Uncertain Systems Motion Synchronization

In the operation of large-scale manufacturing equipment, accurate tracking of the desired trajectory and overall motion synchronizations are the keys to ensuring the products’ high quality. These multi-axis plants are highly coupled nonlinear systems with a range of uncertainties (parametric uncertainties, unmodelled dynamics, cross-coupling between axes, and external disturbances). That makes the control design for such systems a challenging task. In this paper, a Lyapunov-based design for motion tracking and/or cross-coupling synchronization control for multi-axis systems is proposed. The aim is to develop a general framework for the design of motion tracking and/or cross-coupling synchronization. The proposed design is based on a specific structure of the generalized control error and design of control which enforces a predefined form of the Lyapunov function time derivative. The structure of the generalized error allows the application of the same controller design procedure for motion tracking and/or cross-coupled synchronization control in either configuration or operation space. In the proposed design compensation of uncertainties and the convergence of the generalized error are treated separately. The compensation for the uncertainties is realized by the application of an unknown input observer within the controller structure. That yields efficient compensation of the projection of the system uncertainties to the generalized error. In ensuring the desired convergence and stability the Lyapunov function time derivative is used as a design parameter. It could be selected so that closed-loop dynamics exhibits asymptotic or finite-time convergence. The proposed design results in a simple easy-to-implement controller structure with a small number of design parameters. The details of the design procedure and the proposed controller are evaluated in simulation and experiments for a coupled 4-axis system.