{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MEM355W07-08.HW2.soln_stud

MEM355W07-08.HW2.soln_stud - MEM355 PERFORMANCE ENHANCEMENT...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MEM355: PERFORMANCE ENHANCEMENT OF DYNAMIC SYSTEMS Home work #2 solution Problem 1: Unity (negative) feedback system, with the loop transfer function 2 450( 8)( 12)( 15) ( ) ( 38)( 2 28) s s s G s s s s s + + + = + + + Assume the closed loop system is stable. (we need to verify this). This is a type-1 system (presence of one integrator). Hence, it will yield finite error for type-1 (t 1 ) input, zero errors for inputs of lower types, and infinite errors for higher type inputs. The (finite) errors could be evaluated using the error constants, K i . Input Error constant error 25 U(t) ) ( lim ( ) or p s K G s G = = ( ) 1 1 or p e K = = + 37 tU(t) 1 ( ) 450(8)(12)(15) lim ( ) (38)(28) s or v K sG s G = = ) 1 ( 1 1 (38)(28) 450(8) 37 (12)(15) or v e K = = 94 (t 2 /2) U(t) ) 2 ( 2 lim ( ) o s r a K s G s G = = ( ) 2 2 1 or a e K = = Alternately, one could compute the closed loop transfer function, and E(s), the laplace of the error, use the final value theorem to determine the error in time-domain. Such as…. 2 ( ) ( ) 1 1 ( ) 450( 8)( 12)( 15) ( ) 1 ( ) 1 1 ( 38)( 2 28) cl cl C s G E s G s s s s R s G R s G s s s s = = = = + + + + + + + + + 2 2 ( 38)( 2 28) ( ) ( ) ( 38)( 2 28) 450( 8)( 12)( 15) s s s s E s R s s s s s s s s + + + = + + + + + + + (check stability: It is stable, with roots at {-455, -13.34 ± 4.5i, -7.2} . Then by FVT (final value theorem), lim ( ) s e sE s G G = . Thus.....
View Full Document

{[ snackBarMessage ]}

Page1 / 7

MEM355W07-08.HW2.soln_stud - MEM355 PERFORMANCE ENHANCEMENT...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online