I have come across this Proportional Integral- Derivative( PID) control theory. I feel that it is highly beneficial and accurate. I want to create a new algorithm which is more accurate, faster, efficient than PID. Also it should be easily programmable in microcontroller. So what are the prerequisites/ learning materials for a beginner like me. Also, I have heard that we have to mathematically prove that a control algorithm converges to a defined value when applied repeatedly. Could you please provide details about the rigorous math needed.