This paper takes into consideration a combined extended Kalman filter (CEKF) by using a bivariate polynomial for the estimation of Ld and Lq in saturation conditions. In the context of the Kalman filter (KF), Ld and Lq are modelled as nonlinear augmented states to control a permanent magnetic synchronous machine (PMSM). Once Ld and Lq are estimated, continuous monitoring of the machine saturation conditions is achieved to ensure the desired torque even under saturation conditions. The proposed adaptive control method based on maximum torque per ampere (MTPA) consists of an adaptive feedforward and PI controller. A discussion in light of the measured results using Hardware-in-the-loop is also included.