The global focus has recently shifted away from fuel‑based power sources, and one of the most important projects for energy production is wind energy. To maintain low costs, the current research examines the problem of vibrations affecting wind turbine towers’ performance (WTTs). In particular, the tower, resulting from excessive vibrations, can negatively affect a structure’s power output and service life, as it can cause fatigue. Therefore, we conducted numerical tests on various types of controlled systems. Our tests revealed that combining a new technique cubic negative velocity control (CNVC) and linear negative acceleration control (LNAC) was the most effective and cost‑efficient option for vibration damping. This solution was derived by using an approximation method for the averaging technique. The external force is an important component of a nonlinear dynamic system and can be characterized by two‑degree‑of‑freedom (2‑DOF) differential coupled equations. After implementing the control measures, we conducted a numerical analysis of the vibration values before and after the operation. Stability is studied numerically. The numerical and approximate solutions were confirmed through the frequency response equation and time history with fourth‑order Runge– Kutta (RK‑4). Finally, we investigated the effect of parameters and compared our results with those of previously published studies.