Research on magnetic bearing control system based on FPGA

0 Introduction
Magnetic bearings are bearings that support rotating bodies completely contactlessly with magnetic force. In a broad sense, they are bearings that can support linear motion objects and bearings that have partial mechanical contact. The working principle is to use the magnetic levitation force generated by magnetic field induction to resist the force generated by the gravity field and the movement of the shaft, suspending the shaft so that the rotor and the bearing do not contact each other.

1 Magnetic bearing control system
The research on magnetic bearing control system has always been a hot spot and difficulty in the research of magnetic bearing technology. The magnetic bearing control system generally includes four parts: contactless displacement sensor, power amplifier, controller and electromagnetic exciter (i.e. electromagnetic coil and rotating shaft). The structure of the vertical magnetic bearing studied in this paper is shown in Figure 1. For the motor system with vertical structure, the axial bearing mainly bears the dead weight of the rotor itself, which is a unidirectional static load, and its dynamic load is relatively small, so a unilateral working disk electromagnet system can be used. The radial bearing has no static load, but needs to bear bidirectional dynamic load. Therefore, two electromagnets can be designed on each degree of freedom for differential control, so that it can generate positive force and negative force to meet the bidirectional change requirements of dynamic load.
Since the control algorithm is often more complicated, the digital control method is generally used in the design of the magnetic bearing controller, that is, a control platform based on DSP (Digital Signal Processor) is established. However, with the development of microelectronics technology, FPGA (Field Programmable Gate Array) is gradually becoming an indispensable component of various electronic products due to its advantages of good performance, large scale, reprogrammable, and low development investment. Its high-performance parallelism, customization, flexibility, and high cost-effectiveness make FPGA programmable gate array devices one of the preferred devices for high-performance digital signal processing and digital system control.

2 Field Programmable Gate Array (FPGA)
FPGA (Field Programmable Gate Atray) is the abbreviation of Field Programmable Gate Array, which is a type of programmable application-specific integrated circuit (ASIC) (the same category also includes CPLD). In 1984, Xilinx pioneered the innovative technology of Field Programmable Logic Array (FP-GA) and launched the world's first FPGA chip in 1985. In the development process of more than 20 years, the hardware architecture and software development tools of FPGA have been continuously improved and matured. From the initial 1,200 available gates to hundreds of thousands of available gates in the 1990s, to the current single-chip FPGA chips with millions to tens of millions of gates, Xilinx, Ahera and other world-class manufacturers have raised the integration of FPGA devices to a new level.
This article uses the Spartan-3E Starter Kit Board development board, and the chip uses the XC3S500E chip in the Spartan-3E series of Xilinx. The XC3S500E system gate resources include 1164 configurable units (convertible to 4656 chip resources), 4 DCMs, 360K bit block memory, 20 multipliers and 232 usable IO ports. When designing, you can use Matlab from MathWorks and System Generator from Xilinx to be responsible for system-level design.
Matlab, as an analysis and simulation tool for linear systems, has a wide range of applications in engineering and computational science. Simulink, as a toolbox of Matlab, plays a vital role in the entire digital signal processing (DSP) design. It is an interactive tool that can be used to model, simulate and analyze complex systems. System Generator is a blockset of Xilinx and a plug-in of Simulink. It contains Xilinx-specific DSP function IP cores, as well as basic DSP functions and logic operators, such as FIR (Finite Impulse Re-sponse), FFT (Fast Fourier Transform), memory, math functions, converters, delay lines, etc. These pre-defined modules ensure the bit and cycle correctness of FPGA implementation. It can be used to automatically generate VHDL/Verilog language, test vectors and ".do'' files that can be simulated for ModelSim. In order to obtain the best performance, density and predictability, System Generator will also automatically map specific design modules into highly optimized IP core models. Some modules in XilinxBlockset can be directly mapped to hardware, while others correspond to IP cores. Each of them can change parameters according to design requirements and support double-precision and fixed-point algorithms. This module set is an externally expandable library that uses C++ fixed-point algorithms, so users can create their own Simulink library components based on C++ classes to be treated as black boxes in the design. System Generator, combined with Simulink model tools, can parameterize and optimize algorithms. It can also automatically convert from behavioral-level system models to FPGA implementations, and manual reset is no longer required, which greatly saves development time and reduces the probability of errors. Through the software, users can select from the algorithm, performance, energy saving, and silicon area of ​​DSP functions to quickly analyze its computing speed and cost.

