The presence of fast and slow modes in vehicle suspension systems based on a half car model, is utilized in the design of active suspension control using SINGULAR PERTURBATION theory. This strategy is based on the slow-fast control design. The suspension system performance is optimised with respect to ride comfort, road holding and suspension rattle space as expressed by the mean-square-values of body acceleration (including effects of heave and pitch), tire deflections and front and rear suspension travels. The method of design in this study is based on LQG feedback control combined with SINGULAR PERTURBATION theory, and at the end, a composite LQG controller has been proposed. Numerical simulations in the time domain evaluate the performance of the active suspension system. In spite of the simplified structure of the composite model, simulation results indicate that its performance is comparable to that of the full-state feedback design.

In this paper the robust control of multi variable SINGULAR PERTURBATION systems is studied. In order to robust the control of the system, only the additive modeling error is considered. Based on the above bounds of modeling error and the Nyquist criteria and in order to improve the performance of the system a relation is found to determine the robust controller. The SINGULAR PERTURBATION system is decomposed into fast and slow subsystems and the robust controller is designed for reduced order systems. It is explained how to find the new bound to stabilize the system and decrease the sensitivity.

This paper undertakes the synthesis of a logic-based switching H2/H¥ state-feedback controller for continuous-time LTI SINGULAR PERTURBATION systems. Our solution achieves a minimum bound on the H2 performance level, while also satisfying the H¥ performance requirements. The proposed hybrid control scheme is based on a fuzzy supervisor managing the combination of two controllers. A convex LMI-Based formulation of two fast and slow subsystem controllers leads to a structure which ensures a good performance in both transient and steady-state phases. The stability analysis leverages on the Lyapunov technique, inspired from the switching system theory, to prove that a system with the proposed controller remains globally stable in the face of changes in configuration (controller).

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.

In this paper, robust H¥ control of an experimental system is considered. This system consists of a pendulum free to rotate 360 degrees that is attached to a cart. The cart can move in one dimension. The linearized model of the system is used and transformed to a linear diagonal form. The system is separated into slow and fast subsystems. We consider the fast dynamics as disturbance and this is used to design a H¥controller for a system with lower order than the original system. It is shown via a theorem that there is a state feedback controller such that the closed loop system will be stable. Experimental results indicate that the performance is superior to the full-order LQR controller previously used. Material presented at 16th IFAC world congress.

The purpose of this study was to design a logic-based switching H2/H∞ state-feedback controller for continuous-time LTI SINGULAR PERTURBATION systems. To this end, a hybrid control scheme based on a Genetic Algorithm (GA) -based supervisor is proposed which manages the combination of two controllers. A convex LMI-Based formulation of both fast and slow subsystem controllers leads to a structure which ensures a good performance in both transient and steady state phases. The stability analysis uses Lyapunov techniques, inspired from switching system theory, to prove that a system with the proposed controller remains globally stable despite the configuration (controller) changing.

A class of two-parameter SINGULARly perturbed nonlinear second order ordinary differential equations is considered in this article. A fitted mesh method which is a combination of finite difference scheme and a Shishkin mesh is developed to solve the problems. The method is proved to be essentially first order parameter independent convergent. Numerical experiments support the established theoretical results.

A SINGULARly perturbed model is proposed for a system comprised of a PEM Fuel Cell (PEM-FC) with Natural Gas Hydrogen Reformer (NG-HR). This eighteenth order system is decomposed into slow and fast lower order subsystems using SINGULAR PERTURBATION techniques that provides tools for separation and order reduction. Then, three different types of controllers, namely an optimal full-order, a near-optimal composite controller based on the slow and the fast subsystems, and a near-optimal reduced-order controller based on the reduced-order model, are designed. The comparison of closed-loop responses of these three controllers shows that there are minimal degradations in the performance of the composite and the reduced order controllers.

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.