Intersample optimization in a sampled-data control system using the redundancy of a dual-rate system

• Published in: Journal of the Franklin Institute Vol. 358; no. 8; pp. 4483 - 4502
• Main Authors: Yasui, R., Kawaguchi, N., Sato, T., Inoue, A.
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2021; Elsevier Science Ltd
• Subjects: Control methods; Control systems; Control theory; Discrete element method; Indexing; Numerical analysis; Numerical methods; Optimization; Redundancy; Ripples; Steady state; Time response
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.10.048

The present study discusses the design method for controlling a single-input/single-output linear time-invariant dual-rate system, where the sampling interval of the plant output is longer than the holding interval of the control input. In such a dual-rate system, the intersample output might oscillate even when the sampled output converges to the reference input in the steady state. In a conventional ripple-free method, an existing control law is extended by introducing an exogenous variable, which is independent of the discrete-time sampled response, and the exogenous variable is designed for eliminating the steady-state intersample ripples without changing the existing sampled response. In another method, since a control law is designed such that the intersample performance is optimized, the intersample ripples are eliminated in the transient as well as steady states. However, the preservation of an existing sampled response is not taken into account. The present study proposes a new design method for eliminating the intersample ripples subject to the existing sampled response. In the proposed method, the continuous-time index is optimized subject to the existing discrete-time response. As a result, the intersample ripples are eliminated in the transient as well as steady states, and the existing discrete-time sampled response is maintained. The proposed method is compared to the conventional dual-rate design methods in numerical examples, and the effectiveness of the method is demonstrated.