This paper presents a novel electromagnetic induction (EMI) system integrated in magnetorheological (MR) dampers: The added EMI system converts reciprocal motions of MR damper into electiral energy (electromotive force or emf) according to the Faraday's law of electromagnetic induction. Maximum energy dissipation algorithm (MEDA) is employed to regulate the MR dampers because it strives to simplify a complex design process by employing the Lyapunov's direct approach. The emf signal, produced from the EMI, provides the necessary measurement information (i.e., realtive velocity across the damper) for the MEDA controller. Thus, the EMI acts as a sensor in the proposed MREMI system. In order to evaluate the performance and robustness of the MR-EMI sensor system with the NEDA control, this study performed an extensive simulation study using the first generation benchmark cable-stayed bridge. Moreover, it compared the performance and the robustness of proposed system with those of Clipped-Optimal Control (COC) and Sliding Mode Control (SMC), which were previously studied for the benchmark cable-stayed bridge. The results show that the MR-EMI system reduced the vibrations of the bridge structure more than those of COC and SNIC and show more robust performance than that of SMC. These results suggest that EMIs can be used cost-effective sensing devices for MR damper control systems without compromising the performance of them.