Adaptive Control Law for PID

This paper is the final report for my Spring 2019 internship at the Kennedy Space Center in Cape Canaveral, Florida. The official title of my internship is 'Launch Vehicle Control Study internship,' and I spent the spring working in GMRO- Granular Mechanics and Regolith Operations. There are two components to my project involving developing an adaptive control law for a PID controller. The first component involves performing a deep study and analysis of adaptive control laws, with the goal of developing stability proofs about the control law and the gain and phase margins. The second component involves analyzing the data received after implementing the adaptive control law. Unfortunately, as of the time of writing this paper, the data is not considered †̃clean' enough to analyze. Therefore, in this paper I will give an overview of adaptive control law stability proofs and will write about the data analysis separately. Section II includes several general definitions, and the later sections have additional definitions at the end of each section.A PID (proportional integral derivative) controller is a common control algorithm which isimplemented in NASA’s rocket launch system. The idea behind the PID controller is to calculatethe error (current position – desired position) and drive it to zero by using proportional, integral,and derivative influences on the controller. For example, when a sailor steers a ship which isheading towards location x but would like to turn the ship to reach location x∗, he/she wouldinitially turn the wheel significantly, and as the ship proceeds towards x∗ the sailor would slowlyshift the wheel back to its original position, and thereby drive the error, x∗ − x, to zero.