In conventional power systems, most of the power is produced by synchronous generators in the electric grid that have heavy and rotating rotors. As a result, there is an inherent inertia in the rotor of these generators. The presence of inertia in the grid prevents sudden frequency changes during imbalance situations, thus, the frequency stability of the grid is maintained. Today, with the increase of renewable energy sources that are usually connected to the network by power electronic equipment. Such resources do not have rotating materials, therefore, the overall inertia of the grid decreases and the stability of the system deteriorates. To solve the problem of lack of inertia in the power electronic-based grid, the notion of the virtual synchronous generator (VSG) technology has been introduced in recent years. This technology can imitate the behavior of traditional synchronous generators for inverters connected to the grid. In this way, the inverters connected to the grid act like a synchronous generator during imbalance. One of the problems associated with the converters-based microgrid is the existence of DC deviations and additional harmonics, which disrupt the work of the converters. Therefore, in this article, a third-order Generalized Integrator (TOGI) -based VSG for grid-connected inverters is employed so that the system stability is maintained in the conditions of additional harmonics and DC deviation. To show the effectiveness of the proposed method, time domain simulations have been performed in Simulink/MATLAB software. The results of the simulation verify the performance of the proposed method.

The problem of consensus in fractional order single-Integrator multi-agent systems has been studied in this paper. The effect of memory is considered using the Riemann-Liouville fractional derivative in the dynamics of the agents. In order to achieve convergence among the agents, a fractional order control protocol based on the error signal between neighboring agents is proposed. Using Lyapunov's stability theorem, a Lyapunov function is introduced that shows that the agents converge over a specified settling time and the upper bound of the settling time is obtained. The merit of the proposed bound for the settling time is that it is independent of the initial conditions. Finally, some simulations are provided to confirm the introduced method.

In this paper, dynamic equations of motion of a 5 DoF robot manipulator including ‎mechanical arms with revolute joints and their electrical actuators are considered. The ‎application of Integrator backstepping technique for trajectory tracking in presence of ‎parameters of uncertainty and disturbance is studied. The advantage of this control ‎technique is that it imposes the desired properties of stability by fixing the candidate ‎Lyapunov functions initially, then by calculating the other functions in a recursive ‎way. Simulation results are presented in order to evaluate the tracking performance ‎and the global stability of the closed loop system. The validity and usefulness of the ‎proposed technique for robot motion control when the system dynamics including ‎both mechanical arms and electrical actuators become more complex is obtained from ‎the results‏.‏

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of Generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

This paper addresses the problem of fixed-time control for a class of Second-order nonlinear systems in the presence of model uncertainty and external disturbance. By introducing a novel form of non-singular terminal sliding mode control, a fixed-time control is designed to obtain acceptable performance, rapid convergence of the system states, high robustness and singularity elimination. Guaranteeing fixed-time convergence is a significant feature of the proposed control law under which the convergence time of the proposed surface is independent of the initial conditions. Since the upper bound of the system uncertainty and disturbance is quite difficult to obtain, an adaptive mechanism is presented under which there is no need to know this upper bound. Lyapunov analysis proves that the system states converge to small neighborhood of the origin within a fixed time. To assess efficiency of the suggested method, a flexible spacecraft attitude control system is considered and a fixed-time attitude control system is derived. Simulation results verify the effectiveness and performance of the presented approach.

Objective: The purpose of this study was to apply the relative robust approach that minimizes the maximum regret to deal with the present uncertainty in the input data of the Markowitz mean-variance portfolio optimization model by reconstructing that model as a Second-order conic program. Regret is defined as the difference between the obtained solution and the optimal solution under a specified input data set. This approach uses scenarios to consider the present uncertainty in the input data. Moreover, the robust portfolio optimization model introduced by Bertsimas and Sim, which considers uncertainty as an interval, was used to be compared with the relative robust approach and the Markowitz model. Methods: In this research, the return of 50 more active stocks of the Tehran Stock Exchange (TSE) was used to obtain the optimal portfolio using the minimax regret method based on the Markowitz Model. Then, using the out-of-sample Sharpe criterion, the results of the minimax regret method were compared with the classic methods. Results: Based on the research findings, the relative robust approach in the out-of-sample test on most corresponding points of the efficient frontier showed better performance in comparison with the Markowitz model. Also, the Bertsimas and sim approach delivered better performance than the Markowitz model in the out-of-sample test. The results did not prove any significant difference for out-of-sample outputs between the relative robust and Bertsimas and sim approaches. Conclusion: According to the obtained results, the relative robust approach can surpass the mean-variance approach for investors with almost all levels of risk-return preferences. The approach presented in this research can provide investors with a new risk criterion that can be considered in choosing the optimal portfolio. Furthermore, the results confirmed that investors act indifferently in choosing between the relative robust solution and the solution of Bertsimas and Sim's approach. This method can be applied as a portfolio optimization approach and also different markets can be considered under this technique to have a better understanding of its capability.