Adaptive stability margin configuration for second-order systems with unknown parameters and input delay

Stability margins are critical safety indicators for control systems; however, their real-time configuration remains challenging in the presence of uncertain system parameters and input delays. This paper develops an indirect adaptive PI control scheme for second-order linear time-invariant (LTI) systems subject to unknown plant dynamics and an unknown input delay. A delay-aware parameter estimator employing a nonlinear least-squares approach is designed to enable the simultaneous online estimation of plant parameters and time delay. To facilitate real-time implementation, this paper derives explicit closed form approximations that map desired gain and phase margins directly to controller gains, thereby bypassing the computational burden of solving transcendental equations while maintaining high accuracy. The resulting controller achieves high-precision time-domain tracking and regulates frequency-domain stability margins to predefined specifications. Finally, aircraft pitch-rate control simulations demonstrate that the proposed method ensures reliable tracking and precise configuration of the desired stability margins.