Global Monotonic Radio-Frequency Impedance Matching Via Control Lyapunov Function Under Safety Constraints

One of the critical technologies in plasma etching in semiconductor wafers is radio frequency impedance matching control. An impedance matching network is essential to ensure the maximum power transfer in any system, and its application is ubiquitous. Many researches have been proposed control strategies to get a robust performances, reduce convergence speed, and more accurate. However, these proposal present a non-monotonic decreasing behavior of the reflected power, thus affecting the overall matching control performance. In this paper, we propose a controller technique, based on a Control Lyapunov Function (CLF), which ensures global asymptotic stability of the system. This takes place under a safe space of capacitor values defined by a control barrier function (CBF). Numerical simulations on a benchmark setup show the novelty of the proposed control scheme. Concerning others in the literature, it presents lower convergence time and robustness under several non-ideal conditions. Also, our study includes analysis of other indexes like the mean and maximum value of the reflection coefficient integral and reflected power.