Fractional Order Systems-Control Theory and Applications: Fundamentals and Applications

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems, with applications in control theory. Fractional order systems (FOS) are modelled by fractional differential equations, and their application in control theory is important in many engineering applications.

Format: Paperback / softback
Length: 216 pages
Publication date: 01 September 2022
Publisher: Springer Nature Switzerland AG

This book aims to bring together the latest innovative knowledge, analysis, and synthesis of fractional control problems of nonlinear systems, as well as some related applications. Fractional order systems (FOS) are dynamical systems that can be modeled by a fractional differential equation carried with a non-integer derivative. In the last few decades, the growth of science and engineering systems has considerably stimulated the employment of fractional calculus in many subjects of control theory, for example, in stability, stabilization, controllability, observability, observer design, and fault estimation. The application of control theory in FOS is an important issue in many engineering applications. So, to accurately describe these systems, the fractional order differential equations have been introduced.

Fractional order systems (FOS) are a fascinating realm of dynamical systems that can be modeled using fractional differential equations, where the non-integer derivative plays a crucial role. These systems have gained significant attention in recent decades due to their wide-ranging applications in various fields of control theory, including stability, stabilization, controllability, observability, observer design, and fault estimation. The utilization of control theory in FOS has become increasingly important in numerous engineering applications, necessitating the development of accurate models that capture the intricate behavior of these systems.

One of the key challenges in understanding FOS is the description of these systems using fractional order differential equations. These equations provide a mathematical framework that allows for a more comprehensive understanding of the complex dynamics exhibited by FOS. By incorporating fractional derivatives, FOS can be modeled more accurately, capturing phenomena such as non-linearity, time-delay, and chaos, which are often present in real-world systems.

The application of control theory in FOS has led to significant advancements in various fields. In the area of stability, for instance, the use of fractional order controllers has been shown to improve the stability and performance of nonlinear systems. Fractional order controllers can effectively handle system uncertainties and disturbances, leading to improved control performance and reduced system instability.

Stabilization is another important application of control theory in FOS. By designing fractional order controllers, it is possible to stabilize unstable systems, such as those with time-delay or non-minimum phase characteristics. Fractional order controllers can effectively suppress system oscillations and achieve desired steady-state responses, making them valuable in industries such as aerospace, automotive, and power systems.

Observability is another critical aspect of control theory in FOS. By designing observers, it is possible to monitor the state of a system and estimate its parameters. Observers are particularly useful in fault estimation, where they can detect and diagnose system faults early, leading to reduced downtime and maintenance costs.

Observer design is a crucial aspect of control theory in FOS, as it allows for the estimation of unknown system parameters. By designing appropriate observers, it is possible to estimate the state of a system, even when the system is not directly observable. Observer design is particularly useful in systems with complex dynamics, where traditional methods may not be effective.

Fault estimation is another important application of control theory in FOS. By designing fault estimators, it is possible to detect and diagnose system faults early, leading to reduced downtime and maintenance costs. Fault estimators can be based on various techniques, including neural networks, genetic algorithms, and statistical methods.

In conclusion, fractional order systems (FOS) are a fascinating realm of dynamical systems that have gained significant attention in recent decades. The use of control theory in FOS has led to significant advancements in various fields, including stability, stabilization, controllability, observability, observer design, and fault estimation. Fractional order differential equations provide a mathematical framework that allows for a more comprehensive understanding of the complex dynamics exhibited by FOS, and the application of control theory in FOS has led to improved control performance and reduced system instability. As the field of FOS continues to evolve, it is likely to play an increasingly important role in various engineering applications, from aerospace to automotive to power systems.

Weight: 355g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030714482
Edition number: 1st ed. 2022