Minimum settling-time PI control of pure delay processes under a hard non-overshoot constraint: exact boundary-contact characterization and the role of the MID ... (opens in new tab)

We solve, exactly, the problem of minimum settling-time PI control of a pure delay process K e^{-Ls} under the hard time-domain constraint of zero overshoot, y(t) 0 the optimal gains converge to K Kp = e^{-2}, K Ki L = 4 e^{-2}, the generic multiplicity-induced-dominancy (GMID) point of the neutral quasipolynomial. The GMID response satisfies the hard constraint and uniquely maximizes the decay rate; yet at every finite delta the delta-adapted o...