Analytical design of stable delta-domain generalized predictive control

This paper addresses certain fundamental issues related to the discrete-time design problem of the delta-domain generalized predictive control (δ-GPC) for both minimum phase and non-minimum phase linear SISO plants including nominal stability and nominal performance of the closed-loop system. The approach being presented is completely analytical, and the nominal performance of the control system is directly achieved by a prototype design of the closed-loop system characteristics resulting in definite time-domain specifications. Two design methods are offered in which a model-based prediction paradigm is applied to achieve the future output and the future filtered output trajectory of the plant. Prediction of the first type is based on suitable emulations of the output δ-derivatives and is used in the GPC controller design for minimum-phase models of the plant. Prediction of the second type utilizes emulation of derivatives of the output filtered by the numerator polynomial of the transfer function of the controlled part of the plant. It can be employed both for minimum phase and non-minimum phase plants. A numerical example is given that illustrates the δ-GPC method for controller design.