Hybrid Time–Frequency Domain Identification of Second-Order Plus Dead Time Model with Zero and Internal Model Control Design

This paper proposes a hybrid time–frequency domain identification method for second-order plus dead time models with an additional process zero (SOPDT+Z). A dual-relay experiment combined with step response data provides six independent equations for five model parameters, whose mathematical well-posedness is established through Jacobian rank analysis. A cascaded initialization strategy (Sundaresan → SIMC → Jin → proposed) guarantees monotonically improving accuracy. An Internal Model Control (IMC) framework yields equivalent PID parameters with a single tuning parameter λ, supported by a formal robust stability theorem. Simulation studies on five benchmark systems demonstrate 60–100% reduction in open-loop IAE compared to existing SOPDT methods, 36% faster settling, and 100% closed-loop stability under ±20% Monte Carlo perturbation (N = 200). Noise robustness analysis under SNR = 20–40 dB and additional performance metrics (ITAE, ISE) further validate the method.