Continued fractions approximation of the impulse response of fractional-order dynamic systems

A new discrete approximation of the fractional-order operator

“…The Padé and the CFE methods yield the same approximation (causal, stable and minimum phase). A different approach of the CFE method was used in [11]. So-called Muir-recursion scheme can be found in [26].…”

Tuning PI^ν fractional order controllers for position control of DC-servomotors

“…However, there are many rational approximations to s ν at disposal, see for example references in [11]. This paper refers to the following approximation given by one of the authors [10]:…”

Optimizing Continued Fraction Expansion Based IIR Realization of Fractional Order Differ-Integrators with Genetic Algorithm

“…The mapping relation or formula for conversion from continuous time to discrete time operator ( s z ↔ ) is known as the generating function. Among the family of expansion methods, CFE based digital realization has been extensively studied with various types of generating functions like Tustin [10], Simpson [11], Al-Alaoui [12], mixed TustinSimpson [13], mixed Euler-Tustin-Simpson [14], impulse response based [15] and other higher order generating functions [16]- [18]. This paper focuses on the CFE based realization of the fractional order differ-integrators with an optimization based approach for the mixed type generating functions.…”