Model-based control using interval type-2 fuzzy logic systems

Type-2 fuzzy logic introduced new formalisms capable of overcoming the inherent uncertainties of approximating real-world processes by computational models. Yet, despite increasingly present in the nonlinear modeling literature, model-based control theory does not seem to be taking full advantage of the improvements that type-2 fuzzy logic provides. Therefore, the present work proposes the development of a new control methodology based on the generalized predictive control theory supported by interval type-2 Takagi–Sugeno fuzzy logic systems. The developed control system is based on locally linear approximations of the type-2 Takagi–Sugeno model and will be evaluated using a nonlinear process based on the yeast fermentation reaction. For comparison purposes, two additional generalized predictive control implementations based on a linear auto-regressive model with exogenous inputs and a type-1 Takagi–Sugeno fuzzy model will be used. The performance of the closed loop systems will be evaluated by subjecting the process to quick changes in the operation regime and to unmeasured external disturbances. The mean squared error, control effort and typical transient step response metrics (overshoot and settling time) will provide the benchmark criteria. The results achieved demonstrate that at the expense of a small increase in the computational effort, type-2 fuzzy logic systems improve the transient behavior of the closed loop system, presenting significant advantages when the controlled process is subject to unmodeled disturbances.