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Chemical engineering lesson7 high order overdamped processes

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Spring 2006 Process Dynamics, Operations, and Control 10.450 Lesson 7: High Order Overdamped Processes 7.0 context and direction Chemical processing plants are characterized by large time constants and time delays. For control engineering, we can often approximate these high-order systems by the FODT (first-order-dead-time) model. Dead time in a process increases the difficulty of controlling it. DYNAMIC SYSTEM BEHAVIOR 7.1 big and slow - high-order overdamped systems We began our study of process control by considering a mixed tank. Applying a material or energy balance to a well-mixed tank produces a first-order lag system. We subsequently combined two balances to produce a second-order system. In one case, two material balances described storage of material in two tanks. In another case, a single tank stored both material and energy. Energy and material balances show that the tank causes a dynamic lag between input and output, because it takes time to adjust the amount of mass or energy distributed throughout the tank. We might thus expect that more storage elements would lead to higher-order behavior, and require higher-order equations to describe them. The classic illustration of a high-order system is a set of n tanks in series: each tank feeds the next, and a change in the inlet stream composition CA0 must propagate through multiple tanks to be felt at the output CAn. The individual tank models are d Vi C 'Ai = FC 'Ai −1 − FC 'Ai dt (7.1-1) They are combined b ...
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