Summary: In feedforward active noise and vibration control (ANVC) or active noise control (ANC), with online secondary path modeling, fast converging overall modeling algorithms may give high modeling errors. These errors are due to the highly correlated inputs, namely the reference and antinoise signals. These high modeling errors can result in poor performance if ignored. However, it is possible to consider these modeling errors in the control filter design, resulting in a careful controller and good performance, as proposed in this work. Careful control is a dual controller feature, which is the solution to the optimal control problem, but this has not been proposed before in the context of ANC. The modeling error covariance matrix (Sigma(n)) is available in the Kalman filter. However, this requires the knowledge of the time‐varying measurement noise power q(n) and state noise. Instead, this work uses a different approach in which the corresponding linear system is solved in a non‐recursive manner. The resulting maximum error is used for a worst‐case estimate of q(n), and, as it turns out, this can be used to get a worst‐case estimate of Sigma(n). A lower control filter update frequency and other optimizations keep computational complexity similar to other approaches. The resulting algorithm has very few easily selected parameters, good performance, does not require any prior secondary path estimate, and adapts to slow and sudden changes in the physical paths without loss of performance or noise overshoots. However, performance can be impaired by large background noise levels. [ABSTRACT FROM AUTHOR]