Continuous-time fractional linear systems: steady-state responses
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Duarte Valério
Abstract
This chapter presents the frequency responses of several single-input, single-output fractional-order systems-commensurate, noncommensurate, and implicit. Both analytical expressions and the Bode, Nyquist, and Nichols diagrams are shown for several typical transfer functions. The chapter also addresses the Levy identification method for fractional orders, integer-order approximations of fractional-order systems (Crone, Carlson, Matsuda), and the Nyquist stability criterion for closed-loop commensurate systems.
Abstract
This chapter presents the frequency responses of several single-input, single-output fractional-order systems-commensurate, noncommensurate, and implicit. Both analytical expressions and the Bode, Nyquist, and Nichols diagrams are shown for several typical transfer functions. The chapter also addresses the Levy identification method for fractional orders, integer-order approximations of fractional-order systems (Crone, Carlson, Matsuda), and the Nyquist stability criterion for closed-loop commensurate systems.
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
