Abstract
This paper presents a control design for flexible manipulators using piezoelectric actuators bonded on nonprismatic links. The dynamic model of the manipulator is obtained in a closed form through the Lagrange equations. Each link is discretized using finite element modal formulation based on Euler-Bernoulli beam theory. The control uses the motor torques and piezoelectric actuators for controlling vibrations. An optimization problem with genetic algorithm (GA) is formulated for the location and size of the piezoelectric actuator and sensor on the links. The natural frequencies and mode shapes are computed by the finite element method, and the irregular beam geometry is approximated by piecewise prismatic elements. The State-Dependent Riccati Equation (SDRE) technique is used to derive a suboptimal controller for a robot control problem. A state-dependent equation is solved at each new point obtained for the variables from the problem, along the trajectory to obtain a nonlinear feedback controller. Numerical tests verify the efficiency of the proposed optimization and control design.
Highlights
The development of lightweight structures has attracted research attention on coping with flexibility effects
This paper presents a control design for flexible manipulators using piezoelectric actuators bonded on nonprismatic links
The SDRE method is used for positioning control, which implies in a vibration control on the flexible link
Summary
The development of lightweight structures has attracted research attention on coping with flexibility effects. A piezoelectric actuator is applied to single-link flexible manipulators in 8–10 and applied to two-link flexible manipulators in 11 These works considered control torque of the motor, determined based on the rigid link dynamics and the oscillations caused by the torque are suppressed by applying a feedback control voltage to the piezoelectric actuator. In this paper we propose a minimum energy positioning control technique for a robot arm with flexible links, where the motor torque controls the joint angle tracking and reduces the low frequency vibrations on the links. The remainder of this paper is organized as follows: the mathematical formulation of the dynamic model of flexible links with piezoelectric material and a numerical approximation for the vibration modes is presented .
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
