Me330 lecture3

ME 330 Control Systems SP2011 Lecture 3

Example Process ,[object Object],Step 2) Transform f(t) to F(s) Step 1) Represent the system differential equation in Laplace domain “transfer function” Step 3) Multiply “transfer function” with Laplace domain input F(s) Step 4) Solve for time-domain response with inverse Laplace transform f(t)

Partial Fraction Expansion ,[object Object],[object Object],[object Object],[object Object],Nothing in tables for general quadratic equation Sometime even less straightforward when complex roots are involved

Requirement ,[object Object],[object Object],[object Object],order of N(s) < order of D(s)

Methods for Partial Fraction Expansion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Case 1: Real Roots ,[object Object],[object Object],[object Object],0 0 0

Example Case 1 ,[object Object],polynomial long division (shown on board)

Example Case 1 ,[object Object]

Case 2: Real Repeated Roots ,[object Object],[object Object],[object Object],[object Object],0 0 0 0

Example Case 2 ,[object Object],repeated root

Example Case 2 ,[object Object]

Me330 lecture3

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