Francesco Vasca

Discrete-time maps for the analysis of bifurcations and chaos in DC/DC converters

The main aim of this paper is to present a systematic classification of discrete-time models proposed in the literature for the analysis of nonlinear phenomena in power electronic DC/DC converters. It is shown how these models can be applied to different operating conditions and used to analyze the converter dynamics under both voltage-mode and current-mode control. The derivation of simplified maps is discussed together with the Jacobian matrices of the maps that are used for the analysis of several bifurcations and chaotic behaviors. The three most common converter topologies, i.e., boost, buck and buck-boost, operating in continuous conduction mode, are considered. An extensive literature review is also reported.

Switchings, bifurcations, and chaos in DC/DC converters

Nonlinear phenomena in closed-loop pulsewidth modulated (PWM) DC/DC converters are analyzed. We introduce a new discrete time nonlinear map-the A-switching map-which is related to the asynchronous switchings, i.e., the changes of converter configuration occurring within the modulating period. This map is compared with the stroboscopic map, which is typically used in the study of DC/DC converters. Analytical conditions for the occurrence of periodic orbits and flip bifurcations are obtained. Moreover, necessary conditions for infinite local stretching on the phase space are derived. Finally, a possible explanation of the sudden jump to chaos exhibited by DC/DC converters is proposed. Analytical and numerical results can be applied to all fundamental DC/DC converter topologies. The case of the voltage-controlled buck converter is treated in detail.

Gearshift control for automated manual transmissions

A gearshift control strategy for modern automated manual transmissions (AMTs) with dry clutches is proposed. The controller is designed through a hierarchical approach by discriminating among five different AMT operating phases: engaged, slipping-opening, synchronization, go-to-slipping, and slipping-closing. The control schemes consist of decoupled and cascaded feedback loops based on measurements of engine speed, clutch speed, and throwout bearing position, and on estimation of the transmitted torque. Models of driveline, dry clutch, and controlled actuator are estimated on experimental data of a medium size gasoline car and used to check through simulations the effectiveness of the proposed controller.

Self-oscillations and sliding in relay feedback systems : Symmetry and bifurcations

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.

Optimal tracking for automotive dry clutch engagement

Abstract Based on a state space dynamic model of a typical automotive driveline, a new control technique for the dry clutch engagement process is proposed. The feedback controller is designed following an optimal control approach by using the crankshaft speed and the clutch disk speed as state variables: a tracking problem is formulated and solved by using the engine torque and the clutch torque as control variables. The controller guarantees fast engagement, minimum slipping losses and comfortable lock-up. The critical standing start operating conditions are considered. Numerical results show the good performance obtained with the proposed controller.

Control of DC-DC converters with linear optimal feedback and nonlinear feedforward

This paper describes a new control design procedure for PWM DC-DC converters. The control action has two components: a linear feedback, designed via the LQ approach, and a nonlinear feedforward. The proposed control scheme guarantees excellent regulation of the output voltage, even in the presence of large variations of the input reference signal, as pointed out by numerous simulations carried out on different converter topologies. Good performances are also achievable when a suitably designed estimator is inserted into the control loop to reconstruct internal variables and input voltage disturbances from output voltage measurements. >

Averaging of nonsmooth systems using dither

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.

A New Perspective for Modeling Power Electronics Converters: Complementarity Framework

The switching behavior of power converters with ldquoidealrdquo 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 ldquocompleterdquo 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.

Torque Transmissibility Assessment for Automotive Dry-Clutch Engagement

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.

Smooth engagement for automotive dry clutch

Two piecewise linear time-invariant models of the automotive driveline are presented and their hybrid structure due to the presence of the dry clutch is highlighted. Based on a second order model, a slip control technique for the dry clutch engagement process is proposed. The feedback controller is designed by using the crankshaft speed and the clutch disk speed as measured variables. The controller guarantees comfortable lock-up and avoids the engine stall by decoupling the control of engine speed and slip speed. The regulation of the slip acceleration at the lock-up is shown to reduce the undesired driveline oscillations. The critical standing start operating conditions are considered and numerical results show the good performance of the proposed controller.