Paper:

# 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 *t _{c}*, when the input torque of the gear changes from positive to negative. The influence of the viscous friction upon the optimal zero crossing time

*t*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.

_{c}^{*}and Masashi Kanesaka, “Optimal Velocity Function Minimizing Dissipated Energy Considering All Friction in a Position Control System,”

*J. Robot. Mechatron.*, Vol.19, No.1, pp. 97-105, 2007.

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