This brief presentation concerns the stabilisation problem of the input-restricted magnetic levitation system using an input-to-state stabilisable robust control Lyapunov function (ISS-RCLF) controller and a reference management / governor system based on input-to-state stability (ISS) and control Lyapunov function (CLF) approaches.
First, an ISS-RCLF controller is designed to bring the disc of the input-restricted magnetic levitation system to the desired position (stabilisation) in the presence of disturbances. The efficacy of the controller is then verified through computer simulations.
Next, a low-cost computing nonlinear continuous time differential reference management system, also known as the reference governor system is designed and applied to the ISS-RCLF controlled system so that the system can be stabilised for any inputted desired output value while preserving the input within the input constraint. This system acts as a supporting system to the ISS-RCLF controller since it controls the convergence of the state and helps to stabilise the magnetic levitation system in a way that the input is always preserved within the input constraint for any inputted desired output value. The effectiveness of the reference governor system is then verified via computer simulations.
Furthermore, the influence of the reference governor on the controlled system is studied by comparing results of the simulations.