Linear Estimation Strategies Applied to a Spring-Mass-Damper System

Spring-mass-damper (SMD) systems are considered a benchmark setup in vibration-based systems. The system is considered linear for certain ranges during an excitation. For a simple system, the model is considered a second order system with one of the following behaviours for an impulse/unit input: exponential, sinusoidal, polynomial, or combined from the previous performances. The performance depends highly on the values of the parameters including the values of the mass, spring constant, and viscous damper coefficient. In this brief paper, one of the new promising filtering techniques, referred to as the sliding innovation filter (SIF), is used to estimate the system trajectories including the position and velocity. The filter is known for being robust and stable when system parameters change, which makes it a suitable candidate when the SMD system crosses the ranges of its linearized model or one of the parameters changes significantly. To complicate the case, only one state is assumed to be measured, which is the position. In this paper, a revised formulation of the SIF with the Luenberger method is introduced for cases with fewer measurements than states. The results are compared with the well-known Kalman Filter (KF). The results demonstrate that the proposed filter works well with the presence of uncertainties.