Selection/control concurrent optimization of BLDC motors for industrial robots

PLOS ONE RESEARCH ARTICLE Selection/control concurrent optimization of BLDC motors for industrial robots Erick Axel Padilla-Garcı́a ID1, Héctor Cervantes-Culebro ID2, Alejandro RodriguezAngeles ID3*, Carlos Alberto Cruz-Villar3 1 Academia de Ingenierı́a en Robótica, Universidad Politécnica de Atlacomulco, Atlacomulco, Estado de México, México, 2 Escuela de Ingenierı́a y Ciencias, Tecnologico de Monterrey, Atizapán de Zaragoza, Estado de México, México, 3 Departamento de Ingenierı́a Eléctrica, Sección de Mecatrónica, CINVESTAVIPN, Gustavo A. Madero, Mexico City, México a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Padilla-Garcı́a EA, Cervantes-Culebro H, Rodriguez-Angeles A, Cruz-Villar CA (2023) Selection/control concurrent optimization of BLDC motors for industrial robots. PLoS ONE 18(8): e0289717. https://doi.org/10.1371/journal. pone.0289717 Editor: Hongru Ren, Guangdong University of Technology, CHINA Received: May 5, 2023 Accepted: July 23, 2023 Published: August 16, 2023 Copyright: © 2023 Padilla-Garcı́a et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. * Abstract This paper aims to concurrently select and control off-the-shelf BLDC motors of industrial robots by using a synergistic model-based approach. The BLDC motors are considered with trapezoidal back-emf, where the three-phase (a,b,c) dynamics of motors are modeled in a mechatronic powertrain model of the robot for the selection and control problem, defining it as a multi-objective dynamic optimization problem with static and dynamic constraints. Since the mechanical and electrical actuators’ parameters modify the robot’s performance, the selection process considers the actuators’ parameters, their control input, operational limits, and the mechanical output to the transmission of the robot joints. Then, three objective functions are to be minimized, the motor’s energy consumption, the tracking error, and the total weight of installed motors on the robot mechanism. The control parameterization approach via a cascade controller with PI controllers for actuators’ voltage and a PID controller for actuators’ torque is used to solve the multi-objective dynamic optimization problem. Based on simulations of the closed-loop system, a Pareto front is obtained to examine trade-offs among the objective functions before implementing any actuators in the existing robotic system. The proposed method is tested on an experimental platform to verify its effectiveness. The performance of an industrial robot with the actuators originally installed is compared with the results obtained by the synergic approach. The results of this comparison show that 10.85% of electrical power can be saved, and the trajectory tracking error improved up to 57.41% using the proposed methodology. Data Availability Statement: All relevant data are within the paper. Funding: EAPG CB2017-2018-A1-S-26123. The Mexican National Council for Science and Technology https://conacyt.mx/ The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Introduction An industrial robot is a highly integrated system where mechanical, electronic, and information technology subsystems concur to render a mechatronic system, where the balance among subsystems impacts the robot’s overall performance. Several optimization-based methods have been proposed to find an optimal balance or a so-called synergy among subsystems. Typically, optimal design methodologies address the mechanism and controller integration by assuming the actuator or actuators are given. In [1], a serial two-link high-speed arm is PLOS ONE | https://doi.org/10.1371/journal.pone.0289717 August 16, 2023 1 / 23 PLOS ONE Concurrent optimization of BLDC motors for robots optimally designed to minimize the robot settling time. In contrast, the design parameters are actuator locations, feedback gains, and arm link geometry. The desired task plays an essential role for ultrahigh-performance robots and could be considered since the design stage along with kinematic, dynamic, and control parameters, [2]. Most industrial robots are embedded in well-structured environments. However, uncertainties such as manufacturing tolerances or environmental changes are always present, so a robust formulation for the structure/control optimal design of mechatronic systems is proposed in [3]. Recently, ontologies have been introduced to define a set of representational primitives modeling the relationships among two domains intersecting in a mechatronic system, mechanical domain, and feedback control domain, [4]. Industrial robot powertrain design has been performed employing optimization procedures. [5] use an optimization strategy to find the powertrain for new robot concepts when cost and lifetime are considered performance index. The trajectory generation task is included in the design strategy. Service robots should be fulfilled with a lightweight mechanism with desired kinematic performance and compliance. [6] propose an integrated design optimization approach where robot kinematics, dynamics, powertrain design, and strength analysis are considered. In such an approach, kinematic and structural dimensions, motors, and gearboxes are parameterized as design variables. Customized designs of serial manipulators, [7], are usually performed via a two-step optimization strategy. The first step determines the maximum load estimation at each robot joint. In contrast, the second step selects an appropriate motor-gear assembly for the joint, providing an appropriate weight estimation and evaluating the payload capacity of each joint. The optimal mechanical design combined with dynamic control avoids a sub-optimal behavior when path-tracking controller parameters are disregarded in the power-train selection process, [8]. A concurrent multi-objective dynamic optimization method is proposed for optimal selection and control of Permanent Magnet Synchronous Motors (PMSM) driving an industrial parallel robot as in [9]. PMSM motors exhibit high precision and torque in industrial robots and applications. However, the combination of PMSM motors and powertrains is heavy and bulky, [10]. BLDC motors can replace PMSM motors since they are lighter to overcome this problem. In addition, BLDC motors have different control requirements and operating conditions, [11]. For instance, the BLDC rotor spinning induces a trapezoidal-shaped Back Electro-Motive Force (BEMF) instead of sinusoidal, where the magnet flux linkage varies with changes in the motor current, making it unsuitable for the sinusoidal Clark’s and Park’s transformation [12], as used in the (...truncated)