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 inter-sample 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 inter-sample behavior can be taken into account explicitly. For this purpose, we consider a standard sampled-data setting, in which the H∞ norm of the discretization error is minimized. The effectiveness of the proposed methods is demonstrated through benchmark examples.