Reference Trajectory Design Using State Controllability for Batch Processes

Abstract

address: Carrera 80 #65-223, office: M3-100, Medellín, Colombia; zip code: 050041. Abstract:A proposal for the design of a reference trajectory for batch processes was developed, using set theory state controllability concepts. This proposal introduces the Available Control Action Set, which is an indicator of the state controllability and contains the largest amount of possible control actions that reach the desired final state. The volume of Available Control Action Sets can be maximized to improve the safety of batch processes while maintaining consistently high product quality. Thus a closed loop system has sufficient energy to reject disturbances, ensuring end-of-batch product quality. Case studies are presented to demonstrate the applicability of the approach to batch and semi-batch processes and to illustrate how the proposed method for the design of a reference trajectory for batch processes increases safe and robust operation.

PI/PID controller stabilizing sets of uncertain nonlinear systems: an efficient surrogate model-based approach

“…The controllable set, which plays an important role in the analysis of nonlinear systems, is composed of all the states x ∈ X from which the system can be driven to the operating point x * , assumed to be stable in the sense of Lyapunov, by applying a sequence of control actions u(•) ∈ U without any restrictions on the controller design method [28,29,66].…”

“…The controllable set can be approximated accurately with both a bounded error and a risk failure quantification using the randomized algorithm introduced by [28], as summarized in Box 1. The same algorithm was adopted by [29] for the controllability analysis and reference trajectories design of some semi-batch reactors.…”

Input Trajectory Design for the Enhancement of State Estimation through a Set-Theoretic Approach to Observability

“…Moreover, while this article focuses on observability-oriented design, the objective function of the presented approach can be modified via a weighted sum to include other properties of interest. For instance, in the case of batch processes, whose irreversibility represents a common difficulty in control tasks, a combined observability-controllability approach may be developed by adding terms related to the available control actions set to the objective function of the optimization.…”

“…The two most common trajectory design objectives in chemical and biochemical processes are minimizing the batch time ,, and optimizing some terminal quality measures, such as product quantity, , product concentration, , or some properties of the crystal size distribution in crystallization. ,, However, the optimization of other properties is possible and may be desirable. For instance, ref aims to maximize control action availability to prevent the batch process from getting to states from which the desired final condition is no longer reachable.…”

Determination and use of feasible operation region in flash distillation control

“…That expected full range could be obtained by combining all possible values of the n control actions inside their respective spans. The existence of a FOR different to supposed full range operation impacts process engineering tasks executed over the process: design, optimization and control [17]. In this sense, reviewing known textbooks about proposed control structures for flash distillation [3,18], it was evident the lack of mention about the FOR.…”