This paper deals with active noise control (ANC) for impulsive noise sources. The most famous filtered-x least mean square (FxLMS) algorithm for ANC systems, is based on minimization of the variance of the error signal. The impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The FxLMS algorithm, therefore, becomes unstable for the impulsive noise. Among the existing adaptive algorithms for ANC of impulsive noise, one is based on the minimizing fractional lower order moment (p-power of error) that does exist for stable distributions, resulting in filtered-x least mean p-power (FxLMP) algorithm. Another solution is based on modifying; on the basis of statistical properties; the reference signal in the update equation of the FxLMS algorithm. In this paper, we discuss various variants of these two approaches. We see that using saturation nonlinearity in the reference and error signals of update equations of above-mentioned adaptive algorithms greatly improves the convergence performance. Yet as another solution, a modified normalized step-size may also be employed. Computer simulations demonstrate the effectiveness of the modified algorithms. We observe that the modified modifications greatly improve the robustness of existing adaptive algorithms for ANC of impulsive noise sources.