Large sub-millisecond heat pulses due to Type-I edge localized modes (ELMs) have been eliminated reproducibly in DIII-D for periods approaching nine energy confinement times (τE) with small dc currents driven in a simple magnetic perturbation coil. The current required to eliminate all but a few isolated Type-I ELM impulses during a coil pulse is less than 0.4% of plasma current. Based on magnetic field line modelling, the perturbation fields resonate with plasma flux surfaces across most of the pedestal region (0.9 ≤ ψN ≤ 1.0) when q95 ≤ 3.7 ± 0.2, creating small remnant magnetic islands surrounded by weakly stochastic field lines. The stored energy, βN, H-mode quality factor and global energy confinement time are unaltered by the magnetic perturbation. Although some isolated ELMs occur during the coil pulse, long periods free of large Type-I ELMs (Δt > 4-6 τE) have been reproduced numerous times, on multiple experimental run days in high and intermediate triangularity plasmas, including cases matching the baseline ITER scenario 2 flux surface shape. In low triangularity, lower single null plasmas, with collisionalities near that expected in ITER, Type-I ELMs are replaced by small amplitude, high frequency Type-II-like ELMs and are often accompanied by one or more ELM-free periods approaching 1-2 τE. Large Type-I ELM impulses represent a severe constraint on the survivability of the divertor target plates in future burning plasma devices. Results presented in this paper demonstrate that non-axisymmetric edge magnetic perturbations provide a very attractive development path for active ELM control in future tokamaks such as ITER.