108,263 research outputs found
Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems
No full textFeedback control of piecewise smooth discrete-time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasistatically varied. The goal of the control effort in this work is to modify the bifurcation so that the bifurcated steady state is locally attracting and locally unique. To achieve this, Lyapunov-based techniques are used. A sufficient condition for nonbifurcation with persistent stability in piecewise smooth maps of dimension that depend on a parameter is derived. The derived condition is in terms of linear matrix inequalities. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce desirable behavior
Nonlinear Instabilities in TCP-RED
No full textThis work introduces a discrete time model for a simplified TCP network with RED control. It is argued that by sampling the state space at certain instants, the dynamics of the system can be described explicitly as a discrete time feedback control system. This system is used to analyze the operating point of TCP-RED and its stability with respect to various controller and system parameters. With the help of bifurcation diagrams, it is numerically shown that non-trivial (not due to the discontinuity in the system or the control law) instabilities in the system are possible due to the presence of a strong nonlinearity in the characteristics of TCP throughput of a sender as a function of drop probability at the gateway. Some of the bifurcations observed in the system are the period-doubling sequence and border collisions leading to a change in the system periodicity and chaos. Analytical techniques are provided to help in the understanding of this kind of anomalous behavior. An explicit stability condition in terms of different parameters is given
Local Bifurcations in PWM DC-DC Converters
No full textA general sampled-data model of PWM DC-DC converters is employed tostudy types of loss of stability of the nominal (periodic)operating condition andtheir connection with local bifurcations.In this work, the nominal solution's periodic natureis accounted for via the sampled-data model.This results in moreaccurate predictions of instability and bifurcation than can be obtained using the averaging approach.The local bifurcations of the nominal operating conditionstudied here are period-doublingbifurcation, saddle-node bifurcation, and Neimark bifurcation.Examples of bifurcations associated with instabilities in PWM DC-DC convertersare given.In particular, input filter instability is shown to be closely related tothe Neimark bifurcation
Sampled-Data Modeling and Analysis of Closed-Loop PWM DC-DC Converters
No full textSampled-data analysis of converters has been a topic of investigationfor the past two decades. However, this powerful tool is not widelyused in control loop design or in closed-loop performance validation.Instead, averaged models are typically used for control loopdesign, while detailed simulations are used for validatingclosed-loop performance. This paper makes several contributions tothe sampled-data modeling and analysis of closed-loop PWM DC-DC converters,with the aim of increasing appreciation and use of the method. General models are presented in a unified and simple manner, while removingsimplifying approximations present in previous work. These models applyboth for current mode control and voltage mode control.The general models are nonlinear. They are used toobtain {it analytical} linearized models, which are in turn employedto obtain local stability results. Detailed examplesillustrate the modeling and analysis in the paper,and point to situations in which the sampled-data approachgives results superior to alternate methods.For instance, it is shownthat the sampled-data approach will reliablypredict the (local) stability of aconverter for which averaging or simulation predicts instability
Sampled-Data Modeling and Analysis of the Power Stage of PWM DC-DC Converters
No full textThe power stage of the PWM DC-DC converter is modeledand analyzed using the sampled-data approach.The work addressescontinuous and discontinuous conduction mode under voltage mode control,and continuous conduction mode under current mode control.For each configuration, nonlinear and linearized sampled-data models andcontrol-to-output transfer function are derived. Using this approach, both current mode control and discontinuous conduction modecan be handled systematically in a unified framework,making the modeling for these cases simpler than with the use of averaging.The results of this paper are similar to the results of Tymerski,but they are presented in a simpler manner tailored to facilitate immediate application to specific circuits. It is shown howsampling the output at certain instants improves the obtained phase response.Frequency responses obtained from the sampled-data model aremore accurate than those obtained from various averaged models. In addition, a new ("lifted")continuous-time switching frequency-dependent model of the power stage isderived from the sampled-data model. Detailed examples illustrate themodeling tools presented here, and also provide a means of comparingresults obtained from the sampled-data approach with those obtainedfrom averaging
Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems
No full textFeedback controls that stabilize border collision bifurcations are designed for piecewise smooth systems undergoing border collision bifurcations. The paper begins with a summary of the main results on border collision bifurcations, and proceeds to a study of stabilization of these bifurcations for one-dimensional systems using both static and dynamic feedback. The feedback can be applied on one side of the border, or on both sides. To achieve robustness to uncertainty in the border itself, a simultaneous stabilization problem is stated and solved. In this problem, the same control is applied on both sides of the border. Dynamic feedback employing washout filters to maintain fixed points is shown to lead to stabilizability for a greater range of systems than static feedback. The results are obtained with a focus on systems in normal form
Border Collision Bifurcation Control of Cardiac Alternans
No full textThe quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period doubling border collision bifurcation. No smooth period doubling bifurcation occurs in the parameter region of interest. Next, recent results of the authors on feedback control of border collision bifurcation are applied to the model, resulting in control laws that quench the bifurcation and hence result in alternan suppression
Feedback Control of Border Collision Bifurcations in Two-Dimensional Discrete-Time Systems
No full textThe feedback control of border collision bifurcations is consideredfor two-dimensional discrete-time systems. These are bifurcations that can occur when a fixed point of a piecewise smooth system crosses the border between two regions of smooth operation. The goal of the control effort is to modify the bifurcation so that the bifurcated steady state is locally unique and locally attracting. In this way, the system's local behavior is ensured to remain stable and close to the original operating condition. This is in the same spirit as local bifurcation control results for smooth systems, although the presence of a border complicates the bifurcation picture considerably. Indeed, a full classification of border collision bifurcations isn't available, so this paper focuses on the more desirable (from a dynamical behavior viewpoint) cases for which the theory is complete. The needed results from the analysis of border collision bifurcations are succinctly summarized. The control design is found to lead to systems of linear inequalities. Any feedback gains that satisfy these inequalities is then guaranteed to solve the bifurcation control problem. The results are applied to an example to illustrate the ideas
Instability Monitoring and Control of Power Systems
No full textToday's electric power systems are often subject to stress by heavy loading conditions, resulting in operation with a small margin of stability. This has led to research on estimating the distance to instability. Most of these research efforts are solely model-based. In this work, a signal-based approach for real-time detection of impending instability is considered. The main idea pursued here involves using a small additive white Gaussian noise as a probe signal and monitoring the spectral density of one or more measured states for certain signatures of impending instability. Input-to-state participation factors are introduced as a tool to aid in selection of locations for probe inputs and outputs to be monitored. Since these participation factors are model-based, the chapter combines signal-based and model-based ideas toward achieving a robust methodology for instability monitoring
Investigation of microstructure, microhardness and wear behavior of multicomponent Fe-based hardfacing layers applied on carbon steel by GTAW process
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