Research On Predictive Modeling By A Gaussian Process Method And Adaptive Motion Control Of Permanent Magnet Spherical Motors

With the rapid development of modern industrial manufacturing,actuators which are capable of performing precise movement in three-dimensional space,such as robots,pan-tilts,and satellite controllers,are increasingly needed.At present,single-degree-of-freedom motors combined with complex transmission devices are commonly using for realizing multi-degree-of-freedom motion.However,this method has disadvantages such as structural redundancy,poor dynamic performance,and low reliability.Under this background,the multi-degree-of-freedom spherical motor,as an alternative to the single-axis servo motor,provides an excellent solution to the above shortcomings from the actuator and has attracted wide attention from experts and scholars at home and abroad.For the purpose of industrial application,torque modeling and motion control are of great importance for spherical motors.Aiming at a permanent magnet spherical motor with air-core coils,this paper conducts in-depth research on kinematics and dynamics,torque modeling,and motion control.Some results are achieved as follows:1.From the perspective of rigid body rotation,the stator coordinate system,the rotor coordinate system,and the rotor output shaft coordinate system are defined.The rotation mode is specified based on the actual needs of the measurement system and the transformation method between coordinate systems is established.The forward position matrix of the output shaft in the rotor and its converse solution are derived,which lay the foundation for the determination and conversion of the coordinate system in the subsequent torque modeling.The Lagrangian method is used to establish the rotor dynamics model of the permanent magnet spherical motor considering the compound uncertainty,which lay a foundation for the research of motion control algorithms;2.Without loss of generality,the Euler angle-current-torque model of a permanent magnet spherical motor using air-core coils is established.The idea of data-driven is introduced,and the single-task and multi-task Gaussian process methods are used to calculate the torque.In the model,the torque contribution factor related to the motor structure is predicted and modeled by a Gaussian process method.The kernel function suitable for multi-dimensional input is used to train the model,which avoids the complicated magnetic field analysis;3.Considering the requirements and difficulty of obtaining training data,an automated simulation method based on Python script and ANSYS Maxwell is designed.The simulation parameters and simulation operation are automatically controlled through Python scripts.This method improves the efficiency of obtaining training data,and saves time consumption.The experimental results prove the validity of the training data and the accuracy of the Gaussian process prediction model.Moreover,they prove the superiority of the Gaussian process method in the size of the training set.4.Considering the uncertain factors in the dynamic characteristics of the permanent magnet spherical motor,an adaptive control algorithm for the uncertainty of the model is first designed.The simulation analysis proves the effectiveness of the algorithm.Furthermore,considering the influence caused by the friction when the motor is moving,the Lu Gre dynamic friction model is applied to the multi-dimensional spherical motor dynamics model to simulate the friction torque.Based on this,an adaptive control algorithm based on friction observers are designed.The simulation analysis proves that the algorithm is effective for friction compensation.In addition to model uncertainties and friction factors,dynamic models with disturbances are also considered.The factors other than the above nominal models are summarized as compound uncertainties.A robust adaptive sliding mode controller based on dynamic surfaces is designed.A first-order filter is introduced to avoid the differential explosion,so that it can meet the realization requirements of the actual controller.The simulation analysis and experiments have proved the effectiveness of this controller.