E consider a scenario where the chemostat residence

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e) Consider a scenario where the chemostat residence time ! ! ! experiences a positive step change at time = 0 of magnitude 2 hr -1 . What would your input variable function be in Laplace space? Aka what is your function U(s)? Substitute this into your equation for Y(s), and assume the other input variable stays at its steady state value. What are the poles of your function? What does this tell you about the stability of your system to a step change in the residence time? f) Use partial fraction decomposition to separate your expression for Y(s) into three terms with one pole each. Then, convert this expression back into the time domain using your knowledge of Laplace transforms and Table 3-1. g) Plot your final solution to show the response of the system to a step change in the disturbance input variable. Qualitatively comment on this response (i.e. stable/unstable or oscillatory/smooth) and compare to your predictions based on the poles of the system in part e.
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  • Spring '14
  • Pierre-Simon Laplace, chemostat residence time

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