Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 429215, 13 pages

http://dx.doi.org/10.1155/2015/429215

## Second Order Sliding Mode Control Scheme for an Autonomous Underwater Vehicle with Dynamic Region Concept

Centre for Artificial Intelligence & Robotics, Universiti Teknologi Malaysia, Jalan Sultan Yahya Petra, 54100 Kuala Lumpur, Malaysia

Received 17 April 2015; Revised 17 June 2015; Accepted 18 June 2015

Academic Editor: Yong Liu

Copyright © 2015 Zool H. Ismail and Vina W. E. Putranti. 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

The main goal in developing closed loop control system for an Autonomous Underwater Vehicle (AUV) is to make a robust vehicle from natural and exogenous perturbations such as wind, wave, and ocean currents. However a well-known robust control, for instance, Sliding Mode Controller (SMC), gives a chattering effect and it influences the stability of an AUV. Furthermore, some researchers combined other controls to get better result but it tends to present long computational time and causes large energy consumption. Thus, this paper proposed a Super Twisting Sliding Mode Controller (STSMC) with dynamic region concept for an AUV. STSMC or a second order SMC is adopted as a robust controller which is free from chattering effect. Meanwhile, the implementation of dynamic region is useful to reduce the energy usage. As a result, the proposed controller obtains global asymptotic stability which is validated by using Lyapunov-like function. Moreover, some simulations present the efficiency of proposed controller. In conclusion, STSMC with region based control is effective to be applied for the robust tracking of an AUV. It contributes to give a fast response when handling the perturbations, short computational time, and low energy demand.

#### 1. Introduction

The development of control stability for an Autonomous Underwater Vehicle (AUV) has gained much attention from many researchers since several years ago [1]. This happened because of the fundamental role of an AUV for replacing human involved in dangerous underwater activities for instance in underwater rescues, military purposes, underwater pipe inspections, oil and gas explorations, and so forth [2].

The robust tracking of an AUV against some natural disturbances is the main problem in this field [3, 4]. Whereas a precision of tracking desire trajectory is important to be obtained, so that dissipation of energy can be avoided [5]. To cope with this problem, a range number of robust control systems have been introduced. Each control had its advantages and disadvantages. For this reason, many researchers coupled two or three different controllers or unified them with another control technique to improve its performance.

One example of conventional robust control was Proportional-Integral-Derivative (PID) controller [6]. It was a simple control but had difficulties not only for setting an appropriate value of its gain but also for reaching the expected requirement. Then, researchers combined PID with several methods such as PID with Fuzzy Control (FC), PID with self-tuning technique, and PID with Genetic Algorithm (GA) [7–9]. The combination of PID with several methods focused on how to determine the gain value automatically. The control combination showed some improvements although there was a drawback like needed long computational steps which affected low real time execution.

Then, researchers adapted Linear Parameter Verifying (LPV) control and robust technique as the other methods [10, 11]. However, the result of LPV control depicted good achievement only at minimum of sampling time, while robust technique presented smooth performance even though there was misstracking in some places. Furthermore, Sliding Mode Controller (SMC) was used as an alternative robust control. This control was commonly applied for an AUV [12–14]. Designing the closed loop control law of SMC based on Lyapunov candidate was required to remove the rule of linearization equation. Nevertheless, the main disadvantage of using this control was chattering effect. This negative effect appeared during the reaching condition and tended to be sensitive to the inaccurate mathematical model. In addition, chattering effect not only influenced the stability of an AUV but also generated large energy consumption. For this reason, some researchers proposed a dynamic region concept [15, 16]. This method successfully reduced the energy usage.

Meanwhile to reduce the chattering effect, SMC was developed with other controls for instance SMC with fuzzy control or SMC with Neural Network (NN) [17–19]. Fuzzy control and NN were applied to tune the gain and to remove the nonlinearity from error dynamics, respectively. As a result, SMC with fuzzy control could achieve good parameter conditions after arranging many rules, while SMC with NN could perform satisfying condition after proceeding a lot of leanings and adaptations. Thus, this method required long data processes and consequently more energy demand will be spent, so that researcher expanded the formulation of SMC into Second Order Sliding Mode Control (SOSMC) [20–22]. SOSMC was aimed at removing the chattering effect which was produced by the conventional SMC. It worked on the second order of system deviation.

In this paper, Super Twisting Sliding Mode Controller (STSMC) with dynamic region concept for a 6-Degree-of-Freedom (DOF) holonomic AUV is proposed. STSMC ensures the robustness of an AUV when handling natural perturbation while energy consumption issue is overcame using region based concept. The global asymptotic stability of proposed control is analyzed by Lyapunov-like function. The rest of this paper is organized as follows. Section 2 describes the kinematics and dynamic properties of 6-DOF underwater vehicle. Section 3 states the robust control with dynamic region concept. The stability analysis in terms of the Lyapunov technique is also given in this section. Simulation results are presented in Section 4. Finally, Section 5 contains concluding remarks.

#### 2. Kinematics and Dynamics of a 6-DOF AUV

The new formulation of robust control can be designed by considering the modeling system of a 6-DOF underwater vehicle. It involves a study on kinematics and dynamics system. Kinematics model is concerned with the equilibrium of the body at both rest and moving with certain velocity, while dynamics model is concerned with acceleration of the body motion. The studies of these were mainly discussed in [23].

##### 2.1. Kinematic Model

The kinematics model has a correlation between inertial frame and body-fixed velocity of vehicle. It can be described by using the Jacobian matrix in the following form [23]:where denotes the position while denotes the orientation of the vehicle which are expressed in the inertial-fixed frame. and are the transformation matrices described in Euler angles formation. Here, and are the linear and angular velocity vectors, respectively, which are described in terms of the body-fixed frame relative to the earth’s fixed frame. The illustration can be seen in Figure 1.