Phase portraits of pulse-width systems
Systems that are controlled with a pulse width modulator can be described as discrete-time dynamical systems. The choice of state (or phase variables) for modelling such systems will influence the analysis techniques that can be used. In this paper, the duration of the pulse in the current cycle is chosen as a phase variable. With this choice, phase portraits of the system give the sign and duration of the pulse in the current cycle depending on the preceeding cycle. Fixed points of the phase portrait characterize periodic modes. The modified point-mapping method is used to construct the phase portraits. The method can be applied to the analysis of systems with short memory. Also, an example of chaotic behavior in a pulse-width modulated system is given. Finally, phase portraits are used to analysis the stability of periodic modes. A number of examples illustration the ideas are given in the paper.
scientific article; zbMATH DE number 21848