At very high speeds, underwater bodies develop cavitation bubbles at the trailing edges of sharp corners or from contours where adverse pressure gradients are sufficient to induce flow separation. Coupled with a properly designed cavitator at the nose of a vehicle, this natural cavitation can be augmented with gas to induce a cavity to cover nearly the entire body of the vehicle. The formation of the cavity results in a significant reduction in drag on the vehicle and these so-called high-speed supercavitating vehicles (HSSVs) naturally operate at speeds in excess of 75 m s-1. The first part of this paper presents a derivation of a benchmark problem for control of HSSVs. The benchmark problem focuses exclusively on the pitch-plane dynamics of the body which currently appear to present the most severe challenges. A vehicle model is parametrized in terms of generic parameters of body radius, body length, and body density relative to the surrounding fluid. The forebody shape is assumed to be a right cylindrical cone and the aft two-thirds is assumed to be cylindrical. This effectively parametrizes the inertia characteristics of the body. Assuming the cavitator is a flat plate, control surface lift curves are specified relative to the cavitator effectiveness. A force model for a planing afterbody is also presented. The resulting model is generally unstable whenever in contact with the cavity and stable otherwise, provided the fin effectiveness is large enough. If it is assumed that a cavity separation sensor is not available or that the entire weight of the body is not to be carried on control surfaces, limit cycle oscillations generally result. The weight of the body inevitably forces the vehicle into contact with the cavity and the unstable mode; the body effectively skips on the cavity wall. The general motion can be characterized by switching between two nominally linear models and an external constant forcing function. Because of the extremely short duration of the cavity contact, direct suppression of the oscillations and stable planing appear to present severe challenges to the actuator designer. These challenges are investigated in the second half of the paper, along with several approaches to the design of active control systems.

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Active material actuators, sometimes referred to as "smart" actuators, are gaining widespread use for control actuation. Many of these actuators exhibit hysteresis to some degree between their input and output response. There exists an extensive body of research concerning the modeling of hysteresis for the linearization, or compensation, of these hysteresis nonlinearities. However, the models have typically been identified off-line and mainly used in open-loop compensation. When the identified models do not exactly match the actuator nonlinearities, the compensation can create an error between the desired and actual control output. The hysteresis for several of these actuators has been shown to evolve over time, and can render a fixed hysteresis model inadequate to linearize the hysteretic nonlinearities. This paper presents an adaptive hysteresis model for on-line identification and closed-loop compensation. Laboratory experiments with a shape memory alloy wire actuator provide evidence of the success of the adaptive identification and compensation. In addition, the means of determining the saturation of the SMA using updated information from the adaptive hysteresis model is provided.

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A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase transformations, the input–output response at the structural level is also known to be strongly hysteretic. This paper investigates the mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically, the identification of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introduce distributed,hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an ouput least square minimization over probability measures defined on a compact subset of a closed half-plane. In Part II of this paper, consistent and convergent approximation methods for identification of the measure characterizing the hysteresis are derived.