Zero-Crossing Location and Detection Algorithms For Hybrid System Simulation

Fu, Zhang; Yeddanapudi, Murali; Mosterman, Pieter J.

doi:10.3182/20080706-5-kr-1001.01346

Cited by 59 publications

(57 citation statements)

References 9 publications

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“…Signal processing and communication systems have been developed over the years which involve phase based detection of signals. Mostly, such systems interpreted phase as a numerical value for a particular duration of the signal [12]. Digital Phase Locked Loop (DPLL) integrates the operation of a phase detector, low pass filter and voltage controlled oscillator to provide a feedback system for signal regeneration.…”

Section: Model For Dpll Based Phase Recovery Systemmentioning

confidence: 99%

Zero crossing DPLL based phase recovery system and its application in wireless communication

Bhattacharyya

Ahmed

Purkayastha

et al. 2015

2015 International Conference on Computer, Communication and Control (IC4)

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Proper tracking of signals at any intermediate stage of a processing system or at the receiver of modern day communication systems has been given much importance over the last two decades. Proper tracking of the signal envelope is evidently very necessary; for communication systems, to recover the message signal that was transmitted with minimum error whereas for signal processing applications, to regenerate the signal in its most precise form by removing unwanted noise, harmonics, undesired frequency components etc. To develop a system which would be able to track a wide range of signals accurately, a generalized parameter should be available to us which would define all signals accurately. The 'instantaneous phase' information of the signal is kept intact and thus it is a very vital parameter to represent any signal. Thus, if the instantaneous phase of the signal is properly tracked, the signal can be easily regenerated. In recent times, DPLL algorithms have emerged as an efficient technique for phase recovery and considering this aspect, a Zero Crossing Algorithm based DPLL system for phase recovery is proposed.

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Section: Model For Dpll Based Phase Recovery Systemmentioning

confidence: 99%

Zero crossing DPLL based phase recovery system and its application in wireless communication

Bhattacharyya

Ahmed

Purkayastha

et al. 2015

2015 International Conference on Computer, Communication and Control (IC4)

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“…In this case the level is 0, so we refer to it as ZCD. A zero-crossing function g(x(t), x(t + h)), often called a guard function, determines when the level crossing occurs [7] by evaluating to true when sign(x(t)) 6 = sign(x(t + h)). When the function g(x(t), x(t + h)) evaluates to true, a discrete event is generated at t + h. An example developed in Ptolemy II is shown in Figure 2a, the output signals are depicted in Figures 2b and 2c.…”

Section: Combining Continuous Time With Discrete Eventsmentioning

confidence: 99%

“…Techniques to revise the step size in order to more accurately identify the time at which a zero crossing occurred are usually based on bisection search algorithms described by Cellier [4] and Zhang [7]. At each iteration of a bisection search, the output update functions of all components must be evaluated.…”

Section: Combining Continuous Time With Discrete Eventsmentioning

confidence: 99%

“…How h is computed is outside of the scope of our discussion, and its behavior is left unspecified. However, the interested reader can find a detailed description of algorithms for the implementation of f () in [7] and [4]. To finalize this iteration of step revision, the master backtracks the simulation time to t := t h p and saves the computed step size h p := h (with h := f (h p )) in case that also in the next iteration some FMU yields an error flag and a further refinement of the step size is needed.…”

Section: C)mentioning

confidence: 99%

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Step revision in hybrid Co-simulation with FMI

Cremona

Lohstroh

Broman

et al. 2016

2016 ACM/IEEE International Conference on Formal Methods and Models for System Design (MEMOCODE)

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This paper presents a master algorithm for co-simulation of hybrid systems using the Functional Mock-up Interface (FMI) standard. Our algorithm introduces step revision to achieve an accurate and precise handling of mixtures of continuous-time and discrete-event signals, particularly in the situation where components are unable to accurately extrapolate their input. Step revision provides an efficient means to respect the error bounds of numerical approximation algorithms that operate inside co-simulated FMUs. We first explain the most fundamental issues associated with hybrid co-simulation and analyze them in the framework of FMI. We demonstrate the necessity for step revision to address some of these issues and formally describe a master algorithm that supports it. Finally, we present experimental results obtained through our reference implementation that is part of our publicly available open-source toolchain called FIDE

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“…Generally, the discontinuous or PWL version of the Lorenz system presents two discontinuity surfaces, and the problem of nonuniqueness and even non-existence of solutions has to be faced when the trajectories either cross or slide on the discontinuity surfaces. Furthermore, due to the coexistence of several discontinuity surfaces, the problem of specification of the transitions between the system operation modes is critical, and special care has to be taken in the numerical integration [13], [14], [15]. The use of a hybrid automaton to describe the system is presented here as a solution to this problem.…”

Section: Motivationmentioning

confidence: 99%

Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system

Navarro-López

Barajas-Ramírez

2010

2010 11th International Workshop on Variable Structure Systems (VSS)

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Abstract-We propose a computational-oriented perspective within the study of discontinuous chaotic systems, and provide insights into the modelling, control and simulation of chaotic systems with switching dynamics. In particular, the Lorenz system in its piecewise-linear version is studied. This system is reinterpreted within the hybrid-automaton framework, and what is referred to as the Lorenz hybrid automaton is established. Furthermore, a discontinuous control which eliminates the chaotic behaviour and steers the trajectories to a desired equilibrium is proposed. An integral characteristic of the modelling framework is that the controlled system, exhibiting three discontinuity surfaces, is reduced to the composition of several Lorenz hybrid automata. The approach proposed here is especially useful in order to specify the transitions between the different system operation modes, which becomes a crucial problem due to the existence of multiple switching surfaces. I. MOTIVATIONWhat is the best model to describe variable structure systems with multiple switching elements and exhibiting several types of complex behaviours? How to specify all their transitions in a deterministic way to facilitate the simulation? Every mathematical model is an approximation of the real world, and is full of limitations. However, some models are better than others at describing the evolution of certain physical and engineering systems. The hybrid systems framework, in particular, the computational hybridautomaton one is very adequate for modelling and controlling complex systemsThis paper is devoted to the specification and the computational abstraction of a particular discontinuous system with chaotic behaviour: the piecewise-linear (PWL) Lorenz system. The computational framework used is that of hybrid automata [2] faced when the trajectories either cross or slide on the discontinuity surfaces. Furthermore, due to the coexistence of several discontinuity surfaces, the problem of specification of the transitions between the system operation modes is critical, and special care has to be taken in the numerical integration [13], [14], [15]. The use of a hybrid automaton to describe the system is presented here as a solution to this problem. This paper is inspired by Navarro's previous results related to the modelling and discrete abstraction of discontinuous dynamical systems (DDSs) under the hybrid-automaton framework [4], [5], [6].The Lorenz hybrid automaton with 6 discrete locations is given. To prove the efficacy of the hybrid-automaton framework, a second hybrid automaton with 18 locations is proposed. This second automaton corresponds to the controlled PWL Lorenz system with three discontinuity surfaces, which is obtained by considering a sliding-modebased control. The control strategy is based on inserting a discontinuity surface on which the system presents the desired behaviour and forces the system trajectories to slide on this surface. The controlled Lorenz hybrid automaton, by following the computer science divide-and-conq...

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Zero-Crossing Location and Detection Algorithms For Hybrid System Simulation

Cited by 59 publications

References 9 publications

Zero crossing DPLL based phase recovery system and its application in wireless communication

Zero crossing DPLL based phase recovery system and its application in wireless communication

Step revision in hybrid Co-simulation with FMI

Bringing order to chaos: Hybrid modelling of a discontinuous chaotic system

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