Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 573016, 9 pages

http://dx.doi.org/10.1155/2015/573016

## Feedback Linearization and Sliding Mode Control for VIENNA Rectifier Based on Differential Geometry Theory

^{1}School of Electric Power, South China University of Technology, Guangzhou 510641, China^{2}College of Physical Science and Technology, Guangxi University, Nanning 530004, China

Received 6 June 2014; Revised 28 August 2014; Accepted 4 September 2014

Academic Editor: Kang Li

Copyright © 2015 Xiang Lu et al. 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

Aiming at the nonlinear characteristics of VIENNA rectifier and using differential geometry theory, a dual closed-loop control strategy is proposed, that is, outer voltage loop using sliding mode control strategy and inner current loop using feedback linearization control strategy. On the basis of establishing the nonlinear mathematical model of VIENNA rectifier in *d-q* synchronous rotating coordinate system, an affine nonlinear model of VIENNA rectifier is established. The theory of feedback linearization is utilized to linearize the inner current loop so as to realize the *d-q* axis variable decoupling. The control law of outer voltage loop is deduced by utilizing sliding mode control and index reaching law. In order to verify the feasibility of the proposed control strategy, simulation model is built in simulation platform of Matlab/Simulink. Simulation results verify the validity of the proposed control strategy, and the controller has a strong robustness in the case of parameter variations or load disturbances.

#### 1. Introduction

With the development of power electronic technology, three-level pulse width modulation (PWM) rectifiers are widely used in high or medium power converters because of their excellent performance: low switch voltage stress, low input current harmonic distortion, high efficiency, input power factor is unit, and so on [1–7]. Three-phase/switch/level VIENNA rectifier (abbreviated as VIENNA rectifier) is one of the best three-level rectifier, which is proposed in 1994 by Kolar and Zach. Compared with traditional three-level rectifier, such as diode clamping three-level rectifier, VIENNA rectifier has lots advantages, such as small number of power switch tube, simple control circuit, and low design costs, without output voltage bridge arm shoot-through problems. So, more and more scholars and engineers focus their attention on the study of VIENNA rectifier and its control strategy [3–14].

Since VIENNA rectifier is a typical strong coupling nonlinear system, it leads to difficulty in designing the controller. In [8, 9], the mathematical models of large and small signals topology are analyzed in detail, and the controller is designed by using proportion and integral (PI) algorithm. A control method of input/output accurate linearization is proposed in [10]. State-space average model is established, and PI control algorithm is used in the outer voltage loop; hysteresis control is used in the inner current loop in [11–13]. The control methods described above improved the performance of VIENNA rectifier to some extent. However, there are some disadvantages, such as system excessive dependence on the accurate mathematical model, inconvenience of parameter setting, complicated of control algorithm, and poor dynamic. In order to overcome the above drawbacks, this paper proposes a control strategy which combines feedback linearization control and sliding mode control.

In recent decades, nonlinear control theory has made great progress, especially feedback linearization theory based on differential geometry. In this method, nonlinear system can achieve status or input/output linearization by using a certain nonlinear state transformation or feedback transformation. Feedback linearization control has been applied to three-phase voltage PWM rectifier [14–16], which is a multivariable and strong coupling nonlinear system, and achieved well control effect. All these methods can solve the problem of decoupling for original nonlinear system and obviously improve static and dynamic performance for three phase rectifier. Yet, this control method depends on an accurate mathematical model and is sensitive to system parameters. Sliding mode control is different from feedback linearization control method. Sliding mode control shows great robustness and stays out of parameter changes when the system is running in the sliding surface. In [17–20], sliding mode control has been applied to the three-phase PWM rectifier and achieved a good result.

The three-phase PWM rectifier is a two-level rectifier, while the VIENNA rectifier is a three-level rectifier. Although their structure is not the same, there are some similarity in control strategy. Learning from the applications of feedback linearization control and sliding mode control for three-phase PWM rectifier, this paper integrates feedback linearization control method and sliding mode control method and eventually establishes a new type of VIENNA rectifier nonlinear control system. That is, sliding mode control is used in the outer voltage loop and state feedback linearization control is used in the inner current loop. At the same time, space vector pulse width modulation (SVPWM) technology is introduced to modulate the output signal of inner current loop [21]. In order to reduce the chattering phenomenon produced by sliding mode control, index reaching law is adopted to improve the whole approaching process. In order to verify the correctness and superiority of the proposed control strategy, numerical simulation is done.

#### 2. Physical and Modeling Considerations

In this section, the physical system and the mathematical model of VIENNA rectifier are presented. The main circuit of VIENNA rectifier and its simplified model are shown in Figures 1(a) and 1(b), respectively. The main circuit includes six fast-recovery diodes (*D*_{1}–*D*_{6}), three boost inductors, three bidirection power switching tubes (, , and as shown in the dashed box), and two groups of output capacitances. Among them, , , are the AC input power of VIENNA rectifier; and are DC side output voltage filter capacitor, and their voltage across, respectively, are , ; is load resistance and the voltage across is , and is the output current; is the boosting inductor and is defined as an equivalent resistance of inductor. In order to simplify the system, all the power-switching devices are seen as ideal and switching frequency is much higher than the grid frequency.