Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

Review of fractional PID controller

A new jacobi operational matrix: an application for solving fractional differential equations

https://www.kau.edu.sa/Files/130/Researches/61664_32628.pdf

Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations

A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations

This paper deals with robust fractional order PID controller design via numerical multi-objective optimization. The proposed interval-based design scheme uses frequency-domain specifications to ensure a desired closed-loop behavior. By maintaining the desired phase margin quasi-constant in a pre-specified frequency band, it guarantees more robustness to gain uncertainties. This leads to a closed-loop system with an interesting iso-damping property in a more large frequency band than other design methods. A numerical example is presented to show the efficiency of the proposed method and to discuss about the obtained results.

Multi-objective optimization based design of fractional PID controller

This paper develops a new Kalman filter for linear systems described with continuous time fractional model. It extends the classical Kalman filter to deals with fractional differentiation. It is called continuous fractional Kalman Filter. The algorithm of the new filter is detailed and a suboptimal filter can be deduced. A numerical example illustrates the state estimation of a fractional model with the new filter.

Continuous fractional Kalman filter

Quadrotor UAV is a highly coupled and under-actuated system. Estimation of the dynamic model is an important step for the quadrotor control design. In this chapter, two modelling methods are proposed to determine the dynamic model of a quadrotor prototype. Firstly a mathematical model is developed to describe the quadrotor 6 degrees of freedom using Euler–Lagrange formalism. The unknown model parameters are then obtained using calculations and experimental tests. In the second method the roll system is estimated using closed loop identification method and frequency domain analysis. The simulation results are compared with practical responses. Both of the two methods shows good performances.

Dynamic Modeling of a Quadrotor UAV Prototype

This paper presents a new ellipsoidal set-membership method for the identification of linear fractional orders systems. It use the Optimal Bounding Ellipsoid (OBE) algorithm. When the probability distribution of the disturbances is unknown but bounded and when the differentiation orders are known, the proposed method can estimate all the feasible parameters. A numerical example shows the effectiveness of the proposed method.

An ellipsoidal set-membership parameter estimation of fractional orders systems

This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves.

Slaheddine Najar

Papers

Multi-objective optimization based design of fractional PID controller

Continuous fractional Kalman filter

Dynamic Modeling of a Quadrotor UAV Prototype

An ellipsoidal set-membership parameter estimation of fractional orders systems

Resonance study of an elementary fractional transfer function of the third kind