Active vibration control of a flexible robot arm

The control of a flexible robot arm pose new control technologyproblems. One major problem area is the closed-loop stability of the armthat has been mode led with truncated modal dynamics. Stability problemsarise due to the control design process beginning with a deficient model.One possible method of circumventing the problems resultingfromthe increased number of modes to be controlled is by avoiding modalmodels. Working directly with partial-differential equation (PDE) modelsof continuous structure (flexible robot arm) is a viable (workable)alternative for preliminary control designs.This work provides a PDE control problem formulation thatcontains sufficient generality to encompass a wide variety of continuouscontrol system problems within a single analyticalframework. The methodof Lyapunov optimal feedback control is applied to a flexible one linkrobot arm, whose control torque is limited to be at the arm joint. Thismethod combines junction minimization with lyapunov stability criteriaand produces a closed loop feedback control directly.The stability of the system under the proposed control law is derivedin terms of energy dissipation properties of the system and is independentof physical parameters of the plant. The control law is applicable to linear,as well as nonlinear mechanical robot arm with any number of vibrationalmodes. It’s, therefore, unaffected by modal truncation, and as, the stabilityof the proposed controlleris based on globalpropertiesofthe arm, so, it’srobust with respect to plant parameters.