Analytical PI Tuning for Second-Order Plants with Monotonic Response and Minimum Settling Time

Senol Gulgonul has published an analytical PI controller tuning method for second-order plants that guarantees monotonic step response with minimum settling time. The work, available on arXiv (2604.21294), addresses a long-standing gap in control theory: existing methods either only partially meet these objectives or require numerical optimization. The key insight is that designing closed-loop poles slower than the fast plant pole forces pole-zero cancellation of the slow plant pole as a consequence, not an assumption.

The resulting formulas are explicit: K=T1/(4KpT2) and Ti=T1, where T1 and T2 are plant time constants and Kp is plant gain. There are no free parameters. The closed-loop system has universal robustness properties independent of plant parameters: maximum complementary sensitivity Mt=1, maximum sensitivity Ms=1.155, and phase margin PM=76.35°. Simulations across six plant configurations confirm the analytical predictions exactly. This provides engineers with a direct, proven method for tuning PI controllers on stable second-order plants with two real poles.