Incremental and Positional Generalized Predictive Controller for Offset Free Reference Tracking

The traditional design of the Generalized Predictive Control (GPC), to deal with setpoint changes and tracking reference (denoting offset free), is to use an integral control weighted or an incremental plant model. The purpose of this paper is to derive an alternative way of GPC synthesis, from a positional plant model to cover zero steady-state offset, involving the selection of an integral polynomial weighting factor for the setpoint and output of the plant. This control approach introduces an integral control action in a natural way and guarantees an implicit control design. Additionally, the filtered positional GPC proposed in this paper can be hybridized into filtered canonical RST and filtered Internal Model Control (IMC) structures to be used in non-minimum phase, unstable and nonlinear plants, being the filtered positional GPC until now unexplored in nonlinear applications. For validation, this paper brings numerical essays with a nonlinear chemical plant model and an unstable and non-minimum phase model, and a practical test in a nonlinear plant (damped pendulum), showing the efficiency, stability and robustness to setpoint changes and disturbance rejection when moving the operating point of the plant around its nonlinear region. Keywords— integral control, error-free, generalized predictive control, disturbance rejection, target tracking, dynamic stability.