Autonomous underwater vehicles require a motion control system for performing underwater tasks such as exploring and developing marine resources. This study proposes a fractional‐order proportional‐integral (PIλ) controller for autonomous underwater vehicles motion control that simultaneously guarantees frequency and time domain behaviour. First, a stabilisation process is presented for the controlled system, and a three‐dimensional stable surface is obtained. Subsequently, the controller parameters can be tuned. Then, to guarantee frequency and time domain control performance simultaneously, the frequency domain behaviour is studied through a modified flat phase property, and the time domain behaviour is improved through parameter optimisation. The set‐point regulation and noise suppression performances of the autonomous underwater vehicles motion control system indicate that the proposed PIλ controller provides more flexibility in improving the system's robustness and transient performance.
The graphs with a given number n of vertices and given (vertex or edge) connectivity k , having minimum Wiener index are determined. In both cases this is K k + (K 1 ∪ K n−k−1) , the graph obtained by connecting all vertices of the complete graph K k with all vertices of the graph whose two components are K n−k−1 and K 1 .
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