Nonlinear Adaptive Control for Electromagnetic

We study here the problem of robust ”soft-landing ” control for electromagnetic actuators. The soft landing requires accurate control of the actuators moving element between two desired po-sitions. We present here two nonlinear adaptive controllers to solve the problem of robust trajec-tory tracking for the moving element. The first controller is based on classical nonlinear adaptive technique. We show that this controller ensures bounded tracking errors of the reference trajec-tories and bounded estimation error of the uncertain parameters. Second, we present a controller based on the so-called Input-to-State Stability (ISS), merged with gradient descent estimation filters to estimate the uncertain parameters. We show that it ensures bounded tracking errors for bounded estimation errors, furthermore, due to the ISS results we conclude that the tracking errors bounds decrease as function of the estimation errors. We demonstrate the effectiveness of these controllers on a simulation example