1D and 3D co-simulation and self-adaptive position control of electrostatic levitation in China's Space Station.

The greatest challenge of electrostatic levitation for containerless material processing is the stable control of charged material during heating. Recently, high-precision self-adaptive control of electrostatic levitation has been achieved in China's Space Station. Based on the 1D and 3D co-simulation analysis, an optimal scheduling of control strategies of sample release and retrieval in space is developed. Both simulation results and on-orbit experiments demonstrated that the inversion of surface charge is responsible for the heating induced material instability. On-orbit experiments indicated that under laser illuminations, the net surface charge of metal Zr changed from positive to negative at 900 K and from negative to positive at 1300 K. The possible physical mechanism of the charge inversion of heated material is discussed.

Introduction

Containerless material processing using aerodynamic[1,2], acoustic[3,4], electromagnetic[5-7] and electrostatic levitation[8-23], has been widely used in the study of materials science experiments and thermophysical properties measurements. Containerless methods not only avoid chemical contamination at high temperatures caused by the direct contact with the container, but also eliminate extrinsic heterogeneous nucleation. By so doing, melts can often be supercooled to accesses non-equilibrium states, glasses and otherwise unavailable crystalline forms of materials. Among these levitation methods, electrostatic levitation is more valued due to its broad applicability. Since it levitates the charged object by the electrostatic force, it can accommodate a broad range of materials including metal, alloy, and oxide as long as the sample carries sufficient amount of charge. Additionally, it provides a variety of special environments for conducting material experiment such as high-vacuum, inert gas, and high pressure.

Many thermophysical properties of levitated melts can be measured on Earth, but buoyancy-driven convection often masks underlying diffusion phenomena. The microgravity environment greatly reduces buoyancy-driven convection and provides quiescent conditions for thermophysical property measurements and nucleation. Also, only weak electric field is enough for the stable levitation in microgravity while strong electric field is required to overcome the gravity on the ground. Currently, there are two electrostatic levitation furnaces (ELF) in operation in space, including the ELF developed by Japan Aerospace Exploration Agency, which was launched to the International Space Station (ISS) in 2015, and the China’s ELF launched to Tiangong Space Station in May 2021. Recently, several samples have been stably levitated in the ISS and thermophysical properties of them have already been reported[17].

The greatest challenge for conducting electrostatic levitation experiments is the accurate position control of test samples using levitation force, especially at the laser-heating stage, where acute sample instability occurs when the material is heated up over a certain temperature. The prior work recognized that responding to changes in the charge on the sample is an essential requirement for maintaining stable levitation during first heat up from ambient and believed that this phenomenon resulted from the surface charge loss of the sample during heating[8-15,22]. Therefore, a system to compensate positive charge for the heated sample is required for keeping levitation stable. A commonly used method to resolve it is to use a high-power deuterium lamp to maintain the positive charge based on the photoelectric effect[9,11-13,16,17]. Photoelectric charging has been used successfully in some ground-based levitators. However, this method is typically not suitable when a gaseous atmosphere is present. The gas can ionize and cause discharges from the high voltage. Alternatively, in the ground-based experiments, the preheating technique can also ensure the control stability but only for materials with melting temperature higher than 1500 K[12,18].

Various control algorithms were developed to improve system robustness, including fuzzy logic scheme for online tuning of controller parameters and actively identifying the amount of electrical charge in real-time[9,11,15,24,25]. The previous algorithms can actively adjust the controller parameters corresponding to the amount of electrical charge, but they are not valid to deal with the instabilities if the charge polarities flip abruptly. In China’s ELF, instead of using UV lamps to maintain the positive charge, the self-adaptive control strategy has been proposed to resolve the laser heating induced sample instability without having to compensate the surface charge.

As we know, both the time and financial cost can be considerably high in the realization of a new technology, especially for those in space exploration and space science. Therefore, numerical simulation-driven assessments and optimizations is particularly helpful for obtaining an optimal scheduling of control strategies in the complex electrostatic levitation system. In this work, we propose a 1D and 3D co-simulation method and test its validity for optimizing the scheduling of the control strategy on the ELF in China’s Space Station.

