How to implement wavelet-based controller

Hello,

I am working on the wavelet-based controller. However, I am now confusing about how it is implemented. My questions are 1. When the error signal is decomposed, we generate the control signal from the coefficients or the reconstructed signal?

2. If we use coefficients, how can we generate control signal from them ? since at each time step, we have to trap the error signal over a specific interval, decompose them and the resulting coefficients do not have the same length as the error signal.

3. If we use reconstructed signal (which I don't thing this is the case), then how can MRPID work? since normally, the error signal does not contain high frequency. I tried this method and found that almost all information of the error signal will be in the approximated reconstruction of the signal. Thus, even if I apply gains to other components, it will not affect the error signal so my result is just the same as I use only proportional gains to the error signal in PID controller.