简介：Theq-profilecontrolproblemintheramp-upphaseofplasmadischargesisconsid-eredinthiswork.Themagneticdiffusionpartialdifferentialequation(PDE)modelsthedynamicsofthepoloidalmagneticfluxprofile,whichisusedinthisworktoformulateaPDE-constrainedop-timizationproblemunderaquasi-staticassumption.Theminimumsurfacetheoryandconstrainednumericoptimizationarethenappliedtoachievesuboptimalsolutions.Sincethetransientdy-namicsispre-givenbytheminimumsurfacetheory,thenthismethodcandramaticallyacceleratethesolutionprocess.Inordertoberobustunderexternaluncertaintiesinrealimplementations,PID(proportional-integral-derivative)controllersareusedtoforcetheactuatorstofollowthecomputationalinputtrajectories.Ithasthepotentialtoimplementinreal-timeforlongtimedischargesbycombiningthismethodwiththemagneticequilibriumupdate.