Methods

Containerless experiment system

The electrostatic levitation furnace in China’s Space Station is shown in Fig. 1. The rack for containerless material science experiments is composed of an experiment chamber and supporting modules for power supply, information recording and cooling. The core module of the rack is the experiment chamber with 36 optical windows. An axial structure including three pairs of cylindrical electrodes that are pairwise orthogonal is nested in the chamber.

Fig. 1

Drawing of electrostatic levitation furnace in China’s Space Station.

a Containerless material science experiment rack, b Experiment chamber with 36 optical windows, c Electrode configuration.

The stable levitation of charged samples is automatically controlled by the electrostatic force generated by three pairs of high voltage electrodes with a feedback loop. Figure 2 illustrates the simplified model of test sample on x-z plane and the control loop of electrostatic levitation system.

Fig. 2

The simple model of electrostatic levitation control system.

The charged samples is controlled by the electrostatic force generated by three pairs of high voltage electrodes with a feedback loop.

Accurate and high-speed position detection is of great importance to electrostatic levitation. PSD (Position Sensing Device) is commonly used in ground-based electrostatic levitators[8]. By contrast, video imaging method has a better signal to noise ratio and can obtain a clearer sample edge by using the algorithm of image identification[16,17].

In our levitator, the material spatial position is detected by two orthogonal high-speed charge-coupled device (CCD) video cameras (Dalsa M640) in conjunction with two high-intensity backlights (650 nm in wavelength). The high-speed image captured by CCD cameras is analyzed by multi-core graphic processing unit (GPU), and the voltage signal that is required to stabilize material is instantly calculated according to the design of Proportion-Integration-Differentiation (PID) controller. The voltage signal in digital is converted by digital-analog (DA) unit and then the analog signal is fed to high voltage amplifier (Matsusada AS-3B1). Finally, the electric field are generated by three pairs of high voltage electrodes to stabilize charged samples.

The position detection rate is around 700 Hz, due to the limitation of computational ability of GPU for image processing. The change rate of high voltage supplies can reach up to 12 V μs−1 within the range of ±3000 V. The spatial resolution of the position measurement is around 0.04 mm, which is limited to one pixel change on the camera sensor. The accuracy of levitation position can be controlled within ±0.1 mm with the optimal selection of PID parameters.

The pair of electrodes in the z direction are designed to be hollow, which allows two pushing rods transferring samples from the sample cartridge to the levitation area. The diameter of samples should be smaller than 3 mm due to the limitation of the size of sample holder and the hole in the electrode. The two pairs of cylindrical electrodes in the x and y direction provide the lateral electrostatic forces. The interval between z+ and z− electrodes is much less than that in the x and y direction to provide stronger electrostatic force at the stage of sample release and retrieval. The six electrodes are designed in a similar way as described in the ISS-ELF[17].

Four semiconductor lasers (LD) with the wavelength of 915 nm and one CO2 laser with the wavelength of 10.6 μm are used to heat samples. A tetrahedral laser heating configuration for LD lasers was implemented to avoid the destabilizing effect of photon and evaporative anisotropic induced forces[26]. Besides, this multi-beam heating configuration can suppress sample rotation and improve the temperature homogeneity. The maximum optical power of each LD laser and CO2 laser is 75 W and 5 W, respectively. All the lasers have a spot size of nearly 1 mm. Metal samples can be heated by only LD lasers, but upon heating oxide materials, CO2 laser is also required as generally 915 nm wavelength cannot be absorbed well.

The material temperature is simultaneously measured by a single-wavelength infrared pyrometer (IMPAC IGA 5) and a dual-wavelength infrared pyrometer (IMPAC IGAR 12-LO) with a sampling rate of 500 Hz. The operating wavelength of single wavelength pyrometer is from 1.45 μm to 1.8 μm. The dual wavelength pyrometer is operated at 1.28 μm and 1.65 μm wavelength. Both pyrometers are calibrated to true temperature using the known melting plateau of the material and they have a repeat accuracy of ±1%.

