Adaptive pole assignment using an auto-recurrence model-based state feedback control scheme

Abstract

A parameter control scheme is developed for control of a single-input single-output (SISO) process. An auto-recurrence model is used for the identification of structural and coefficient parameters. Adaptive model state feedback control is used based upon a pole-placement design. Around this, adaptive explicit Closed-Loop Model-Reset (C-L M-R) is used for offset elimination. Different parts of the complete scheme, as noted below, were considered, developed, and tested. Reviews are given of various state models, the weighted least-squares methodology, and iterative search algorithms for batch optimization with respect to formulations, terminology, features, and attributes. Several sequential (coefficient) parameter estimation methods are tested and evaluated. These include ordinary recursive least-squares (RLS) and those based upon a steepest descent search, an orthogonal directions search, a conjugate directional search, Broyden's (Rank 1) search, and the Davidon-Fletcher-Powell (DFP) search method. The last three methods utilize periodic resetting to a steepest descent step. They preformed well on noise-free test data. However, on data with inherent process (and measurement) inaccuracies (or noise), they showed an undesirable parameter spiking tendency. The overall evaluations led to the selection of RLS with simultaneous noise filter design for use in the complete adaptive control scheme. A new method to adapt the structure of the adaptive controller's models is developed and tested. This adapts the structural parameters as the numbers of delay (deadtime) elements, poles, and zeroes. A new pole-placement design is developed and tested. The design is formulated and solved as a constrained optimization problem. It can provide control even when "uncontrollable" models are encountered. The actual process control algorithm employs model state-variable control with explicit C-L M-R. Procedures are developed and tested to update the state variables of these control models as the models are adapted. The complete adaptive control scheme is shown to operate successfully for a simulated test involving a switch between processes with significantly different structural and coefficient parameters.