Selective updating (SU)-based adaptive algorithms are proposed for secondary path estimation and noise control in active noise control systems. Use of the proposed variable threshold (VT) for noise control filter aids in reducing the computational complexity of filtered-x LMS-Newton algorithm to achieve fast convergence and improved noise reduction irrespective of the eigen-spread of input signal correlation matrix. A VT-SU least mean square algorithm is presented for the online estimation of the secondary path that reduces computational cost while maintaining estimation accuracy and convergence speed. A power scheduling scheme is presented that requires only one tunable parameter and discontinues auxiliary noise for power level below a predefined limit to reduce the residual error signal. The proposed VT-SU algorithms allow frequent updates in the transition phase and fewer updates in the steady state. Simulations are performed under benchmark conditions to validate the improved performance of the proposed method in comparison with established state-of-the-art methods in terms of estimation accuracy, steady-state residual error, convergence speed, number of tunable parameters, tracking capability, and computational complexity.