Structural testing often involves the use of servo-hydraulic actuators. The inherent nonlinearity of a servo-hydraulic actuator as well as the nonlinear response of experimental specimens results in an amplitude-dependent behavior of the entire servo-hydraulic system, making it difficult to accurately control the actuator. The existence of the nonlinear response in the servo-hydraulic system can be a critical issue that must be addressed to achieve a successful real-time hybrid simulation involving a large-scale experimental substructure controlled by multiple actuators. In order to achieve improved control of servo-hydraulic systems with nonlinearities, an adaptive time series (ATS) compensator is introduced in this paper. The ATS compensator continuously updates the coefficients of the system transfer function during a real-time hybrid simulation using on-line real-time linear regression analysis. Unlike most existing adaptive methods, the system identification procedure of the ATS compensator does not involve user-defined adaptive gains. Through the on-line updating of the coefficients of the system transfer function, the ATS compensator can effectively account for nonlinearities in the servo-hydraulic system and experimental specimen, resulting in improved accuracy in actuator control. In this study, the exceptional performance achieved in actuator control using the ATS compensator is demonstrated through a real-time hybrid simulation of a large-scale 3-story steel frame structure with large-scale magneto-rheological (MR) dampers.