H∞-optimal digital redesign method

The plant input mapping (PIM) method is a digital redesign technique which guarantees the closed-loop stability for all non-pathological sampling periods. The PIM method, however, has some possible drawbacks observed in the closed-loop step response: (1) a steady-state error, and (2) a pure time delay. The first problem might occur when the plant is unstable, and the second one occurs, when the analog controller is not bi-proper. In the present study, we first modify the original PIM method such that these two drawbacks are resolved. Although the PIM method does not, in general, lead to undesirable inter-sample ripples, yet, its formulation does not explicitly address the intersample behavior of the resulting digital control system. Therefore, the main contribution of the paper is to extend the idea of the PIM method in the context of sampled-data systems, so that the intersample behavior can be taken into account explicitly. For this purpose, we consider a standard sampled-data setting, in which the H-infinity. norm of the discretization error is minimized. The effectiveness of the proposed methods is demonstrated through benchmark examples. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.