Two fractional differential controllers, described and validated by using the fractional order stability theorem and the Gershgorin circle theorem for a self-sustained electromechanical system consisting of a van der Pol-Duffing coupled oscillator, were studied in this paper. Based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Finally, the circuit simulation results demonstrate the correctness and the effectiveness of the proposed control and GS strategy.