As is well known, large-scale type-I edge localized modes (ELMs) may pose serious risks to machine components in future large fusion devices. The resonant magnetic perturbation (RMP), generated by magnetic coils external to the plasma, can either suppress or mitigate ELMs, as has been shown in recent experiments on several present-day fusion devices. Understanding the ELM control with RMP may involve various physics. This work focuses on the understanding of the roles played by three key physical quantities: the edge safety factor, the RMP coil current, and the particle drift kinetic effects resulting from thermal and fusion-born α-particles. Full toroidal computations are performed by using the MARS-F/K codes. The results show that the plasma response based figures-of-merit i.e. the pitch resonant radial field component near the plasma edge and the plasma displacement near the X-point of the separatrix,consistently yield the same periodic amplification as q_95 varies. The number of peaks, y, is positively correlated with the toroidal number n, i.e. y \approx n\Delta q_95 with \Delta q_95 = 3.5. The peak window in q_95 occurs when a new resonant surface passes through a specific region of the plasma edge. Two-dimensional parameter scans, for the edge safety factor and the coil phasing between the upper and lower rows of coils, yield a linear relationship between the optimal/worst current phase difference and q_95 , which can be well fitted by a simple analytic model. The optimal value of coil current amplitude is sensitive to n. Compared with the same current amplitude assumed for the two/three rows of coils, the optimal current amplitude can increase the \xi _\textX but does not change the prediction of the relative toroidal phase difference. More advanced response model, including kinetic resonances between the RMP perturbation and drift motions of thermal particles and fusion-born alphas, shows that the modification of kinetic effects should be considered in order to better describe the plasma response to RMP fields in high-β plasmas. The fluid response model with a strong parallel sound wave damping (\kappa _\parallel = 1.5) can well predict the plasma response for the ‘DEMO-like’ equilibria. For low β plasma, the kinetic response is consistent with the fluid response, whether a strong parallel sound wave damping exists or not.