Backstepping-based levitation control design for linear magnetic levitation rail system

The levitation control in a linear magnetic levitation (maglev) rail system is a subject of considerable scientific interest because of highly nonlinear and unstable behaviours. The authors mainly focus on the sequential developments of backstepping-based control systems including a backstepping control (BSC), an adaptive BSC (ABSC) and an adaptive dynamic surface control (ADSC) for the levitated positioning of the linear maglev rail system. In the proposed ADSC system, a filter mechanism is incorporated with BSC to cope with the problem of the explosion terms caused by repeated differentiations in backstepping design procedure. Moreover, a robust observer is designed for predicting system uncertainties to solve the trouble of chattering phenomena caused by a sign function in BSC and ABSC law despite the utilisation of a fixed value or an adaptive tuning algorithm for the lumped uncertainty bound. The effectiveness of the proposed control schemes for the levitation control of a maglev system is verified by numerical simulations and experimental results, and the superiority of the ADSC system is indicated in comparison with the BSC and ABSC systems.