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Control Systems

by: Lionel Hansen

Control Systems MECH 417

Lionel Hansen
GPA 3.87

David Alciatore

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David Alciatore
Class Notes
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This 2 page Class Notes was uploaded by Lionel Hansen on Tuesday September 22, 2015. The Class Notes belongs to MECH 417 at Colorado State University taught by David Alciatore in Fall. Since its upload, it has received 80 views. For similar materials see /class/210251/mech-417-colorado-state-university in Mechanical Engineering at Colorado State University.

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Date Created: 09/22/15
In summary the six rules for sketching the root locus of a closedloop system with the char 5 acteristic equation lKGsHs 039 i are given in Table 72 Recall that the root locus is a plot of the roots of the system charac teristic equation poles of the closed loop system as the parameter E is varied Some exam ples will be given new to illustrate the use of these rules TABLE 124 RULES FOR ROOT LOCUS DEVELOPMENT l The root locus is symmetrical with respect to the real axis 2 The root locus originates on thepoles of GsHs for K 0 and terminates on the zeros 391 of GsHs as Kquot gt on including those at in nity If the open loop function has a zeros at in nity a 2 l the root locus will approach a asymptotes as K approaches infinity The asymme are located at the angles r180 a 3 Q 0amp3 r ili3 and those asymptotes intersect theatealaxislat the point Z finite poles E nite zeros quot finite poles nite zeros where the symbol denotes number 4 The root locus includes all points on the real axis to the left of an odd number of real critical frequencies poles and zerosla I I p 5 The breakaway points on39aquot39root locus5le appear among the of the polynomial obtained from either d ammo z 0 is or equivalently menses Mtgmesa 0 where Ms amt Ds are the numerator and denominator polynomials respectively of CSl k Loci will depart from a pole pj arrive at a zero 2 of GsHs at the angle 949a Where ed 293 29p r 180 139 iii ea 29quot 293 r 180 quot ti and where r i1 i3 and 9m Bzi represent the angles from pole 5 zero zi respectively to pjzj 9quot 103106 1144 AM MATLAB Command Window gtgt help margin MARGIN Gain and phase margins and crossover frequencies gtgt GmPmchch MARGINSYS computes the gain margin Gm the phase margin Pm and the associated frequencies ch and ch for the 8180 open loop model SYS continuous or discrete The gain margin Gm is defined as 16 where G is the gain at the l8O phase crossing The phase margin Pm is in degrees The gain margin in dB is derived by GmdB 20loglOGm The loop gain at ch can increase or decrease by this many st before losing stability and GmdBltO Gmltl means that stability is most sensitive to loop gain reduction If there are several crossover points MARGIN returns the smallest margins gain margin nearest to 0 dB and phase margin nearest to 0 degrees For a Sl by by Sp array SYS of LTI models arrays of size Si Sp such that Gmjl jpPmjljp MARGINSYS jl MARGIN returns jp GmPmchch MARGINMAGPHASEW derives the gain and phase margins fromthe Bode magnitude phase and frequency vectors MAG PHASE and W produced by BODE Interpolation is performed between the frequency points to estimate the values MARGINSYS by itself plot the open loop Bode plot with the gain and phase margins marked with a vertical line See also ALLMARGIN bode ltiview ltimodels Overloaded functions or methods help ltimarginm ones with the same name in other directories Reference page in Help browser doc margin 1 of l


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