Fixed frequency sliding mode-based robust inversion with a full-bridge current DC-link buck-boost
Introduction
Full-Bridge Buck-based power supply equipments require a transformer in order to perform step-up tasks (see, for example, [1]), thus resulting in a significant increase of weight and size of the source inverter. This fact has opened a research branch that assesses the possibility of replacing the former structure by a transformerless DC–AC converter, derived from a nonlinear switched DC–DC converter and capable of carrying out step-down and step-up inversion as well.
One of the main challenges in this field deals with the non-minimum phase character exhibited by nonlinear switch-mode DC–DC converters. Direct control of the output voltage by means of passivity-based schemes [2] and PID-type sliding mode controllers [3] has been successfully used for regulation purposes but, as far as these authors know, no results on tracking tasks have been reported. Alternatively, serious attempts to overcome the problem trying current-based indirect control strategies in Boost and Buck-Boost DC–AC inverters [4], [5] cannot avoid sensitivity to external perturbations and parameter uncertainties. PI controllers also offer interesting performance in full-bridge nonlinear inverters [6], [7], [8], [9]; however, it is well known that PI control designs are based on small signal models obtained for nominal parameters, which include a nominal resistive output load. This leads to output waveforms sensitive to power stage parameter variations, such as the output load. The reader has to bear in mind the high variability of the load in case of connection to nonlinear elements as, for example, a full-wave rectifier.
The Full-Bridge Current DC-Link Buck-Boost (FBBB) inverter, which is essentially constituted by a full-bridge inverter in series with a Boost converter, has two control inputs. Hence, it is possible to design control strategies that yield robust tracking of periodic signals by the output voltage and, at the same time, keep the input current regulated at a prescribed level [10].
Sliding mode control [11], [12] is here shown to render an efficient performance of the FBBB in inversion tasks. The proposed scheme uses an error-based switching surface that does not depend on the plant parameters. This, combined with the fact that all disturbances are matched, guarantees robustness in the face of bounded nonlinear and resistive loads. Moreover, a decoupling of the control actions, which allows a fixed-frequency implementation of the sliding mode control law by means of the Zero Average Dynamics (ZAD) algorithm, maintains the robustness properties inherent to sliding mode control and renders null mean tracking error for the output voltage. As a result, highly accurate robust tracking performance of periodic references is achieved. This technique has already shown efficient experimental results in a power inverter. A complete survey about the ZAD algorithm including both theoretical and experimental considerations, together with a comparative study between ZAD and other control implementation techniques, may be found in [13]. Finally, restrictions for candidate signals to be tracked are derived demanding non-saturation of the control action – which has fixed control gains – in the steady state.
It is already known that proper energy transfer constitutes the main goal of power converters, this meaning good efficiency and high output signal quality. Maximizing power efficiency requires minimization of the Root Mean Square (RMS) of the current flowing in the switching converter, this leading to two different effects, namely, optimization of the losses due to the power switching and minimization of the resistive losses in the inductors. Hence, the design incorporates a procedure to reduce power losses that has been successfully applied to the robust tracking of offset sinusoidal signals in a Non-Inverting Buck-Boost under bounded resistive load variation [14]. This technique, which is based on semi-infinite programming theory [15], is here adapted to deal with a family of nonlinear currents that is assumed to be bounded by a known resistive load current. Eventually, the resulting method generalizes that of [14] by relaxing a continuous differentiability condition to Lipschitz continuity and it is also applicable to linear loads.
The proposal is validated by means of illustrative simulations with the realistic power electronics software package PSIMR.
This paper is structured as follows. The mathematical model of the FBBB inverter is established in Section 2. A sliding mode control strategy to achieve the output voltage tracking target is developed in Section 3. The selection of a current reference profile that reduces power losses is studied in Section 4. Simulation results are presented in Section 5, while Conclusions are in Section 6. Appendix A contains the proofs of some of the results stated in Section 4.
Section snippets
The full-bridge current DC-link buck-boost inverter
The FBBB inverter, depicted in Fig. 1, is derived by replacing each one of the original switches of a Non-Inverting Buck-Boost converter [16], [17] by a full bridge of switches allowing bi-directional current flows.
Its dynamical behavior can be modelled by means of a two-dimensional, bilinear system with the inductor current iL and the capacitor voltage vC as state variablesThe variable iR stands for the load current. The control actions envisage the
Sliding mode control of the full-bridge current DC-link buck-boost inverter
The sliding surface used in [10] for system (5), (6) requires a somehow complicated variable switching frequency implementation due to the coupling suffered by the control actions. However, a fixed frequency implementation is possible with a selection of switching surfaces that result in a decoupling of the control actions.
With this aim, consider the switching surfaces candidates Proposition 1 Let Assumption A be fulfilled. Then, the control law
Power loss reduction
According to Remark 3 and to the definition of the unsaturation region in Eqs. (10), (11), the selection of a constant and high enough inductor current reference signal x1d may suffice to guarantee the desired performance. However, due to both technical and economical reasons, it is extremely convenient to reduce as much as possible power losses in the converters. These losses are of two types, namely switching losses and conduction losses; in this article we focus on the second ones.
The power
Simulation results
The power electronics software PSIMR is used to carry out the simulations, the numerical integration time step being . The reader is referred to the PSIMR User's Manual for further details.
The parameters of the FBBB inverter simulation prototype are: a DC source of , an inductance of with an internal resistance of and a capacitor of . The inverter also has two switches: the first one is a unidirectional voltage and bidirectional current full-bridge, and has
Conclusions and suggestions for further research
This article presents an inverter obtained from the replacement of the original switches by a full bridge in a Non-Inverting Buck-Boost converter. Operating under a sliding regime that yields a control action decoupling, the converter performance involves step-down and step-up tasks which are robust in the face of nonlinear and resistive loads with known bounds. The control law is implemented by means of the ZAD algorithm, which provides a fixed operation frequency and guarantees null error in
Acknowledgment
This work has been partially supported by the spanish Ministerio de Educación under projects DPI2009-14713-C03-03 and DPI2010-15110.
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