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In this paper, fractional calculus is used to develop a generalized fractional dynamic model of an electrohydraulic system composed of a servo valve and a hydraulic cylinder, where a fractional position controller P I γ D μ is proposed for minimizing the performance index according to the integral of the time-weighted absolute error (ITAE). First, the general mathematical equations of the cylinder and servo valve are used to obtain the transfer functions in fractional order by applying Caputo's definition and a Laplace transform. Then, through a block diagram of the closed-loop system without a controller, the fractional model is validated by comparing its performance concerning the integer-order electrohydraulic system model reported in the literature. Subsequently, a fractional PID controller is designed to control the cylinder position. This controller is included in the closed-loop system to determine the fractional exponents of the transfer functions of the servo valve, cylinder, and control, as well as to tune the controller gains, by using the ITAE objective function, with a comparison of the following: (1) the electrohydraulic system model in integer order and the controller in fractional order; (2) the electrohydraulic system model in fractional order and the controller in integer order; and (3) both the system model and the controller in fractional order. For each of the above alternatives, numerical simulations were carried out using MATLAB®/Simulink® R2023b and adding white noise as a perturbation. The results show that strategy (3), where electrohydraulic system and controller model are given in fractional order, develops the best performance because it generates the minimum value of ITAE. [ABSTRACT FROM AUTHOR]

A complete modeling (including the actuator dynamics) of a robot manipulator that uses three-phase induction motors is presented in this paper. A control scheme is designed to synchronize robot manipulators actuated by induction motors under a master-slave scheme in the case where the joint velocity of the slave robots is estimated. All of the research on the synchronization of robot manipulators assumes the use of ideal actuators to drive the joints; for that reason, in this work, a three-phase induction motor is considered to be a direct-drive actuator for each joint. An entire model of the mated system is obtained by a combination of the dynamics of the induction motor and robot manipulator. Thus, the synchronization control algorithm for a master-slave scheme in both the joint space and workspace of robot manipulators driven by induction motors is developed. An observer based on the entire model is proposed to estimate the joint velocity of the slave robot manipulators. Through the Lyapunov criterion, a stability analysis of the synchronization control with a velocity estimator is detailed. The analytical results show the synchronization and estimation errors are globally, uniformly, and ultimately bounded. Simulations with multiple robots demonstrate the performance of the proposed control algorithm. [ABSTRACT FROM AUTHOR]