My first thought: Why not just use max gain? of course that would leas to catastrophic failure over short or long. Second thought: Why not both? Just like speed

My first thought: Why not just use max gain? of course that would leas to catastrophic failure over short or long. Second thought: Why not both? Just like speed is a derivative, so perhaps you want a set of differential equations, also gain per square time, too. On another note, "not to play" should be a zero-division error.