Birhythmicity arises in several physical, biological and chemical systems. Although, many control schemes are proposed for various forms of multistability, only a few exist for controlling birhythmicity. In this paper we investigate the control of birhythmic oscillation by introducing a self-feedback mechanism that incorporates the variable to be controlled and its canonical conjugate. Using a detailed analytical treatment, bifurcation analysis and experimental demonstrations we establish that the proposed technique is capable of eliminating birhythmicity and generates monorhythmic oscillation. Further, the detailed parameter space study reveals that, apart from monorhythmicity, the system shows transition between birhythmicity and other dynamical forms of bistability. This study may have practical applications in controlling birhythmic behavior of several systems, in particular in biochemical and mechanical processes. ; Comment: Accepted in Physical Review E