Electrical and Electronic Engineering - Research Publications
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ItemExplicit Lyapunov functions for stability and performance characterizations of FOREs connected to an integrator(IEEE, 2006)In this paper we provide explicit Lyapunov functions that prove that a First Order Reset Element (FORE) in negative feedback interconnection with an integrator is exponentially stable for any, positive or negative, value of the pole of the FORE. The Lyapunov functions also allow to establish finite gain L2 stability from a disturbance input acting at the input of the plant to the plant output. L2 stability is established by giving a bound on the corresponding L2 gains. The framework used for the characterization of the system dynamics and for the stability and performance analysis corresponds to the ideas first proposed in (Nesic et al. IFAC 2005) and (Zaccarian et al. ACC 2005).
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ItemSet-point stabilization of SISO linear systems using First Order Reset Elements(IEEE, 2007-01-01)In this paper we further develop on a novel representation of first order reset elements (FORE) control systems for SISO plants. We study here the problem of guaranteeing asymptotic tracking of constant references for general plants, which may or may not contain an integrator (namely, an internal model of the constant reference signal). We propose a generalization of the FORE which allows to guarantee asymptotic tracking of constant references when the plant parameters are perfectly known. Robustness of the scheme follows from the L infin stability properties of the FORE control schemes. The proposed approach is successfully illustrated on a simulation example.
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ItemElectrical Stimulation of Neural Tissue Modeled as a Cellular Composite: Point Source Electrode in an Isotropic Tissue(IEEE, 2014-01-01)Standard volume conductor models of neural electrical stimulation assume that the electrical properties of the tissue are well described by a conductivity that is smooth and homogeneous at a microscopic scale. However, neural tissue is composed of tightly packed cells whose membranes have markedly different electrical properties to either the intra- or extracellular space. Consequently, the electrical properties of tissue are highly heterogeneous at the microscopic scale: a fact not accounted for in standard volume conductor models. Here we apply a recently developed framework for volume conductor models that accounts for the cellular composition of tissue. We consider the case of a point source electrode in tissue comprised of neural fibers crossing each other equally in all directions. We derive the tissue admittivity (that replaces the standard tissue conductivity) from single cell properties, and then calculate the extracellular potential. Our findings indicate that the cellular composition of tissue affects the spatiotemporal profile of the extracellular potential. In particular, the full solution asymptotically approaches a near-field limit close to the electrode and a far-field limit far from the electrode. The near-field and far-field approximations are solutions to standard volume conductor models, but differ from each other by nearly an order or magnitude. Consequently the full solution is expected to provide a more accurate estimate of electrical potentials over the full range of electrode-neurite separations.
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ItemAveraging for nonlinear systems on Riemannian manifolds(IEEE, 2013)This paper provides a derivation of the averaging methods for nonlinear time-varying dynamical systems defined on Riemannian manifolds. We extend the results on ℝ n to Riemannian manifolds by employing the language of differential geometry.
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ItemPWM hybrid control systems: averaging tools for analysis and design(IEEE, 2010)We consider averaging for a class of hybrid systems that are motivated by Pulse Width Modulated (PWM) implementation of hybrid control laws for general nonlinear plants. Rapid time variations in the flow map of a hybrid system generate solutions that are also solutions of a time-invariant average hybrid system that is slightly perturbed. Results relating solutions of the time-varying system to solutions of the average system ensue. In the absence of finite escape times for the average system, on compact time domains each solution of the time-varying system is close to a solution of the average system. In the presence of asymptotic stability for the average system, the time-varying system exhibits semi-global, practical asymptotic stability. These results rely on mild regularity properties for the average system. In particular, the average system is not required to exhibit unique solutions. Both periodic and non-periodic flow maps are considered.
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ItemLyapunov functions for L-2 and input-to-state stability in a class of quantized control systems(IEEE, 2011-01-01)ℒ 2 and input-to-state stability (ISS) properties of a class of linear quantized control systems are considered. The quantized control system differs slightly from the ones considered in the literature previously. A recently proposed hybrid modeling framework and corresponding Lyapunov analysis tools are used to calculate the finite gains of the closed loop system.
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ItemControl oriented modeling of turbocharged (TC) spark ignition (SI) engine(SAE International, 2009-01-01)
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ItemIdle speed control using linear time varying model predictive control and discrete time approximations(IEEE, 2010-01-01)This paper addresses the problem of idle speed control of hydrogen fueled internal combustion engine (H2ICE) using model predictive control (MPC) and sampled data control (SDC) theories. In the first step, results from SDC theory and a version of MPC are collectively employed to obtain a rigorously developed new generic control strategy. Here, a controller, based on a family of approximate discrete time models, is designed within a previously proposed framework to have guaranteed practical asymptotic stability of the exact (unknown) discrete time model. Controller design, accomplished using MPC theory, is facilitated by successive online linearizations of the nonlinear discrete time model at each sampling instant. In the second step, the technique is implemented in the idle speed control of hydrogen internal combustion engine (H2ICE). Various conditions under which this theory can be implemented are presented and their validity for idle speed control problem are discussed. Simulations are presented to illustrate the effectiveness of the control scheme.
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ItemModel Reduction of Automotive Engines using Perturbation Theory(IEEE, 2009-01-01)In this paper, a new constructive and versatile procedure to systematically reduce the order of control oriented engine models is presented. The technique is governed by the identification of time scale separation within the dynamics of various engine state variables and hence makes extensive use of the perturbation theory. On the basis of the dynamic characteristics and the geometry of engines, two methods for model reduction are proposed. Method 1 involves collective use of the regular and singular perturbation theories to eliminate temperature dynamics and approximate them with their quasi-steady state values, while Method 2 deals with the elimination of fast pressures. The result is a library of engine models which are associated with each other on a sound theoretical basis and simultaneously allow sufficient flexibility in terms of the reduced order modeling of a variety of engines. Different assumptions under which this model reduction is justified are presented and their implications are discussed.