Theoretical Analysis of Long-Range Predictive Controllers

In this paper a rigorous and elegant formulation of long-range predictive control (LRPC) laws is developed in terms of transfer function operators. The controller structure for a variety of LRPCs is shown to consist of four parts: i) a set of controller gains, ii) a set of predictor filters, iii) a battery of set-point conditioning elements, and iv) an integration element. Two specific LRPC algorithms, Generalized Predictive Control and Dynamic Matrix Control, are analyzed using this framework to expose differences between the techniques. The GPC control law is formulated in standard feedback control form which is then used to characterize the closed-loop stability in the z-domain rather than the state-space domain commonly pursued in the literature. The form of the predictor model is reformulated to show explicitly the role of the plant step-response coefficients. Important properties of the technique are demonstrated analytically, including th capability of producing offset-free set-point tracking, furthermore, the stability and tracking properties of the control system are unaffected by stable or unstable pole-zero cancellations. The GPC technique possesses a certain degree of tolerance for near pole-zero cancellations. It is also shown that the control law exactly inverts the numerator dynamics of the plant under control, even when the plant contains time delay, provided that the controller gain vector is calculated using the Moore-Penrose pseudoinverse and the user-specified control-horizon parametr is chosen equal to the rank of the Dynamic Matrix.