On-Line Calculation ofFeedforward Trajectories forTokamakPlasma ShapeControl*

Inthis paper, wereport ontheimplementation andexperimental testofanalgorithm forcomputing feed- forward coil current trajectories thatcanproduce anapproxi- mately correct evolution ofplasmashape, using anonlinear on- line optimization methodthatmaintains coil currents farfrom their limits. Thevoltage trajectory thatproduces these currents canbeusedasthefeedforward component ofplasmashape control whencombined withamultivariable linear feedback control algorithm. I.INTRODUCTION Inthepast fewyears, muchworkhasbeendoneatvarious institutions onapplication ofmultivariable linear controllers fortokamak plasma shape control, including several design studies andexperimental implementations (see(1) forasur- vey). A great dealhasbeenlearned aboutshapecontrol through thesestudies. Someofthepractical constraints imposed byworking tokamaks mustnowbeaddressed in order tomakethebenefits ofmultivariable control available toworking experimental devices. Because ofthelarge plant sizetypical fortokamak plasma shape control, developers arelargely constrained touseofmaturelinear design tools formultivariable controllers. Bycontrast, formanyofthe nonlinear problems faced, wemustappeal torather imma- tureorevenyettobedeveloped nonlinear control techniques. Multiple current andvoltage constraints suchaslimits on coil current andaconstraint onasumofcurrents atDIII-D (seebelow) implythattherangeofaccessible plasma equilibria isconstrained. Programmed attempts toreach equilibria outside these constraints canlead toproblems such asexceeding coil current limits orsaturation ofactuators leading tolossofcontrol. Inthispaper, we describe a nonlinear on-line optimization method forcomputing afeed- forward coil current trajectory that canproduce anapproxi- mately correct evolution ofplasma shape. Thevoltage tra- jectory that produces these currents canbeusedasthefeed- forward component ofshape control whencombined witha multivariable linear control algorithm. Thisonline optimiza- tion calculation isabletoexploit theexistence ofreal time reconstructed equilibria andtheprediction accuracy of