Performance improvement demonstration of an NMP system using sample and hold inputs

Earlier investigation analyzed the minimum-phase (MP) characteristics of a discrete-time system obtained by sampling a continuous-time non-minimum-phase (NMP) system using sample and hold inputs (SHIs). The proposed SHIs, compared to a conventional zero order hold, are able to increase the range of sampling rates for obtaining an MP discrete-time system. As a result, the negative effect of the NMP system can be reduced in discrete-time domain and controllers with high gains can be used to improve performance. This paper demonstrates the advantages of using the SHIs for the single inverted pendulum through simulations and experiments. In particular, it is shown that the performance of the stabilized closed-loop system can be improved by designing an outer-loop controller based on the MP discrete system obtained using the SHIs. Simulation results in the presence of Coulomb friction show that the additional controller reduces cart oscillations significantly; for a particular SHI, the steady state amplitude of oscillation was reduced by up to 68.95%. Experiments confirmed the results obtained in simulations.