Interval-Based Sliding Mode Control Design for Solid Oxide Fuel Cells With State and Actuator Constraints

The control design for many practical applications involves a need to specifically treat parameter uncertainty and disturbances. As shown in previous work of the authors, techniques from interval analysis can be used for this purpose in an efficient way. The two options that have been considered so far are the use of interval analysis in either a framework for model predictive control or in a framework for variable-structure sliding mode design. In the latter case, interval techniques can be used efficiently for a robust stabilization of continuous-time dynamic systems despite bounded uncertainty. To avoid unnecessarily conservative control strategies, it has to be shown in real time that the closed-loop control system is guaranteed to remain asymptotically stable despite bounded error variables. This online stability proof is performed on the basis of suitable candidates for Lyapunov functions, whereas functionalities for interval analysis are provided by C++ software libraries. Required partial derivatives, for transformations of state equations into suitable canonical forms and for the estimation of a finite number of time derivatives of the controlled variables, are efficiently computed by algorithmic differentiation. This paper presents an overview of interval-based variable-structure control approaches for the thermal behavior of solid oxide fuel cells. These approaches consist of trajectory tracking during nonstationary heating phases and disturbance compensation at high-temperature operating points. Finally, they rigorously account for state and actuator constraints.