Motion control of towed underwater vehicles with movable wings using a high-gain observer based approach

Stability analyses on a towed underwater vehicle motion control system using a high‐gain observer

“…We have already designed a high‐gain‐observer‐based output‐feedback controller with LQ state‐feedback gain, where the regulation simulations were performed using the lowest‐order case of the dynamical model and relatively short length of the cable 33 . For our purpose of taking account of the full nonlinear dynamics, the high‐gain‐observer technique is an appropriate and well‐established nonlinear design technique, which is relatively simple to apply for nonlinear mechanical systems to produce an output‐feedback controller 34,35 .…”

“…On the other hand, a detailed theoretical stability analysis of the proposed control system in the articles 33,38 has not been presented yet. We have already investigated fundamental properties of a TUV as a plant to be controlled, that is, without a controller, such as controllability, observability and stability, and shown that the system has desirable properties in the sense of depth and attitude control 39 .…”

“…In general, it is so difficult to ascertain a region of attraction strictly that an estimate of the region of attraction is calculated. To clarify the essential property of the control system and make analyses tractable, this paper focuses on the LQ state‐feedback‐control law with a high‐gain observer, which has been already presented in our previous articles, 33,38 and the lowest‐order case of the dynamical model, that is, one cable segment. The method utilized in our study is based on singularly perturbed systems by Saberi and Khalil 40 and output‐feedback control for input‐output‐linearizable systems by Esfandiari and Khalil, 41 where some theorems to analyze the stability of the closed‐loop system were presented.…”

“…Here, important contributions of this paper are listed as in the following: Detailed stability analyses on the high‐gain‐observer‐based control system of a TUV are presented, using the singular perturbation method and computing estimates of the region of attraction with consideration of control input saturation that is significantly important for motion control of underwater vehicles and high‐gain‐observer‐based control systems; For the analyses, we have devised useful mathematical tools, which are our original contributions, for quadratic Lyapunov functions the state‐space‐scaling method that can provide a less conservative estimate of region of attraction than the conventional one, the hyper‐rhombus representation for regions of attraction; Discussions on the relation between the analyses and control simulation results clarify their consistency and gap; Robustness evaluation against model variations via control simulations; A switching control method is proposed for the full‐range‐depth operation, which is associated with the configuration of multiple regions of attraction with different depth equilibria. Note that this approach is not presented in our previous articles 33,38 …”

“…A switching control method is proposed for the full‐range‐depth operation, which is associated with the configuration of multiple regions of attraction with different depth equilibria. Note that this approach is not presented in our previous articles 33,38 …”