In this paper‎, ‎a modern method is presented to solve a class of fractional optimal control problems (FOCPs) indirectly‎. ‎First‎, ‎the necessary optimality conditions for the FOCP are obtained in the form of two fractional differential equations (FDEs)‎. ‎Then‎, ‎the unknown functions are approximated by the hybrid functions‎, ‎including Bernoulli polynomials and Block-pulse functions based o...

*Correspondence: [email protected] Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, P.R. China Abstract In this paper, a new rectifying action is combined into different proportional-α-order-derivative-type iterative learning control algorithms for a class of fractional order linear time-invariant systems. Unlike the existing fractional...

In this work, a class of fractional order controller (FOPID) is tuned based on internal model control (IMC). This tuning rule has been obtained without any approximation of time delay. Moreover to show usefulness of fractional order controller in comparison with classical integer order controllers, an industrial PID controller tuned in a similar way, is compared with FOPID and then robust stabi...

The aim of this paper is to employ fractional order proportional integral derivative (FO-PID) controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system (MLS), which is inherently nonlinear and unstable system. The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order con...

In this article, a fractional-order proportional-integral-differential (FOPID) controller and its modified structure, called MFOPID controller, are presented. To guarantee optimal system performance, the gains of proposed FOPID controllers well-tuned, employing Jellyfish Search Optimizer (JSO), novel highly effective bioinspired metaheuristic approach. The assessed in hybrid with two domains, w...

this paper presents a self-tuning pid (proportional and integral and derivative) controller for regulating terminal voltage synchronous generators. in order to modify the system reponse and to overcome the difficulties of self tuning controllers, a dual rate sampling control system was used. system results demonstrated usfulness of the proposed regulator. the designed controller is simple and c...

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

<p style='text-indent:20px;'>The approximation of the fractional-order controller (FOC) has already been recognized as a distinguished field research in literature system and control. In this paper, two-step design approach is presented to realize proportional integral (FOPI) for class plant model. The goals are based on some frequency domain specifications. first stage work focused devel...

The previous work in [1], Tseng et al. have designed a fractional order differentiator using radial basis function by directly truncating the coefficients to approximate the fractional order derivative Dα of the given digital signal. This paper presents the designing of fractional order differentiator using radial basis function and window. Three design examples are given to illustrate that the...