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unsw ceic3000 tutorial w5 process modeling and analysis

unsw ceic3000 tutorial w5 process modeling and analysis -...

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School of Chemical Engineering CEIC3000 Process Modelling and Analysis Tutorial 5 1. Consider the following linearized process model of an exothermic reactor: ˙ x 1 = 2 x 1 + x 2 (1) ˙ x 2 = 2 x 1 - 2 x 2 (2) where x 1 and x 2 are the temperature of the reactor and the mass of the product in the reactor. (a) Sketch the phase-plane plot. (b) On what initial condition, the temperature of the reactor will not keep on increasing? 2. Consider the following linear system: ˙ x = [ a - b b a ] x (3) How would the value of a affect the shape of the phase-plane plots? 3. Show that the following system exhibits a pitchfork bifurcation with three real
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Unformatted text preview: μ < 0 and a single unstable real solution for μ > 0. ˙ x = f ( x, μ ) = μx + x 3 (4) 4. Another type of bifurcation displays a saddle-node behavior. That is with different choices of μ , there will be either no equilibriums or one stable and one unstable equilibriums. This type of bifurcation will be discussed next week in class. Show that the following two-variable system ˙ x 1 = f 1 ( x, μ ) = μ-x 2 1 (5) ˙ x 2 = f 2 ( x, μ ) =-x 2 (6) exhibits saddle-node behavior in the phase plane. 1...
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