Phase-Space Nonlinear Control Toolbox: The Maglev Experience

We describe the Phase-Space Nonlinear Control Toolbox, a suite of computational tools for synthesizing and evaluating control laws for a broad class of nonlinear dynamical systems. The Toolbox comprises computational algorithms for identifying optimal control reference trajectories in the phase space of dynamical systems and experimental methods for evaluating performance of the control laws. These algorithms combine knowledge of the geometric theory of modern nonlinear dynamical systems with eecient computational methods for geometric reasoning and graph search; they deene the properties of con-trollability and robustness in terms of phase-space geometric structures and exploit the phase-space neighborhood adjacencies to obtain computational eeciency. Compared to the traditional analytic control design methods, the phase-space based control synthesis and evaluation rely on high-performance computational techniques and are applicable to physical systems operating in large nonlinear regimes. Using a proof-of-concept physical experiment for stabilizing a nonlinear magnetic levitation system, we have successfully demonstrated the feasibility of the phase-space control technology.