Xue D. Fractional-Order Control Systems Fundamentals and Numerical Implem. 2017

Textbook in PDF format

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