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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.
Contents
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
Contents
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