Generalized predictive control in the delta-domain

This paper describes new approaches to generalized predictive control formulated in the delta (δ) domain. A new δ-domain version of the continuous-time emulator-based predictor is presented. It produces the optimal estimate in the deterministic case whenever the predictor order is chosen greater than or equal to the number of future predicted samples, however a “good” estimate is usually obtained in a much longer range of samples.

This is particularly advantageous at fast sampling rates where a “conventional” predictor is bound to become very computationally demanding. Two controllers are considered: one having a well-defined limit as the sampling period tends to zero, the other being a close approximation to the conventional discrete-time GPC.

Both algorithms are discrete in nature and well-suited for adaptive control. The fact, that δ-domain model are used does not introduce an approximation since such a model can be obtained by an exact sampling of a continuous-time model.