(706b) Model Predictive Control of Atmospheric Pressure Plasma Jets for Biomedical Applications

Model Predictive
Control of Atmospheric Pressure Plasma Jets for Biomedical Applications

D. Gidon, D. B. Graves, A. Mesbah

Department of
Chemical and Biomolecular Engineering, University of California Berkeley

E-mail: dgidon@berkeley.edu

Atmospheric
Pressure Plasma Jets (APPJs) are a class of cold, ambient pressure plasma
devices that are increasingly used for biomedical purposes. Energetic electrons
in these plasmas drive the production of therapeutically relevant components
such as reactive oxygen and nitrogen species (RONs), UV-range photons, heat,
and electric field. However, under atmospheric pressure, the characteristics of
the plasma and the associated therapeutic effects can vary drastically with
changing environmental conditions and disturbances [1]. Multiple modes observed
in both radio frequency (RF) range [2] and kilohertz range [3] excited APPJs
exemplifies this phenomenon. The change in plasma behavior is often associated
with a heterogeneous, filamentary discharge structure and can lead to ‘arcing’
where all the current is concentrated in a thin conductive plasma channel. This
sensitivity of the plasma behavior to external conditions makes reliable and
reproducible operation of APPJs difficult, in particular for safety-critical
applications. The large amount of heat and current delivered to the treated
surface with arcing is also generally undesirable for biomedical applications
due to safety considerations. The latter operational considerations and the
requirements for high performance and strict constraint handling necessitate application
of advanced control strategies for regulating the intricate dynamics of APPJs.

Dynamics
of APPJs are commonly described by a set of coupled, high dimensional fluid
equations. Small spatial discretization and small time steps are necessary to
capture the non-equilibrium behavior of the plasma and the spatial distribution
of variables of interest [1]. Consequently, the computational cost associated
the solution of such fluid models becomes prohibitive for use in on-line
optimal control strategies, such as model predictive control (MPC). Recent
developments in analytical and numerical ‘global’ (zero-dimensional) modeling
of APPJs [4] have revealed that simpler models can provide adequate
descriptions of dynamical characteristics of plasmas. Moreover, for control,
such global models must be extended to account for the full complexity of
operation; including the electrical circuit associated with the device and the
effects of the plasma on the treated surface. These requirements motivate our
approach to control-oriented, lumped-parameter modeling of APPJs based on first
principles.

In this
work, a nonlinear MPC (NMPC) is designed based on a control-oriented lumped
parameter model of the argon RF-APPJ reported in [5]. The control-oriented thermal
model of the APPJ coupled with a biological surface, presented in [6], is
extended by a lumped-parameter equivalent circuit model and a truncated
reaction network to adequately represent system physics. The performance of the
proposed NMPC approach is evaluated in terms of regulating the target surface
temperature and the current delivered to the surface. The closed-loop simulation
results of NMPC are compared to those of an internal model control system for
various scenarios inspired from biomedical applications of the APPJ under study.

References

[1] H. W. Lee G. Y. Park, Y. S. Seo,
Y. H. Im, S. B. Shim, and H. J. Lee, Journal of Physics D: Applied Physics,
44, 053001 (2011).

[2] J. J. Shi, X. T. Deng, R. Hall,
J. D. Punnett, and M. G. Kong, Journal of Applied Physics, 94:10,
6303 (2003).

[3] J. Walsh, F. Iza, N.  B. Jason,
V. J. Law, and M. G. Kong, Journal of Physics D: Applied Physics, 43,
075201 (2010).

[4] M. Lieberman, Plasma Sources
Science and Technology, 24, 025009 (2015)

[5] S. Hofmann, K. van Gils, S. van der Linden, S.
Iseni. P. Bruggeman, European Physical Journal D, 68:3 (2014)

[6] D. Gidon, D. B. Graves, A. Mesbah, Proceedings of the
American Control Conference, Accepted, Boston (2016).