Electrical and Electronic Engineering - Research Publications
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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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ItemFurther results on robustness of linear control systems with quantized feedback(IEEE, 2007-01-01)This paper extends results from [5], where input-to-state stabilization (ISS) of linear systems with quantized feedback was considered. In this paper, we show that using the scheme proposed in [5] it is also possible to achieve (nonlinear gain) l2 stabilization for linear systems.
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ItemPath-following in the presence of unstable zero dynamics: An averaging solution for nonlinear systems(IEEE, 2007-01-01)We consider a path-following problem in which the goal is to ensure that the error between the output and the geometric path asymptotically is less than a prespecifled constant, while guaranteeing output's forward motion along the path and boundedness of all states. For a class of nonlinear systems in which the only input into unstable zero dynamics is system's output and paths satisfying certain geometric condition a solution to this problem was given in [12]. For the same class of systems but under more stringent conditions on the path geometry here we develop a simpler solution to the above problem. We assume here that the path is periodic which allows us to exploit averaging tools to construct an open-loop timeperiodic control law for the path parameter instead of a hybrid control law developed in [12].
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ItemA note on the control of a spherical inverted pendulum(IFAC, 2007-01-01)We carry out extensive numerical simulations of a spherical inverted pendulum with various controllers to verify our theoretical developments. The simulations are useful in quantitatively understanding the operation of the system with different controllers and checking that the theoretical results are consistent with the numerical results. Using the numerical simulations, we also discuss in some detail various important aspects of the performance of the closed loop systems in order to compare the controllers.
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ItemA note on robustness of linear spatially distributed parameter systems and their numerical approximations(IEEE, 2007-01-01)In this paper, we investigate a relationship between robust stability properties of linear spatially distributed parameter systems (LSDPS) with disturbances and robust stability properties of their numerical approximations. Since it is hard to analytically find solutions of a partial differential equation, numerical methods, such as finite-difference methods, are always used to approximately find the solutions. Moreover, it is crucial that the numerical method reproduces (approximately) the behavior of the actual system model. For instance, if the actual system is stable in some sense, then the numerical method should possess (approximately) the same stability property and vice versa. Our results show that input-to-state exponential stability (ISES) properties of the numerical approximation with respect to disturbances are equivalent to practical ISES of the LSDPS provided that: (i) the finite-difference approximation is consistent with the model; (ii) an appropriate uniform boundedness condition holds for the numerical method. Our results can be regarded as an extension of the celebrated Lax-Richtmyer theorem to systems with disturbances, as well as its application to analysis of ISES. This question is typically not considered in the numerical analysis literature and yet it is very well noticed by in control applications.
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ItemA unified approach to controller design for systems with quantization and time scheduling(IEEE, 2007-01-01)We generalize and unify a range of recent results in quantized control systems (QCS) and networked control systems (NCS) literature and provide a unified framework for controller design for control systems with quantization and time scheduling via an emulation-like approach. A crucial step in our approach is finding an appropriate Lyapunov function for the quantization/time-scheduling protocol which verifies its uniform global exponential stability (UGES). We construct Lyapunov functions for several representative protocols that are commonly found in the literature, as well as some new protocols not considered previously.
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ItemObserver design for linear networked control systems using matrix inequalities(IEEE, 2007-01-01)We design an observer-protocol pair to asymptotically reconstruct the states of a linear time-invariant (LTI) plant under network-induced communication constraints. We parameterize a class of observers and dynamic protocols, and for a given network transmission interval we derive sufficient conditions in terms of matrix inequalities for existence of an observer-protocol pair in the considered class that asymptotically reconstructs the plant states. The derived matrix inequalities are always feasible for sufficiently small transmission intervals if the underlying plant is observable from the measured output.
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ItemFurther results on stability of networked control systems: a Lyapunov approach(IEEE, 2007-01-01)Simple Lyapunov proofs are given for an improved (relative to previous results that have appeared in the literature) bound on the maximum allowable transfer interval to guarantee global asymptotic or exponential stability in networked control systems and also for semiglobal practical asymptotic stability with respect to the length of the maximum allowable transfer interval. We apply our results to emulation of nonlinear controllers in sampled-data systems.