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1 2004

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GPC in state space with robust observer: constraint satisfaction based on invariant sets

Salcedo J. V., Martinez M., Sanchis J., Blasco F. X.

Systems Science

2004

Vol. 30, no 1

77-90

The Generalized Predictive Controller (GPC) [1], [2] belongs to the general class of predictive controllers. The authors have proposed an alternative (although equivalent) formulation for the GPC in state space [7]. This formulation is based on a robust observer [5], and the poles selection is closely related to the controller robustness. An important feature of predictive controllers consists of their ability to take explicitly into account hard constraints in their formulation. However, their design must be accompanied by a guarantee of feasibility. There are some papers which deal with (his problem [4], [9], [8], [3], although all of them suppose that the state of the process can be measured on-line. However, in some cases, the design of the GPC proposed by the authors cannot measure online the process states since they are artificial states, that is to say, not related to physical magnitudes. The authors in paper [6] extend the results of [3] to the GPC in the case where all the states are online measurable. So the state estimation will be presented employing the same ideas of this previous work [6]. When the states have to be observed with the robust observer proposed, the authors show that there appears in the analysis a linear but time varying system perturbed with the error in the initial estimation of states. This initial error belongs to a known and bounded set. The main result states that if it is possible to find a collection of non-empty sets K_j that converge to the maximal robust control invariant set when j increases, the feasibility of GPC control law is guaranteed for all the sampling instants. Finally, this result is verified in a numerical example with a 2 states process.