3 Simulation of magnetic bearing system
The structural diagram of a general magnetic bearing system is shown in Figure 1. It can be seen from the figure that the axial magnetic bearing mainly uses the electromagnetic attraction of the axial electromagnet to balance the weight of the rotor itself and constrain the axial movement of the rotor. The axial bearing mainly carries the dead weight of the rotor itself, which is a unidirectional static load, and its dynamic load is relatively small, so a unilateral working disk electromagnet system can be used. Figure 2 is a simple structural diagram of the axial magnet/thrust disk suspension system conversion. In the figure, x0 is the gap of the axial bearing at the equilibrium position, i0, ic are the bias current and control current of the electromagnet coil respectively, and F is the electromagnetic force generated by the electromagnet on the rotor.

In the simplified model shown in Figure 2, the total suction force between the magnet and the thrust plate is:

Due to the electromagnetic force F∝i(t)2/x(t)2, where i(t) is the excitation current and x(t) is the corresponding air gap, f=F-mg=0 must be satisfied to make the rotor stably suspended in the equilibrium position. Assuming that the input initial current is i0 and the air gap between the rotor and the electromagnet is x0, if the rotor is treated as a single particle total concentrated mass, then when the rotor mass center has an upward offset X in the Y direction (the rotor only has translation and no interference force exists), the central motion equation of the rotor can be expressed as:

In fact, the axial magnet and the radial magnet have the same linearized mathematical model, but the current stiffness and displacement stiffness are different. Therefore, the same control method can be used for the axial and radial directions.
In analog control systems, the most commonly used control of the controller is PID control. Due to its own advantages, PID control is still widely used in industrial production processes. The analog PID controller is mainly composed of three typical links, namely the proportional link (P), the integral link (I), and the differential link (D). According to the mathematical model of the magnetic bearing system mentioned above, the Simulink simulation tool can be used in the Matlab environment to simulate the axial system of the magnetic bearing to observe its output response curve. The simulation data is taken from the actual magnetic bearing experimental device. Since the electromagnetic bearing itself is to be applied to actual production, it often encounters load changes during operation, just like ordinary motors. For example, there are axial and radial loading and unloading in applications such as fans, punching machines and milling machines. The following takes the axial bearing as an example to analyze the impact of loading and unloading on the system. In order to facilitate the comparison between analog and digital, the top-level module shown in Figure 3 can be established first, where the simulation block diagram of the analog control system is shown in Figure 4, and the simulation block diagram of the digital control system is shown in Figure 5.

In the simulation of this system, its digital PID is constructed using the blockset provided by Xilinx, as shown in Figure 6.

In the above simulation, the bias current i0 is 3.3 A (for the convenience of simulation, 3.3 A is taken and expanded by 1,000 times), the balanced air gap x0 is 1 mm, the cross-sectional area S of the magnetic pole is 10,500 mm2, the number of turns of the electromagnetic coil is 150 turns, and the vacuum permeability μ0 is 4π×10-7 Vs/Am. In addition, take: mg=733 N, 1/m=0.013 (for the convenience of simulation, expanded by 1,000 times), kp=8,800, ki=18.5, kd=1,000,000, kp1=9,000, ki1=220,000, kd1=50, T=2×10-5.

Loading/unloading can be described by Flux*, which is used to represent step loading and unloading of 400 N at 0.2 s and 0.6 s. The simulation results are shown in Figure 7. The upper part of the obtained suspension air gap waveform is analog control, and the lower part is digital control.

The current output result is reduced by 1000 times. Figure 8 shows the magnet current curve (unit A), where the actual rated current value is set to 3.3 A. The upper part is analog control and the lower part is digital control.

4 Hardware co-simulation
Hardware co-simulation means that after simulating the algorithm model designed in the Matlab-Simulink environment, the "System Generator" can combine the actual "Xilinx-FPGA" hardware resources to generate a "hard core" that integrates the algorithm; then download the "hard core" to the FPGA through the FPGA. Finally, with the same signal as the input, one signal is connected to the "software algorithm model" and the other signal is connected to the "hard core", and the outputs of both are observed at the same time. If the processing results are consistent, it can be proved that the DSP model designed in the Matlab-Simulink environment is hardware feasible.
After running the co-simulation of the digital control system simulation, a new digital PID module will be generated. Then reconnect it to the digital control system simulation block diagram, and you will get the hardware co-simulation system block diagram shown in Figure 9.

Compare the theoretical control of Figure 5 with that of Figure 9, then connect the development board, turn on the power, and run the model for simulation. It can be clearly seen from the simulation waveform that the results of the hardware co-simulation are exactly the same as the theoretical results.

5 Conclusion
This paper uses System Generator to simulate the FPGA-based magnetic bearing control system and downloads it to the FP-GA development board for hardware collaboration. The results show that when loading/reducing 400N force, the designed digital PID controller can better control the magnetic bearing system and achieve stable suspension.