Active noise blocking: Non-minimal modeling, robust control, and implementation

This paper presents a new modeling and robust control approach for active noise blocking (ANB). The proposed modeling technique is based on a new non-minimal state-space realization (NSSR) of continuous-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. The NSSR model generates a non-minimal set of states for a given system, using measured inputs and outputs, without differentation. From the NSSR model, using an Hinfin model reduction technique, a reduced-order state space (RSS) model is derived with known states. A multi-model Hinfin state-feedback (MHSF) control is then designed, in an LMI framework, for multiple RSS models of the system. This control design has an increased robustness against modeling uncertainty when different frequency responses of the system belong to a bounded convex set. Hardware experiments using a digital signal processor (DSP) have been carried out in order to verify the applicability and the performance of the proposed NSSR-based modeling and vibration control of a plate for active noise blocking (ANB) in a 3D acoustic enclosure.