H∞ controller design for a ball and plate system using normalized coprime factors

In this paper, we discuss how to synthesize a stabilizably robust controller for a ball and plate system (BPS). In order to reduce the fragility in its robust controller synthesis, a loop-shaping method in terms of a normalized right coprime factor (NRCF) uncertainty description for the BPS is thus employed. In effect, the design of weighting functions for the BPS loop-shaping is a decisive factor to determine good performance of the resulting closed-loop system. As a result, the well-known lead-lag series compensation design methods are innovatively adopted to obtain appropriate pre and post compensators as the weighting functions to guaranteed the BPS time-domain performance requirements. Finally, a numerical simulation on the BPS is used to verify the effectiveness of the proposed design method for the shaping weighting functions.