新型仿人机器人关节用永磁球形步进电机控制算法及驱动器研究
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摘要
随着现代工业技术的不断发展，电机设计研究领域的不断深入，国内外学者相继开发研究了各种新型的多自由度三维电机。三自由度球形电机设计概念及样机的出现，使得机器人关节的空间三维运动可以在一个较小的工作空间中完成，简化了系统结构，减小了机构体积，有利于提高系统的动、静态性能和定位精度。然而，各类球形电机的控制相关问题的研究较为匮乏，始终是限制其发展和实用化的瓶颈。永磁球形步进电机作为一种新型的三自由度步进式结构球形电机，与其它结构模式的球形电机相比，无需叠片结构，具有力能指标高、运行原理相对简单、便于制造实现等优点。本文针对永磁球形步进电机的控制，就电机转矩建模，转子动力学建模，控制方式和算法，控制驱动器设计等方面展开了探讨。
本文的主要工作具体包括：
1．在简要介绍永磁球形步进电机结构特点及磁场转矩计算的基础上，将电机矩角特性细分为三类加以计算并作拟合，总结出简化的电机转矩模型与表达式。
2．简化了电机的整体模型，用瞎子爬山法针对永磁球形步进电机单步步进运动时，单个或两个定子线圈通电，转子球可能运行的稳定位置进行了计算，为继电器控制模式下的电机转子位置提供了参考。
3．在永磁球形步进电机继电器控制模式下，基于四元数旋转，提出了一种运动轨迹分段绕定轴旋转的开环控制算法，解决了电机做定点运动时可完成的运动轨迹有限的问题。
4．运用卡尔丹角旋转结合拉格朗日第二类方程，建立了转子固连坐标系下电机转子动力学模型，解决了长期以来永磁球形步进电机转子运动没有一个精确的数学模型，无法在运动力学上结合电机转矩进行定量分析的问题。
5．把电流控制方案应用在永磁球形步进电机的控制中，提出闭环控制。针对空载状态下电机转子作定点(PTP)运动的情况应用了PD控制算法。针对空载状态下电机转子作连续轨迹(CP)运动的情况引入了具有偏置的PD控制算法。使永磁球形步进电机不仅可以完成简单的PTP运动任务，也可以做到复杂的CP运动。
6．提出了一种基于输入—输出稳定性理论的控制算法，以完成空载状态下CP运动的控制任务，该算法无需转子各轴向的加速度反馈信号，减轻了转子位置检测系统的压力。在该算法的基础上，提出了自适应控制算法和变结构控制算法。以适应电机负载运行时，转子各轴向转动惯量发生变化，电机仍需完成CP运动的控制要求。解决了一直以来，各控制算法及方案均要假设电机空载运行的问题，拓展了永磁球形步进电机的应用范围。
7．完成了各类控制算法的仿真实例，分别针对继电器控制方案和电流控制方案提供了控制系统的完整解决方案，设计了永磁球形步进电机控制驱动器。
With the continuous development of the technology and the expansion of the research on the motor, all kinds of novel multi-degree-of-freedom motors were designed one after the other by the scholars all of the world. While the idea and the prototype of the three-degree-of-freedom (three DOF) motor came into being, it is more convenient to realize the motion of the robot joint where the demand on workspace is low but three DOF is required. It also combines the merits of simplified system construction, minimized machine volume, improved dynamic and static performance with high position accuracy. However, control relative problems have seldom been discussed which becomes the bottleneck of the development and practicability of the three DOF motors. The permanent magnet spherical stepper motor (PMSSM) is a novel three DOF stepping configuration spherical motor that laminations are not required, so the realization of a prototype is much easier. It has higher energy and simple working principle with respect to other spherical motors. In view of control problems of the PMSSM, this dissertation is devoted to an in-depth study on the torque model, dynamic model of the rotor, control strategy and algorithm, design of the driver and the controller and so on.
The main contribution of this dissertation includes:
1. Based on the simple presentation of the configuration characteristic and the calculation of the magnetic field and torque of the PMSSM, the torque-angle characteristic is divided into three kinds to calculate. Then the curves of the torque are approximated with different functions. The simplified torque model and the expressions are concluded.
2. The whole model of the motor was simplified to a system using active solenoids. The possible stable positions of the rotor with one or a pair of active stator coils are discussed using Hill-Climbing method while the motor is in stepping mode. It affords the reference of the rotor position for the relay control mode.
3. One open loop control algorithm based on quaternion rotation for the PMSSM in relay control mode is proposed. It divides the kinetic trajectory into sections. Thus each segment corresponds one arc and circles around one fixed axis individually, and the continuous movement of the rotor is feasible. This solves the problem of the limited motion trajectory while in point-to-point motion.
4. The dynamic model of the rotor expressed with Cardan angle rotation was set up in rotor-fixed coordinates frame using Lagrange equation of second kind. The problem that the PMSSM has no exact mathematical description leading to the trouble of quantitative analysis combined with the torque model and the dynamic model is then resolved.
5. The current control method is applied in the controller to construct the closed loop control of the PMSSM. Later the PD control algorithm for the point-to-point (PTP) motion and the adjusted PD control algorithm for the continuous path (CP) motion in unloaded mode are presented. So the PMSSM can accomplish not only the PTP motion but also the CP motion.
