Stochastic analysis of dead-time systems using a hybrid spectral method

• Published in: International journal of control, automation, and systems Vol. 13; no. 5; pp. 1306 - 1312
• Main Authors: Duong, Pham Luu Trung, Lee, Moonyong
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01-10-2015; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Approximation; Closed loop systems; Control; Control systems; Engineering; Hybrid systems; Mathematical models; Mechatronics; Monte Carlo methods; Monte Carlo simulation; Process controls; Random variables; Robotics; Spectral methods; Statistical analysis; Stochasticity; Studies; Technical Notes and Correspondence; Uncertainty; 제어계측공학; Dead-time process; Monte-Carlo; uncertainty quantification; operational matrix; polynomial chaos
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-013-0468-z

Control systems often operate in the presence of dead-time. However, in most works, these dead-time systems are studied in a deterministic manner, which have low precision and reliability. Many natural systems often suffer stochastic noise that causes fluctuations in their behavior, making their responses deviate from nominal models. Therefore, it is important to investigate such statistical characteristic of states (mean, variance, etc.) for those stochastic systems. This problem is often called statistical analysis of a system. A hybrid spectral method represents a powerful numerical tool for statistical analysis of stochastic linear system. Thus, a hybrid spectral technique is proposed for statistical analysis of the time delay system under affections of random parameters and inputs. Numerical examples are considered to demonstrate the validity of the proposed method. Comparison with the traditional Monte-Carlo and the polynomial chaos methods is made to demonstrate the computationally lessdemanding feature of the proposed method.