Multivariable GPC for processes with multiple time delays: Implementation issues

In this work, implementation issues related to multivariable Generalized Predictive Control (GPC) for processes with multiple time delays are analyzed. Due to specific properties of those processes, the resulting control system has to account for the existing delays between control variables changes and their effect on controlled outputs. In the case of Model Predictive Control (MPC) techniques, such as GPC, the dead-time issue can be captured in the process model and thus considered in the predictive mechanism of the controller. However, this working principle results in augmented matrix dimensions that considers input-output time delays as additional zero entries. This fact increases the computational load and has to be accounted for in the control system design, specially in systems where computing resources are scarce (eg. embedded systems). The reduction of the matrix dimension, and hence the computation required, depends on how the delay terms are structured. The presented analysis considers two different GPC implementations for multivariable dead-time processes, which are used to compensate for internal matrix dimensions for the multiple time delays. Each implementation mode is evaluated for two industrial multivariable processes, providing several performance indexes. Performed simulations show that the required computational load can be reduced when adequate implementation mode is selected.