Discrete mechanics optimal control (DMOC) and model predictive control (MPC) synthesis for reaction-diffusion process system with moving actuator

This paper is concerned with the computation of optimal motion control as well as the optimal input injection policy of an actuator arm regulating the temperature in a reaction-diffusion system. The system has two dynamical components consisting of the arm mechanics with inertial, elastic and damping properties, which is driven by bounded mechanical actuation controls and an underlying reaction-diffusion system described by the parabolic PDE. The state of the actuator arm parametrizes the input injection operator of the parabolic PDE systems model and causes coupling between the two dynamical systems generally operating at different time scales. The method proposed in this paper is aimed at solving this coupled problem. The actuator mechanics and its control are achieved in the discrete mechanics and optimal control (DMOC) framework, while the input injection for the reaction diffusion system is calculated by the modal model predictive control (MMPC) algorithm suitable for the dissipative systems. The actuation arm policy and input to the parabolic PDE system include in its realization low-order discrete representation of the parabolic PDE evolution and incorporate optimality with respect to both the state of the PDE and the actuator displacement cost from current to some more optimal control position as well as naturally present input and PDE state constraints. The proposed actuation arm policy and optimal stabilization of the unstable reaction-diffusion system in the presence of constraints in the full state-feedback controller realization have been evaluated through simulations.