Nonlinear Control Tools for Fused Magnesium Furnaces: Design and Implementation

This paper employs the recently developed nonlinear control tools to solve the engineering problem of stable current control of fused magnesium furnaces (FMFs). By fully taking into account the nonlinearity, uncertainty, and couplings in FMFs, this paper first develops a dynamic model for controller design. A mild assumption for controller design is verified by using experimental data. Based on the dynamic model, this paper proposes a class of stable control rules for the disturbance-free model. Then, the result is extended to handle both measurement errors and external disturbances. With the proposed control algorithm, it is proved that the closed-loop system is robustly stable, and the three-phase currents ultimately converge to neighborhoods of the setpoints. If the system is disturbance-free, then asymptotic stability can be guaranteed. It is shown that the proposed control algorithm can be readily implemented as rule-based control. The notion of input-to-state stability and the nonlinear small-gain theorem are employed as tools for the designs. An industrial application is demonstrated to show the validity of the proposed design in solving practical engineering problems.