In Stochastic Controls Power Spectral Densities (PSDs) are often used to represent or define disturbance and noise environments. However, there are several implementation issues that must be dealt with when using PSDs.
The basics of a PSD are as follows:
- The PSD is represented in MATLAB by a vector of frequencies and magnitudes at those frequencies.
- PSDs typically (but not always) have units of magnitude squared (^2) over Hz.
- The primary metric used to compare one PSD to another is the Root Mean Square (RMS).
- As with most metrics the RMS does not tell you everything.
- Particularly important is where in the frequency range does most of the PSD energy resides. More specifically, "Is the energy in the low, mid, or high frequency range by comparison to your designed rejection and performance requirements?"
Some of the PSD implementation issues are:
- PSD measurements are often very coarse particularly in the low frequencies. The result of this is that low frequency measurements might be at 0.01 Hz, 0.1 Hz, 1 Hz, 2 Hz, 5 Hz, 10 Hz, ... For noise PSDs this is not usually an issue. However, disturbance PSDs are often dominated by low frequency content. The RMS is an integration under the curve and coarse measurements often lead to inaccurate RMS calculations.
- Addition and subtraction of PSDs must occur at the same frequency and this often dictates the use of an interpolated PSD.
- Measured data comes in the form that is easiest to capture with the least noise. This often leads to measurements in rate (from good MEMS gyros) or acceleration (from good MEMS accelerometers). While the measurements are in rate or acceleration the disturbances that need to be in any simulation may need to be integrated to a position PSD.