Mathematical Solution ODEs Laplace Procedure 1.Linearize ODE 2.Subtract original steady state 3.Find τ’s and k’s 4.Laplace 5.Rearrange to find transfer functions 6.Substitute to get one equation 7.Inverse Laplace with Maple®
Impulse Response Simulink® Output for Tryptophan
Final Thoughts Linear approximation is valid Step response is as expected Impulse response as expected Matlab® & Simulink® agree Model will provide basis for more complex systems Conclusions Vary k values Explore larger/smaller step and impulse values Make model more realistic Model multiple food components Recommendations
References Biglione, N., Yousef, M., & Rodgers, V.G.J., (2004). Process Dynamics & Control in Design 52:185: Lab # 1: Programming and Simulation using Matlab® and Simulink®. Seborg, D.E., Edgar, T.F., & Millichamp, D.A. (2004). Process Dynamics and Control (2nd ed.). Hoboken, NJ: John Wiley & Sons. Vander, A., Sherman, J., Luciano, D. (2001). Human Physiology: The Mechanisms of Body Function (8th ed.). Boston: McGraw Hill.
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