This study is aimed at development of a nonlinear IMC controller that can handle a larger class of nonlinear systems than hitherto, including the singular systems that exhibit change in the sign of the steady state gain. The construction of the model inverse is achieved through inversion of successive quadratic approximation of the nonlinear model operator. The controller synthesis problem is formulated as minimization of 2-norm of single step prediction error. Using the theory of solutions of the multidimensional quadratic equations, a closed form dead-beat type quadratic control law is evolved. The performance of the proposed control law is demonstrated by simulating control of two highly nonlinear systems and also a singular system. In the case of singular system, it has been shown that the proposed quadratic control law can be effectively used for handling a difficult robust control problem arising out of non-attainability of set point due to plant-model mismatch.