I'm a Junior computer engineer working on a project involving a 3d printer. It is a mobile printer with the print head attached to wheels which move along the x,y axis of the surface it is printing on. The wheel movements may be off by less than a millimeter as the printer is moving. This causes a serious problem after printing a few layers as each layer does not land on top of the other.
I am in the process of implementing a sensor to detect the location of the print head with respect to some arbitrary reference point. My task is to implement a feedback control loop to correct the printer's movements and have the object printed properly.
I have an idea of how I want to solve this; using the sensor to detect the current location, then read the code to check what is the desired location, I then implement code to move the difference.
My question is where does the concept of PID control even fit in? The following equations were taken from wikipedia for time/frequency domains.
I am confused about the values of t and s in the above equations. I have numeric values for input, output, error and the K constants. None of the values are functions so I don't understand what happens with the derivative and integration involved. Sorry if this seems like a dumb question but I am a complete novice to control theory and have been learning from online articles.