R. Leyva

Robust LQR Control for PWM Converters: An LMI Approach

A consistent framework for robust linear quadratic regulators (LQRs) control of power converters is presented. Systems with conventional LQR controllers present good stability properties and are optimal with respect to a certain performance index. However, LQR control does not assure robust stability when the system is highly uncertain. In this paper, a convex model of converter dynamics is obtained taking into account uncertainty of parameters. In addition, the LQR control for switching converters is reviewed. In order to apply the LQR control in the uncertain converter case, we propose to optimize the performance index by using linear matrix inequalities (LMIs). As a consequence, a new robust control method for dc-dc converters is derived. This LMI-LQR control is compared with classical LQR control when designing a boost regulator. Performance of both cases is discussed for load and line perturbations, working at nominal and non nominal conditions. Finally, the correctness of the proposed approach is verified with experimental prototypes.

Quasi-periodic route to chaos in a PWM voltage-controlled DC-DC boost converter

A quasi-periodic route to chaos is studied both numerically and experimentally in a DC-DC boost switching regulator. After undergoing a Neimark-Sacker bifurcation of a one-periodic orbit, quasi-periodic behavior is obtained and the corresponding attractor is a T/sup 2/ torus, Under parameter changes, such a torus may breakdown to give chaotic behavior. Two different scenarios are possible for the destruction of the torus. One is obtained by means of period doubling of a phase-locking orbit while the other is achieved by losing the torus smoothness. An approximated two-dimensional mapping is built up to predict the nonlinear phenomena detected in this system.

A Design-Oriented Combined Approach for Bifurcation Prediction in Switched-Mode Power Converters

In this brief, two different approaches are combined for studying the stability of a buck switching power dc-dc converter and for predicting its bifurcations. Instability indexes derived from both approaches are combined to get a complete design-oriented perspective of bifurcation analysis in terms of practical circuit parameter and to show the effect of each parameter on the system behavior. The first approach is based on the conventional Routh-Hurwitz criterion applied to the averaged converter dynamics, and it is suitable for detecting low-frequency oscillations but is unsuitable for predicting fast-scale period-doubling instabilities. Complementarily, the second approach considers the ripple component before the pulsewidth modulator to quantitatively predict the occurrence of subharmonic oscillations. The usefulness of the combined approach is shown by analytically deriving inequalities that compress the complete design space into simple instability indexes, which, used complementarily, allow a division of the design space into the different instability regions (both period-doubling or fast-scale instability, and Hopf or slow-scale instability). Comparison of the design-oriented complete map obtained combining both methods and their related stability indexes with the results obtained both from time-domain numerical simulations of the exact switched state equations, as well as the stability border obtained from discrete recurrent maps, corroborates the approach.

Paralleling DC–DC Switching Converters by Means of Power Gyrators

In this paper, the problem of paralleling DC-DC switching converters is solved by means of power gyrators. The key element of the parallel connection is a buck converter with input filter acting as a power gyrator of type G with controlled output current, i.e., with its DC output current being proportional to its DC input voltage. electromagnetic interference minimization, current distribution among converters, stability, and voltage regulation are ensured by this approach. It is shown that a voltage regulator based on the parallel operation of power gyrators with democratic current sharing is always stable regardless of the number of connected modules. Experimental results of a DC-DC voltage regulator based on the parallel connection of three power gyrators with democratic current sharing are in perfect agreement with the theoretical predictions.

Analysis and Comparison of Extremum Seeking Control Techniques

Two non-perturvative extremum seeking control approaches are analyzed; the first approach needs the sensing of the functions gradient while the second one does not. Relationships between the algorithms parameters and their dynamic behavior are found. Also expressions for the steady state error of both approaches are derived. Finally, these results are used to verify and to compare, by means of simulation, the performance of both methods.

