An Introduction to Fractional Control

Fractional control techniques provide an effective way to control dynamic behaviours, 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 pseudo-state-space 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 time-varying 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.