Robust Nonlinear Control of Two Links Robot manipulator and Computing Maximum Load Hasanifard, Goran Engineering Department, Islamic Azad University of Sanandaj, Sanandaj, Iran g_hasanifard@yahoo.com Habib Nejad Korayem, Moharam Mechanical Department, Iran University of Science & Technology, Tehran, Iran hkorayem@iust.ac.ir Nikoobin, Amin Engineering Department, Semnan university, Semnan, Iran anikoobin@iust.ac.ir Abstract—A new robust nonlinear control scheme of a manipulator is proposed in this paper which is robust against modeling errors and unknown disturbances. It is based on the principle of variable structure control, with sliding mode control (SMC) method. The variable structure control method is a robust method that appears to be well suited for robotic manipulators because it requers only bounds on the robotic arm parameters. But there is no single systematic procedure that is guaranteed to produce a suitable control law. Also, to reduce chattring of the control signal, we replaced the sgn function in the control law by a continuous approximation such as tangant function. We can compute the maximum load with regard to applied torque into joints. The effectivness of the proposed approach has been evaluated analitically demonstrated through computer simulations for the cases of variable load and robot arm parameters. Keywords—Variable structure control, robust control, switching surface, robot manipulator. I. INTRODUCTION HE robotic control and its application are very popular research topics in control field as well as in industry automation. A robot manipulator is a highly nonlinear and dynamically coupled system, which is subject to disturbances and model uncertainties. The general control methods, such as computed torque method, PD control method, etc., will not render the expected performance with the presence of disturbances and model uncertainties. Also, a number of approaches have been proposed to develop controllers that are more robust so that their performance is not sensitive to modeling errors. The sliding mode control (SMC) theory has been applied to robot manipulators for the last decade [1-5]. SMC is commonly favored as a powerful robust control method for its independence from parametric uncertainties and external disturbances under matching conditions. In general, SMC comprises a discontinuous control input that drives the control system toward a specified sliding surface. Usually, a large control gain formula is applied to handle the unknown parametric variations and external disturbances [6]. Here, we develop a class of sliding mode controllers to the case of two link elbow robot manipulator with variable structure control method [7, 8]. This paper organized as follows: the basic concept of sliding mode is presented in section III the manipulator dynamics is introduced and a new control structure is proposed developed. Simulation results are presented in section IV. Section V gives the conclusion. II. SLIDING MODE CONCEPT The basic idea behind adaptive control is that the controller gains gradually changes as parameters of the system being controlled evolve.[9] It is also possible to change the control signal abruptly on the basis of the state of system being controlled. Control systems of this type are referred to as variable structure systems (VSS)[10-12]. A block diagram of a variable structure controller for a robotic arm is shown in Fig. 1. Fig. 1 Variable structure control of a robotic arm To apply variable structure control, we do not have to know the exact robotic arm parameters, instead only bounds on these parameters. Variable structure controllers are robust in the sense that they are insensitive to errors in the estimates of the parameters as long as reliable bounds on the parameters are known. To formulate a variable structure control law, it is helpful to first recast the state equations in terms of the tracking error and its derivative. Suppose the reference input ݎሺݐሻ is sufficiently smooth that is has at least one derivative. Define the state vector as ݔ൦ ݔ ଵ ݔ ଶ ݔ ଷ ݔ ସ ൪ where: ൜ ݔ ଵ ൌ  ଵ ൌ ݎ ଵ െ ݍ ଵ , ݔ ଶ ൌ  ଵ ሶ ൌ ݎ ଵ ሶ െ ݍ ଵ ሶ ݔ ଷ ൌ  ଶ ൌ ݎ ଶ െ ݍ ଶ , ݔ ସ ൌ  ଶ ሶ ൌ ݎ ଶ ሶ െ ݍ ଶ ሶ (1) T q + r - w e Robotic arm Torque regulator f S World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:3, No:2, 2009 231 International Scholarly and Scientific Research & Innovation 3(2) 2009 scholar.waset.org/1307-6892/5007 International Science Index, Mechanical and Mechatronics Engineering Vol:3, No:2, 2009 waset.org/Publication/5007