Carles Batlle

Stabilization of periodic orbits of the buck converter by time‐delayed feedback

Time-delay autosynchronization (TDAS) can be used to stabilize unstable periodic orbits in dynamic systems. The technique involves continuous feedback of signals delayed by the orbits period so that the feedback signal vanishes on the target orbit and hence the latter is a solution of the original dynamic system. Furthermore, this control method only requires the knowledge of the period of the unstable orbit. The feedback gain needed to achieve stabilization varies with the bifurcation parameter(s) of the system, resulting in a domain of control, the computation of which requires, in general, detailed information about the target orbit(s). In this paper we compute the domain of control of the unstable periodic orbits of the PWM controlled buck converter for a couple of TDAS schemes. For both schemes we get an analytical expression for the closed curve whose index determines the stability, and this index is then numerically computed. We run several simulations of the controlled systems and discuss the results. The main result is that TDAS greatly increases the range of values of the input voltage where the PWM control yields a periodic orbit with a small rippling. Copyright

Power Flow Control of a Doubly-Fed Induction Machine Coupled to a Flywheel*

We consider a doubly-fed induction machine-controlled through the rotor voltage and connected to a variable local load-that acts as an energy-switching device between a local prime mover (a flywheel) and the electrical power network. The control objective is to optimally regulate the power flow, and this is achieved by commuting between two different steady-state regimes. The marginal stability of the zero dynamics of the system hampers its control via feedback linearization. Instead, we apply the energy-based interconnection and damping assignment passivity-based control technique, which does not require stable invertibility. It is shown that the partial differential equation that appears in this method can be obviated fixing the desired closed-loop total energy and adding new terms to the interconnection structure. Furthermore, to obtain a globally defined control law we introduce a state-dependent damping term that has the nice interpretation of effectively decoupling the electrical and mechanical parts of the system. This results in a globally asymptotically stabilizing controller parameterized by two degrees of freedom, which can be used to implement the power management policy. The controller is simulated and shown to work satisfactorily for various realistic load changes.

Simultaneous interconnection and damping assignment passivity-based control: the induction machine case study

We argue in this article that the standard two-stage procedure used in interconnection and damping assignment passivity-based control (IDA–PBC)–consisting of splitting the control action into the sum of energy-shaping and damping injection terms–is not without loss of generality, and effectively reduces the set of systems that can be stabilised with IDA–PBC. To overcome this problem we carry out, simultaneously, both stages and refer to this variation of the method as SIDA–PBC. To illustrate the application of SIDA–PBC we consider the practically important example given by the control problem of the induction machine. First, we show that torque and rotor flux regulation of the induction motor cannot be solved with two stage IDA–PBC. It is, however, solvable with SIDA–PBC. Second, we prove that with SIDA–PBC we can shape the total energy of the full (electrical and mechanical) dynamics of a doubly-fed induction generator used in power flow regulation tasks, while with two stage IDA–PBC only the electrical energy can be shaped. Simulation results of these examples are presented to illustrate the performance improvement obtained with SIDA–PBC.

IDA-PBC controller for a bidirectional power flow full-bridge rectifier

A controller able to support bidirectional power flow in a full-bridge rectifier with boost-like topology is obtained. The controller is computed using port Hamiltonian passivity techniques for a suitable generalized state space averaging truncation of the system, which transforms the control objectives, namely constant output voltage dc-bus and unity input power factor, into a regulation problem. Simulation results for the full system show the correctness of the simplifi-cations introduced to obtain the controller.

Energy-based modelling and simulation of the interconnection of a back-to-back converter and a doubly-fed induction machine

This paper describes the port interconnection of two subsystems: a power electronics subsystem (a back-to-back AC/AC converter (B2B), coupled to a phase of the power grid), and an electromechanical subsystem (a doubly-fed induction machine (DFIM). The B2B is a variable structure system (VSS), due to the presence of control-actuated switches; however, from a modelling and simulation, as well as a control-design, point of view, it is sensible to consider modulated transformers (MTF in the bond graph language) instead of the pairs of complementary switches. The port-Hamiltonian models of both subsystems are presented and, using a power-preserving interconnection, the Hamiltonian description of the whole system is obtained; detailed bond graphs of all subsystems and the complete system are also provided. Using passivity-based controllers computed in the Hamiltonian formalism for both subsystems, the whole model is simulated; simulations are run to test the correctness and efficiency of the Hamiltonian network modelling approach used in this work

Generalized discontinuous conduction modes in the complementarity formalism

We model dc-dc power converters using the complementarity formalism. For each position of the switches, the dynamics is given by a linear complementarity system which incorporates, in a natural way, the description of generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM can be stated. As an example, this result is used to identify the GDCM for the switch configurations of the C/spl caron/uk converter. Simulation results, showing a variety of behaviors, such as persistent or re-entering GDCM, are presented.

A Robustly Stable PI Controller For The Doubly-Fed Induction Machine

In this paper we propose a new control scheme for the doubly-fed induction machine (DFIM) that offers significant advantages, and is considerably simpler, than the classical vector control method. In contrast with the latter, where the DFIM is represented in a stator flux-oriented frame, we propose here a model with orientation of the stator voltage. This allows for an easy decomposition of the active and reactive powers on the stator side and their regulation - acting on the rotor voltage - via stator current control. Our main contribution is the proof that a linear PI control around the stator currents ensures global stability for a feedback linearized DFIM, provided the gains are suitably selected. The feedback linearization stage requires only measurement of the rotor and stator currents, hence is easily implementable. Finally, an outer loop control for the mechanical speed is introduced. The complete control system is tested both in simulations and experiments, showing good transient performance and robustness properties

Extended Galilean symmetries of non-relativistic strings

A bstractWe consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.

Distributed parameter model simulation tool for PEM fuel cells

In this work, a simulation tool for proton exchange membrane fuel cells (PEMFC) has been developed, based on a distributed parameter model. The tool is designed to perform studies of time and space variations in the direction of the gas channels. Results for steady-state and dynamic simulations for a single cell of one channel are presented and analyzed. Considered variables are concentrations of reactants, pressures, temperatures, humidication, membrane water content, current, among others that have signicant eects on the performance and durability of PEMFC.

Simultaneous Interconnection and Damping Assignment Passivity-Based Control: Two Practical Examples

Passivity-based control (PBC) is a generic name given to a family of controller design techniques that achieves system stabilization via the route of passivation, that is, rendering the closed-loop system passive with a desired storage function (that usually qualifies as a Lyapunov function for the stability analysis.) If the passivity property turns out to be output strict, with an output signal with respect to which the system is detectable, then asymptotic stability is ensured. See the monographs [5, 12], and [6] for a recent survey.