Control of systems with asymmetric bounds using linear programming: Application to a hydrogen reformer

Abstract

This paper studies controller design for feedback systems in the presence of asymmetrically bounded signals, using a case study. An asymmetric objective functional is used to consider the asymmetrically bounded signals, which makes possible to derive a linear programming problem. Solving this LP makes possible to design controllers that minimize certain outputs, fulfilling at the same time hard constraints on certain signals. The method is presented by application to a hydrogen reformer, a system in petrochemical plants that produces hydrogen from hydrocarbons: a mixed sensitivity problem is stated and solved, with an additional constraint given by the asymmetric limitations on the magnitude and rate of the control signal, and the asymmetricity in the disturbances.

On Improving the Convergence Rate of Linear Continuous-Time Systems Under Constrained Control With State Observers

“…The two cases where the full-order observer and the minimal order observer are used to reconstruct the inaccessible state are considered. The proposed technique is developed for asymmetric constraints, as they are very frequent in practice [7], [19].…”

“…Thus, we wish to generate the remaining state combinations as (15) Using (1) is chosen such that the required matrix inverse exists. To obtain , we must use a minimal-order observer described by (16) The reconstructed state is then given by (17) The observer reconstruction error is given by (18) where and (19) Using the previous requirements, one obtains (20) Following the steps of the design method proposed in [2], the controller is computed in two steps: The first consists in computing a regulator gain which gives a large set of admissible initial states, but might give poor convergence performance of the closed-loop system. In the second step, regulator gains , are computed and the control law is switched from to when the state comes inside the set .…”

“…In this case, matrix is selected to be that is and Taking account of (19), one can have and Let and , this implies that…”