![]() ![]() The first formulation, which will be explained in section 2.5, is inspired by DeHaan and Guay, (19) who proposed a continuous-time MPC method for a lumped-parameter system. Sections 2.5 and 2.6 describe the differences between the two formulations. ![]() Sections 2.1– 2.4 are equally applicable to both formulations. In this paper, we describe two very similar suboptimal MPC formulations. To ensure that the MPC can be executed in real time, we describe a discrete-time system formulation in section 2.1, define a receding horizon in section 2.2, formulate an optimal control problem in section 2.3, and present a real-time MPC algorithm based on a suboptimal nonlinear programming method in section 2.4. Especially for fast dynamical systems and distributed-parameter systems, this is still a major challenge for MPC. MPC typically involves the solution or suboptimal solution of a dynamic optimization problem. The control objectives are to limit the maximum reactor temperature (avoid hot spots) and to maximize the process output. The robustness of the controllers is evaluated for an example problem, where a nonisothermal plug-flow reactor with irreversible exothermic reactions is considered. An analysis of the nominal stability is provided for one NMPC scheme. With this suboptimal solution strategy, a fixed maximum evaluation time and execution in real time are guaranteed. The NMPC algorithms perform a single step or several steps of an iterative solution routine of the optimal control problem at every sampling point. ![]() For the resulting lumped-parameter system, a constrained optimal control problem is formulated and state constraints are implemented in the form of barrier functions. The system is modeled by a hyperbolic partial differential equation and discretized by means of a two-time-level semi-implicit semi-Lagrangian scheme. Two real-time nonlinear model predictive control (NMPC) algorithms for a transport–reaction system are designed. ![]()
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