Session: MSNDC-05-01 Motion Planning, Dynamics, and Control of Robots

Paper Number: 89838

89838 - Nonlinear Oscillations in Delayed Collocated Control of Pendulum on Trolley 

The paper investigates the nonlinear dynamics of the collocated position control of a trolley that carries a pendulum. Delayed proportional derivative control force is considered, which is based on the position and velocity of the trolley only. This means that the relevant nonlinearity of the system is related to the not detected motion of the pendulum. Stability charts are constructed for different parameter combinations, which show intricate structures in the plane of the control parameters. As the time delay or the angular natural frequency of the system is increased the stable area shrinks and disappears, but increasing these parameters further, the stable domain reappears and then disappears and reappears alternately. To examine the nonlinear behavior of the system, the Hopf bifurcation calculation is carried out after an infinite dimensional center manifold reduction. Closed form algebraic solutions are given for the Poincaré-Lyapunov coefficient and for the amplitude of the emerging self-excited oscillations. This indicates that at the boundary of the first stable lobe always supercritical Hopf bifurcations exist, however, for increasing time delays, the reappearing stable lobes may be bounded with subcritical Hopf bifurcations as well, and even quasi-periodic oscillations may occur. The analytical bifurcation diagrams match well with the ones created with DDE-BIFTOOL .

Presenting Author: Bence Mate Szaksz Budapest University of Technology and Economics

Presenting Author Biography: Bence Szaksz got his BSc and MSc degree in Mechanical Engineering at the Budapest University of Technology and Economics. He is a PhD student at the Department of Applied Mechanics at the same university, where he works in the dynamics group. He spent a semester at the Universtity of Bristol in 2018, where he completed his master project. His special interest includes stability and bifurcation theory of delayed dynamical systems with special applications in robotics and vehicle control.

Authors:

Bence Mate Szaksz Budapest University of Technology and Economics
Gabor Stepan Budapest University of Technology and Economics