Active control of the ideal external kink mode and the resistive wall mode (RWM) is numerically investigated using the MARS-F code (Liu et al 2000 Phys. Plasmas7 3681), for a reactor relevant tokamak plasma shaped with negative triangularity (NTR). Magnetic coils are used as the actuators of the control system. An ideal feedback system (i.e. with no time delays), located inside the vacuum vessel, is shown to be capable of stabilizing the external kink mode and moderately increasing the ideal-wall beta limit by up to 10%. Despite the rather different plasma boundary shape as compared to the conventional D-shaped plasma, the optimal poloidal location of the active coils is still the low-field-side of the torus. The eddy currents in the wall may enhance or cancel the control field produced by active coils depending on the poloidal location of the active coils, thus improving or deteriorating the feedback performance. For a single row of active coils, the optimal poloidal width is about 50° for the RWM stabilization, for the NTR plasmas considered in this study. With two rows of coils, optimization of the feedback gain phasing helps to substantially improve the RWM control. The control performance experiences jumps as the radial location of the active coils is shifted across the poloidal sensor location, as shown in both MARS-F computations and by an analytic model.