Table 1 System parameters for simulation and experimental validation of the simulator.
From: Improved mirror position estimation using resonant quantum smoothing
Parameter | Simulation | Experiment | Description |
|---|---|---|---|
h(ω) | \(\frac{c_{1}s + c_{2}\omega_{m}}{s^{2} + \beta s + \omega_{m}^{2}} e^{-s\tau}\) | \(\frac{c_{1}s + c_{2}\omega_{m}}{s^{2} + \beta s + \omega_{m}^{2}}e^{-s\tau}\) | Plant transfer function |
\(S_{f}(\omega)\) | \(\frac{Q}{2}[\frac{1}{(\omega-\omega_{i})^{2} + \gamma ^{2}} + \frac{1}{(\omega+\omega_{i})^{2} + \gamma^{2}}]\) | \(\frac{Q}{2}[\frac{1}{(\omega-\omega_{i})^{2} + \gamma^{2}} + \frac {1}{(\omega +\omega_{i})^{2} + \gamma^{2}}]\) | Forcing function PSD |
R | 7.7 × 10−11 | 7.7 × 10−11 | Measurement noise magnitude term where \(R\delta(t-t') = \sigma(\eta(t),\eta(t))\), η(t) is white Gaussian noise |
Q | 7.4 × 10−2 | 7.4 × 10−2 | Forcing function magnitude term where \(Q\delta(t-t') = \sigma(\xi(t),\xi(t))\), ξ(t) is white Gaussian noise |
γ | 1,333 | 1,333 | Forcing function damping factor |
\(\omega_{m}\) | 2π⋅7,930 | 2π⋅7,930 | Frequency of PZT resonance |
\(\omega_{i}\) | 2π⋅7,930 | 2π⋅7,930 | Frequency of forcing function resonance |
\(c_{1}\) | 131 | 131 | Constant |
\(c_{2}\) | 196 | 196 | Constant |
β | 2,494 | 2,494 | PZT resonance damping factor |
τ | 0 and 18.5 × 10−6 | system | Time delay |
F | 250 kS/s | 250 kS/s | Sample rate |
N | 215 | 216 | Number of samples |
Averages | 21 | 5 | Number of data sets averaged |