There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

More than a decade of research in the field of thermal, motion, vibration and electromagnetic radiation energy harvesting has yielded increasing power output and smaller embodiments. Power management circuits for rectification and DC-DC conversion are becoming able to efficiently convert the power from these energy harvesters. This paper summarizes recent energy harvesting results and their power management circuits.

Micropower energy harvesting

Energy harvesting technologies have been explored by researchers for more than two decades as an alternative to conventional power sources (e.g. batteries) for small-sized and low-power electronic devices. The limited life-time and necessity for periodic recharging or replacement of batteries has been a consistent issue in portable, remote, and implantable devices. Ambient energy can usually be found in the form of solar energy, thermal energy, and vibration energy. Amongst these energy sources, vibration energy presents a persistent presence in nature and manmade structures. Various materials and transduction mechanisms have the ability to convert vibratory energy to useful electrical energy, such as piezoelectric, electromagnetic, and electrostatic generators. Piezoelectric transducers, with their inherent electromechanical coupling and high power density compared to electromagnetic and electrostatic transducers, have been widely explored to generate power from vibration energy sources. A topical review of piezoelectric energy harvesting methods was carried out and published in this journal by the authors in 2007. Since 2007, countless researchers have introduced novel materials, transduction mechanisms, electrical circuits, and analytical models to improve various aspects of piezoelectric energy harvesting devices. Additionally, many researchers have also reported novel applications of piezoelectric energy harvesting technology in the past decade. While the body of literature in the field of piezoelectric energy harvesting has grown significantly since 2007, this paper presents an update to the authors' previous review paper by summarizing the notable developments in the field of piezoelectric energy harvesting through the past decade.

https://iopscience.iop.org/article/10.1088/1361-665X/ab36e4/pdf

A review of energy harvesting using piezoelectric materials: state-of-the-art a decade later (2008–2018)

Let the unknown linear system x = Ax + Bu; y = Cx, be given, together with the a priori information that for a known, nonnegative integer l, there is a (nonadaptive) regulator of order l which stabilizes the system. It is shown that this suffices as a priori information for an adaptive stabilizing controller. An example of such an algorithm is given. This yields a continuous regulator, which does not utilize probing signals. It is based on a dense search through parameter space, and does not utilize high-gain properties, as opposed to the ‘universal regulators’ proposed before [3–6]. In the absence of information of such an l, it is shown how to modify the algorithm to search over the regulator structures, i.e. the controller's dimension.

The Order of Any Stabilizing Regulator is Sufficient a Priori Information for Adaptive Stabilization

This paper proposes a sensorless vector control that combines two discrete-time observers to estimate the rotor speed and position of permanent magnet synchronous machines (PMSM). The first one is a sliding mode (DSM) current observer and the second one is an adaptive electromotive force (EMF) observer. Initially, the sliding conditions that assure the sliding motion around the sliding surface are derived and a design procedure to the DSM current observer is developed. Moreover, using discrete-time adaptive Lyapunov based EMF observer the rotor speed and position are obtained. Experimental results validate the theoretical analysis and demonstrate the very good performance of the proposed discrete-time sensorless vector control.

Discrete-Time Sliding Mode Observer for Sensorless Vector Control of Permanent Magnet Synchronous Machine

Switching dc–dc converters are widely used to interface the dc output of renewable energy resources with power distribution systems in order to facilitate the use of energy at the customer side. In the case of residential photovoltaic (PV) applications, high conversion ratio is usually required, in order to adapt the low output voltages of PV modules to a dc bus voltage, while dealing with the appropriate impedance matching. In this paper, a system connected to a PV panel consisting of two cascaded dc–dc boost converters under sliding-mode control and working as loss-free resistors is studied. The modeling, simulation, and design of the system are addressed. First, an ideal reduced-order sliding-mode dynamics model is derived from the full-order switched model taking into account the sliding constraints, the nonlinear characteristic of the PV module, and the dynamics of the MPPT controller. For this model, a design-oriented averaged model is obtained and its dynamic behavior is analyzed showing that the system is asymptotically globally stable. Moreover, the proposed system can achieve a high conversion ratio with an efficiency close to 95 $\%$ for a wide range of working power. Numerical simulations and experimental results corroborate the theoretical analysis and illustrate the advantages of this architecture in PV systems.

