Multiscale modeling and model predictive control of processing systems

Abstract

Traditional approaches in Model Predictive Control (MPC) suffer from several weaknesses such as: (a) Satisfying the output constraints over a finite control horizon and guaranteeing closed loop stability. (b) The need for infinite horizon for robust stability and performance. (c) Limited representation of plant-model mismatch. (d) Inability to shape frequency response characteristics of the outputs through systematically selected weights in the objective function. (e) Significant numerical complexity which depends on the number of input constraints. These weaknesses are addressed by formulating and solving the MPC in a multiscale (time/scale) domain. Based on the wavelet transformation of time domain models, the multiscale models are defined on dyadic or higher-order trees, whose nodes are used to index the values of any variable, localized in both time and scale (range of frequencies). The objective function, state equations, output equations and constraints on inputs and outputs are transformed into the multiscale domain. Moreover, feedback information is also generated for all scales using a multiscale constrained state estimator, providing rich depiction of the plant-model mismatch (including modeling errors, external disturbances and measurement noise) than the pure time domain formulation. This problem formulation: (i) incorporates rich depiction of feedback errors and provides an environment to identify plant-model mismatch at multiple scales, (ii) it provides a natural framework for optimum fusion of multirate measurements and control actions. The solution to this problem, (i) satisfies all the constraints on inputs and outputs if the problem is feasible at least over an infinite horizon and (ii) satisfies the frequency response specifications on the controlled outputs. In addition it reduces the computational load through two very effective mechanisms. (l) Sets horizon to the required length at each open loop optimization step. (2) It minimizes the search space for active constraints, because once a constraint is determined to be active at a scale, all the lower scale depictions of the constraint emanating from that node, will also be active, and can be solved using parallelized algorithms thus reducing the complexity further and allowing handling of larger problems with more constraints.