A nonlinear signal-based control (NSBC) method utilises the ‘nonlinear signal’ that is obtained from the outputs of a controlled system and its linear model under the same input signal. Although this method has been examined in numerical simulations of nonlinear systems, its application in physical experiments has not been studied. In this paper, we study an application of NSBC in physical experiments and incorporate an error feedback action into the method to minimise the error and enhance the feasibility in practice. Focusing on NSBC in substructure testing methods, we propose nonlinear substructuring control (NLSC), that is a more general form of linear substructuring control (LSC) developed for dynamical substructured systems. In this study, we experimentally and numerically verified the proposed NLSC via substructuring tests on a rubber bearing used in base-isolated structures. In the examinations, NLSC succeeded in gaining accurate results despite significant nonlinear hysteresis and unknown parameters in the substructures. The nonlinear signal feedback action in NLSC was found to be notably effective in minimising the error caused by nonlinearity or unknown properties in the controlled system. In addition, the error feedback action in NLSC was found to be essential for maintaining stability. A stability analysis based on the Nyquist criterion, which is used particularly for linear systems, was also found to be efficient for predicting the instability conditions of substructuring tests with NLSC and useful for the error feedback controller design.