An optimal two-input approach for impulse measurements in the nanoN·s range produced by contact forces

The performances of an optimal two-input filter technique for measuring impulses, caused by contact forces, in the nanoN·s range have been investigated. The instrument is based on a sensing element (proof mass) suspended by a simple pendulum. The impulse is exerted to the proof mass and is measured by applying the optimal filter to the measured signal of the resulting swing motion of the pendulum. Since the contact forces cause the mass to rest out of the pendulum equilibrium before the application of an unknown impulse, the resulting swing motion is also affected by such an undesired and unknown input. As a consequence, the pendulum initial position must be included as an additional input of the optimal filter. Main objectives of this article are to: (a) present the mathematical formulation of the two-input optimal filter, (b) apply this formulation to a harmonic oscillator initially set out of the equilibrium position and subjected to an impulse, (c) analyze the performances of the filtering technique in terms of an achievable measurement accuracy taking into account the effect of noise, sampling frequency, width of the sampling window and an unknown instant of an impulse application.