FOTF Toolbox for fractional-order control systems
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Dingyü Xue
Abstract
Handy and reliable computer tools are helpful for the researchers to handle their research problems. In Section 1, a brief review to MATLAB toolboxes in fractional-order systems is given, and the main toolbox involved in this chapter, FOTF Toolbox, is briefly addressed. The use of the major functions in the FOTF Toolbox is described and demonstrated through examples. In Section 2, numerical functions for computing Mittag-Leffler function, fractional-order derivatives and integrals are presented. The Grünwald-Letnikov and Caputo definitions are both considered. In particular, o(hp) high precision algorithms are proposed and implemented in the FOTF Toolbox, with much higher accuracy than any other existing algorithms and tools. MATLAB solvers for linear and fractionalorder differential equations are provided. In Section 3, a Simulink based blockset, fotflib, is introduced and its applications in solving fractional-order differential equations are addressed. A unified modeling strategy for nonlinear Caputo equation with any complexity is introduced, and illustrated through examples. In Section 4, two classes for linear fractional-order control components are designed and demonstrated. With these classes, complicated linear system models can be constructed, and time and frequency domain analysis can be carried out easily, as if one is processing integer-order models. In Section 5, several controller design examples are proposed, where an optimal fractional-order PID controller design function and interface are proposed first, followed by two examples in multivariable fractional-order controller design: pseudodiagonalization controller design and parameter optimization controller design. Simulation methods of closed-loop multivariable control systems are also demonstrated.
Abstract
Handy and reliable computer tools are helpful for the researchers to handle their research problems. In Section 1, a brief review to MATLAB toolboxes in fractional-order systems is given, and the main toolbox involved in this chapter, FOTF Toolbox, is briefly addressed. The use of the major functions in the FOTF Toolbox is described and demonstrated through examples. In Section 2, numerical functions for computing Mittag-Leffler function, fractional-order derivatives and integrals are presented. The Grünwald-Letnikov and Caputo definitions are both considered. In particular, o(hp) high precision algorithms are proposed and implemented in the FOTF Toolbox, with much higher accuracy than any other existing algorithms and tools. MATLAB solvers for linear and fractionalorder differential equations are provided. In Section 3, a Simulink based blockset, fotflib, is introduced and its applications in solving fractional-order differential equations are addressed. A unified modeling strategy for nonlinear Caputo equation with any complexity is introduced, and illustrated through examples. In Section 4, two classes for linear fractional-order control components are designed and demonstrated. With these classes, complicated linear system models can be constructed, and time and frequency domain analysis can be carried out easily, as if one is processing integer-order models. In Section 5, several controller design examples are proposed, where an optimal fractional-order PID controller design function and interface are proposed first, followed by two examples in multivariable fractional-order controller design: pseudodiagonalization controller design and parameter optimization controller design. Simulation methods of closed-loop multivariable control systems are also demonstrated.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Nonlinear control methods 1
- Dynamical properties of fractional models 29
- Modified versions of the fractional-order PID controller 57
- H∞ and H2 control of fractional models 73
- Stability analysis of discrete time distributed order LTI dynamic systems 101
- Continuous-time fractional linear systems: transient responses 119
- Continuous-time fractional linear systems: steady-state responses 149
- State space methods for fractional controllers design 175
- Posicast control of fractional-order systems 201
- FOMCON toolbox for modeling, design and implementation of fractional-order control systems 211
- FOTF Toolbox for fractional-order control systems 237
- Fractional-order controllers for mechatronics and automotive applications 267
- Fractional-order modeling and control of selected physical systems 293
- Control of a soft robotic link using a fractional-order controller 321
- Fractional-order precision motion control for mechatronic applications 339
- Development of fractional-order analog integrated controllers – application examples 357
- Synchronizations in fractional complex networks 379
- New trends in synchronization of fractional-order chaotic systems 397
- Index 423
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Nonlinear control methods 1
- Dynamical properties of fractional models 29
- Modified versions of the fractional-order PID controller 57
- H∞ and H2 control of fractional models 73
- Stability analysis of discrete time distributed order LTI dynamic systems 101
- Continuous-time fractional linear systems: transient responses 119
- Continuous-time fractional linear systems: steady-state responses 149
- State space methods for fractional controllers design 175
- Posicast control of fractional-order systems 201
- FOMCON toolbox for modeling, design and implementation of fractional-order control systems 211
- FOTF Toolbox for fractional-order control systems 237
- Fractional-order controllers for mechatronics and automotive applications 267
- Fractional-order modeling and control of selected physical systems 293
- Control of a soft robotic link using a fractional-order controller 321
- Fractional-order precision motion control for mechatronic applications 339
- Development of fractional-order analog integrated controllers – application examples 357
- Synchronizations in fractional complex networks 379
- New trends in synchronization of fractional-order chaotic systems 397
- Index 423
