M. Asadi, H. Toossian Shandiz,
Volume 12, Issue 2 (6-2016)
Abstract
This paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer results have been proposed for pure-feedback systems because the cascade and non-affine properties of pure-feedback systems make it difficult to find the explicit virtual controls and actual control. Therefore, by employing the singular perturbation theory in back-stepping control procedure, the virtual/actual control inputs are derived from the solutions of a series of fast dynamical equations which can avoid the “explosion of complexity’’ inherently existing in the conventional back-stepping design. The stability of the resulting closed-loop system is proved by Tikhonov’s theorem in the singular perturbation theory. Finally, the detailed simulation results are provided to demonstrate the effectiveness of the proposed controller, which can overcome the non-affine property of pure-feedback systems with lower complexity and fewer design parameters.
Y. McHaouar, A. Abouloifa, I. Lachkar, H. Katir, F. Giri, A. El Aroudi, A. Elallali, C. Taghzaoui,
Volume 18, Issue 1 (3-2022)
Abstract
In this paper, the problem of controlling PWM single-phase AC/DC converters is addressed. The control objectives are twofold: (i) regulating the output voltage to a selected reference value, and (ii) ensuring a unitary power factor by forcing the grid current to be in phase with the grid voltage. To achieve these objectives, the singular perturbation technique is used to prove that the power factor correction can be done in the open-loop system with respect to certain conditions that are not likely to take place in reality. It is also applied to fulfill the control objectives in the closed-loop through a cascade nonlinear controller based on the three-time scale singular perturbation theory. Additionally, this study develops a rigorous and complete formal stability analysis, based on multi-time-scale singular perturbation and averaging theory, to examine the performance of the proposed controller. The theoretical results have been validated by numerical simulation in MATLAB/Simulink/SimPowerSystems environment.
