Nonlinear Control of a Transient Inductrack System Using State Feedback

The concept of Inductrack refers to the magnetic levitation technology achieved by Halbach arrays of permanent magnets. In an Inductrack system, the dynamic behaviors involved with transient responses are difficult to capture due to the highly nonlinear, time-varying, electromagnetic-mechanical couplings. In the literature, dynamic modeling of Inductrack systems that aims to analyze the transient behaviors has been widely addressed. However, one common issue with the previous investigations is that most of the dynamic models either partly or completely adopted certain steady-state and ideal case assumptions. These assumptions are extremely difficult to maintain in a transient scenario, if not impossible. Therefore, while providing good understanding of Inductrack systems, the previous results in dynamic modeling have a limited utility in providing guidance for feedback control of Inductrack systems. Recently, a benchmark transient Inductrack model was created for characterizing the transient time response of the system with fidelity, which enables model-based feedback control design. In this work, based on the transient model, a new control method for the Inductrack dynamic system is developed. The proposed control method consists of a linear part and a nonlinear part. The linear part is devised based on a state feedback configuration; the nonlinear part is accomplished by fitting a nonlinear “force-current” mapping function. With this nonlinear feedback controller, the levitation gap of the Inductrack vehicle can be effectively stabilized at both constant and time-dependent traveling speed. The proposed control law is demonstrated in numerical examples. The nonlinear control design is potentially extensible to more complicated Inductrack systems with higher degrees of freedom.