Electrical and Electronic Engineering - Research Publications
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ItemOn Extremum Seeking in Bioprocesses with Multivalued Cost Functions(WILEY, 2009-05-01)Finding optimal operating modes for bioprocesses has been, for a long time, a relevant issue in bioengineering. The problem is of special interest when it implies the simultaneous optimization of competing objectives. In this paper, we address the problem of finding optimal steady states that achieve the best tradeoff between yield and productivity by using nonmodel-based extremum-seeking control with semiglobal practical stability and convergence properties. A special attention is paid to processes with multiple steady states and multivalued cost functions.
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ItemOn global extremum seeking in the presence of local extrema(PERGAMON-ELSEVIER SCIENCE LTD, 2009-01-01)We propose a global extremum seeking scheme which can seek the global optimal value in the presence of local extrema. It is shown that the proposed global extremum seeking scheme can converge to an arbitrarily small neighborhood of the global extremum from an arbitrarily large set of initial conditions if sufficient conditions are satisfied. A simple example illustrates the effectiveness of the proposed scheme.
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ItemDecentralized control design of interconnected chains of integrators: A case study(PERGAMON-ELSEVIER SCIENCE LTD, 2008-08-01)We develop a constructive decentralized control design procedure for a class of systems that may be loosely described as chained integrators which are dynamically coupled. The design method is inspired by nested saturation control ideas and formulated by applying the singular perturbation theory. We demonstrate that the proposed design provides a Lyapunov function for an associated closed loop system from which semi-global stability may be deduced. Using the proposed idea, we design a semi-globally stabilizing control law for a four degree of freedom spherical inverted pendulum.
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ItemOn the choice of dither in extremum seeking systems: A case study(PERGAMON-ELSEVIER SCIENCE LTD, 2008-05-01)We discuss how the choice of dither (excitation signal) affects the performance of extremum seeking using a benchmark situation: a static scalar map; and a simple scalar extremum seeking scheme. Our comparisons are based on the performance of the system with different dithers in terms of three performance indicators: the speed of convergence, domain of attraction and accuracy (i.e. the ultimate bound on trajectories). Our analysis explicitly shows how the dither shape affects each of these performance indicators. Our study suggests that the practitioners using extremum seeking control should consider the dither shape as an important design parameter. Computer simulations support our theoretical findings.
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ItemNon-local stabilization of a spherical inverted pendulum(TAYLOR & FRANCIS LTD, 2008-01-01)We design a non-linear stabilizing control law for a four degree of freedom spherical inverted pendulum. The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that it stabilizes the upright position starting from any position in the upper hemisphere with arbitrary velocity. We achieve this by first transforming the original system to an appropriate upper triangular form and then designing a controller which incorporates a high gain design with the method of non-linear forwarding. The control law is evaluated through computer simulations.
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ItemNon-linear stable inversion-based output tracking control for a spherical inverted pendulum(TAYLOR & FRANCIS LTD, 2008-01-01)We design an exact output tracking control law for a four degree of freedom spherical inverted pendulum based on the non-linear stable inversion tool proposed by Devasia et al. (1989). The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that the pendulum can be steered to track some smooth desired translational trajectories while keeping the pendulum tightly around the upright position. The design proceeds in three steps: 1. identification of the internal dynamics; 2. feedforward control design for achievable trajectories; 3. feedback design to stabilize the achievable trajectories. The computer simulations show that the proposed controller can deliver excellent tracking performance.
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ItemOn non-local stability properties of extrernum seeking control(PERGAMON-ELSEVIER SCIENCE LTD, 2006-06-01)In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.
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ItemMinimum phase properties for input nonaffine nonlinear systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-04-01)For input nonaffine nonlinear control systems, the minimum phase property of the system in general depends on the control law. Switching or discontinuous controllers may offer advantages in this context. In particular, there may not exist a continuous control law which would keep the output identically equal to zero and for which the zero output constrained dynamics are locally stable, whereas a discontinuous controller which achieves this exists. For single-input/single-output input nonaffine nonlinear systems we give sufficient conditions for existence and present a method for the design of discontinuous switching controllers which yield locally stable zero dynamics.
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ItemControllability of structured polynomial systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 1999-04-01)Two algorithms, based on the Grobner basis method, which facilitate the controllability analysis for a class of polynomial systems are presented. The authors combine these algorithms with some recent results on output dead-beat controllability in order to obtain sufficient, as well as necessary, conditions for complete and state dead-beat controllability for a surprisingly large class of polynomial systems. Our results are generically applicable to the class of polynomial systems in strict feedback form.
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ItemDiscussion on: 'Stabilisability and stability for explicit and implicit polynomial systems: A symbolic computation approach' by D. Nesic and I.M.Y. Mareels(SPRINGER-VERLAG LONDON LTD, 1999-01-01)