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This article deals with the control of a repetitive impacting elastic link in rotational motion. A fuzzy logic controller was designed and employed to suppress the vibrations resulting after the impact with an external rigid body. The momentum balance method and an empirical coefficient of restitution were used in the collision of the two bodies. It was shown that the controller had a good behavior for different ranges of the restitution coefficient.

In this paper the stability and control of a parametrically excited, rotating flexible beam is considered. The equations of motion for such a system contain time periodic coefficients. Floquet theory and a numerical integration are used to evaluate the stability of the linearized system. Stability charts for various sets of damping, parametric excitation, and rotation parameters are obtained. Several resonance conditions are found and it is shown that the system stability can be significantly changed due to the rotation. Such systems can be used as preliminary models for studying the flap dynamics and control of helicopter rotor blades and flexible mechanisms among other systems. To control the motion of the system, an observer based controller is designed via Lyapunov-Floquet transformation. In this approach the time periodic equations are transformed into a time invariant form, which are suitable for the application of standard time invariant controller design techniques. Simulations for several combinations of excitation and rotation parameters are shown.

In this article, the control of a repetitive impacting elastic link with parametrically excited base in rotational motion is considered. A fuzzy-logic controller is designed and employed to suppress the vibrations resulting after the impact with an external rigid body. The momentum balance method and an empirical coef®cient of restitution is used in the collision of the two bodies. The controller is applied successfully to reduce the vibrations of the parametrically excited impacting¯exible system. Simulations for several combinations of excitation and rotation parameters are provided. IntroductionTheories for rigid or elastic multibody systems have considerably in¯uenced progress in mechanical engineering. Within the past few years, robot and teleoperator systems utilizing mechanical manipulators have gained wide-spread acceptance in the area of manufacturing, especially with regard to parts handling and assembly. Manipulators are being used as orthopedic and orthotic devices. In environments where radioactive materials are present, master-slave manipulator systems are now a standard tool for safe handling of dangerous materials. Even the space shuttle craft is equipped with manipulators for use in parts handling in outer space.Impact dynamics of colliding bodies is one of the classical problems of mechanics, which appears in design of manipulators. Impact is also prominent in mechanical part feeding systems and pneumatic impact tools. The control is necessary to suppress the vibrations that appear during the motion of the robot arm and those resulted from collision with other external bodies.Both linear and nonlinear controllers were constructed, and different kinds of strategies were implemented for the vibrations control of systems with¯exible elements. Adaptive control algorithms and on-line parameter identi®cation techniques have been common features of the last generation controllers.The problem of controlling an elastic arm of two links based on variable structure system theory and pole assignment technique for stabilization was treated in [13]. This design approach was motivated by a simple observation that the nonlinearity in the dynamics of an elastic robotic system is essentially due to the rigid modes (joint angles), and, as the time derivatives of the rigid modes vanish, the remaining motion is only due to the elasticity. For the rigid modes, a sliding-mode controller was designed. The controller of the elastic modes was