Seite - (000016) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

4 1 Introduction Tracking concerns the ability of a system to follow a changing environmental setpoint.For example, a systemmaybenefitbyaltering its responseas theenviron- mental temperaturechanges.Howcloselycanthesystemtracktheoptimal response to the changing environmental input?Once again, the analysis of performance and robustnessmay be developed by considering explicit measures of system charac- teristics.With explicitmeasures, one can analyze the tradeoffs between competing goals andhowalternativeassumptions lead toalternativeoptimaldesigns. All of these topics build on the essential benefits of feedback control. The par- ticular information that canbemeasured andused for feedbackplays a key role in controldesign. 1.2.3 Part III:CommonChallenges Thethirdpartpresentschallenges incontroldesign.Challenges includenonlinearity anduncertaintyof systemdynamics. Classical control theory assumes linear dynamics, whereas essentially all pro- cessesarenonlinear.Onedefenseof linear theoryis that itoftenworksforrealprob- lems.Feedbackprovidespowerfulerrorcorrection,oftencompensatingforunknown nonlinearities.Robust lineardesignmethodsgracefullyhandleuncertainties in sys- temdynamics, includingnonlinearities. One can also consider the nonlinearity explicitly.With assumptions about the formofnonlinearity, onecandevelopdesigns fornonlinear control. Other general design approachesworkwell for uncertainties in intrinsic system dynamics,includingnonlinearity.Adaptivecontroladjustsestimatesfortheunknown parameters of intrinsic systemdynamics. Feedbackgives ameasure of error in the current parameter estimates. That error is used to learn better parameter values. Adaptive control can often be used to adjust a controllerwith respect to nonlinear intrinsicdynamics. Model predictive control uses the current system state and extrinsic inputs to calculate an optimal sequence of future control steps. Those future control steps ideallymove the system toward the desired trajectory at the lowest possible cost. At eachcontrol point in time, thefirst control step in the ideal sequence is applied. Then, at the next update, the ideal control steps are recalculated, and the first new step is applied. Byusingmultiplelinesofinformationandrecalculatingtheoptimalresponse, the system corrects for perturbations and for uncertainties in systemdynamics. Those uncertaintiescan includenonlinearities,providinganother strongapproachfornon- linear control.