Dynamic performance of maximum power point tracking circuits using sinusoidal extremum seeking control for photovoltaic generation

The article studies the dynamic performance of a family of maximum power point tracking circuits used for photovoltaic generation. It revisits the sinusoidal extremum seeking control (ESC) technique which can be considered as a particular subgroup of the Perturb and Observe algorithms. The sinusoidal ESC technique consists of adding a small sinusoidal disturbance to the input and processing the perturbed output to drive the operating point at its maximum. The output processing involves a synchronous multiplication and a filtering stage. The filter instance determines the dynamic performance of the MPPT based on sinusoidal ESC principle. The approach uses the well-known root-locus method to give insight about damping degree and settlement time of maximum-seeking waveforms. This article shows the transient waveforms in three different filter instances to illustrate the approach. Finally, an experimental prototype corroborates the dynamic analysis.

QFT robust control of current-mode converters: application to power conditioning regulators

A design method using quantitative feedback theory (QFT) for robust control of PWM DC–DC converters is developed. Parametric and nonparametric uncertainty can be described accurately with this technique. Besides, with the proposed method, the controller can consider both continuous and discontinuous conduction mode models (CCM and DCM respectively). Considering these sources of uncertainty results in a robust controller insensitive to parametric variations and also to different plant cases due to different conduction modes. A power converter satisfying a well-known industry standard is presented as a design example, in order to demonstrate that, with the proposed procedure, the performance of the regulated system can be tightly specified not only in terms of frequency requirements, but also in terms of time-domain characteristics, like overshoot and establishment time. The synthesised robust controller has been verified with experimental data from a power converter prototype, achieving satisfactory results.

Sliding mode control of a high voltage DC-DC buck converter

In this paper, a sliding mode approach is used in order to design a high voltage two-cell DC-DC buck converter. The studied system is derived from the elementary DC-DC buck converter where the single switch is substituted by two ones connected between them through a capacitor. One of the control objectives is to get a good voltage sharing between the two switches while the other is to maintain the output voltage to a desired value. Steady state analysis, dynamic behavior and control design of the system are presented. After identifying the switching surfaces, a linear model is derived and a sliding mode control for the system is designed in order to maintain a regulated output voltage and at the same time to share the high input voltage between the two switches. Numerical simulations show that the system presents a good response in front of line and load variations.

H∞ control of DC-DC converters with saturated inputs

A consistent framework for robust control of power converters subject to saturated inputs is presented. Usually, linear control design methods do not take into account the effects of duty-cycle saturations, which can lead to degradation of performance and even to destabilization of the converter. An illustrative example of this problem is presented and a possible solution is proposed. Such solution consists of a saturation model based on a deadzone nonlinearity and a controller design method based on a sector condition expressed in LMI form. The objective of the proposed design method is to maximize the region of stability of the closed-loop saturated system. The method has been verified with numerical simulations and it has been compared with the conventional results of the controller design method that does not consider the input saturations.

Combined Photovoltaic / Thermal Energy System for Stand-alone Operation

The utilization of solar energy can be made by photovoltaic (PV) cells to generate electric power directly and solar thermal (T) panels can be applied to generate heat power. When the utilization of the solar energy is necessary to generate electric power, the option of using T panels in combination with some heat / electric power conversion technology can be a viable solution. The power generated by utilizing the solar energy absorbed by a given area of solar panel can be increased if the two technologies, PV and T cells, are combined in such a way that the resulting unit will be capable of co-generation of heat and electric power. In the present paper combined Photovoltaic / Thermal panels are suggested to generate heat power to produce hot water, while the photovoltaic part is used to obtain electric power mainly for covering the electric power consumption of the system, to supply the electronic control units and to operate pump drives etc. Ac and dc supplies are provided by converters for covering self-consumption and possibly the need of some household appliances. The development and design of the system is made by extensive use of modeling and simulation techniques. In the paper a part of the simulation studies, carried out to determine the energy balance in the electric energy conversion section of the system and the control structure, assuming stand-alone operation is presented.