This brief paper treats the question of adaptive control of a projectile fin using a piezoelectric actuator. The hollow projectile fin is rigid, within which a flexible cantilever beam with a piezoelectric active layer is mounted. The model of the fin-beam system includes the aerodynamic moment, which is a function of angle of attack of the projectile. The rotation angle of the fin is controlled by deforming the flexible beam, which is hinged at the tip of the rigid fin. An adaptive servoregulator is designed for the control of the fin angle using the fin angle and its derivative for feedback. Interestingly, the knowledge of the dimension and parameters of the system is not essenstial for the synthesis of the control law. In the closed-loop system, the fin angle asymptotically converges to the desired set point and the elastic modes converge to their equilibrium values. Computer simulation and laboratory test results are presented to show the performance of the controller.

This paper treats the question of control of a biorobotic autonomous undersea vehicle (BAUV) in the yaw plane using a biomimetic mechanism resembling the pectoral fins of fish. These fins are assumed to undergo a combined sway-yaw motion and the bias angle is treated as a control input, which is varied in time to accomplish the maneuver in the yaw-plane. The forces and moments produced by the flapping foil are parametrized using computational fluid dynamics. A finite-difference-based, Cartesian grid immersed boundary solver is used to simulate flow past the flapping foils. The periodic forces and moments are expanded as a Fourier series and a discrete-time model of the BAUV is developed for the purpose of control. An optimal control system for the set point control of the yaw angle and an inverse control law for the tracking of time-varying yaw angle trajectories are designed. Simulation results show that in the closed-loop system, the yaw angle follows commanded sinusoidal trajectories and the segments of the intersample yaw trajectory remain close to the discrete-time reference trajectory. It is also found that the fins suitably located near the center of mass of the vehicle provide better maneuverability.

This paper treats the question of control of two-dimensional incompressible, unsteady wake flow behind a circular cylinder at Reynolds number Re=100. Two finite-dimensional lower order models based on proper orthogonal decomposition (POD) are considered for the control system design. Control action is achieved via cylinder rotation. Linear optimal control theory is used for obtaining stabilizing feedback control systems. An expression for the region of stability of the system is derived. Simulation results for 18-mode POD models obtained using the control function and penalty methods are presented. These results show that in the closed-loop system mode amplitudes asymptotically converge to the chosen equilibrium state for each flow model for large perturbations in the initial states.

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.

This paper presents a new approach to end-point trajectory control of flexible macro-micro manipulator based on nonlinear inversion and predictive control techniques. In this approach, precise control of the end-effector trajectory is accomplished by the inverse controller of the rigid micro manipulator, and the predictive controller steers the end point of the flexible macro manipulator with limited elastic oscillation. The predictive control law is obtained by minimizing a quadratic function of the tip tracking error, the elastic deflection, and the input torque of the flexible macro manipulator. The feedback parameters of the predictive controller are chosen such that zero dynamics are asymptotically stable. The combination of the inverse and the predictive controllers accomplishes precise end-effector trajectory tracking and elastic mode stabilization. These results are applied to a planar macro-micro manipulator system consisting of one flexible link and two micro rigid links. Simulation results are presented to show that in the closed-loop system time varying end point trajectory control and elastic mode stabilization are accomplished.

We treat the question of position and force control of a three-axis elastic robotic system on a constraint surface based on nonlinear inversion of an input-output map and linear feedback stabilization. Unlike the rigid robots, the feedback linearizing control of end point motion gives rise to unstable zero dynamics. Instability of zero dynamics is avoided by controlling a parameterized output vector corresponding to a point close to the end point of the arm. Zero dynamics are stable or almost stable as long as the parameter in the output vector does not exceed a critical value. Using the inverse controller, the control of the force and the position of the end point is possible while the end effector moves on the constraint surface. However, this excites the elastic modes. For the final capture of the terminal state and vibration suppression, a linear stabilizer is designed. Simulation results are presented to show that in the closed-loop system trajectory and force control on the constraint surface is accomplished.