Stability of active disturbance rejection control (ADRC) is analysed in the presence of unknown, nonlinear, and time-varying dynamics. In the framework of singular perturbations, the closed-loop ...error dynamics are semi-decoupled into a relatively slow subsystem (the feedback loop) and a relatively fast subsystem (the extended state observer), respectively. It is shown, analytically and geometrically, that there exists a unique exponential stable solution if the size of the initial observer error is sufficiently small, i.e. in the same order of the inverse of the observer bandwidth. The process of developing the uniformly asymptotic solution of the system reveals the condition on the stability of the ADRC and the relationship between the rate of change in the total disturbance and the size of the estimation error. The differentiability of the total disturbance is the only assumption made.
This paper concerns the persistence of kink and periodic waves to singularly perturbed two-component Drinfel’d-Sokolov-Wilson system. Geometric singular perturbation theory is first employed to ...reduce the high-dimensional system to the perturbed planar system. By perturbation analysis and Abelian integrals theory, we then are able to find the sufficient conditions about the wave speed to guarantee the existence of heteroclinic orbit and periodic orbits, which indicates the existence of kink and periodic waves. Furthermore, we also show that the limit wave speed
c
0
(
k
)
is increasing.
Under partial shading conditions, photovoltaic (PV) systems exhibit multiple peaks in their power-voltage (<inline-formula><tex-math notation="LaTeX">\mathbf{P-V}</tex-math></inline-formula>) ...characteristics. It is essential to extract maximum energy from the PV system. The global maximum power point tracking (GMPPT) algorithms presented in the literature, track the global peak using different methods. It is imperative to have minimal convergence time for GMPPT process. This paper proposes a novel algorithm to track the global peak using voltage and current perturbation. The new GMPPT algorithm operates in a current perturbation or voltage perturbation mode, based on the value of a control variable. In either mode, the proposed technique generates reference current or reference voltage, for navigating the operating point to GMPP location. The proposed algorithm is compared with two GMPPT algorithms, namely, modified maximum power trapezium (M-MPT) and high-performance GMPPT algorithms. The simulation studies are performed in MATLAB and is validated using a laboratory prototype, with dSPACE 1202 MicroLabBox controller for implementing GMPPT methods. Simulation and experimental results show that the new technique exhibits superior performance in terms of tracking time. Also, the energy efficiency is improved by 40% while using the proposed GMPPT algorithm for the irradiance profiles considered in this paper compared to the other two techniques.
This work is devoted to propose a distributed control hybrid algorithm for the primary and secondary control loops of AC-bus microgrids in islanded mode and to provide a large-signal stability. A ...primary control loop based on Hybrid Dynamical System (HDS) theory manages the DC/AC inverters considering structural non-linearities in the model (affine terms and hybrid dynamics of their signals) and implementation constraints (dwell-time) and ensures the robustness of the output voltage with respect to any model variation. Moreover, the secondary control loop is designed based on the droop concept, which ensures that SOCs, reactive and active powers converge to their reference values, and on Multi-Agent System (MAS) theory to get a consensus among the reactive power and the State Of Charge (SOC) of the batteries in discharging mode. Moreover, it guarantees reliability and robustness with respect to any disconnection. The tuned system parameters are chosen in order to fit a three-time scale model (a time scale for each control objective: power converter control, droop control and consensus controls), which allows providing a large-signal stability analysis for the complete hybrid system based on HDS, MAS and singular perturbation theory.
•Perturbed Painlevé-2 equation.•The bifurcation boundary separates solutions of two types.•The border has a spiral structure.•Both analytical and numerical results are given.
Solutions of the ...perturbed Painlevé-2 equation are typical for describing a dynamic bifurcation of soft loss of stability. The bifurcation boundary separates solutions of different types before bifurcation and before loss of stability. This border has a spiral structure. The equations of modulation of the bifurcation boundary depending on the perturbation are obtained. Both analytic and numeric results are given.
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