Dynamic Modeling and Simulation for Robust Control of Distributed Processes and Bioprocesses

Abstract

370 11 Dynamic Modeling and Simulation for Robust Control dimensional space of particle positions and velocities into a reduced order formulation which usually takes the form of the Boltzmann equation. Finally, coarse graining methods will zoom out the view point of the system and take the description back to the mesoscopic and macroscopic world of continuum [29].One conclusion to be drawn from this picture is that for any given time and length scales there will be a number of states dynamically active, coupled with others either relaxed (those states active at shorter scales) or frozen (as they are associated with much slower dynamics). Mathematically, such description translates into a highly coupled stiff system obeying a nonlinear set of algebraic, partial, and ordinary differential equations, which is usually difficult to solve. In this way, the stiffness of the resulting problem is the effect of the diversity of time scales coexisting in the system. From a control point of view or even from the more general perspective of "decision making," stiffness must be avoided, what calls for model reduction methods able to provide the simplest robust dynamic description representative of the system at the scales of interest.The application to process control should be considered not just in the restricted sense of a PID regulator or any other such device equipped with a "compensation" rule which responds to deviations between the prescribed operation condition and the current one. From a broader perspective a controller consists of a virtual representation of the system one wants to operate (the plant), and a sort of agent which at regular time instants inspects the current state of the process and employs the system representation to screen future scenarios by asking whether a given decision should be made or not. Once the best possible action is found, the agent implements it in the real plant and waits for the response given by the sensors to initiate further corrective actions. This logic, properly repeated during the process operation, is what is known as a feedback control scheme. In its simple version a PID contains one such representation of the linear dynamic range, which in this case is explicitly inverted in some smart way as the internal model control (IMC) theory clearly highlights [39].More sophisticated control algorithms will also share the same construction logic, namely a virtual representation of the system dynamics, an agent devising future operation, and a comparison rule which evaluates the real effect of the control actions on the process. Such control methods would include adaptive control [41], feedback linearization control [34], slide mode control [48], or model predictive control (MPC) in all its flavors (linear, nonlinear, constrained, etc.) [23,32,42].In constructing a reliable dynamic representation for the system to be controlled, and depending on the class of description employed, there are a wide variety of methods at hand. However, they all rely on the very same basic principle, n...

Derivation of Postharvest Fruit Behavior Reduced Order Models for Online Monitoring and Control of Quality Parameters During Refrigeration

“…; Alonso et al . ). Depending on the way of computing the basis functions, different techniques arise, for instance the proper orthogonal decomposition (POD) or laplacian spectral decomposition (for more details see Vilas et al .…”

“…Reduced order models (ROM) emerged as an efficient alternative to the classical techniques for real time applications. These techniques are based on projection of the original PDEs system over a set of globally defined basis functions (Sirovich 1987;Balsa-Canto et al 2002;Alonso et al 2010). Depending on the way of computing the basis functions, different techniques arise, for instance the proper orthogonal decomposition (POD) or laplacian spectral decomposition (for more details see Vilas et al 2006) to name a few.…”