Inductively coupled plasma (ICP) torches have been widely used in various materials processing. To improve the control of their processes, there has been a growing demand for simplified numerical models which can rapidly predict the dynamics of plasma jets subject to time-varying inputs or external disturbances. In this paper, control-oriented dynamic models of an ICP torch are developed as an alternative to the complex, high-level 2D time-dependent numerical model (i.e. a model based on magneto-hydrodynamic equations). Prior to model development, the detailed dynamic and nonlinear nature of the ICP torch to its time-varying operation conditions was numerically investigated using a 2D numerical model to gain insight into choosing appropriate dynamic model structures. Linear ARX (AutoRegressive with eXogenous input) and ARX-type neural network models were selected in the model identification, and their parameters or weightings were determined using the input/output data obtained from the 2D time-dependent numerical model. The dynamic behaviours of the ICP torch predicted from the developed models were in good agreement with the data from the 2D time-dependent numerical model. Using the developed models, a simple control system for the plasma temperature and axial velocity regulations was also designed and tested. The feedback control simulations demonstrated good set point tracking and disturbance rejection performances, indicating that the developed approach can be directly applied to the model-based control system design of an ICP torch as well as other thermal plasma torches.
First-principles-driven model-based current profile control for the DIII-D tokamak via LQI optimal control