International Journal of Control and Automation Vol. 7, No. x, xxxxx, 2014 1 Proportional-Integral Sliding Mode Control for Trajectory Tracking and Vibration Control of a Flexible Single Link Manipulator Mohammed Rachidi and Badr Bououlid Idrissi Université Moulay Ismaïl, Ecole Nationale Supérieure d’Arts et Métiers, BP 4024, Marjane II, Beni Hamed, 50000, Meknès, Morocco morachidi@yahoo.fr, badr.bououlid@gmail.com Abstract This paper presents investigations into the development of a Proportional-Integral Sliding Mode Control (PISMC) for trajectory tracking and vibration control of a flexible single link manipulator. The motor at the single rotating joint is the control actuator. Two SMC control laws are reviewed. The classical discontinuous control based on the signum function and a modified control law where the servomotor output voltage depends on the instantaneous values of the states. The selection of the discontinuity gain is reviewed in the case of exact model (certain case) as well as when the parameter variations are present in the system (uncertain case). To prove the reaching condition, we use the Lyapunov stability criteria. It is proven that this design is equivalent to a full state feedback with its steady state motion constrained to the sliding hyper-surfaces. Simulation results of the response of the flexible manipulator with both controllers are presented. The performances of the control schemes are examined in terms of input tracking capability, level of vibration reduction and time response specifications. A comparative assessment of both control techniques shows the effectiveness of the second control law and its invariance to so-called matched uncertainty. Keywords: Vibration reduction, flexible manipulator, sliding mode control, model uncertainties. 1. Introduction Current generation of industrial robots need to be rigid to achieve precise control with today’s established control methodologies. Rigidity, however, necessitates massive construction, which results in slow operation, low load to weight ratio and high energy consumption. To enhance the performance of the robots, they must be made ever lighter which will eventually lead to link flexibility in robot manipulators. The expected advantages of using such flexible manipulators in industry include higher speed, higher load to weight ratio, low material and energy consumption, higher mobility and efficiency. Control systems for light weight flexible arms, however, have to overcome more problems. Being flexible, the arms are prone to vibration; hence precise position control is much more difficult [1] [2] [3] [4]. Unlike a rigid arm, a flexible arm is basically a distributed parameter system of infinite order. But due to the limitations of nowadays control processors, the sensor accuracy and the presence of noise, it is common to approximate a flexible arm by a finite order system and control it by a controller of finite order. In this study, only the first two vibration modes are considered.