Virtual Platform Design and Implementation for Magnetic Levitation Actuator Digital Twin With AI-Based Modeling and Control

Abstract

Magnetic levitation (maglev) planar actuators (MLPAs) utilize electromagnetic forces and torques between the stator array and movers to achieve frictionless and contactless precision motion. In this thesis, research works were developed and implemented for the existing MLPAs, specifically the Maglev floor (MagFloor) and the prototype (Testbench) at the University of Waterloo.

This thesis proposed a real-time magnet-coil role-switching force and torque (wrench) model for the levitation movement of disc-magnet movers (DMMs), through modeling the disc-magnet as a thin-walled conductor solenoid and the square coils as stacked coil-geometry magnets. The role-switching technique was achieved by utilizing equivalent magnetic dipole moments of the coil and magnet. The wrench model is the first online DMM wrench model in the literature, which computes the wrench between magnet and coil in 80 μs. A weighted pseudoinverse commutation law was proposed to extend the operating ranges of the DMMs. The single 4 inch DMM could be levitated with a maximum air gap of 70 mm and rotated with a maximum rotational angle of 45◦. The control resolutions were ±10 μm and ±20 mdegree for translations and rotations, respectively.

To further accelerate the implementation speed of the wrench model, a deep-learning residual-based model was established using an eight-million-point dataset generated from the above wrench model. Such a wrench model covered the extensive operating range of the above DMM, and computed the wrench results in 4.1 to 14.0 μs per coil-magnet pair without compromising the model accuracy. The 3σ error intervals of the model were equivalent to those of a lookup table with 20,645,504 mover poses. Furthermore, the wrench results were verified using measurements of the load cell and simulations. The deep-learning wrench model successfully controlled a 3 × 2 inch DMM, which could be levitated with a maximum air gap of 60 mm and rotated with a maximum rotational angle of 25◦. The same control resolutions were obtained.

The above wrench models were integrated into a novel virtual platform (VRP) for future digital twin (DT) applications, aiding research on MLPAs. This research proposed a VRP architecture that incorporated customized physics engines and uncertainties in physical replicas. Additionally, the virtual performance and motion results, considering uncertainties, were verified using physical experiments. The proposed VRP was fully open-source and constructed using PyBullet module and a parallel-operated graphic user interface (GUI) implemented with the PyQt5 module. The VRP simplified the processes of mover design, the wrench model comparison, and motion control verification. Furthermore, MLPA VRP was time-, material-, labor-, and cost-efficient to develop, which provided a virtual safeguard environment for the next stage of machine learning research and multiple magnet-mover motion control studies. Besides the advantages for MLPA development, the VRP could be embraced for remote operations and collaborative task research for FMSs. For future MagFloor and Testbench applications, the VRP system can be utilized as a training platform for researchers.

After establishing the VRP, a deep reinforcement learning (DRL) controller was implemented and trained for MLPAs, and its performance was verified using a DMM on the Testbench. The novel controller investigated the DRL approaches and verified the VRP for machine learning tasks. A linear controller was trained using proximal policy optimization (PPO) and soft actor-critic (SAC) models, which sampled at 455 μs, where the actions were continuous horizontal control forces. The remaining degrees of freedom were controlled using basic controllers. A reward function was proposed to minimize current saturation effects and power consumption while maintaining the dynamic responses. The model results were improved by using an additional sigmoid state machine to mitigate the oscillation issue of DRL policies when settling at references. After the successful demonstration of the DRL using the VRP for a single DMM, path planning for multiple movers could be considered.

Before initiating a machine learning approach for path planning in multiple mover control, a relative map path planning model was developed for operating a two-dimensional (2D) Halbach array mover (HAM) and a DMM. The model established an avoidance boundary for magnetic movers by analyzing the end effect of HAM and MLPA safety power consumption details, which determined mover operation speeds for the manufacturing process. Since the HAM experienced larger damping forces and required more power than the DMM, it was selected as the frame of reference to create the relative map. The optimal path obtained in the relative map was proven to preserve its optimality in the global frame for trajectory tracking. When no feasible optimal path existed, a speed-variant path was proposed. The algorithm was verified through 10,000 simulation cases and compared with the Lifelong Planning A* and Rapid Random Tree* methods, which demonstrated the fastest implementation speed (mean time of 0.05 s) and a 100 % success rate.