Sample-and-Hold Inputs for Minimum-Phase Behavior of Nonminimum-Phase Systems

Abstract

The advantages of minimum-phase (MP) systems for control applications are well known. Prior research has shown that a non-MP (NMP) system can be discretized to an MP system using either a zero-order hold (ZOH) or a square-pulse sample-and-hold input (SHI). This paper investigates the MP characteristics of the discrete-time (DT) system obtained by discretizing a continuous-time single-input single-output NMP system using different SHIs. Two new SHIs (forward and backward triangular) are studied in addition to the square pulse. Numerical simulations were adopted for studying the MP property of the resulting DT system as a function of sample-and-hold parameters. The simulation results show that it is possible to find a smaller sampling period that results in an MP DT system using the proposed SHIs compared with the ZOH. The $q$ -Markov cover system identification with pseudorandom binary signal was then used for a hardware-in-the-loop (HIL) simulation study. A resistor–capacitor filter was used to represent the implementation error of the SHI due to unmodeled actuator dynamics. The HIL simulation results show that the proposed SHI scheme is robust to actuator modeling error. The MP properties of the DT systems with three SHIs are compared. The results show that the forward triangle SHI has the best performance due to its robustness to unmodeled actuator dynamics and the capability of retaining the MP property of the discretized system at small sampling periods.