Algebraic estimation of impact times: Juggling a ball with a magnetically levitated plate

Abstract

A plate that may freely move in the field of four electromagnets is automatically controlled such as to keep a ping-pong ball bouncing. A simple mathematical model of the process is used together with an algebraic derivative estimator in order to estimate the impact times of the ball. This information is used to predict the next impact. The only measurement used in this process is the plate position measurement. It is related with the reference forces in order to generate a motion appropriate to keep the ball bouncing. Precision and robustness against measurement noise, mechanical vibrations, and fast motions of the plate are achieved by a suitable parameterization of the algebraic derivative estimator and an automatic calibration. Experimental results are shown.

Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification

“…The parameters α and T can now be chosen such that the zeros of G (α,α) 0,T,ϑ coincide with specific frequencies. This has been used in Kiltz (2017); Kiltz, Janocha, and Rudolph (2013); to compute derivatives of experimental signals corrupted by a harmonic disturbance with a known frequency without resorting to further filtering methods. The approach is extended in Othmane, Mounier, and Rudolph (2021) to approximately annihilate disturbances with Fourier transforms showing repetitive peaks and applied to the estimation of derivatives of quantised signals.…”

Motion Signals With Velocity Jumps: Velocity Estimation Employing Only Quantized Position Data

“…We look for an upper bound for |e k+1 | under the assumption that no velocity jump has occurred in the domain [t k−m k ,t k+1 ]. In order to do so, the vectorq k containing the measured position for the sample times in the domain [t k−M ,t k ] is split in three components, namelỹ In (15),…”

“…Existing techniques for just detecting impacts and estimating the corresponding times can be found in e.g. [14] and [15]. These works, however, require the use of a model of the impacting system as well as the input signal and do not focus on instantaneous detection of impact events, contrary to our assumptions and needs.…”