Notes-4B

# Notes-4B - 4.4 SteadyState Response and System Type...

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4.4 Steady State Response and System Type L(s)=P(s)C(s)

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Error Constants System type k

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Example: DC motor is a type 1 system
PID Controller

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Example: PI Controller
Example: DC Motor

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Example

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Disturbance Rejection Summary: when z ( )= 0 step input (l=0, d(t)=1(t)): if k 1 (i.e., more than one integrators) ramp input (l=1, d(t)=t): if k 2 (i.e., more than two integrators) acceleration input (l=2, d(t)=t 2 /2): if k 3 (i.e., more than three integrators)

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Example: DC motor 0 0 By the previous results, if the disturnbance is a step, we need at least 1 integrator in the controller to achieve zero error. () L e t , Then the error is ( ) lim pi i p s Ks K KP s Cs K Ps ss s PsD es + =+= = ∞= 0 0 0 0 00 0 0 () () lim 1 1 0, for ( ) 1( ) lim lim ,for ( ) s i sP s D s s PsCs dt d t s D s sD s d s C s C s K →→ = ++ = == = = +
Internal Model Principle To achieve this robustly, we need a(s)p(s) and b(s)[q 2 (s) q 1 (s)] contain s l+1 as factors respectively, so P(s)C 2 (s) has to be type l+1 and [q 2 (s) q 1 (s)] contain s l+1 as a factor. Similarly, C 2 (s) has to be type l+1 if d(t) is an l th order polynomial of

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## This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Notes-4B - 4.4 SteadyState Response and System Type...

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