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When to use integral to calculate phase lag?
The integral will be greatest when the signals ‘line-up’ and the time-shift corresponding to this position can then be used with the signal frequency to calculate the phase-lag ( 2 π f ∗ t i m e D e l a y = p h a s e L a g ). What worked best for me was to continuously record the signal over two or more periods.
This article describes the phase relationship between the command signal and the stage response. The response is monitored using the internal (in this case capacitive) sensor. The bandwidth of a system is the key element to phase lag. Using control parameters one can easily obtain a bandwidth of approximately 1/3 the loaded resonance of the system.
How does phase lag affect the driving frequency?
Phase lag results at different frequencies can be seen here. Please also note that as the driving frequency increases, the phase lag (in time) stays mostly the same as a consequence of the control-loop tuning, but the lag takes up more and more of the input period.
How is the lag between two signals determined?
You can use the cross-correlation function to determine the lag between the two signals. Answers about using cross-correlation are correct. But if your input and output signals are sinusoid you can use more simple and faster method. eliminate high-frequency part.
How to calculate the phase of a sinusoidal signal?
Then calculate phase by: This method worked well for sinusoidal signals of the same frequency. Becomes problematic when various frequency components are mixed in the signals. For the phase between 2 blocks of sinusoidal data, block1 and block2: (using classical phase detector mapping) Note the above is for phase angles between 0 and 180 degrees.
How is cross correlation used to determine phase lag?
A cross-correlation of your signals could be used to determine the phase lag. Cross-correlation basically consists of sliding one function along the time-axis while keeping the other fixed, calculating the integral of their products at each time-shifted position.