CHEN 4601 Lecture Notes - Lecture 4: Ddb Worldwide, Paga, Energy Economics

• School: UMN
• Department: Chemical Engineering
• Course: CHEN 4601
• Professor: Prodromos Daoutidious

Document Summary

Last time: general form of process models this is linear set of 1st order odes nonlinear (this is the general form of eqns we will use) This is principle of superposition for linear systems, if you change parameters, you get proportional change in response but not for nonlinear systemsdon"t get proportional changes. A diff. eqn is linear is linear if the dependent variable and its derivatives appear linearly. For non-linearity --> look for x2, x1x2, x1u (product of output variable with input variable), ex, lnx Nonlinearities lead to multiple steady states --> necessitate numerical solutions vs. analytical, complex phenomena. Non-linearity is the rule (but creates problems when we deal with it --> that"s why we want linear) rather than the exceptionbut control theory and engineering focus/assumes linear behavior --> valid close to a steady state. Recall: taylor series expansion of functions around a point. If x is close to x0, we can truncate the series @ the linear term.