Page - (000094) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

Chapter12 ModelPredictiveControl Control design often seeks the best trajectory alongwhich tomove a system from its current state to a target state.Most control methods approximate this goal by using thecurrent inputsandsystemstate tocalculate thenextcontrol signal todrive system dynamics. That standard approach considers only the first step of the full trajectory toward the target state. The idea is that estimating a good first step in the right direction is sufficient,without considerationof the full trajectory fromthe current location to thefinal target. Model predictive control considers the full sequence of input steps required to move the system optimally from its current state to a future target. The control system then applies thefirst inputs to start the systemalong that optimal trajectory (Rossiter2004;CamachoandBordons2007;Ellisetal.2014;RawlingsandMayne 2015). Afterapplying the initial inputs, thesystemdoesnotuse theadditional sequence ofcalculatedinputstocontinuealongtheplannedtrajectory.Instead,thesystemtakes updatedmeasuresof the external target and the internal state.Thenew information isusedtorecalculateanupdatedoptimal trajectory.Usingtheupdatedtrajectory, the newlycalculatedfirst inputsare thenappliedtothesystem.Theprocessrepeatswith eachnewroundofupdatedexternal and internal signals. This approach considers a receding future horizon. At each point in time, the systemcalculates theoptimal trajectory toaparticular timepoint in the future—the horizon.Then,afterasmallamountof timepasses relative to thefuturehorizon, the systemrecalculatesbytakingcurrent inputsandadvancingthefuturehorizonbythe timeelapsed. Intuitively, this approach seemssimilar tomanydecisionsmadebyhumans.We estimate howwewill get to a goal, start off in the best direction, then update our planasnewinformationarrives. Our estimate of howwewill get to a goal depends on an internalmodel of our dynamicsandonthemodulatingcontrolsignalsthatwewillusetoalterourdynamics. Theself-correctingprocessof recalculating theplannedtrajectorymeans thatwedo notneedanaccuratemodelofourinternaldynamicstoperformwell.Anapproximate ormisspecifiedmodelofdynamicsoftenworkswell, even fornonlinearprocesses. ©TheAuthor(s)2018 S.A.Frank,ControlTheoryTutorial, SpringerBriefs inAppliedSciences andTechnology,https://doi.org/10.1007/978-3-319-91707-8_12 91