Fractional-order Systems and Controls

Discrete-Time Implementation and Experimental Validation of a Fractional Order PD Controller for Vibration Suppression in Airplane Wings

“…The fractional order approach represents a generalization of differentiation and integration to an arbitrary order. Compared to the integer order controllers, the fractional order ones offer increased flexibility and can honor more closed loop performance constraints simultaneously [7]. For this reason, a fractional order PD controller has been previously designed for a similar cantilever beam, as the case study in this paper, and the experimental results demonstrated the advantages of using a fractional order PD controller instead of the classical integer order PD [8], [9].…”

On Digital Realizations of Non-integer Order Filters

“…It was observed in earlier authors' works [7] that it can become destabilized very easily. On the other hand, CFE method shows inferior quality in frequency characteristic representation [25]. Detailed analysis of CFE approximation in discrete time can be found in [12,44,45].…”

“…The original approach, developed by Oustaloup [26,27], is based on approximation of fractional systems in frequency domain. This approach is widely used, e.g., [11,22,25,32] and many others. However, this method has some flaws which cannot be neglected-when discretized, it does not guarantee stability of the system (the poles of discrete system are outside unit circle) (see, e.g., [30]).…”

Bounded real lemmas for fractional order systems

“…Moreover, with the theoretical development of fractional differential equations [3] , fractional controllers have been proposed which possess more flexibilities and robustness, e.g., the P I λ D u controller [4] , the CRONE principle [5] , and other variations [6] . Many fundamentals and applications of fractional order control systems can be found in [7] and the references therein.…”