First of all we are talking about “actuation”. A system is openly (open loop) controlled is the feedback of the actuation is not played back. Otherwise, if the (feedback) sensing is included, we call it closed loop.
A common mechanism to reduce the actuation error of a noisy system is a PID controller. Three components reduce the continuous error:
- P-roportional (view on current) error correction, if the deviation is +5 the error reduction feedback is -5.
- I-ntegral (view in the past) error, if the past error was high we have to give a high error correction. Area of the error function.
- D-ifferential (outlook to the future) error, if the error increases we have to give a decreasing error correction. It is the function slope of tangent.
To avoid noise in the sensing – the closed loop thing- filters such as the Kalman-filter are quite supportive.
Keep in mind, the Kalman-filter assumes that the variables describing the system are normal distributed (Gaussian) and can be linear (if not extended Kalman), iterative extrapolated, because the mean value is seen as the expected value. The variance around the mean is the uncertainty.
Kalman-filter happens in two steps:
- Prediction the process according its model e.g., velocity = distance / time
- Measurement and correction (calculate the gain) with an probabilistic approach
As prognoses (aka prediction) model the “Monte Carlo” approach is commonly used if no historical data exists. The variables will be simulated by random variables, but we have to know the possible value range.
Keep in mind, the random “Monte Carlo” variable must be between 0 and 1. The value will be mapped to the expected value range e.g., -4 to 4. This allows to reduce the noise of the system.