Real-time implementation of delayed model predictive control in active noise control systems

The filtered-x normalized least mean square (FxNLMS) algorithm is widely used in industrial active noise control (ANC) systems due to its simple implementation and robust stability. In contrast, model predictive control (MPC) is known for handling multivariable and constrained optimization problems but remains underutilized in active noise control due to its high computational demand and the strict latency requirements of ANC systems. Additionally, existing MPC based ANC schemes often rely on external disturbance predictors, limiting their accuracy and applicability to predictable noise. This paper addresses these shortcomings by formulating a delayed joint state space model that integrates the primary and secondary acoustic paths, thereby removing the need for disturbance prediction. Building on this model, we derive an unconstrained causal MPC algorithm combined with saturation that directly computes the optimal control signals for the secondary loudspeaker in real time. Compared to the standard FxNLMS algorithm, the proposed method achieves improved noise attenuation while maintaining computational complexity comparable to FxNLMS. The performance of the approach is demonstrated through numerical simulations and real time experiments.