Stability Margin Configuration for Second-Order Systems with Output Delay

Stability margins serve as critical safety indicators for control systems. However, real-time margin configuration remains a significant challenge. This paper develops a margin configuration scheme for typical second-order linear time-invariant systems with output delay. To facilitate practical implementation, explicit closed-form approximations are proposed to eliminate the need for solving complex transcendental equations and constructing a nominal PI control law. Crucially, these approximation techniques demonstrate broader applicability while maintaining high precision. The proposed method is applicable to regulating the system's stability margins near the desired values with low computational burden while achieving command tracking in the time domain. Finally, a pitch-rate control simulation of an aircraft demonstrates that the proposed method ensures reliable tracking and desired stability margin configuration, with an average error of error of 4.725%.