This paper discusses the dependence of the convergence rate on the acoustic error path in these popular algorithms and introduces new algorithms which increase the convergence region regardless of the time-delay in the acoustic error path. We also Propose a novel control algorithm (AFC/CAFC) for tonal noise cancellation. The proposed algorithm estimates the magnitude and phase of the tonal noise. The algorithm uses the steepest descent method for the phase/magnitude estimation. Performances of tile CAFC algorithm are presented in comparison with those by the AFC algorithm based on computer simulations and experiments.