Application of multivariable GPC to a four tank process with unstable transmission zeros

This paper presents in which conditions instability problems arise when Generalized Predictive Controller is applied to a multivariable system with unstable transmission zeros. The four tank process is a nonlinear multivariable process commonly used to study this kind of process. The paper shows how the instability problems are produced by cancellations of unstable transmission zero with an unstable pole, which lead to a loss of internal stability of the feedback system. A guideline about tuning GPC for this kind of processes are also presented and controller performance is judged using the nonlinear multivariable system.