This article focuses on theoretical developments in modeling and control of High-Speed Supercavitating Vehicles (HSSV). A simplified model of longitudinal dynamics is developed for control, and a dynamic inversion based inner-loop control technique is proposed to handle the switched, time-delay dependent behavior of the vehicle. Two outer-loop control schemes are compared for guidance level tracking. Various aspects of disturbance characteristics and actuator dynamics are investigated and analyzed.
Abstract-A control system based on feedback linearization is developed for a high-speed supercavitating underwater vehicle. The supercavitation bubble surrounding the body leads to reduced drag but is also responsible for the undesired switched, nonlinear and delay dependent behavior caused by the phenomena known as planing. The theoretical contributions of the switched control design are discussed in connection with the mathematical description of the system. Special attention is made to understand and handle the complex and novel dynamics of the vehicle.I. PROBLEM DESCRIPTION Based on the recent advancements [8], [6], [7] in simulation and control of a High-Speed Supercavitating Underwater Vehicle (HSSV), a new mathematical model was developed [1] to capture more details of the vehicle dynamics. The nonlinear interaction of the body with the cavity wall, showing memory effect, is very important, hence the way the cavity surface is described (cavity shape is a function of the history of the vehicle motion and cavitator area) plays an important role in the vehicle dynamics (Fig. 1). The theoretical aspects, i.e. controller design, controllability and tracking, raised by the novel system type are discussed in the following sections. The layout of the paper is as follows: a brief description of the generalized vehicle model developed in [1] is presented in Sec.II followed by the basic overview of the proposed control methodology (Sec.III). Section IV describes the theoretical design and controllability properties, including a solution for the reference signal tracking. Simulation results are presented in Section V. The future direction of this research and conclusions are presented in Sec.VI. II. MODEL DESCRIPTIONThe system equations for the longitudinal motion of the HSSV are written in a local tangent reference frame attached to the nose of the vehicle (Fig. 2) [rad/s] body pitch rate. The two control inputs are δ cav and δ fin the cavitator and fins deflection. In addition to the gravity force (F g ) another force (F p ) caused by the contact of the vehicle with the fluid surface can be present. It depends on the relative immersion depth (h ) and immersion angle (α) of the transom. Due to the lack of space the details of the system equations for the HSSV are omitted but the reader is referred to [1] for further details. The overall system equations can be written as: 0] with δ denoting the delay operator: δx(t) = x(t − τ ). Using this notation, F p (t, x, δ) can be written as:where c , δ/v, 0]. Eqs.1-4 describe the system as a bimodal, switched system. In the first (linear) mode the vehicle is flying inside the cavity and in the second mode it is planing e.g. on the bottom (or top) of the cavity. Note the characteristics of the switched system: (i) the switching hyperplane depends on the delayed state variable x(t − τ ), (ii) in the first mode the system dynamics is linear and in the second mode it is nonlinear input affine, i.e. the control inputs effect the dynamics linearly in both modes, and (iii) the s...
The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently reduced by parameter varying reduction methods. The decomposition starts with the construction of a modal transformation that separates the modal subsystems. Hierarchical clustering is applied then to collect the dynamically similar modal subsystems into larger groups. The subsystems formed from the groups are then independently reduced. This approach substantially differs from most of the previously proposed LPV model reduction techniques, since it performs manipulations on the LPV model and not on a set of linear time-invariant (LTI) models defined at fixed scheduling parameter values. Therefore the model interpolation, which is the most challenging part of most reduction techniques, is avoided. The applicability of the developed algorithm is thoroughly investigated and demonstrated by numerical case studies.
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