Damped One-Mode Vibration Model State and Parameter Estimation via Pre-Filtered Moving Horizon Observer

Abstract

The estimation of parameters and states is one of the core data-processing algorithms used for the monitoring and control of continuum or structured mechatronical systems (e.g., flexible robotic arms and cantilevers). The measurements taken from the sensors combined with an appropriate model can filter the states and extract information about vibration dynamics parameters such as damping and spring constants. This paper presents a method based on the application of a Moving Horizon Observer (MHO) for state and parameter estimation of a lightly-damped vibrating system. A numerical experiment on a single-degree-of-freedom (SDOF) system is performed to demonstrate the method on noisy measurements and to compare the MHO with the benchmark Extended Kalman Filter (EKF). Test scenarios show that the MHO appears to be more robust with respect to modeling errors.

Moving Horizon Observer for vibration dynamics with plant uncertainties in nanopositioning system estimation

“…The objective and novel contribution of this study is the experimental application of nonlinear least-squares estimation of states, parameters and force disturbance of nanopositioning device with MHO [6]. While the EKF accumulates past history measurement information in the a priori estimate of the state and the error covariance matrix estimate, the MHO uses finite moving horizon data window to extract the information from the actually measured and past measured data.…”

Adaptive Model Predictive Vibration Control of a Cantilever Beam with Real-Time Parameter Estimation

“…Such a second-order differential equation representing a 1 DOF vibrating system only takes the first resonant frequency into account; however, from the viewpoint of the control system, this is not an issue, since the first resonance dominates the response. Single degree of freedom models are routinely used in literature to identify the physical parameters of vibrating structures using the EKF and other statistical estimation methods [32,41,42].…”

“…The EKF was previously used as a benchmark algorithm for the open-loop state and parameter estimation of the free vibrations of the cantilever beam considered in this work, contrasting the results to moving horizon observer (MHO) in an offline simulation [32].…”

Regularized Nonlinear Moving Horizon Observer for Detectable Systems

“…Due to knowledge of the mapping H t (·), this uniquely defines the state estimates at the entire horizon, including the current state estimatê x t,t that is usually the main target of estimation. It is further remarked that the formulation can be extended with process noise (as in [2], [4]) or a Kalman-filter corrected predictor for pre-filtering of the a priori estimate (as in [37], [38]) in order to reduce the estimator's sensitivity to model errors and disturbances. For simplicity, we leave out this extension in the present paper.…”