Lyapunov-Based Controller Using Nonlinear Observer for Planar Motors

In general, it is not easy work to design controllers and observers for high-order nonlinear systems. Planar motors that are applied to semiconductor wafer-stage processes have 14th-order nonlinear dynamics and require high resolution for position tracking. Thus, many sensors are required to achieve enhanced tracking performance because there are many state variables. To handle these problems, we developed a Lyapunov-based controller to improve the position tracking performance. Consequently, a nonlinear observer (NOB) was also developed to estimate all of the state variables including the position, the velocity, and the phase current using only position feedback. The closed-loop stability is proved through Lyapunov theory and the input-to-state stability (ISS) property. The proposed method was evaluated based on the simulation results and compared with the conventional proportional-integral-derivative (PID) control method to show the improvement in the position tracking performance.