In the context of problem 1, suppose that no one is really sure whether Y is affected by changes in X and, if it is, whether the relationship is "direct" or "inverse".
(a) Speculate on what might happen if the PID controller of part (c) above is implemented where Y is completely unrelated to X. What might happen if in fact Y is inversely related to X?
(b) How would you propose to figure out what, if any, PID control based on X might be fruitful?