• accelerometri
• controlli digitali
• demodulatori
• filtri digitali
• onde gravitazionali
• rumore sismico
• virgo

Gravitational waves, predicted on the basis of the General Relativity, are ripples in the curvature of space-time that propagate as a wave. The passage of a gravitational wave induces tiny oscillations in the relative separation between two test masses, that can be measured. Nevertheless these oscillations are extremely small, so that only a very sensitive detector is able to measure them. The Advanced Virgo project is a major upgrade of the 3 km-long interferometric gravitational wave detector Virgo, with the goal of increasing its sensitivity by about one order of magnitude in the whole detection band. We expect to have a maximum strain amplitude sensitivity of 4 × 10^−24 1/√Hz at ∼ 300 Hz. In other words this means that it will be able to detect a relative displacement between mirrors of about 10^−20 m, by averaging for one second. This sensitivity should allow to detect several tens of events per year.

Among the various ongoing updates, an important improvement is represented by the new electronics used to control the Superattenuators, complex mechanical structures that isolate optical elements from seismic noise by a factor 10^15 at 1 Hz. Using the information of several inertial sensors, a digital control system keeps the structures as stable as possible. A new board for the Superattenuator control has been designed, that incorporates analog-to-digital and digital-to-analog converters, a Field Programmable Gate Array (FPGA) and a Digital Signal Processor (DSP) into a single unit. This board is enough to handle every single part of the Superattenuator inertial control. It performs the computation of feedback forces, and is used to synthesize sine wave to drive the coils of the inertial sensors, as well as to read their output. Furthermore it interfaces with all the other structures of Virgo.

In this thesis I have studied the horizontal accelerometers, feedback-controlled sensors used in the Superattenuator inertial control to measure the seismic noise in the frequency band from DC to 100 Hz. Using the computing power of the new electronics (the new DSP has 8 cores and can compute 8.4 GFLOPS per core for double precision floating point indeed), I have designed a new control system for the accelerometers, exploiting the properties of a critically damped harmonic oscillator. This system allows to improve by about one order of magnitude the sensitivity of these sensors, with respect to the system used in Virgo, by reducing the root mean square of the force needed for the control by a factor 2. In this way, the accelerometer sensitivity can reach about 10^−9 (m/s^2)/√Hz at 1 Hz.

In the last part of the thesis I have studied the Linear Variable Differential Transformer (LVDT), a kind of displacement sensor widely used in Superattenuator control. I have designed a system to read the output of LVDT using a FPGA. It consists of a Direct Digital Synthesizer (DDS) that is used both to drive the primary coil of the LVDT with a sine wave at 50 kHz, and then to demodulate the signal induced on the secondary coils, whose amplitude is modulated by a signal proportional to displacement. An algorithm, based on a Phase-Locked Loop (PLL), allows the detection of the phase shift of the signal induced on the secondary coils, and tunes the system in order to maximize the signal-to-noise ratio of the measurement of displacement.