6. One control algorithm is designed based on input-output stability theory for the CP motion in unloaded mode. It can drive the motor without the angular accelerations feedback, which reduces the pressure on the position measuring system. Inheriting the advantage of this algorithm, the adaptive control algorithm and the switching control algorithm applied in the situation that the load affected the rotation inertia of the axes are developed to satisfy the requirements of the CP motion. It resolves the problem of assuming the unloaded mode for all the existent control algorithms. It has extended the applications of the PMSSM significantly.
7. The simulation examples of all the control algorithms are accomplished. The entire solvent of the control system based on the relay control and the current control are presented, also the driver and controller for the permanent magnet spherical stepper motor is developed.
本文的主要工作具体包括：
1．在简要介绍永磁球形步进电机结构特点及磁场转矩计算的基础上，将电机矩角特性细分为三类加以计算并作拟合，总结出简化的电机转矩模型与表达式。
2．简化了电机的整体模型，用瞎子爬山法针对永磁球形步进电机单步步进运动时，单个或两个定子线圈通电，转子球可能运行的稳定位置进行了计算，为继电器控制模式下的电机转子位置提供了参考。
3．在永磁球形步进电机继电器控制模式下，基于四元数旋转，提出了一种运动轨迹分段绕定轴旋转的开环控制算法，解决了电机做定点运动时可完成的运动轨迹有限的问题。
4．运用卡尔丹角旋转结合拉格朗日第二类方程，建立了转子固连坐标系下电机转子动力学模型，解决了长期以来永磁球形步进电机转子运动没有一个精确的数学模型，无法在运动力学上结合电机转矩进行定量分析的问题。
5．把电流控制方案应用在永磁球形步进电机的控制中，提出闭环控制。针对空载状态下电机转子作定点(PTP)运动的情况应用了PD控制算法。针对空载状态下电机转子作连续轨迹(CP)运动的情况引入了具有偏置的PD控制算法。使永磁球形步进电机不仅可以完成简单的PTP运动任务，也可以做到复杂的CP运动。
6．提出了一种基于输入—输出稳定性理论的控制算法，以完成空载状态下CP运动的控制任务，该算法无需转子各轴向的加速度反馈信号，减轻了转子位置检测系统的压力。在该算法的基础上，提出了自适应控制算法和变结构控制算法。以适应电机负载运行时，转子各轴向转动惯量发生变化，电机仍需完成CP运动的控制要求。解决了一直以来，各控制算法及方案均要假设电机空载运行的问题，拓展了永磁球形步进电机的应用范围。
7．完成了各类控制算法的仿真实例，分别针对继电器控制方案和电流控制方案提供了控制系统的完整解决方案，设计了永磁球形步进电机控制驱动器。
With the continuous development of the technology and the expansion of the research on the motor, all kinds of novel multi-degree-of-freedom motors were designed one after the other by the scholars all of the world. While the idea and the prototype of the three-degree-of-freedom (three DOF) motor came into being, it is more convenient to realize the motion of the robot joint where the demand on workspace is low but three DOF is required. It also combines the merits of simplified system construction, minimized machine volume, improved dynamic and static performance with high position accuracy. However, control relative problems have seldom been discussed which becomes the bottleneck of the development and practicability of the three DOF motors. The permanent magnet spherical stepper motor (PMSSM) is a novel three DOF stepping configuration spherical motor that laminations are not required, so the realization of a prototype is much easier. It has higher energy and simple working principle with respect to other spherical motors. In view of control problems of the PMSSM, this dissertation is devoted to an in-depth study on the torque model, dynamic model of the rotor, control strategy and algorithm, design of the driver and the controller and so on.
The main contribution of this dissertation includes:
1. Based on the simple presentation of the configuration characteristic and the calculation of the magnetic field and torque of the PMSSM, the torque-angle characteristic is divided into three kinds to calculate. Then the curves of the torque are approximated with different functions. The simplified torque model and the expressions are concluded.
2. The whole model of the motor was simplified to a system using active solenoids. The possible stable positions of the rotor with one or a pair of active stator coils are discussed using Hill-Climbing method while the motor is in stepping mode. It affords the reference of the rotor position for the relay control mode.
3. One open loop control algorithm based on quaternion rotation for the PMSSM in relay control mode is proposed. It divides the kinetic trajectory into sections. Thus each segment corresponds one arc and circles around one fixed axis individually, and the continuous movement of the rotor is feasible. This solves the problem of the limited motion trajectory while in point-to-point motion.
4. The dynamic model of the rotor expressed with Cardan angle rotation was set up in rotor-fixed coordinates frame using Lagrange equation of second kind. The problem that the PMSSM has no exact mathematical description leading to the trouble of quantitative analysis combined with the torque model and the dynamic model is then resolved.
5. The current control method is applied in the controller to construct the closed loop control of the PMSSM. Later the PD control algorithm for the point-to-point (PTP) motion and the adjusted PD control algorithm for the continuous path (CP) motion in unloaded mode are presented. So the PMSSM can accomplish not only the PTP motion but also the CP motion.
6. One control algorithm is designed based on input-output stability theory for the CP motion in unloaded mode. It can drive the motor without the angular accelerations feedback, which reduces the pressure on the position measuring system. Inheriting the advantage of this algorithm, the adaptive control algorithm and the switching control algorithm applied in the situation that the load affected the rotation inertia of the axes are developed to satisfy the requirements of the CP motion. It resolves the problem of assuming the unloaded mode for all the existent control algorithms. It has extended the applications of the PMSSM significantly.
7. The simulation examples of all the control algorithms are accomplished. The entire solvent of the control system based on the relay control and the current control are presented, also the driver and controller for the permanent magnet spherical stepper motor is developed.
引文
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