Emulation design for a class of extremum seeking controllers: Case studies in ABS design and spark timing calibration

The vast majority of extremum seeking designs in the literature are in continuous-time, however their practical implementation is typically done using digital technology. In this paper, a sampled-data implementation of extremum seeking controllers using emulation design methods is studied to address this gap. The conditions under which the emulated controller preserves the performance of the continuous-time plant are investigated. The main result also provides a guideline on how to tune the controller parameters including sample period in order to achieve the desired performance. The examples of anti-lock braking and spark timing calibration are used to illustrate the proposed design method through simulation and experimental tests.