Minimum-Phase Criterion on Sampling Time for Sampled-Data Interval Systems Using Genetic Algorithms

[[abstract]]In this paper, a genetic algorithm-based approach is proposed to determine a desired sampling-time range which guarantees minimum phase behaviour for the sampled-data system of an interval plant preceded by a zero-order hold (ZOH). Based on a worst-case analysis, the identification problem of the sampling-time range is first formulated as an optimization problem, which is subsequently solved under a GA-based framework incorporating two genetic algorithms. The first genetic algorithm searches both the uncertain plant parameters and sampling time to dynamically reduce the search range for locating the desired sampling-time boundaries based on verification results from the second genetic algorithm. As a result, the desired sampling-time range ensuring minimum phase behaviour of the sampled-data interval system can be evolutionarily obtained. Because of the time-consuming process that genetic algorithms generally exhibit, particularly the problem nature which requires undertaking a large number of evolution cycles, parallel computation for the proposed genetic algorithm is therefore proposed to accelerate the derivation process. Illustrated examples in this paper have demonstrated that the proposed GA-based approach is capable of accurately locating the boundaries of the desired sampling-time range.