Nanoforce estimation based on Kalman filtering and applied to a force sensor using diamagnetic levitation

Abstract

International audienceNanoforce sensors based on passive diamagnetic levitation with a macroscopic seismic mass are a possible alternative to classical Atomic Force Microscopes when the force bandwidth to be measured is limited to a few Hertz. When an external unknown force is applied to the levitating seismic mass, this one acts as a transducer that converts this unknown input into a displacement that is the measured output signal. Because the under-damped and long transient response of this kind of macroscopic transducer cannot be neglected for time-varying force measurement, it is then necessary to deconvolve the output to correctly estimate the unknown input force. The deconvolution approach proposed in this paper is based on a Kalman filter that use an uncertain a priori model to represent the unknown nanoforce to be estimated. The main advantage of this approach is that the end-user can directly control the unavoidable trade-off that exists between the wished resolution on the estimated force and the response time of the estimation

State Observation of a Specific Class of Unknown Nonlinear SISO Systems using Linear Kalman Filtering

“…In most implementation of Kalman filtering, this point is tricky and lead to some heuristic choices. We show in the following that the approach previously developed in [23] for a secondorder system with u = 0 can be adapted to solve this point in our framework.…”

“…The observation strategy presented in this paper takes its roots in the ADRC framework and also in an unknown input observation technique for known linear systems that uses a LFK [23]. For SISO systems, ADRC addresses the observation and the control of dynamical uncertain nonlinear systems of order p whose state-space representation is given by [10]:…”

“…Using an appropriate equivalent state-space representation introduced in Section IV, the proposed approach will also consider that the extended state component is here a virtual additive unknown input. Estimating an unknown input with a LKF has been proposed in [23], but exclusively for a perfectly known linear system having a null control input. The challenge to face consists in merging these two approaches, with one related to an unknown nonlinear system and extended state and the other to a known linear system with unknown additive input and Gaussian measurement error.…”

Review on Carbon Nanomaterials-Based Nano-Mass and Nano-Force Sensors by Theoretical Analysis of Vibration Behavior

“…Regarding force sensors, for manipulating nano particles, biomolecular or cells, development of high sensitivity force sensors with mechanical types [ 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ], electrical types [ 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 ], and optical types [ 65 , 66 , 67 , 68 ], it has been a great challenge for advanced micro/nano-assembly and bio-engineering. Willemsen et al [ 49 ] summarized the works of the detection of biomolecular interaction forces using AFM with silicon nitride probes by that time, in which the AFM probes were considered as force sensors that could detect the interaction forces between individual molecules in nN (10 −9 N) range by mechanical evaluations, such as strain change or frequency shift.…”

Design and Experimental Validation of Novel Force Sensor

“…Many different types of force sensors are available on the market, using several basic principles for the realization of the transduction of force into mechanical or electrical signals. As a result, many force sensors have been continually developed in the literature, such as spring force sensors [5][6][7][8], load-cell [9], Strain gauge dynamometer [10][11], piezoelectric force sensor [12][13], nanoforce sensor [14], magnetostrictive force sensor [15][16], cantilever force sensor [17], mechanoelectrical force sensors [18], high-sensitivity MEMS force sensor [19], and dual-range force sensor [20], and so on. Amongst the various force sensors which have been proposed, those spring force sensors are particularly popular since they are characterized by a low cost and simplicity.…”