Page - (000097) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

94 12 ModelPredictiveControl 12.3 MixedFeedforwardandFeedback In some cases, the sensor and calculation costs of updating in each time stepmay not provide sufficient benefit. Instead, the systemcould apply the first few control inputs of the sequence,u(0),u(1),...,u(τ), and thenupdate the sequence at time τ <T . Asystemthatuses feedback inputs at one timepoint tocalculate and thenapply a future sequence of control inputs is running in partial feedforward mode. The feedback inputs arrive, and then the systemruns forward fromthose inputswithout the feedback correction obtained by comparing the changing systemoutput to the potentiallychanging target reference signal. After awhile, the systemmay takenew input readings andupdate theprojected sequence of future control signals. Eachmeasurement and recalculation acts as a feedback correction process. Thus, systemsmay combine the simplicity and rela- tively lowcostof feedforwardcontrolwith thecorrectionandrobustnessbenefitsof feedback. 12.4 NonlinearityorUnknownParameters This section’s example used a simplemodel of internal dynamics, x¨=u, given in Eq.12.1.Thatexpression,equatingaccelerationandforce,providedasimplewayin whichtoanalyzetrajectories.That internalmodelmayoftenperformwellevenif the truemodel is nonlinear because thefirstmovealong the calculated trajectoryoften dependsonhowthe forceof theapplied input alters theaccelerationof the system. Alternatively, one could use amore general expression for the internal model dynamics,withasetofunknownparameters.Onecouldthenaddanadaptivecontrol layer to the system to provide updated parameter estimates. In some cases, this combinationofmodelpredictivecontrol andadaptivecontrolmayperformwell. OpenAccess This chapter is licensed under the terms of theCreativeCommonsAttribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation,distributionandreproduction inanymediumorformat,as longasyougiveappropriate credit to theoriginal author(s) and thesource,providea link to theCreativeCommons licenseand indicate if changesweremade. The images or other third partymaterial in this chapter are included in the chapter’sCreative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter’s Creative Commons license and your intended use is not permitted by statutory regulationorexceeds thepermitteduse,youwillneed toobtainpermissiondirectly from thecopyrightholder.