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. 1. Introduction The development of lightweight structures has attracted research attention on coping with flexibility effects. Structures with a reduced weight are essential to improve the performance in mobile applications, such as flexible robots, aircrafts, and spacecrafts. The design of these structures requires a control system, which takes into account the interaction of the applied forces and the elastic modes. Structure vibration suppression depends not only on control design, but also on the sensor/actuator (S/A) selection and placement [1]. This paper considers piezoelectric S/A pairs bounded on a beam. Piezoelectric coupling is defined as a relation between an applied electric field and mechanical strain, or an applied strain and electric field in certain crystals, ceramics, and films. In general, flexible robot manipulators feature surface bonded or embedded piezoelectric actuators and/or sensor. The piezoelectric actuator generates a large actuating force and has a fast response time. Moreover it is smaller than other actuating systems as electrical motor or hydraulics for the same force [2]. A flexible beam optimization and control design is composed by two parts: control gain and the placement of actuators and sensors. The proposed control must stabilize the system against the motion-induced vibration. Design of a smart structure system requires more than accurate structural modeling, since both structural dynamics and control need to be considered for active
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