Xue D. Fractional-Order Control Systems Fundamentals and Numerical Implementations

De Gruyter, Berlin, 2017. — 388 p. — ISBN 978-3-11-049999-5.This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MatLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems.Introduction to fractional calculus and fractional-order control.
Mathematical prerequisites.
Definitions and computation algorithms of fractional-order derivatives and Integrals.
Solutions of linear fractional-order differential equations.
Approximation of fractional-order operators.
Modelling and analysis of multivariable fractional-order transfer function Matrices.
State space modelling and analysis of linear fractional-order Systems.
Numerical solutions of nonlinear fractional-order differential Equations.
Design of fractional-order PID controllers.
Frequency domain controller design for multivariable fractional-order Systems.
Inverse Laplace transforms involving fractional and irrational Operations.
FOTF Toolbox functions and models.
Benchmark problems for the assessment of fractional-order differential equation algorithms.