Journal of Control Science and Engineering

Volume 2019, Article ID 6761784, 5 pages

https://doi.org/10.1155/2019/6761784

## Nonlinear Voltage Regulation Algorithm for DC-DC Boost Converter with Finite-Time Convergence

^{1}Anhui Vocational College of Press and Publishing, Hefei, Anhui 230601, China^{2}School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, Anhui 230009, China

Correspondence should be addressed to Chun Duan; moc.621@97nuhcnaud

Received 13 November 2018; Accepted 19 March 2019; Published 1 April 2019

Academic Editor: Radek Matušů

Copyright © 2019 Chun Duan and Di Wu. 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

For the DC-DC Boost converter system, this paper employs the finite-time control technique to design a new nonlinear fast voltage regulation control algorithm. Compared with the existing algorithm, the main advantage of the proposed algorithm lies in the fact that it can offer a fast convergent rate, i.e., finite-time convergence. Based on the average state space model of Boost converter system and finite-time control theory, rigorous stability analysis showed that the output voltage converges to the reference voltage in a finite time. Simulation results demonstrate the efficiency of the proposed method. Compared with PI control algorithm, it is shown that the proposed algorithm has a faster regulation performance and stronger robust performance on load-variation.

#### 1. Introduction

As a kind of important power electronic devices, the main function of DC-DC converters is used to achieve energy conversion, which has been widely applied in many industrial occasions, such as switching power supply, direct current motor drives, and communication equipment. Boost type direct current-direct current (DC-DC) converter is a typical power converter which has many industrial applications such as direct current (DC) motor drives, computer systems, and communication equipment [1]. With the development of distributed power generations, it is required that the DC-DC converter has the high-quality, reliable, efficient power supplies, and other features. However, from the control viewpoint, how to improve the control system performance for DC-DC converter is challenging since DC-DC converters are usually time-varying systems due to their switching operation.

In the past decades, many researchers from automatic control and power electronic have investigated the control problem for this kind of devices. It is well-known that DC-DC power converters are typical switch systems and the Boost type DC-DC converter is non-minimum-phase system, which is a main obstacle for controller’s design.

So far, many researchers have employed different nonlinear control methods to design control algorithms for Boost converter. In [2, 3], based on sliding mode control (SMC) method, some SMC algorithms were given and the analog control circuits were set up. In [4], combining SMC and feedback linearization technique, the corresponding SMC algorithm was also designed. Based on LMI technique and saturation control technique, the work [5] proposed a saturated nonlinear control algorithm. In [6], time-delayed compensation technique was employed to design a time-delayed control algorithm.

Actually, for a control system, the steady-state and dynamical performances (e.g., convergent rate) are two key indexes. Note that the most of existing voltage regulation algorithms for Boost converter system only guarantee that the convergence is at best exponential with infinite settling time. Clearly, in practice, it is more desirable if the output voltage can converges to the reference voltage in a finite time. Motivated by this, finite-time control theory has been introduced and developed in the literate [7–13], which guarantees that the system states converge to equilibrium in a finite time. Besides faster convergence rates, the closed-loop systems under finite-time control usually have some other nice features such as higher accuracies and better disturbance rejection properties [7, 14]. Because of the advantages of finite-time control, the work [15] employed the terminal sliding mode technique to design the finite-time voltage regulation algorithm for Buck converter. The works [16, 17] considered the finite-time control law for the DC-DC buck converter system. As for the Boost converter, the work [18] designed a class of finite-time voltage control algorithms, where the input voltage and load resistance are assumed to be known.

This paper will also employ the finite-time control technique to solve the voltage regulation problem for DC-DC Boost converter systems. Different from the existing work [18], this paper considers the design of fast finite-time control algorithm. The contribution/novelty of this paper is that a new nonlinear control algorithm is designed, i.e., the finite-time control algorithm. The main advantage of this algorithm is that the fast convergent rate of the closed-loop system can be guaranteed when the state is near the equilibrium. First, since the DC-DC Boost converter system has a nonlinear structure, a coordinate transform based on the total energy storage function is used to the average state space mode. Then the voltage control problem is equivalent to control the total storage energy. Based on the finite-time control theory, a second-order finite control algorithm is given. Finally, a rigorous proof is given to prove the global finite-time stability of the closed-loop system under the proposed controller. At the end, simulation results are provided to show the potentials of the proposed techniques.

#### 2. Preliminaries and Problem Formulation

##### 2.1. System Model

Figure 1 shows a typical boost type DC-DC converter. is a DC input voltage source, is a controlled switch, is a diode, is sensed output voltage, denotes the inductance current, and are the inductance, capacitance, and load resistance, respectively. If the switching frequency for is sufficiently high, the dynamic of DC-DC converters can be described by an average state space model [3]. Based on the average state space model [3], the dynamic equation for the Boost converter iswhere is the duty ratio function (called control input) and . The Boost type DC-DC converters are used in applications where the required output voltage is larger than the input voltage. Let be the desired DC output reference voltage; then the reference current can be described by