George Zhu, York University

Dr. Zheng Hong (George) Zhu is Professor of Mechanical Engineering and founding Co-Director of Centre for Manufacturing, Technology, and Entrepreneurship, and Director of Space Engineering Lab at York University. He also served as the Director of Space Engineering undergraduate program in the Department of Earth and Space Science and Engineering, Chair of Mechanical Engineering Department, and Inaugural Academic Director of Research Commons in the Office of Vice-President Research & Innovation. His research interests include dynamics and control of tethered space systems, space robotics, computational mechanics and control, machine learning, 3D printing in space, and CubeSat. He has authored 200+ peer-reviewed journal papers and 160+ conference articles. Dr. Zhu is an elected member of International Academy of Astronautics, College Member of the Royal Society of Canada, Fellows of the Canadian Academy of Canada, Engineering Institute of Canada, Canadian Society for Mechanical Engineering, and American Society of Mechanical Engineers; an Associate Fellow of the American Institute of Aeronautics and Astronautics, and Senior Member of IEEE. He is the recipient of the 2019 Engineering Medal R&D from Professional Engineers Ontario, the 2021 Robert W. Angus Medal from CSME, the 2022 President's Research Excellence Award from York University, and the 2024 Solid Mechanics Medal from CSME.

From Computational Mechanics to Computational Control

Accurate control of spacecraft position and orientation, especially those with flexible structures like tethers, solar panels, and booms, is crucial for mission success. This task typically demands experts with extensive training and specialized knowledge in control systems. One wonders if it is possible to algorithmically synthesize stable feedback laws for controlling the complex coupled rigid-flexible dynamics of spacecraft structures, or more broadly, for dynamic systems with infinite degrees of freedom, analogous to how the finite element method (FEM) solves physical problems in modern engineering. Currently, we find no definitive answer to this in the field of control.

This talk will present our recent efforts to bridge this gap by developing a novel model-based computational control framework. This framework algorithmically synthesizes stable feedback laws for dynamic systems with flexible bodies governed by Hamiltonian mechanics and elasticity in a manner analogous to FEM. It is based on the principles of Lyapunov stability theory, Hamiltonian mechanics, and computational solid mechanics. The key achievement is to synthesize feedback control laws in each finite element, rather than piecewise in the discretized regions in the across state space. This involves a piecewise affine local control Lyapunov function within each element and Sontag’s universal formula for local stability. Control inputs are assigned at each element node, with non-actuated elements receiving null inputs. The global feedback system is formed using standard FEM assembly, ensuring stability and controllability through the Popov-Belevitch-Hautus criterion and Lyapunov’s method. Ultimately, our framework integrates with existing FEM programs, simplifying nonlinear feedback control for engineers in rigid-flexible dynamic systems. Once implemented, this framework can be applied to controlling generalized coupled rigid-flexible dynamic systems like using FEA codes.