On the optimal trajectory generation for servomotors: A Hamiltonian approach

Abstract

This note considers the energy optimal trajectory control design approach. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. The minimum principle is applied to establish piecewise necessary optimality conditions. An approximate optimal control is proposed to circumvent the difficulty due to the nonlinearity of the cost function. Simulation is performed to illustrate the generation of the approximate optimal trajectory. IEEE Annual Conference on Decision and Control (CDC)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. On the optimal trajectory generation for servomotors: a Hamiltonian approach Yebin Wang, Koichiro Ueda, and Scott A. BortoffAbstract-This note considers the energy optimal trajectory generation of servo systems through open-loop optimal control design approach. Solving the exact optimal solution is challenging because of the nonlinear and switching cost function, and various constraints. The minimum principle is applied to establish piecewise necessary optimality conditions. An approximate optimal control is proposed to circumvent the difficulty due to the nonlinearity of the cost function. Simulation is performed to illustrate the generation of the approximate optimal trajectory.

Comparison of energy consumption for position controlled PMSM using various energy near-optimal control techniques

“…Such possibility exploits another two generators described further. The individual approaches to energy efficient position control of electric drives differ mainly by description of velocity time profile [8] and [9].…”

“…for constant cruising speed is defined by(9).Prescribed function of position is gained by subsequent derivation of acceleration and angular speed. Prescribed time functions of position, speed and acceleration shows Fig.…”

Energy-Efficient Trajectory Planning for a Mobile Agent by Using a Two-Stage Decomposition Approach

“…Although it is still challenging to apply the indirect method to Problem 2, introducing the switch time instant t s does simplify the derivation of necessary conditions from the minimum principle Bryson and Ho [1975]. Necessary conditions could be potentially useful to get insight on the properties of the optimal solutions as Wang et al [2012Wang et al [ , 2013.…”