An SOS Observer-Based Sensorless Control for PMLSM Drive System

Sum-of-squares (SOS) approach is an effective technique for analysis and design of nonlinear systems. Due to the advantage, this study presents an SOS observer-based control approach for sensorless position servo of permanent magnet linear synchronous motor. To apply the SOS approach, a nonlinear polynomial model is firstly established to describe motor dynamics. Based on this model, a full-order Luenberger observer is developed to estimate the system state. The observer gain that ensures the convergence of state estimation is deduced via the stability analysis and solved by using the third-party toolbox SOSTOOLS. Compared with earlier studies, the advantage of the proposed observer is that the exact motor dynamics is used. Therefore, no further hypothesis or adaptive mechanism on the mover speed is required, which is usually utilized to solve the problem of speed variation with the state observation. According to the principle of backstepping control, the controller is systematically designed to guarantee the asymptotic stability of the closed-loop system. Since both the mechanical and electrical dynamics have been considered, the control signal is directly presented as a voltage. This is different from the conventional current control strategy, which applies the proportional–integral controller to produce a voltage command. The experiment results are provided to validate the proposed control scheme. Moreover, a recent work that is based on the sensorless linear quadratic regulator optimal control is adopted as a comparison study.