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The effective force testing is a promising seismic testing method for evaluating the structural dynamic response to earthquakes for conciseness and efficiency. However, two challenging loading issues are associated with this method, i.e. the natural velocity feedback (NVF) and nonlinearities related to the interaction between the loading system and specimen, thereby hindering its development and extensive applications. To address these issues, this study proposes a dynamic force loading strategy using a hybrid algorithm with linear compensation for NVF and model reference adaptive control via the minimal control synthesis (MCS) method. Online identification of linear compensation gain in preliminary tests is conceived based on the gradient descent method. A series of numerical simulations on a nonlinear loading system model with linear/trilinear single/two degree(s)-of-freedom specimens are conducted using five loading strategies, including linear and nonlinear compensations and MCS method. Comparative studies show that the proposed method and nonlinear compensation strategy outperform the other three methods, and sometimes the proposed method performs best. In summary, the proposed method is promising because of its accuracy and robustness as well as its ease of implementation and cost-effectiveness. [ABSTRACT FROM AUTHOR]