Valerio D., da Costa J.Sa. An Introduction to Fractional Control

The Institution of Engineering and Technology, UK, 2013. — 382 p. — (IET Control Engineering Series 91) — ISBN: 9781849195461.Fractional control techniques provide an effective way to control dynamic behaviors, using fractional differential equations. This can include the control of fractional plants, the control of a plant using a fractional controller, or the control of a plant so that the controlled system will have a fractional behaviour to achieve a performance that would otherwise be hard to come by.
An Introduction to Fractional Control outlines the theory, techniques and applications of fractional control. The theoretical background covers fractional calculus with real, complex and variable orders, fractional transfer functions, fractional identification and pseudostatespace representations, while the control systems explored include: fractional lead control, fractional lag control, first, second and third generation Crone control, fractional PID, PI and PD control, fractional sliding mode control, logarithmic phase Crone control, fractional reset control, fractional H2 and H8 control, fractional predictive control, trajectory planning and fractional timevarying control. Each chapter contains solved examples, where the subject addressed is either expanded or applied to concrete cases, and references for further reading. Common definitions and proofs are included, along with a bibliography, and a discussion of how MatLAB can be used to assist in the design and implementation of fractional control. This is an essential guide for researchers and advanced students of control engineering in academia and industry.Preliminaries
Fractional derivatives with real orders
Fractional calculus: real orders
Fractional transfer functions
Approximations of fractional transfer functions
Fractional identification
First and second-generation Crone control
Fractional PIDs
Fractional reset control
Fractional H₂ and H₁ control
Pseudo-state-space representations
Fractional sliding mode control
Trajectory planning
Fractional derivatives with complex orders
Fractional calculus: complex orders
Complex order transfer functions
Third generation Crone control
Fractional derivatives with variable orders
Fractional calculus: variable orders
Fractional time-varying control
General considerations