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Verriest, Vibrational Control of Nonlinear Time Lag Systems with Bounded Delay: Averaging Theory
 Stabilizability, and Transient Behavior, IEEE Trans. Automat. Contr
, 1994
"... AbstractThis paper develops the theory of vibrational control Of "lhJear time Systems with arbitrarily large but bounded delay. theory for fast Oscillating, differential delay equations is presented and then applied to vibrational control. conditions B1p given which ensure the e*ne ot parametr ..."
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Cited by 9 (0 self)
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AbstractThis paper develops the theory of vibrational control Of "lhJear time Systems with arbitrarily large but bounded delay. theory for fast Oscillating, differential delay equations is presented and then applied to vibrational control. conditions B1p given which ensure the e*ne ot parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also discussed. Illustrative examples are given which Show 1) the fbfiv O f t h e theory to hP0t aPPfiatiOm and 2, the differences in the presented and the eKisw known theory for vibrational control of ordinary differential equations. the vibrations depended only on time (and not on the value of the state), there no longer was a need to take measurements of concentration, thus reducing the cost of the reaction even more. For similar reasons, the vibrational control described by [61 has many benefits. A number of practical, important systems, however, are best described by including time delays in their states. In particular, if the exothermic reaction vibrationally controlled in [5] includes a recycle stream, as in [7], the model must I.
Dither for smoothing relay feedback systems
 IEEE Trans. on Circuits and SystemsI: Fundamental Theory and Applications
, 2003
"... Dither signals are commonly used for compensating nonlinearities in feedback systems in electronics and mechanics. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumpt ..."
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Cited by 7 (5 self)
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Dither signals are commonly used for compensating nonlinearities in feedback systems in electronics and mechanics. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. The aim of this thesis is to provide some ideas and tools on how to analyse and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system. Stability results based on Popovlike and ZamesFalb criteria jointly with some Linear Matrix Inequalities are proposed. Moreover it is argued that in dithered relay feedback systems the shape of dither signals is relevant for stabilization. Some peculiar behaviours of relay feedback systems dithered with a particular class of dither signals are presented. When the dither signal is a square wave, the dithered system can exhibit an asymmetric periodic orbit, though the smoothed system is asymptotically stable. We even show an example in which, by using a trapezoidal dither signal, both systems have a stable oscillation, but the period time for the oscillation of the smoothed system is different from the one of the dithered system. Finally some engineering applications are presented in order to show the usefulness of techniques and results discussed in the thesis. Thesis Supervisor: Franco Garofalo, Professor of Automatic Control Thesis Supervisor: Francesco Vasca, Associate Professor of Automatic Control Acknowledgements Yes, ...it's fina...
Averaging of nonsmooth systems using dither
, 2006
"... It was shown by Zames and Shneydor and later by Mossaheb that a highfrequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems ..."
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Cited by 6 (2 self)
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It was shown by Zames and Shneydor and later by Mossaheb that a highfrequency dither signal of a quite arbitrary shape can be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period.
An Overview on Averaging for Pulsemodulated Switched Systems
, 2011
"... Averaging of fast switching systems is an effective technique used in many engineering applications. Practical stability and control design for a nonsmooth switched system can be inferred by analyzing the smooth averaged system. In this paper we overview the few formal approaches proposed in the li ..."
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Cited by 6 (4 self)
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Averaging of fast switching systems is an effective technique used in many engineering applications. Practical stability and control design for a nonsmooth switched system can be inferred by analyzing the smooth averaged system. In this paper we overview the few formal approaches proposed in the literature to deal with the averaging of nonsmooth systems. The dithering, the phasor dynamics and the hybrid framework techniques are recast and compared by considering pulsemodulated switched linear systems as the common modeling platform.
Limits of Achievable Performance of Controlled Combustion Processes
"... Abstract—This paper presents a fundamental limitationsbased analysis to quantify limits on obtainable performance for active control of combustion (thermoacoustic) instability. Experimental data from combustor rigs and physicsbased models are used to motivate the relevance of both the linear and n ..."
