Boundary control of a vertical nonlinear flexible manipulator considering disturbance observer and deflection constraint with torque and boundary force feedback signals

Abstract

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to prevent the amount of boundary deflection from violating the constraints and avoiding any simplifications, in the presence of external boundary disturbance, proper control feedbacks and boundary disturbance observer are adopted in order to reach control objectives and to compensate external boundary disturbance effects simultaneously. By choosing proper boundary feedback, system states are proven to be uniform ultimate bounded and converge exponentially toward a small neighbourhood of zero. In order to illustrate the performance of the proposed control approach, numerical simulation results are provided.

KEYWORDS:

• Nonlinear flexible vertical manipulator
• distributed parameter system
• vibration control
• boundary control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Farshid Entessari

Farshid Entessari received the B.Sc. and the M.Sc. degree in Mechatronics from the School of Science and Engineering, Sharif University of Technology (SUT), International Campus, I.R. Iran, in 2009 and 2012, respectively, and the Ph.D. degree in Mechanics from the School of Science and Engineering, Sharif University of Technology (SUT), International Campus, I.R. Iran, in 2020. He is currently with the Department of Mechanical Engineering, SUT. His current research interests include Nonlinear Control and infinite-dimensional systems.

Ali Najafi Ardekany

Ali Najafi Ardekany received his B.Sc., M.Sc. and PhD degrees in Mechanical engineering from Shiraz University, Shiraz, Iran in 2005, 2007 and 2011. He also worked as a Postdoctoral Researchers in the Sharif University of Technology. At present, he is an assistant professor of mechanical engineering in K. N. Toosi University of Technology. He is the head of mechatronics Laboratory. His fields of research are mainly in Mechatronics, new emerging technologies for the care of dementia patients, deep learning and control of distributed parameter systems.

Aria Alasty

Aria Alasty received his B.Sc. and M.Sc. degrees in Mechanical engineering from Sharif University of Technology (SUT), Tehran, Iran in 1987 and 1989. He also received his Ph.D. degree in Mechanical engineering from Carleton University, Ottawa, Canada, in 1996. At present, he is a professor of mechanical engineering in Sharif University of Technology. He has been a member of Center of Excellence in Design, Robotics, and Automation (CEDRA) since 2001. His fields of research are mainly in Nonlinear and Chaotic systems control, Computational Nano/Micro mechanics and control, special purpose robotics, robotic swarm control, and fuzzy system control.