This paper presents a control design for flexible manipulators using piezoelectric actuators bonded\r\non nonprismatic links. The dynamic model of the manipulator is obtained in a closed form through\r\nthe Lagrange equations. Each link is discretized using finite element modal formulation based on\r\nEuler-Bernoulli beam theory. The control uses the motor torques and piezoelectric actuators for\r\ncontrolling vibrations. An optimization problem with genetic algorithm GA is formulated for\r\nthe location and size of the piezoelectric actuator and sensor on the links. The natural frequencies\r\nand mode shapes are computed by the finite element method, and the irregular beam geometry\r\nis approximated by piecewise prismatic elements. The State-Dependent Riccati Equation SDRE\r\ntechnique is used to derive a suboptimal controller for a robot control problem. A state-dependent\r\nequation is solved at each new point obtained for the variables from the problem, along the\r\ntrajectory to obtain a nonlinear feedback controller. Numerical tests verify the efficiency of the\r\nproposed optimization and control design.
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