Performance and gain and phase margins of well-known PI tuning formulas

The performance and robustness of well-known proportional-integral formulas are discussed. Tuning formulas that optimize load disturbance response have gain and phase margins that are smaller than those that optimize for setpoint response. Tuning formulas that optimize setpoint response mostly make use of the PI controller zero to cancel the process pole. They typically have a gain margin of three and a phase margin of 60 degrees. The Ziegler-Nichols tuning formula gives phase margin that varies greatly. Hence its performance varies greatly too. Approximate analytical formulas to compute gain margin and phase margin are also derived in this paper to facilitate online computation which could be particularly useful for implementing adaptive control or auto-tuning