An S-plane compensation transfer function implemented in a computer requires that the computer calculate the values of the transfer function many times a second for a typical control loop. This is at least twice the frequency of the highest frequency in the loop, which often means a large number of complex-number calculations per second. If it is too many for standard microcontrollers, than you may need to use a DSP (Digital Signal Processor) controller which is optiminzed for doing such calculations.
Also, if the control loop signals are analog, then they will have to be converted by an ADC to digital for the microcontroller, and then back to analog by a DAC after the calculations. Some DSP chips have the ADC and DAC converters built in for this purpose.