###### Abstract  
Previous control methods were designed based on cascade structure and consist of position and current controllers for permanent magnet-synchronous motors (PMSMs). Thus, the structures of the previous methods are necessarily complex although the stability is guaranteed. Thus, the gain tuning is difficult to obtain for the desired control performance for the PMSMs. To overcome this problem, this paper proposes a nonlinear optimal position control method with an observer to improve the position tracking performance of PMSMs. The proposed method consists of a desired state generator, controller, and nonlinear observer. The desired states and inputs are derived using the PMSM model. Then, the state feedback controller is designed based on the whole tracking error dynamics including both mechanical and electrical dynamics. The nonlinear observer  
regulator based controller was proposed to reduce sideband harmonics for the PMSM [14]. A nonlinear control method using neural network and terminal sliding mode control was proposed for the PMSM [15]. Control methods using the combination of linear quadratic regulator (LQR) method and observer were developed [16; 17].  
Although these methods improve the control performance of a PMSM, they require velocity and load torque measurements. Actually, it is difficult to measure both velocity and load torque because of space and/or cost limitations. Thus, several observers were proposed to estimate the state variables for the PMSM [18; 19; 20; 21]. However, these methods did not consider the load torque or were complex for the implementation for the PMSM. Furthermore, these methods are based on a cascade structure that consists of a mechanical dynamics controller and an electrical dynamics controller. Thus, it is difficult to choose the control gains for the mechanical and electrical dynamics controllers because electrical dynamics change much faster than mechanical dynamics. Another problem is that these methods are designed using a direct-quadrature (DQ) transformation. DQ transformation has been used for commutation in the control of PMSMs [22]. However, such a commutation is not exact because of the time delay of the position and current sensors. The commutation delay causes strikingly qualitative changes in motor behavior [23].  
Furthermore, the previous methods are designed based on the cascade control concept for both current and position tracking, where currents track the desired currents that generate the torque required by the electrical controller and the position tracker tracks the position required by the mechanical controller. Therefore, the structures of the previous methods are necessarily complex although the stability is guaranteed. Thus, the gain tuning is difficult to obtain the desired control performance for the PMSMs.  
This paper proposes a nonlinear optimal position control method with an observer to improve the position tracking performance of a surface mounted PMSM. The proposed method consists of a desired state generator, controller, and nonlinear observer without DQ transformation. The desired states and inputs are derived using the PMSM model. Then, the state feedback controller is designed based on the whole tracking error dynamics including both mechanical and electrical dynamics. The control and observer gains are chosen using an optimal control method. A nonlinear observer is designed to estimate the velocity and load torque. The closed-loop stability is proven using the input-to-state stability. The proposed method is not designed based on the cascade structure. Furthermore, the control and observer gains are chosen using an optimal control method to obtain the desired performance for the PMSMs. Thus, the gains can be easily tuned compared to the previous methods. This approach simplifies the design process such that the control algorithm is suitable for real-time control. The performance of the proposed method is validated via simulations.