Generalized Predictive Control in the Presence of Constraints
OXFORD UNIV (UNITED KINGDOM) DEPT OF ENGINEERING SCIENCE
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Several predictive control strategies which handle physical system constraints have been proposed in the literature. The difficulty with these approaches is that, in an attempt to optimize output tracking over a finite horizon and guarantee stability, they define an optimization problem which can be infeasible in the case of systems with poles andor zeros outside the unit circle, this can lead to instability. In this thesis we develop stability conditions which ensure the continuing existence of a stabilizing solution and propose improved algorithms which overcome finite horizon infeasibility of making the output reach its set-point within a finite horizon. Here, we propose two algorithms which overcome these difficulties the first does so by mixing two- and infinity-norm objectives and the second retains only a two-norm objective, but introduces an additional constraint to ensure stability. We then examine the necessity of the strategy of requiring the predicted errors and input increments to reach zero within some finite horizon and show that, for a guarantee of stability, one needs only require these predictions to be stable. We propose algorithms which implement these relaxed restrictions and thus yield optimizations which, for a given number of degrees of freedom, utilize the entire class of stabilizing solutions rather than the sub-class of finite length sequences. Previous work does not consider the case of systems subject to physical constraints and disturbances. To guarantee feasibility, any inputoutput predictions must take into account the effects of disturbances. The final purpose of this thesis is to derive stability conditions for systems subject to disturbances, and then to develop algorithms which reserve enough control authority to reject the effects of bounded disturbances and thus retain the guarantee of stability.
- Numerical Mathematics