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| Director: Prof. Andreas A. Linninger |
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Integrating Design and Control: Dynamic Analysis of Flexible Operation Andres Malcolm and Andreas A. Linninger Key words: Conceptual Design Phase, Dynamic Control, Flexibility Index, Process Modeling, Stability, Frequency Analysis. Motivation The usual practice to handle uncertainty in designing systems in chemical engineering is by overdesign applying a 'safety factor'. Once the design of the system is obtained in a second stage the control system is devised. Overdesign has at least three shortcomings:
i. the degree of safety factor is unknown (usually determined by experience),
On the other hand, process control aims at dissipating disturbances (or uncertainty) and hence pursues similar objectives as conceptual design. It would appear advantageous to consider process design and control system design simultaneously in order to achieve the best overall performance under operational uncertain with an implementable control. Background Grossmann and coworkers1-2-3 introduced the concept flexible design with a static considering a steady state analysis. Unfortunately this approach does not render implementable control strategies. Recently, Pistikopoulos and coworkers3-4 have shown that considering a steady-state point of view leads to unrealistic control scheme and that a dynamic analysis is needed. Another approach to handling uncertainties/disturbances leads to robust control. This theory aims at producing stable closed-loop systems in the presence of model and parameter uncertainty5-6. The main focus is in the stability of the controlled system under uncertain inputs but with fixed design decisions (e.g. reactor size, residence time, etc). Unfortunately, no consideration of end-point constraints is given in this analysis, nor can it guarantee thr quality constraint satisfaction of the dynamic operation. Currently a systematic tractable framework to solve for the simultaneous system design and control design is in its infancy and much work needs to be done to overcome this challenging problem.
Challenges Between the many challenges the simultaneous design and control problem comprises, we will like to point the following: i. Numerical tractability of the problem: the uncertain space together with the time domain, leads to an infinity domain optimization problem.ii. Time varying models for critical uncertain scenarios are still missing; therefore there are no guarantees about the robustness of the design with the current methodologies. iii. The controlled system can observe an unstable response for certain control configurations, a global stability criterion has to be adopted. iv. The current optimal controller design relies on a previously fixed process design decisions, objectives and trade-offs for simultaneous control and design optimization techniques have to be developed. v. Checking flexibility of a system usually often leads to large MINLP; convergence of this kind of problem in never assured and there exist no reliable global optimization method. Proposed methodology We propose a methodology that aims at obtaining best trade-offs between design and control decisions in a dynamic view of process control and design. Our method will include an extension of stochastic flexibility, dynamic feasibility test and robust control theory. We will also demonstrate, with the help of this dynamic approach, that integration of design and control at conceptual level yields better cost performance and higher flexibility as compared to designs, which consider process control separately. In particular we would like to: i. Reduce the infinite dimensional problem by the use of spectral methods.ii. Model different uncertain sources in time. iii. Discuss the impact of periodical uncertainty and the influence of their frequency of occurrence. Case Study Using a controlled heat exchanger design under uncertainty (Figure 1a), as our case study7, we have found out that a dynamic flexible design obtained considering constant or low frequency uncertain variables, can still violate constraints if the frequency of the uncertain variables reaches a critical value (Figure 1c-d). This indicates that a dynamic flexible design is not sufficient to ensure flexibility and a proper model of the uncertain variables in time is needed to do a robust design. Conclusions It is needed to consider process design and control system design simultaneously so as to achieve the best overall performance of the system under realistic implementable control and operational uncertainty. The available methodologies offer insufficient insight to the problem. We propose a new method include the elements of stochastic flexibility, dynamic feasibility test and robust control theory so as to obtain a robust simultaneous process and control system design under uncertainty.
References:
1. Halemane,
K. P; Grossmann, I. E.: Optimal
Process Design under Uncertainty, AIChE J. 1983, 29, 425.
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