Biologically-Inspired Bodies Under Surface Waves—Part 2: Theoretical Control of Maneuvering

Abstract

The theoretical control of low-speed maneuvering of small underwater vehicles in the dive plane using dorsal and caudal fin-based control surfaces is considered. The two dorsal fins are long and are actually mounted in the horizontal plane. The caudal fin is also horizontal and is akin to the fluke of a whale. Dorsal-like fins mounted on a flow aligned vehicle produce a normal force when they are cambered. Using such a device, depth control can be accomplished. A flapping foil device mounted at the end of the tailcone of the vehicle produces vehicle motion that is somewhat similar to the motion produced by the caudal fins of fish. The moment produced by the flapping foils is used here for pitch angle control. A continuous adaptive sliding mode control law is derived for depth control via the dorsal fins in the presence of surface waves. The flapping foils have periodic motion and they can produce only periodic forces. A discrete adaptive predictive control law is designed for varying the maximum tip excursion of the foils in each cycle for the pitch angle control and for the attenuation of disturbance caused by waves. Strouhal number of the foils is the key control variable. The derivation of control laws requires only imprecise knowledge of the hydrodynamic parameters and large uncertainty in system parameters is allowed. In the closed-loop system, depth trajectory tracking and pitch angle control are accomplished using caudal and dorsal fin-based control surfaces in the presence of system parameter uncertainty and surface waves. A control law for the trajectory control of depth and regulation of the pitch angle is also presented, which uses only the dorsal fins and simulation results are presented to show the controller performance.