Non-linear adaptive control for electromagnetic actuators

The authors study here the problem of adaptive ‘soft-landing’ control for electromagnetic actuators. The soft landing requires accurate control of the actuator´s moving element between two desired positions. They propose a non-linear adaptive controller to solve the problem of robust trajectory tracking for the moving element, when considering model uncertainties with linear parametrisation. The controller is an integral input-to-state stability (iISS) backstepping controller, merged with gradient descent estimation filters to estimate model uncertainties with linear parametrisation. They show that it ensures bounded tracking errors for bounded estimation errors. Furthermore, iISS result allows us to represent the bound on tracking error as a decreasing function of the estimation error. They demonstrate the effectiveness of this controller with numerical tests.