No abstract

This paper is concerned with the bifurcation analysis of linear dynamical systems with relay feedback. The emphasis is on the bifurcations of the system periodic solutions and their symmetry. It is shown that, despite what has been conjectured in the literature, a symmetric and unforced relay feedback system can exhibit asymmetric periodic solutions. Moreover, the occurrence of periodic solutions characterized by one or more sections lying within the system discontinuity set is outlined. The mechanisms underlying their formation are carefully studied and shown to be due to an interesting, novel class of local bifurcations.

No abstract

No abstract

Abstract-Three-phase inverters subject to droop control are widely used in islanded microgrids to interface distributed energy resources to the network and to properly share the loads among different units. In this paper, a mathematical model for islanded microgrids with linear loads and inverters under frequency and voltage droop control is proposed. The model is constructed by introducing a suitable state space transformation which allows to write the closed loop model in an explicit state space form. Then, the singular perturbations technique is used to obtain reduced order models which reproduce the stability properties of the original closed loop model. The analysis shows that the currents dynamics influence the stability of the microgrid particularly for high values of the frequency droop control parameters. It is also shown that a further reduction of the model order leads to the typical oscillator model which is not able to predict the possible instability of the droop controlled system. Numerical and experimental results demonstrate the validity of the proposed models.

It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency 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. ᭧

Dry clutches are widely used in conventional and innovative automotive drivelines and represent a key element for automated manual transmissions (AMTs). In practical applications, it is fundamental to model the clutch behavior through its torque transmissibility characteristic, i.e., the relationship between the throwout bearing position (or the pressure applied by the clutch actuator) and the torque transmitted through the clutch during the engagement phase. In this paper, a new model for the torque transmissibility of dry clutches is proposed. It is analyzed how the transmissibility characteristic depends on: friction pads geometry, cushion spring compression, cushion spring load, and slip-speed-dependent friction. Corresponding functions are suitably composed determining the torque transmissibility expression. An experimental procedure for tuning the characteristic parameters is presented. The clutch-torque transmissibility model is tested on a detailed cosimulation model with a typical AMT controller

The switching behavior of power converters with "ideal" electronic devices (EDs) makes it difficult to define a switched model that describes the dynamics of the converter in all possible operating conditions, i.e., a "complete" model. Indeed, simplifying assumptions on the sequences of modes are usually adopted, also in order to obtain averaged models and discrete-time maps. In this paper, we show how the complementarity framework can be used to represent complete switched models of a wide class of power converters, with EDs having characteristics represented by piecewise-affine (even complicated) relations. The model equations can be written in an easy and compact way without the enumeration of all converter modes, eventually formalizing the procedure to an algorithm. The complementarity model can be used to perform transient simulations and time-domain analysis. Mathematical tools coming from nonlinear programming allow to simulate numerically the transient behavior of even complex power converters. Also rigorous time-domain analysis is possible without excluding pathological situations like, for instance, inconsistent initial conditions and simultaneous switchings. Basic converter topologies are used as examples to show the construction procedure for the complementarity models and their usefulness for simulating the dynamic evolution also for nontrivial operating conditions.