Proportional–Derivative Output Feedback Vibration Control with Antiresonance for Systems with Time Delay in Actuators

Active vibration control is crucial for mitigating harmful resonant vibrations in structures subjected to harmonic loads. While antiresonant (zero-placement) methods are effective for this purpose, existing state-feedback solutions require full state measurement, and output-feedback approaches often prioritize resonance assignment over direct harmonic cancellation. This work bridges this gap by proposing a novel systematic design for a proportional–derivative (PD) output-feedback controller to achieve antiresonance for second-order linear systems with a time delay in the actuators. The method first computes a homogeneous gain solution. It then leverages the parametrization of all antiresonant solutions as a constraint within a genetic algorithm optimization. The algorithm optimizes both the stability margin, characterized by an Ms-disk criterion, and the number of encirclements of the critical point (−1,0) in the complex plane, as assessed by the Generalized Nyquist Stability Criterion. The proposed approach provides a practical, optimized output-feedback strategy for precise rejection of harmonic disturbances, as demonstrated through a collection of numerical examples from real-world applications. The results confirm the method’s effectiveness in synthesizing stabilizing controllers that enforce antiresonance while ensuring robust stability margins.