STUDY ON SAVING ENERGY FOR MECHATRONICS USING NOLINEAR CHARACTERISTICS

减少机械机械和伺服系统等机电系统的能量耗散，对改善因火电厂排放的二氧化碳而升温的地球环境具有重要意义。因此，本项目研究了在包含减速齿轮的位置控制系统中使耗散能量最小的最优速度函数和最优传动比。在机电系统中耗散的能量由电机电枢电阻引起的焦耳损耗和齿轮引起的摩擦损耗组成。首先用齿轮效率来表示减速器的库仑摩擦，并建立了减速器的动力学方程。从最优控制理论出发，求出耗散能量最小的最优电流和速度函数。针对减速器库仑摩擦引起的非线性问题，引入过零时间，得到了解析解。通过仿真研究了系统各参数对最佳过零时间的影响。最后，利用最优速度函数进行了位置控制实验。将最优速度函数的能量耗散与梯形速度函数的能量耗散进行了比较。实验和仿真结果表明，在较大的负载惯性矩下，最优速度函数具有显著的节能效果。耗散的能量还取决于功率变送器（如齿轮和滚珠丝杠）的传动比。耗散的能量由传输比、发射机效率和负载表示。为了使耗散能量最小，对齿轮和滚珠丝杠的传动比进行了数值和解析计算。与传统的惯性匹配方法相比，得到的最优传动比可以降低耗散能量。

It is important to reduce the dissipated energy even for mechatronic systems such as manipulators and servo systems for improving the environment of the earth that is warmed up by CO_2 gas emitted from thermal power plants. Hence, this project has studied on optimal velocity functions and optimal gear ratios that minimize the dissipated energy in a position control system including reduction gears.The energy dissipated in the mechatronic systems is composed of Joule loss due to motor armature resistances and friction loss due to gears. First, Coulomb friction of a reduction gear is represented using efficiency of the gear and the dynamic equation is expressed. Te optimal current and velocity functions that minimize the dissipated energy are obtained from optimal control theory. For nonlinearity due to the Coulomb friction of a reduction gear, the zero crossing time is introduced in order to obtain analytical solutions. The effect of each parameter of the system on the optimal zero crossing time is investigated by simulation. Finally, an experiment on position control is performed using the optimal velocity functions. The energy dissipated with the optimal velocity function is compared to the energy dissipated with a trapezoidal velocity function. The results of the experiment and simulations indicate that the optimal velocity function can provide remarkable energy saving for a larger moment of load inertia.The dissipated energy also depends on a transmission ratio of power transmitter such as gears and ball-screws. The dissipated energy is expressed by a transmission ratio, efficiency of the transmitter and load. In order to minimize the dissipated energy, the transmission ratios of gears and ball-screws are obtained by numerically and analytically. The obtained optimal transmission ratios can reduce the dissipated energy compare to the conventional inertia matching method.