978-1-4799-6743-8/14/$31.00 ©2014 IEEE A Comparative Study on SMC, OSMC and SDRE for Robot Control Moharam Habibnejad Korayem, Alireza Khademi and Saeed Rafee Nekoo Robotic Research Laboratory, School of Mechanical Engineering Iran University of Science and Technology (IUST), 1684613114, Tehran, Iran Emails: hkorayem@iust.ac.ir, a_8590@yahoo.com, rafee@iust.ac.ir Abstract—In this paper, a comparative study is conducted to investigate the capability of three nonlinear methods in controlling manipulators. The sliding mode control (SMC) as a nonlinear method with robust nature and state-dependent Riccati equation (SDRE) as a nonlinear suboptimal technique are performed to illustrate the effectiveness of robustness and optimality combination. The optimal sliding mode control (OSMC) has both mentioned essence. The OSMC benefits from linear quadratic regulator (LQR) to define its gains. This reduces the magnitude of input signals and eliminates the chattering phenomenon. The end-effector error, norm of control inputs and dynamic load carrying capacity (DLCC) are computed as some important criteria of industrial robots to assess the controllers. Simulation results showed that the OSMC method, in addition to control input reduction has also the robustness properties and it can be considered as a suitable approach in this area. Keywords— SMC; Optimal SMC; SDRE; Robot; Nonlinear; Simulation I. INTRODUCTION This document investigates manipulator’s control. They have complex dynamics and uncertainty in the model. The external load for carrying is always variable; as a result, this load is considered as unknown external disturbance of the system. To control a nonlinear system with external disturbance and uncertainty, sliding mode control could be a good choice because of its robust nature. Ohri et al. compared PID and sliding mode controls of manipulator in terms of robustness and expressed that by varying load, SMC method was more robust [1]. Chattering phenomenon is one of the SMC’s difficulties. It is unwanted and leads to an excessive usage of actuators; therefore the control law may become impractical. Many methods have been proposed for eliminating or reducing the chattering including the boundary layer, continuous approximations and higher order SMC approaches. Azlan et al. applied proportional integral sliding mode control for a hydraulic robot manipulator. They eliminated chattering phenomena with replacing discontinuous controller sign function with a proper continues function [2]. Ertugrul et al. used the MIT rule for gain adaptation of sliding mode control and introduced sliding surface’s function for adaptation [3]. The proposed controller was applied for a two-link SCARA robot and experimental result illustrated that adaption removes chattering phenomena. Park et al. introduced sliding mode controller for manipulators with adaptive law to regulate controller’s gain and boundary layer thickness [4]. This decreased discontinues control input and provided better performance for the system. Kuo et al. used adaptive sliding mode control for manipulators [5]. They used adaptive law for input switching gain and boundary layer parameters. In addition to accuracy of a control law, energy consumption should be regarded too. Optimal control method allows a trade-off between the precision and consumption of energy in its process and algorithm. The SDRE controller has been recently applied for practical systems such as robots [6- 12]. Erdem and Alleyne used it for an underactuated arm experimentally and reported good performance of it [6]. Comparison of the SDRE with successive Galerkin approximation [7], using it for a complex manipulator [8] and for flexible joint robots [9] showed significant ability of this controller. So, a new control law with all the advantages such as robustness and optimality would be amazing. Amato et al. presented a robust and optimal control problem for uncertain bilinear system via a guaranteed cost approach and applied it to tracking control design of a robotic arm [13]. Esfahani et al. introduced a robust optimal sliding mode controller based on new algorithm of artificial immune system and employed it for trajectory tracking of an underwater manipulator [14]. Dogan and Istefanopulos developed nonlinear adaptive and robust controllers for a two link flexible robot arm and optimized stabilizer part of this controller with a new evolutionary algorithm [15]. In this present work, we tried to avoid chattering and reduce energy consumption by optimization of controller’s coefficient and present a simple structure. The LQR is used to provide this reconciliation. The rest of the work is as follows. The mathematical model of the arm is presented in Section II. Controller designs are expressed in Section III in three parts: sliding mode control, optimal sliding mode control and state-dependent Riccati equation. Section IV presents the simulation results and finally, concluding remarks are presented in Section V. II. MATHEMATICAL MODEL OF THE ROBOT Spherical robot that is shown in Fig. 1 is one of the most well-known arms. This manipulator consists of two main parts: main body and wrist. The main body includes two ﻣﺘﻠﺐ ﺳﺎﯾﺖ MatlabSite.com MatlabSite.com ﻣﺘﻠﺐ ﺳﺎﯾﺖ