Complexity

Volume 2017, Article ID 4143901, 11 pages

https://doi.org/10.1155/2017/4143901

## On Control of a Boost DC-DC Power Converter under Constrained Input

Instituto Politécnico Nacional-CITEDI, Ave. Instituto Politécnico Nacional 1310, Nueva Tijuana, 22435 Tijuana, BC, Mexico

Correspondence should be addressed to Javier Moreno-Valenzuela; xm.idetic@onerom

Received 30 July 2016; Revised 14 November 2016; Accepted 6 December 2016; Published 15 January 2017

Academic Editor: Alfred Hubler

Copyright © 2017 Javier Moreno-Valenzuela and Octavio García-Alarcón. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, a new controller for a boost DC-DC (direct current to direct current) power converter is proposed. The discussed DC-DC boost converter model considers the losses coming from the inductor and capacitor. The novel control scheme takes into account that the duty cycle is constrained to physically admissible values. The analysis of the closed-loop trajectories provides the conclusion that output voltage regulation is achieved in asymptotic form. In addition, the problem of uncertain supply voltage and unmeasurable inductor current is also addressed by using an observer together with the proposed control law. Our theoretical results are supported by using numerical simulations and experimental tests. Comparisons with respect to known approaches are presented.

#### 1. Introduction

The voltage of many electrical and electronic systems is often higher than the voltage of the main source, for example, in systems powered by batteries. A conventional solution employs the so called boost DC-DC (direct current to direct current) converter where the increase of the output voltage is accomplished. Textbooks giving introduction to the history, construction, and control of the boost power converters are [1–4].

The boost power converter is applied in photovoltaic systems [5], mobile communication circuits [6], power factor correction [7], and hybrid electric vehicle systems [8]. This power converter is a bilinear second order nonminimum phase system and under certain operation conditions can be affected by disturbances and other nonlinearities.

The perspective in power electronics engineering to control a boost power converter relies on the characterization of the devices and in the design of compensation circuits. On the other hand, in control engineering, the approach to regulate the output voltage is to modify the duty cycle, thus compensating the losses due to the operation of the components.

In order to provide a degree of robustness to compensate uncertainties in the load, supply voltage, and unmodeled disturbances, many control algorithms have been devised to achieve voltage output regulation; see, for example, [9–12]. More recently, the work in [13] presented a comparison of nonlinear controllers for the DC-DC boost power converter. In [14], the problem of output feedback regulation via Lyapunov’s theory was addressed.

Usually, the duty cycle percentage is the control input for the boost power converter. This a number that is into the set and this constraint is rarely taken into account to design a control system. The reason probably is the increasing in the complexity of the closed-loop system stability analysis. As pointed out in the textbook [15, p. 171]: “saturation is probably the most commonly encountered nonlinearity in control engineering.”

Works considering saturation of duty cycle in control input for buck converters can be found in [16, 17]. Specifically, the research in [16] used a LMI approach supported by simulation results. Paper [17] presented a comparison between two controllers and included a discussion of stability analysis. More recently, in the work in [18], an adaptive neural network controller is introduced. However, this scheme is based on the concept of inverting a saturation function, which is not globally possible. More recently, in [19], the problem of robust stability and tracking of a saturated control buck DC-DC converter was considered. There, LMIs were used to insert the constraints in the design phase while imposing positivity in the closed-loop state. Other problems with saturation in the dynamics (not in the system input) have been addressed in, for example, [20], where a nonlinear controller with an inherent current limiting capability was presented for different types of DC-DC power converters.

There have been only a few works that address the problem of voltage regulation for boost converters control under constrained duty cycle percentage. For example, in [21] a model-based full state-feedback controller was introduced. The efficiency of the controller was proven by real-time experiments. A more sophisticated scheme was given by Karagiannis et al. [22] addressing the problem of controlling the boost converter by using only output voltage measurement while the supply voltage is unknown. More recently, in [23] a saturated state-feedback control law for a battery-driven boost converter was introduced. In [24], a control design procedure for boost power converters was reported, and, although this procedure ensures robustness for the supply voltage and output load variations, input saturation is avoided.

Many of the controllers reported in literature do not take into account the parasitic resistance in the inductor and capacitor, including the works cited earlier. Although the parasitic resistances are relatively small, they cannot be ignored in the practical DC-DC boost converter because it increases the model uncertainty. The proposed controller in this paper is designed on the basis that the losses due to parasitic resistances are present.

The contributions of this paper are the following. Firstly, we introduce a new controller for an input-constraint boost power converter. We prove asymptotic convergence of the output voltage error in spite of the fact that the system is affected by input saturation. Secondly, an observer for the supply voltage is revisited. The implications of using this new observer together with new controller are studied. A simulation study complements the theoretical results, where comparisons are given. Besides, a real-time experimental study supports the practical viability of the proposed scheme.

Better results are obtained with the new controller.

The present document is organized as follows. Section 2 deals with the modeling of DC-DC boost converters and the control goal. In Section 3, the new controller is introduced. The implications of using an observer to estimate the supply voltage with the new controller are discussed in Section 4. The simulation results are presented in Section 5. Experimental results are given in Section 6. Finally, Section 7 presents some concluding remarks.

#### 2. Boost DC-DC Power Converter Model and Control Goal

##### 2.1. Boost DC-DC Power Converter Model

This paper deals with the output voltage regulation problem of the DC-DC boost converter shown in Figure 1. We consider a practical inductor with a parasitic resistance. This model also includes a resistor to represent unavoidable loss, which dissipates power as the capacitor is charged or discharged. The nominal values of the resistors are assumed to be known. By using an average switching method, the mathematical model of Figure 1 is described by [2, 3]where is a continuous control signal representing the duty cycle percentage of the PWM circuit controlling the switch, the positive quantity represents the external voltage supply, is the current through inductor , is the voltage through capacitor , and , , and denote the inductance, the capacitance, and the load resistance, respectively.