Two direct Tustin discretization methods for fractional-order differentiator/integrator

By Blas M. Vinagre, YangQuan Chen, Ivo Petrás. Journal of the Franklin Institute, 2003

365 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/3fcbd09163aad2f4d5c92d6c269d94f263ae3c91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Ivo Petrás
2. YangQuan Chen
3. Dingyu Xue
4. Zhe Gao
5. Xiaozhong Liao
6. Chunna Zhao
7. A. Charef
8. Samir Ladaci

In Electrical and Electronic Engineering

1. Xiaozhong Liao
2. Zhe Gao
3. Ivo Petrás
4. Samir Ladaci
5. A. Charef
6. YangQuan Chen

Citations in the corpus

• Stability of Fractional-Order Systems with Rational Orders (2008, neutral): “The fractional order calculus plays an important role in physics [45,60,67], thermodynamics [31,57], electrical circuits theory and fractances [7,12,14,21,40,71], mechatronics systems [55], signal processing [56, 68], chemical mixing [41], chaos theory [62, 64], and biological system as well [23].”
• A note on the fractional-order Chua’s system (2008, methodology): “It is also a high order system but numerical error is much smaller than in methods in the form of IIR filter [23,24].”
• Tuning and implementation methods for fractional-order controllers (2012, background): “Some proposals we can be found in the work [38].”
• Fractional control of heat diffusion systems (2008, background): “ous operators of type s adopts the Euler, Tustin, and Al-Alaoui generating functions [6–8].”
• On Fractional Adaptive Control (2006, methodology): “Vinagre et al. [ 25 ] developed a new method for the discretisation of fractional order operators using Tustin approach.”
• Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics (2010, neutral): “Different numerical approximations are reported in [36, 37].”
• Rational approximation for fractional-order system by particle swarm optimization (2012, background): “in engineering [1], for example, in heat diffusion modeling and control [2‐4], the fractional-order PID controller [5‐7], fractional-order chaotic systems [8‐10], the fractional-order digital filter [ 11 , 12], etc.”
• A Modified Approximation Method of Fractional Order System (2006, background): “For example, in [ 14 ], continued fraction expansion is used for a approximation due to the fact that the continued fraction expansion often converges much more rapidly than power series expansion yet with a larger domain of convergence in the complex plane.”