(357e) Synthesis of Moving Actuator Arm Controller in Reaction-Diffusion System within the Framework of Model Predictive Control (MPC) and Discrete Mechanics Optimal Control (DMOC)

This work considers the control design of a temperature regulating actuator mounted over a catalytic bar in a multiscale mechanical & reaction-diffusion system. The controller synthesis is based on two different types of dynamics present - the reaction-diffusion system dynamics describing the catalytic rod temperature in terms of a parabolic PDE, and the standard rigid body dynamics of the actuator arm.

While the problem of temperature control in the reaction-diffusion systems is well studied [1], the issue of a moving actuator incorporated in the temperature controller synthesis has not been explored due to the complexity of an integrating mechanical system control realization, which also needs to obey optimality and actuator constraints. Therefore, we are interested in the following optimal control problem:

``compute the actuator force over a given finite time interval which brings the system to a desired state while minimizing a user-specified cost function given as a balanced between control effort, time, and heating/cooling injected by the actuator, subject to the dynamics of the catalytic rod and the actuator as well as to temperature and input injection constraints.''

The subsystem dynamics describing the evolution of the temperature in the catalytic rod is treated by a model predictive control (MPC) formulation, which includes constraints on the available input injection and on allowable temperature profile. The actuator dynamics is numerically represented through a discrete Lagrange-d'Alembert variational principle [2] which is suitable for robust numerical integration and optimization purposes. The resulting discrete mechanical optimal control (DMOC) problem is combined with the constrained optimization structure emerging from the MPC realization. Bounds on the arm motion velocity can also be included as additional constraints in the proposed framework.

In this work, we report initial results in incorporating the actuator dynamics and actuator constraints in the temperature controller synthesis for reaction-diffusion systems. In this way, the multiscale features of the mechanical systems dynamics and temperature evolution of conventional process systems are merged in the realizable controller synthesis which obeys inevitably present constraints.

[1] P.D. Christofides, Nonlinear and Robust Control of PDE Systems: Methods and Applications to the Transport-Reaction Processes, Birkhauser, Boston, 2001.

[2] J. Marsden and M. West, Discrete Mechanics and Variational Integrators, Acta Numerica, 2001, 10, pp 357-514.