so on. These dynamic systems require continuous control to ensure that their function in question is maintained. Engineers in automatic control work in the fields of domestic appliances, automobiles, aerospace, chemical process, wastewater management, 3D printers and so on.

Fractional calculus is used to add up new solutions to the problematics presented in automation, but considering the basiest case: The linear systems case. This case, even though considered as “mature”, enable us to find new possibilities due to the generalization of calculus definitions of integrals and derivatives to the real or even complex order case.

Fractional calculus will be used in this work as a tool to design a control feedback algorithm for linear fractional and non fractional order, time-invariant systems with time-delay and as a mathematical modeling tool for large-scale mechanical systems.