摘要：In this paper, a new analysis and design method for proportional-integrative-derivative （PID） tuning is proposed based on control.er scaling analysis. Integral of time absolute error （ITAE） index is minimized for specified gain and phase margins （GPM） constraints, so that the transient performance and robustness are both satisfied. The requirements on gain and phase margins are ingeniously formulated by real part constraints （RPC） and imaginary part constraints （IPC）. This set of new constraints is simply related with three parameters and decoupling of the remaining four unknowns, including three control.er parameters and the gain margin, in the nonlinear and coupled characteristic equation simultaneously. The formulas of the optimal GPM-PID are derived based on control.er scaling analysis. Finally, this method is applied to liquid level control.of coke fractionation tower, which demonstrate that the proposed method provides better disturbance rejection and robust tracking performance than some commonly used PID tuning methods.