Recently, fractional order systems (FOS) have attractedmore andmore attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and syste...

The robotic manipulator is considered one of the complex systems that include multi-input, multi-output, non-linearity, and highly coupled. uncertainty in parameters external disturbances have a negative influence on performance system. Therefore, controllers will be designed for these must able to deal with complexities difficulties. Proportional, Integral, Derivative (PID) controller known si...

The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the s...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

Reducing the emissions of greenhouse gases has directed energy sectors toward using renewable sources (RESs) and decreasing dependency on conventional sources. Recently, developing efficient load frequency control (LFC) schemes become essential to face reduced inertia due RESs installations. This paper presents a modified tilt fractional order (FO) integral–tilt FO derivative with filter (TFOI-...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

Poor control of the power grid can lead to a total system collapse, causing significant economic losses and possible damage security social peace. Therefore, improving stability, particularly transient has become one major research topics. This paper proposes developed modeling approach that provides optimal stabilizer parameters devices, aiming at electrical network stability by minimizing ang...