Experimental procedure

The sealed chamber can provide experimental environment ranging from near vacuum (10−4 Pa) to highly pressurized environment (300 kPa) with inert gas (Ar) for the processing of metal and oxide materials. Although a purity (99.999 at. %) Ar atmosphere can be used to study Zr, possible chemical reactions between the highly reactive molten metals and residual gas could alter the intrinsic surface tension or viscosity values. Very small amounts of oxygen can decrease the surface tension of metals[27,28]. Hence, we conduct the experiments of Zr samples under a ~10−4 Pa vacuum condition.

The technique for sample release and retrieval in microgravity experiments is first proposed in the ISS-ELF[16,17], where a rod is used to push samples to hit the bottom electrode for initial charging and the sample is retrieved by using electrostatic force. However, the hitting approach has some uncertainty in the position and velocity after the bounce of charged sample, which may cause the loss of control. Accordingly, we design a new approach for the levitation initiation.

The Zr samples are ~2.7 mm in diameter and are firstly transferred by the pushing rods from the sample holder to the hole of the z+ electrode. A constant high voltage signal is then fed to the z+ electrode. Under electrostatic attraction, the sample contacts the bottom electrode and gets like electric charges by contact. After a few seconds, the sample is electrostatically repelled from the z+ electrode. Once the charged sample enters the control area, its position is detected by the CCD camera and the feedback control starts to work.

When the sample is controlled in the right position, four LD lasers is used to heat samples and a self-adaptive control algorithm is enabled to actively identify the charge polarity of heated samples. Following the thermophysical property measurements of the melt, the heating lasers are turned off and the melts solidifies rapidly.

Finally, the processed samples are retrieved to the sample holder by constantly supplying the bottom electrode with a high voltage, so it repels the charged sample quickly into the hole of the top electrode.

It is worth noting that no UV lamps are used to maintain the positive surface charge during heating. Instead, a well-designed self-adaptive control strategy is utilized to avoid the laser heating induced material instability. The above optimal scheduling of experimental procedure and control strategies is based on a series of simulation-based analyses and is proven to be extraordinarily effective in on-orbit experiments.

1D and 3D co-simulation method

To obtain optimal control strategy and a robust control system, high-precision numerical simulation of electrostatic levitation is necessary. System dynamics simulation tools such as Simulink are usually used for modeling one dimensional (1D) complex control systems[11,19] due to the short computing time. Considering the lack of accuracy in 1D system model when estimating the electrostatic force between charged samples and high voltage electrodes[20,21], performing a three dimensional (3D) electrostatic simulation to obtain an accurate electrical force could significantly improve the overall accuracy of 1D system model. Therefore, a coupled 1D and 3D co-simulation approach is very attractive considering their complementary advantages and is to be implemented in the present work.

The co-simulation proposed here is the implementation of 1D control system modeling in Simulink and the 3D electrostatic modeling in COMSOL Multiphysics version 5.6, as illustrated in Fig. 3. The method uses the Simulink system model as the simulation master, while the 3D model is used as a sub-model with more detailed physical information of electric field and electrostatic force, which is represented by a Functional Mock-up Unit (FMU). COMSOL is integrated into Simulink via the LiveLink for Simulink, which can co-simulate using FMU files in a Simulink diagram. As shown in Fig. 3, the Simulink inputs the position and the voltage information of the electrodes to the COMSOL model while the COMSOL model subsequently computes the electrostatic force applied on charged samples and feeds it back to the Simulink.

Fig. 3

1D and 3D co-simulation model.

It implements system model in Simulink and 3D electrostatics model in Comsol Multiphysics.

According to the detected position of test samples, the voltage of the electrodes is computed by the PID feedback withwhere denotes the position deviation in the loop. is the target position and x is the center position of the levitated sample. , K and K are the PID parameters.

The motion of the levitated object is described bywhere m and are the mass and the acceleration, respectively, F is the electrostatic force and g is the gravitational acceleration in space.

In the Simulink system model, the error and time delay in position measurement as well as ripple voltage are taken into consideration to improve the accuracy of simulations. The COMSOL package enables an accurate computation of the electrostatic force of a charged sample. Consider a charged conductive sphere in the electric field of six cylindrical electrodes. The electric potential ϕ is described by the Poisson equation

The boundary conditions of the six electrodes are given by setting the potential aswhere is computed in the Simulink system model. The initial surface charge of the conductive sphere is given according to the electrostatic simulation.