LPV identification of high performance positioning devices

Abstract

High performance positioning devices exhibit position dependent dynamics in the form of varying flexible modes, which are expected to dominate the dynamic behavior in the new generation of lightweight positioning structures.To handle such position-dependent behavior, the framework of Linear Parameter-Varying (LPV) systems offers powerful tools in terms of control synthesis with many successful practical applications. However, to achieve the desired performance, a low complexity but accurate LPV model of the underlying plant is of crucial importance. Obtaining LPV models for positioning devices based on first principle laws is a rigorous and costly process often resulting in models with inadequate accuracy. Therefore a data driven-modeling approach using Orthonormal Basis Functions (OBF's) is studied for the controloriented modeling of xy-positioning table dynamics. Through a simulation study it is demonstrated that the proposed modeling procedure, using only measurement data, can provide models whose accuracy is very close to the analytic models derived with the full knowledge of the system.

LPV system identification using series expansion models

“…The linearized (or so called local) dynamics of this device varies with its actual position, often manifesting in terms of position-dependent resonant dynamics. Based on [Tóth et al (2011d)], we present in the following an LPV identification study of an xy-table aiming at a highly accurate fit of the resulting model w.r.t. the frozen frequency responses of the original plant.…”

“…By taking p = x 1 as In Eq. (33), forces in one direction have influence on the movements in other directions (see [Tóth et al (2011d)]). Thus, to enable the design of SISO controllers, the plant dynamics are commonly decoupled in practice by using pre-and post-transformation matrices T u and T y implemented directly into the hardware.…”

Gaussian Process Position-Dependent Feedforward: With Application to a Wire Bonder

“…First, LTI dynamics can be scheduled according to the current configuration of the LPV system, resulting in high control performance for e.g. wafer stages [5] or xy-positioning tables [6]. Second, data-driven learning techniques, such as Iterative Learning Control (ILC) or adaptive control, can be extended to LPV systems, which results in high performance through learning [7], [8].…”

Frequency Response Data Based LPV Controller Synthesis Applied to a Control Moment Gyroscope

“…The associated dynamics are nonlinear and characterized by coupled behavior and challenging rotational dynamics that change based on the operating conditions of the system. Locally, these behaviors manifest in terms of operating condition-dependent resonant dynamics, also commonly encountered in mechatronic systems [3]. Flexible phenomena introduce severe practical limitations on the achievable performance, which become even more severe in case of operating condition-dependent dynamics.…”