Nonminimal Model based Long Range Predictive Control

A new, Nonminimal Predictive Controller (NPC) is formulated by combining the nonminimal FIR output predictor developed by Lu et. al [10] with a long range predictive control strategy. The predictor structure used in the proposed NPC does not have the truncation error associated with the truncated, impulse or step response predictor structure used in DMC or MAC. Furthermore, the adaptive version of the proposed NPC does not require the on-line solution of a Diaphantine equation as required in GPC. It uses a single adaptive predictor to produce a trajectory of predicted output values with equal error variances at each predicted point. The conditions under which this can be achieved are formally generalized and proven as the Equal-variance Principle. Obeying this principle facilitates minimization of a parameter identification cost function which is the sum of long-range (multi-step) prediction error squares instead of the sum of single step prediction error squares. Therefore the identification algorithm is the dual of the the control calculation which aims at minimizing the long-range tracking error squares. This results in improved, robust, system performance even in the presence of noise and unmodeled dynamics. Reduced versions of adaptive NPC are also possible, which significantly reduce the number of parameters to be identified on-line. Simulation results confirm the advantages of using the nonminimal FIR predictor and show that NPC can outperform existing long range predictive controllers such as GPC.