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Cited by 3 (1 self)
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Abstract—This paper presents a fundamental limitationsbased analysis to quantify limits on obtainable performance for active control of combustion (thermoacoustic) instability. Experimental data from combustor rigs and physicsbased models are used to motivate the relevance of both the linear and nonlinear thermoacoustic models. For linear models, Bode integralbased analysis is used to explain peaksplitting observed in experiments. It is shown that large delay in the feedback loop and limited actuator bandwidth are the primary factors that limits the effectiveness of the active control. Explicit bounds on obtainable performance in the presence of delay, unstable dynamics, and limited controller bandwidth are obtained. A multiinput describing function framework is proposed to extend this analysis to the study of nonlinear models that also incorporate the effects of noise. The fundamental limitations are interpreted for a modified sensitivity function defined with respect to noise balance. The framework is applied to the analysis of linear thermoacoustic models with nonlinear ONOFF actuators and Gaussian noise. The results of the analysis are wellsupported by experiments and model simulations. In particular, we reproduce in model simulations and explain analytically the peaksplitting phenomenon observed in experiments. Index Terms—Active control, combustion instability, describing function, fundamental limitation, nonlinear analysis. Sensitivity function. Performance bandwidth. Control bandwidth. Lower frequency for control bandwidth. Higher frequency for control bandwidth. Relative degree of openloop transfer function. Required attenuation level for sensitivity function over performance bandwidth. Powerspectral density function of the input disturbance. Powerspectral density function of the combustor pressure.
On the Averaging of a Class of Hybrid Systems
, 2004
"... Modeling abstraction and timescale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a ..."
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Cited by 3 (2 self)
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Modeling abstraction and timescale separation in the design of complex systems often leads to hybrid dynamics. Discontinuities in the continuous evolution of a hybrid system may however create difficulties in the formal analysis, as well as in numerical simulation and verification. Here we study a class of hybrid systems that are excited by highfrequency external signals. These systems arise in the modeling of switched power converters, mechanical systems with friction and quantized systems. For a quite general class of excitation signals, an averaging result is shown stating that the hybrid system can be approximated by a Lipschitzcontinuous system. The approximation is in the order of the maximal repetition interval of the excitation signal.
CONTROL OF CHAOS: SURVEY 1997–2000
, 2002
"... A brief survey of the emerging field termed ”Control of Chaos” is given based on about 200 publications in peer reviewed journals. Three major branches of research are discussed in detail: ”nonfeedback control” (based on periodic excitation of the system); ”OGY method” (based on linearization of Poi ..."
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Cited by 2 (1 self)
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A brief survey of the emerging field termed ”Control of Chaos” is given based on about 200 publications in peer reviewed journals. Three major branches of research are discussed in detail: ”nonfeedback control” (based on periodic excitation of the system); ”OGY method” (based on linearization of Poincaré map) and ”Pyragas method” (based on a timedelay feedback). Some unsolved problems concerning the justification of chaos control methods are presented.
Analysis of dither in relay feedback systems
 in Proc. of IEEE Conference on Decision and Control, Las Vegas
, 2002
"... Dither signals provide an effective way of compensating for nonlinearities in control systems. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinear ..."
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Cited by 2 (2 self)
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Dither signals provide an effective way of compensating for nonlinearities in control systems. The seminal works by Zames and Shneydor and more recently by Mossaheb present rigorous tools for systematic design of dithered systems. Their results rely however on a Lipschitz assumption on the nonlinearity and thus do not cover important applications with discontinuities. This paper presents initial results on how to analyze and design dither in nonsmooth systems. In particular, it is shown that a dithered relay feedback system can be approximated by a smoothed system obtained through an averaging approach. Guidelines are given for tuning the amplitude and the period time of the dither signal, in order to stabilize the nonsmooth system. 1
PRACTICAL STABILITY AND LIMIT CYCLES OF DITHERED RELAY FEEDBACK SYSTEMS
"... relay feedback systems. ..."
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