Generalized Predictive Proportional Integral Controller Design for Unstable Plant Models with Long-Dead Times

Low order plant models with long dead-times require controllers to have some type of predictive structure. In control engineering practice it is very common to consider for such type of plant models a proportional-integral (PI) controller. However, another option is the Predictive PI (PPI) control structure, which has proven to surpass in performance the traditional PID controller structure for plant models with long dominant dead-times. Very recently a third, more flexible and novel control structure alternative has been developed, named the Generalized Predictive PI (GPPI) controller structure, which has proved to have better performance than the PI and even the PPI controller structures. Here we extend the study and analysis of these three controller structures to unstable low order systems with long dead-times. Such unstable plant models can result from linearization of linear plant models at unstable equilibrium points and/or due to the presence of faults. We show that neither the PI, nor the PPI controller structures, will in general suffice to stabilize such a challenging class of plant models. However, the GPPI controller structure design, tuned with a previously presented signal-to-noise ratio (SNR) approach, will prove to be up to the task for an arbitrary long dead-time unstable plant models.