Application ofNMI totheDesign ofFACTSDampingControl with Multiple Operating Points

. . . . inequalities (LMI)throughsuitable parameterization and pint. Inthepteshappiain fof LM tehniquina transformation. Thiscan beapplicable tothedesign of damping controller desIgn hasbeen focused onthenominal FACTSdamping control that canguarantee thesatisfactory model, since LMIformulations ofthecontrol specifications performance overawiderange ofoperating conditions ratherfromH2andH,.performance toregional poleplacement, thanoneoperating condition. Therearetwocontrol designregulation, andsettling constraints fortheoutput feedback strategies that canbeapplied inapplying theLMIapproach. controller havebeenwidely discussed inthecontrol area Thefirst control design strategy isthatasingle damping[7-11].Software packages, including M/ATLABLMI controller isdetermined andusedforall operating points. The Control Toolbox, forsolving LMIproblems havebeen second control strategy isthatinstead ofusing a singleavailable [12, 13]. damping controller foralloperating points, multiple damping However, ifthepost-fault operating condition isfarfrom controllers aredesigned andutilized. Eachofthemultiple thenormal condition, acontroller tunedaround thenormal damping controllers iscorresponding toa fewoperating points. Theadvantage ofthesecond control design strategy is condition maynotoperate asexpected intermsofcontrol that theLMIdesign problem isrelatively small andeasy to performance. Whenonly afewoperating conditions undera solve, andthecorresponding damping controllers mayproviderelatively large disturbance areofinterest, multiple linear better control performance incomparison tothesinglemodels canbeapplied toconsider these different operating damping controller ofthefirst design strategy. TheLMI points. Inthis situation, thedamping controller design isto approach alongwiththetwo designstrategies are find acommonoutput feedback controller forthemultidemonstrated ona4-machine 2-area system. Numerical resultsmodelsystem. However, there aredifficulties toextend the showthatthedamping controller designed bythetwomultipleLMI formulation andassociated parameterization and operating point basedapproaches canensuresimultaneous stablitanadeutdampnforthe.... muliploperatintransformation techniques totheoutput feedback control for points,