The current paper introduces an efficient tilt-integral-derivative-acceleration (TIDA) controller for regulating nonlinear systems. The suggested control system structure consists of the conventional TID controller with added accelerator term to improve the transient response. The accelerator term augments the control signal based on the rate of change of the error signal, enabling faster response to sudden changes or disturbances in the system dynamics. Furthermore, the optimization of TIDA parameters is achieved through the Grey Wolf Optimization (GWO) algorithm. As a result, it provides a high level of flexibility in dealing with disruptions and uncertainties in system output that affect system performance. The Grey Wolf Optimizer (GWO) is used to optimize the proposed TIDA controller parameters, and the optimal range for those parameters is determined by minimizing an integral time absolute error (ITAE) fitness function. The applicability and superiority of the given TIDA controller based on GWO are evaluated by simulating a nonlinear DC servomotor and comparing the results with that of existing controllers. Simulation tasks show that the proposed TIDA controller has a higher superiority response for system disturbances and step changes to the other approaches.