Pole-zero placement through the robust receptance method for multi-input active vibration control with time delay

Vibration control is fundamental to improve the performances of lightweight flexible systems. However, the introduction of sensors and actuators in the control loop introduces time-delays which must be carefully considered during the tuning stage to obtain effective controllers. This paper proposes a novel approach for the design of state and state-derivative feedback active vibration controllers in multi-input systems with time delay. The method exploits the versatility provided by the system receptances: two procedures are presented to compute the control gain matrices that simultaneously assign the antiresonance frequencies (zero assignment) and a subset of the desired closed-loop poles (partial pole placement). The notion of eigenloci of the loop gain, an extension of the Nyquist plot for multi-input systems, is used to impose closed-loop stability and guaranteed robustness margins to the closed-loop system. A Genetic Algorithm is exploited to search a solution of the control non-convex optimization problem. The effectiveness of the proposed method is assessed through numerical simulations on some benchmark systems taken from the literature. The obtained results highlight that besides assigning the prescribed zeros and poles, the proposed method enables to obtain stable closed-loop systems with guaranteed phase and gain margins.