Sharif Digital Repository

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order α is a known constant belonging to 0 < α < 1. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and... 

This letter presents new sufficient conditions for robust Hurwitz stability of interval matrices. The proposed conditions are based on two approaches: (i) finding a common Lyapunov matrix for the interval family and (ii) converting the robust stability problem into a robust non-singularity problem using Kronecker operations. The main contribution of the letter is to derive accurate and computationally simple optimal estimates of the robustness margin and spectral bound of general interval matrices. The evaluation of the condition relies on the solutions of linear matrix inequalities (LMIs) and eigenvalue problems, both of which are solved very efficiently. The improvements gained by using... 

This paper proposes a control strategy for the autonomous (islanded) operation of a four-wire, electronically-coupled distributed generation (DG) unit which can feed a highly unbalanced load, e.g., due to the presence of single-phase loads. In the grid-connected mode, the power-electronic interface of the DG unit enables the exchange of real and reactive power with the distribution network, based on the conventional dq-frame current control strategy. The current control scheme is disabled subsequent to the detection of an islanding event, and the proposed controller is activated. The proposed control strategy utilizes: i) an internal oscillator to maintain the island frequency and ii) a... 

Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex... 

This study investigates the dynamic participation of wind power plants (WPPs) in the automatic generation control (AGC) task. The pre-specified model of wind farm in the AGC studies has been used. It is shown that operating of WPPs at the command mode results in a significant improvement in the frequency behaviour of power system due to their faster response. However, the WPPs may change their operation mode from the command mode to the maximum power point mode according to the wind speed conditions and load variations. This reduces the improvement in the frequency response. In this condition, the shortage in the wind power should be compensated by the conventional units. Thus, the share of... 

This study addresses the robust stability analysis for an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). Owing to large load changes, microgrid structure reconfiguration, and higher-power demands, the low-frequency (LF) dominant modes of a microgrid stir toward unstable zone and make the system more oscillatory or even unstable. In this study, a robust two-degree-of-freedom (2DOF) decentralised droop controller, which is the combination of the conventional droop with a robust transient droop function, is utilised for each inverter-based DG unit. Unlike conventional tuning of 2DOF droop controllers, a new design procedure is proposed to robustly... 

Robust stability analysis of multiorder fractional linear time-invariant systems is studied in this paper. In the present study, first, conservative stability boundaries with respect to the eigenvalues of a dynamic matrix for this kind of systems are found by using Young and Jensen inequalities. Then, considering uncertainty on the dynamic matrix, fractional orders, and fractional derivative coefficients, some sufficient conditions are derived for the stability analysis of uncertain multiorder fractional systems. Numerical examples are presented to confirm the obtained analytical results. Copyright © 2017 John Wiley & Sons, Ltd  

This paper investigates the robust stability analysis of fractional-order interval systems with multiple time delays, including retarded and neutral systems. A bound on the poles of fractional-order interval systems of retarded and neutral type is obtained. Then, the concept of the value set and zero exclusion principle is extended to these systems, and a necessary and sufficient condition is produced for checking the robust stability of them. The value set of the characteristic equation of the systems is obtained analytically and, based on it, an auxiliary function is introduced to check the zero exclusion principle. Finally, two numerical examples are given to illustrate the effectiveness... 

This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore... 

This paper presents a robust control scheme for an islanded microgrid in the presence of structured uncertainties. The microgrid consists of parallel connection of two Distributed Generation (DG) units and a passive load. The DG units are connected to the passive load by using the power electronics converters. The microgrid model is structurally uncertain due to the large perturbations in the load parameters. To deal with the uncertainties, a Linear Fractional Representation (LFR) of the parametrically uncertain system is obtained. To achieve robust performance, the μ-synthesis approach is applied to the derived LFR model to design a μ controller. The resultant controller is structurally...