Energy-Optimal Motion Trajectory Accounting for Machine Efficiency for a Servo Motor Drive

This article addresses the energy-optimal trajectory planning problem for servomotor systems. Previous research typically considers only the copper losses of the motor in the cost function, neglecting iron losses and mechanical losses, or incorporates iron losses using empirical formulas. However, the loss mechanisms of the motor are complex, and empirical formulas often fail to accurately model motor losses, resulting in suboptimal trajectory planning. In contrast, motor efficiency maps, obtained through experimental measurements or finite element analysis (FEA), can accurately represent motor efficiency across various combinations of torque and speed, facilitating a comprehensive evaluation of overall motor losses. In this article, the efficiency map of a surface-mounted permanent magnet synchronous motor (SPMSM) is experimentally measured. With the measured efficiency map, total motor losses are incorporated into the cost function. However, integrating the efficiency map into the cost function complicates the optimal control problem. To address this challenge, a dynamic programming (DP) approach is introduced, transforming the optimal control problem into a multi-stage decision-making process, thereby ensuring an effective and accurate solution. Experimental results demonstrate that the energy-optimal trajectory, accounting for total machine losses, is more energy-efficient than one considering only copper losses.