Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems.
Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.
A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO) time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order PI λ D μ controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of PI λ D μ controller with respect to a traditional optimized PID controller.
In this paper, a neuro-fuzzy fast terminal sliding mode control method is proposed for controlling a class of nonlinear systems with bounded uncertainties and disturbances. In this method, a nonlinear terminal sliding surface is firstly designed. Then, this sliding surface is considered as input for an adaptive neuro-fuzzy inference system which is the main controller. A proportinal-integral-derivative controller is also used to asist the neuro-fuzzy controller in order to improve the performance of the system at the begining stage of control operation. In addition, bee algorithm is used in this paper to update the weights of neuro-fuzzy system as well as the parameters of the proportinal-integral-derivative controller. The proposed control scheme is simulated for vibration control in a model of atomic force microscope system and the results are compared with conventional sliding mode controllers. The simulation results show that the chattering effect in the proposed controller is decreased in comparison with the sliding mode and the terminal sliding mode controllers. Also, the method provides the advantages of fast convergence and low model dependency compared to the conventional methods.
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