2017 International Conference on System Science and Engineering (ICSSE) Hybrid Control for Swing up and Balancing Pendubot System: An Experimental Result Tran Vinh Toan , Tran Thu Ha and Tran Vi Do Abstract- This paper presents a hybrid control which includes swing-up and balancing control for pendubot system - a two-link under-actuated robot. The parameters of the pendubot system are measured in the actual pendubot system built in the automation lab, University of Technology and Education HCM City. A hybrid controller which drives the system close to the equilibrium manifold and maintains the system stabilization in the upright position will be developed. The proposed control consists of two stages: swing-up control using partial feedback linearization, and balancing control using linear quadratic regulator. Finally, the controller is verified through both simulation and experimental results. The stability of the pendubot system in simulation showed that the proposed hybrid controller works well. However, the control quality in the experimental model still has some limitations. Keywords- Under-actuated system, hybrid control, partial feedback linearization, LQR, pendubot. I. INTRODUCTION The pendubot system is a two-link, under-actuated robotic mechanism which has the number of control inputs less than the controlled actuators degree of freedom (DOF) [1]. This system is widely used for research in nonlinear control as one of the typical under-actuated mechanical systems. Controlling pendubot system consists of two folds: swing-up from the stable initial position and stabilizing both of two links toward the unstable vertical upright position [2]. The swing-up problem for pendubot is highly nonlinear and challenging because of its complicated characteristics [3]. The swing-up and balancing control of the pendubot system have been proposed and tested in several previous studies. Spong and Block used partial feedback linearization for swing-up control and linear quadratic regulator (LQR) for balancing and stabilizing [1] . An energy based approach to establish the control law has been proposed by Fantoni et aI. , 2000 [2] . The swing up and balancing control problems for an under-actuated robot, pendubot, from the point view of fuzzy logic control were investigated by Ma et ai. , 2002 [4]. A model orbit stabilization approach to swing up control of pendubot was implemented and tested by Orlov [5] , [6]. In [7] , the dual fuzzy PD controller is applied to balance the pendulum. More recently, Eom et ai., 2015 proposed a robust swing-up and balancing control method for the pendubot Tran Vinh Toan is with Ho Chi Minh city University of Technology and Education (email: vinhtoanspkt@gmail.com). Tran Thu Ha is with Ho Chi Minh city University of Technology and Education (email: thuhaspkt@hcmute.edu.vn). Tran Vi Do (corresponding author) is with the BioRobotics Institute, Scuola Superiore Sant'Anna, Polo Sant'Anna Valdera, Viale R. Piaggio 34, Pontedera, Italy; Laboratory of Rehabilitation Bioengineering, Volterra, Italy and Ho Chi Minh city University of Technology and Education (email: vido.tran@santannapisa. it ). 978-1-5386-3422-6/17/$31.00 ©2017 IEEE 450 system in the presence of the friction [8]. The swing-up and balancing controller in this study compensate for the friction , system uncertainties, and external disturbance by incorporating a nonlinear disturbance observer for the uncertain pendubot system. These previous studies, however, evaluated the controller with simulation results or implemented with a commercial system such as the planar single inverted pendulum model (Produced by Quanser Consulting Inc.) in which the physical parameters are easily obtained using the manual of the system. Building a pendubot system and evaluating a controller on self-built system seem necessary for control research and education, especially for student. This paper proposes a hybrid control for swing-up and balancing a self-built pendubot system. We fIrst determine the parameters of the system, some parameters are easily achieved by measure but some are estimated through experimental results. Then, the proposed controller will be applied to swing-up and balance our system. This study is organized as follow: the dynamic equations of the pendubot system are described in Section II. In Section III a hybrid control which includes a swing-up control and balancing control is proposed. Then, the proposed hybrid control is verifIed through the simulation and the experimental results in Section IV and Section V respectively. Finally, the conclusion is presented in Section VI. II . SYSTEM DYNAMICS Consider the two-link under-actuated planar robot which is called the pendubot in Figure 1. With the standard assumption that there is no friction in the joints, the equation of motion for the pendubot system can be obtained using the Euler-Lagrange formulation as follows [2]: Y x Figure I. Pendubot system.