Maple and BlockBuilder for Simulink® from Maplesoft help advance Maglev train technology - User Case Studies - Maplesoft


User Case Study: Maple and BlockBuilder for Simulink® from Maplesoft help advance Maglev train technology

Introduction

The concept of a magnetically levitated (Maglev) train is not new to science, but not much progress has been made to make it a successful commercial venture. However, research continues to make Maglev train technology faster, cheaper, and more marketable.

The principal behind a Maglev train is that it floats on a magnetic field, about 10mm above the guideway. It follows the guidance tracks using changing magnetic fields, created by the linear induction motor rather than an onboard engine.

The complex design of a Maglev train is a disadvantage as the design process is extremely long. Dr. Richard Gran, Director (rtd) of Advanced Concepts Laboratories, Grumman, led a project funded by the U. S. Department of Transportation to develop a new model of Maglev trains using superconducting magnets mounted below the vehicle to attract the train to an iron rail. 

Significant time savings

The original simulation development process took several months, but Dr. Gran and his team used Maple™ and BlockBuilder for Simulink® to reduce the design and simulation time from months to just a few weeks.
 

How was the model developed?

Lift, propulsion, control, and ride comfort are all created from the configuration of the magnets and the large air gap that the control system maintains. During the development of this system, engineers working in propulsion (linear motors in particular), superconductivity, structural dynamics, control systems, and aerodynamics had to develop a simulation that would answer a myriad of design questions, and take human factors such as ride quality into account. Maple provided a common environment, which made this task possible.
 
The first step in simulating the vehicle was to obtain simulation models for the nonlinear magnet dynamics. Therefore the nonlinear differential equation model was created using BlockBuilder for Simulink® and exported to Simulink® to build the Simulink® Library that ultimately stored all of the Maglev subsystems as building blocks for the final simulation.

Notably, when there is no current in the coils, the vehicle drops under the influence of gravity and the under-carriage hits the guideway. Similarly, when the current in the magnet is very large, the magnet is attracted to the rail and again, possibly hits it. Therefore, the analysis of the nonlinear differential equations resulting from the simulation assumed that the dynamics were unstable. 

 
The team then moved on to the development of the control system, starting with an investigation of the underlying dynamics to understand how best to control the vehicle. The developed linear model allowed the team to use BlockBuilder to analyze the system and, ultimately, to build a block in Simulink®. The goal of the simulation was to model the entire vehicle’s dynamics in a system with five degrees of freedom. To simulate the 12 magnet pairs along the bottom of the vehicle, the team then copied the control systems that came from the Maple analysis into Simulink®. The ability to design the control system and develop the model that was exported to Simulink® was a critical time-saving step. This process was possible because the Maple analysis flowed seamlessly into Simulink®. Furthermore, Maple both documented the analysis and provided the annotations for the Simulink® block. The BlockBuilder could then be used to create the system with five degrees of freedom.
 

The final results

This simulation used three important products - Maple, BlockBuilder, and Simulink® - to create a complex interdisciplinary model of a system. The combined power helped to drastically reduce development time, at the same time provided the ability to accurately analyze the system, design the components, and produce very complex simulations that can be used to optimize the design. The importance of having a common environment to synthesize data (using mathematics), analyze equations (using both mathematics and math models), and work across multiple disciplines (by sharing a common set of results and simulation models) cannot be overemphasized. BlockBuilder was a critical tool in this process because it allowed the results of the mathematical manipulations to be converted rapidly into a simulation that was accurate and easy to document, both because it was based on detailed math, and the transcription of the mathematical calculations to the model was automated.   

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