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The EffĘcts of In Partial 3ėĄLfil1n€nt of Tle B€qüireûents for Eh ...

The EffĘcts of In Partial 3ėĄLfil1n€nt of Tle B€qüireûents for Eh ...

The EffĘcts of In Partial 3ėĄLfil1n€nt of Tle B€qüireûents for Eh ...

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pr axj-s .<br />

At the higher-crd€r ccntrol syst€Bs thê control<br />

signal {ni) rân be experlmentaty aIplj-ed. or reftoved rela-<br />

tive to the state- space re lat€¡ .iiscreFaÐcy display.Thj-s<br />

sj"gnal is applieð o!€r a¡d abcve the ¡estoriag <strong>for</strong>ces<br />

esse¡tial in the a¡rtÕ-detêrûinÉd stal,ilj-zation <strong>of</strong> perfo¡-<br />

¡na:lcê. Uathematically, it is<br />

ilpi/di=gi lPi, Pii +di (r) +ni í4i<br />

n: is ge¡era.l1y b j.nary {0,cr 1l ,cca<strong>for</strong>ning "{ith optima.li-<br />

ty priacipl€ €f ccrltlcl cr ,rbang-bangrt co¡trol {Tûfirvic,<br />

1966) . Eriefly, th€ baag-barg crnt.rol- action ipi, pi)<br />

ut j"lizes strategi.caì switcàing in and Õut <strong>of</strong> mi in such a<br />

raï as to mak€ tbe conditic¡ed action nost rapid a¡d<br />

stab.l-e.Às the trajectory int€rsects ths sHj.tching .1iïie,<br />

cortect.iÐnal üi is activaÈ€d. <strong>The</strong> positia! and the asqle<br />

<strong>of</strong> the suitcTì-ng line describes the ccntrol policy in<br />

<strong>for</strong>c€. {A vertj.cal sr.itching Linê neâns that mi uill be<br />

appli.ed ¡hen er¡or index pj" has €xceeded a tolêrated<br />

l-evel, an cbligue l-ile statês that thê derivative pi, or<br />

a.ûtj-cipêtion is incl-{¡d€d in the p oc€ss <strong>of</strong> conÈrol<br />

decj-sio¡.Thè optinal- control policy caa be de¡ived nathe-<br />

naticallÏ <strong>for</strong> a. slstÈn i"f we ¡

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