Impedance Matching in Photovoltaic Systems Using Cascaded Boost Converters and Sliding-Mode Control

A novel dc-dc switching converter consisting of a boost stage cascaded with a buck converter with their coils magnetically coupled is presented. The disclosed converter has the same step-up or step-down voltage conversion properties than the single inductor noninverting buck-boost converter but exhibits nonpulsating I/O currents. The converter control-to-output transfer function is continuous between operation modes if a particular magnetic coupling is selected. The addition of a damping network improves the dynamics and results in a control-to-output transfer function that has, even in boost mode, two dominant complex poles without right-half-plane zeros. An example shows that an output voltage controller can be designed with the same well-known techniques usually applied to the second-order buck regulator. Details of a prototype and experimental results including efficiency, frequency, and time domain responses are presented. The experimental results validate the theoretical expected advantages of the converter, namely, good efficiency, wide bandwidth, and simplicity of control design.

A Noninverting Buck–Boost DC–DC Switching Converter With High Efficiency and Wide Bandwidth

In distributed power generation systems a pivotal role is played by DC-DC power converters that are employed to connect local loads to local power sources. These converters are used either in combinations of series/parallel connections or as stand-alone devices. A lot of work has taken place in the stability analysis of these converters and several methods have been used/proposed with different properties, strengths and weaknesses. Describing all existing methods is probably a never ending task and therefore in this tutorial paper four different methods will be presented by pointing out their main properties and explaining briefly how they can be used in applications that involve power converters. More specifically, the chosen methods are based on 1) the Poincare map, 2) Saltation matrix, 3) trajectory sensitivity, and 4) steady-state-response analysis of the discrete-time model. Simple case studies from previous publications are collected and presented in order to further explain these methodologies. Finally, this paper intents to describe some of the future challenges that exist in the area of stability analysis of power converters especially when these are employed in distributed generation applications.

A Review on Stability Analysis Methods for Switching Mode Power Converters

Switched power converters are used to interface the dc output in modern distributed power generation systems, which are usually aggregated to the main grid to yield the necessary power using interconnected modules. Synthesis, modeling, and stability analysis of interconnected systems using cascaded converters working under sliding-mode control are considered in this paper. A systematic procedure to synthesize cascaded connection of dc-dc boost converters is introduced. The approach is based on making each module to behave as a suitable canonical element for power processing. Three different elements are considered, which are the dc power gyrator, the dc transformer, and the dc loss-free resistor. These canonical elements are designed by means of a sliding-mode control theory and then their dynamic behavior is studied in detail. The sliding-mode conditions for each case are derived in closed form to obtain design-oriented criteria for selecting the parameters of the system. The aforementioned canonical elements are compared to select the most suitable one for a distributed power system. Simulation results ensure the correctness of the proposed approach. Experimental measurements corroborate the theoretical predictions and the numerical simulations.

Synthesis of Canonical Elements for Power Processing in DC Distribution Systems Using Cascaded Converters and Sliding-Mode Control

This paper is concerned with the study of nonlinear phenomena in a closed loop voltage-controlled DC–DC Buck–Boost converter when suitable parameters are varied. The dynamics is analyzed using both the continuous-time model and the numerically computed stroboscopic map. The analysis of the one-dimensional bifurcation diagram shows that Neimarck–Sacker bifurcation occurs at certain values of the parameters. Phase-locking periodic windows, the period-adding sequence, and transition from quasiperiodicity to period-doubling via torus breakdown are also obtained. The two-dimensional bifurcation diagram is carefully computed. This shows that phase-locking orbits produce so-called Arnold tongues in the parameter space. It is shown that the winding number plotted as a function of the bifurcation parameter is a devil's staircase. As typically occurs in general circle maps, the fine structures of the Arnold tongues and the devil's staircase show self-similarity.

Abdelali El Aroudi

Papers

Impedance Matching in Photovoltaic Systems Using Cascaded Boost Converters and Sliding-Mode Control

A Noninverting Buck–Boost DC–DC Switching Converter With High Efficiency and Wide Bandwidth

A Review on Stability Analysis Methods for Switching Mode Power Converters

Synthesis of Canonical Elements for Power Processing in DC Distribution Systems Using Cascaded Converters and Sliding-Mode Control

Quasiperiodicity and chaos in the dc–dc buck–boost converter