(740b) Learning-Based Model Predictive Control for Non-Equilibrium Plasmas

Learning-based control is a form of adaptive control, whereby controller and/or process model parameters are modified based on system measurements [1]. Learning-based control can create unprecedented opportunities for process control of non-equilibrium plasmas (NEPs) [2]. NEPs are weakly ionized gases, typically helium, argon, or air, generated in ambient conditions via the application of a modulated electric field. NEPs have recently gained increasing attention for treatment of heat and pressure sensitive (bio)materials in surface etching/functionalization, environmental, and biomedical applications. Some of the main challenges in process control of NEP applications arise from their inherent complexity and variability. Firstly, the dynamics of NEPs are highly nonlinear and spatio-temporally distributed, which are both expensive and also difficult to model due to their mechanistic complexity. Secondly, the NEP effects on complex surfaces are generally poorly understood. And thirdly, NEPs exhibit run-to-run variations and time-varying dynamics, whereby the same experiment may be carried out under similar conditions, but yield different results [3,4].

In this talk, we demonstrate the usefulness of a learning-based robust model predictive control (LB-RMPC) strategy for NEP treatment of complex surfaces via closed-loop control experiments on a kHz-excited atmospheric pressure plasma jet (APPJ) in Helium [5]. APPJs are a particular type of NEP devices widely used in plasma medicine and materials processing applications. Inspired by [6], we consider a linear dynamic model and a nonlinear additive state-dependent noise, which can be predicted using Gaussian Process (GP) regression. We show that GP provides a way to obtain state-dependent uncertainty bounds as the predictions will depend on current as well as past states and inputs. Thus, the LB-RMPC strategy allows system operation closer to the constraints, while guaranteeing that the constraints are not violated. Furthermore, online training of the GP model can eliminate the plant-model mismatch and reduce the uncertainty, improving the performance of the controller. Closed-loop experiments show that the proposed LB-RMPC strategy is less conservative than a RMPC strategy that uses worst-case uncertainty bounds. Most importantly, constraint violations in the key state variables such as the plasma intensity and the target surface temperature are eliminated, ensuring safe and reliable operation despite possible disturbances. Additionally, plant-model mismatch is effectively suppressed without the need to resort to offset-free MPC techniques.

[1] A. Aswani, H. Gonzalez, S. Shankar Sastry and C. Tomlin, "Provably safe and robust learning-based model predictive control," Automatica, 49, pp. 1216-1226, 2013.

[2] A. Mesbah and D. Graves, "Machine Learning for Modeling, Diagnostics, and Control of Non-equilibrium Plasmas," Journal of Physics D: Applied Physics, 2019.

[3] J. Shin and L. L. Raja, "Run-to-run variations, asymmetric pulses, and long time-scale transient phenomena in dielectric-barrier atmospheric pressure glow discharges," Journal of Physics D: Applied Physics, 40, pp. 3145-3154, 2007. [4] D. Gidon, D. B. Graves and A. Mesbah, "Effective dose delivery in atmospheric pressure plasma jets for plasma medicine: A model predictive control approach," Plasma Sources Science and Technology, 26, pp. 85005-85019, 2017. [5] D. Gidon, B. Curtis, J.A. Paulson, D.B. Graves, and A. Mesbah. “Model-based feedback control of a kHz-excited atmospheric pressure plasma jet,” IEEE Transactions on Radiation and Plasma Medical Sciences, 2, pp. 129-137, 2018.

[6] R. Soloperto, M. A. Müller, S. Trimpe and F. Allgöwer, "Learning-Based Robust Model Predictive Control with State-Dependent Uncertainty," in Proceedings of the IFAC Conference on Nonlinear Model Predictive Control, pp. 442-447, Madison, WI, 2018.