A novel nonlinear fractional order sliding mode controller is proposed to control the chaotic atomic force microscope system in presence of uncertainties and disturbances. In the design of the suggested fractional order controller, conformable fractional order derivative is applied. The stability of the scheme is proved by means of the Lyapunov theory based on conformable fractional order deriv...

This paper presents a modified numerical scheme for a class of Fractional Optimal Control Problems (FOCPs) formulated in Agrawal (2004) where a Fractional Derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire time domain is divided into several subdomains, and a fractional derivative (FDs) at a time node point is approximated using a modified Grünwald-Letnikov ap...

Robust stability is a major concern for real-world control applications. Realization of optimal robust requires stabilization scheme, which ensures that the system stable and presents performance predefined range perturbations. This study presented an approach closed-loop fractional order proportional integral derivative (FOPID) systems with interval parametric uncertainty uncertain time delay....

The pumped storage unit has good adjustment characteristics of a fast power response and convenient start stop, which provides support for the safe stable operation system. To this end, paper proposes fractional order PID (FOPID) optimization control method regional load frequency pumped-storage plants. Specifically, based on IEEE standards, established single-region model storage. Then, contro...

non-fragile observer design is the main problem of this paper. using continuous frequency distribution, the stability conditions based on integer order lyapunov theorem are derived for lipschitz class of nonlinear fractional order systems. the proposed observer is stable beside the existence of both gain perturbation and input disturbance. for the first time, in this paper a systematic method i...

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then next-generation matrix method used to calculate threshold. Furthermore, stability rumor-free/spreading equilibrium discussed based on Routh–Hurwitz criterion, Lyapunov function method, invariance principle. Next, necessary conditions for frac...

This paper presents a novel robust fractional PIλ controller design for flexible joint electrically driven robots. Because of using voltage control strategy, the proposed approach is free of problems arising from torque control strategy in the design and implementation. In fact, the motor's current includes the effects of nonlinearities and coupling in the robot manipulator. Therefore, cancella...

This paper addresses the problem of the fractional sliding mode control (FSMC) for a MEMS optical switch. The proposed scheme utilizes a fractional sliding surface to describe dynamic behavior of the system in the sliding mode stage. After a comparison with the classical integer-order counterpart, it is seen that the control system with the proposed sliding surface displays better transient per...