Simultaneous Piezoelectric Actuator and Sensor Placement Optimization and Control Design of Manipulators with Flexible Links Using SDRE Method

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.

SDRE Control Applied to the Wheel Speed of a Compressed Air Engine with Crank-Connecting-Rod Mechanism

“…The pressures and forces values were obtained through applying (28), (29) excitation force a converted into pressure a through (12). This variation of force does not impact on the motor and its machinery elements for there are the characteristics of compressibility and damping of energy by compressed air with the overpressure being equalized during the movement.…”

“…The advantage of this control technique is that it does not cancel possible benefits provided by nonlinearities of the system, due to the fact that it is not necessary to linearize the system when applying this technique [12][13][14][15][16]. Among successful techniques implemented in real applications, there is the classical proportional-derivative (PD) controllers [17][18][19].…”

Practical Tracking Control of Piezoelectric Actuators with Time-delay Estimation and Nonsingular Terminal Sliding Mode

“…In recent years, the high-precision micro/nano-operation technology has played an increasingly important role in modern industrial systems [1]. Piezoelectric actuators (PEAs), such as micromanipulators [2], atomic force microscopes [3], MEMS manufacturing [4], micro-operation robot [5], and intracytoplasmic sperm injection [6], are widely used in micro/nano-operations due to their advantages (e.g., large output force, high resolution, and high response frequency) [7]. However, uncertain nonlinear factors, such as hysteresis, creep, and high-frequency vibration, severely restrict the application of PEAs [8].…”

On Positioning and Vibration Control Application to Robotic Manipulators with a Nonideal Load Carrying

“…erefore, to improve the efficiency of using the manipulators, control strategies are required. e SDRE control is being applied in many nonlinear systems due to its easy application and advantage of considering the influence of nonlinearities of the system, i.e., there is no need to linearize the system to be applied [10][11][12][13][14]. Such control has been widely used in rigid and flexible robotic manipulators as the works of authors [8,[14][15][16][17][18][19][20][21][22][23].…”