Circuit-Based Mathematical Model of an Arc Heater for Control System Development

A novel circuit-based mathematical model of an electric arc heater is presented so that an arc heater system can be modeled, and a control algorithm can be developed and simulated. Due to inherent arc nonlinearities and complexities, as well as low amounts of arc heater data, the new model was developed by establishing a holistic approach to implementing the arc as a circuit element, where common circuit analysis and control techniques can be easily applied. The response of the arc heater system was examined at various voltage and current operating points that represent different regions of operation within the arc's characteristic curve. The simulated data of the arc heater model were compared to the arc characteristics of the experimental data. The experimental data set used for comparison was collected at the Hypersonic Materials Environmental Test System (HyMETS) arc-jet wind tunnel by the NASA Langley Research Center in Hampton, Virginia. Data analysis and simulations were executed utilizing MATLAB and Simulink to compare the newly developed model with the experimental data. The simulations demonstrate a strong correlation between these datasets, indicating the model's ability to accurately replicate the physical system, while also allowing initial control system development to begin with simplistic proportional-integral-derivative (PID) control of the arc heater.