Optimal Velocity Function Minimizing Dissipated Energy Considering All Friction in a Position Control System
Yiting Zhu*, Xuejun Zhu**, Teruyuki Izumi*,
and Masashi Kanesaka*
*Department of Electronic and Control Systems Engineering, Shimane University, 1060 Nishi-Kawatsu, Matsue, Simane 690-8504, Japan
**Department of Mechanical Engineering, Ningxia University, 90-5-075 Yinchuan 750021, China
In order to help reduce global warming, the amount of dissipated energy of machines should be decreased. The present paper discusses optimal current and velocity functions that minimize the dissipated energy in a servo system with friction of all types. The Coulomb friction of a gear in the servo system is represented by the efficiency of the gear and is assumed to be proportional to the absolute value of the output torque of the motor. Even if the system is nonlinear due to Coulomb friction, an analytical optimal function can be solved by introducing a zero crossing time tc, when the input torque of the gear changes from positive to negative. The influence of the viscous friction upon the optimal zero crossing time tc* is examined by simulations. The energy dissipated with the optimal velocity function is compared to the energy dissipated with a conventional trapezoidal velocity function. The results of the simulations and the experiment indicate that the optimal velocity function can greatly reduce the amount of energy dissipated when the moment of inertia is large.
-  H. Machida and F. Kobayashi, “An Implementation of the One-Chip PLL/PWM Motor Control System,” T. of the Institute of Electrical Engineers of Japan, Vol.122-C, No.12, pp. 2144-2148, 2002.
-  S. Arimoto, “Robot Dynamics and Control,” Asakura Co., 1995.
-  H. Kojima, “Dynamic Finite Element Analysis of the Position Control System of a Horizontal Flexible Robot Arm with Two Links,” T. of the Japan Society of Mechanical Engineers Series C, Vol.55, No.513, pp. 2179-2186, 1989.
-  M. Hamaguchi and K. Terashima, “Design Method for Optimum Shape of Container and Velocity Pattern in Liquid Transfer Considering Damping of Sloshing,” Journal of Japan Foundry Engineering Society, Vol.71, No.5, pp. 307-313, 1999.
-  C. Tai, S. Sakai, and Y. Hori, “Proposal of a Novel Method of Motion Control of Electric Vehicles Utilizing Speed Trajectory Shaping,” P. of the 2002 Japan Industry Applications Society Conference, No.245, 2002.
-  E. Sergaki and G. Stavrakakis, “Optimal Robot Speed Trajectory by Minimization of the Actuator Motor Electromechanical Losses,” Journal of Intelligent and Robotic Systems, Vol.33, pp. 187-207, 2002.
-  T. Izumi, Y. Yokose, and R. Tamai, “Minimum Energy Path Search for a Manipulator in Consideration of All Non-linear Characteristics by GA and Its Experiments,” T. of the Institute of Electrical Engineers of Japan, Vol.125-C, No.11, pp. 1751-1757, 2005.
-  Y. Zhu, T. Izumi, and H. Zhou, “Minimization of Dissipated Energy in a Position Control System with Coulomb Friction of Gears,” SICE Annual Conference 2005 in Okayama, pp. 2798-2803, 2005.
-  T. Izumi, Y. Zhu, and H. Zhou, “Optimal Velocity Function and Gear Ratio Minimizing Dissipated Energy in Position Control System with Coulomb Friction,” P. of the 2006 JSME Conference on Robotics and Mechatronics, 2P1-B35, 2006.
-  H. Kanoh, “Theory and Computational Methods in Optimization,” Corona Publishing Co., 1987.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.
Copyright© 2007 by Fuji Technology Press Ltd. and Japan Society of Mechanical Engineers. All right reserved.