Constrained predictive control using orthogonal expansions

Abstract

AbstractIn this article, we approximate bounded operators by orthogonal expansion. The rate of convergence depends on the choice of basis functions. Markov‐Laguerre functions give rapid convergence for open‐loop stable systems with long delay. The Markov‐Kautz model can be used for lightly damped systems, and a more general orthogonal expansion is developed for modeling multivariable systems with widely scattered poles. The finite impulse response model is a special case of these models. A‐priori knowledge about dominant time constants, time delay and oscillatory modes is used to reduce the model complexity and to improve conditioning of the parameter estimation algorithm. Algorithms for predictive control are developed, as well as conditions for constraint compatibility, closed‐loop stability and constraint satisfaction for the ideal case. An H∞‐like design technique proposed guarantees robust stability in the presence of input constraints; output constraints may give “chatter.” A chatter‐free algorithm is proposed.