Chapter 1: Introduction To Adaptive Control - Grenoble INP

Adaptive ControlChapter 1: Introduction to Adaptive ControlAdaptive Control – Landau, Lozano, M’Saad, Karimi

Chapter 1: Introduction to Adaptive ControlAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive ControlA set of techniques for automatic adjustment of the controllersin real time, in order to achieve or to maintain a desired levelof performance of the control system when the parameters of theplant (disturbance) dynamic model are unknown and/or changein timeParticular cases:1 Automatic tuning of the controllers for unknown but constant plant parameters2 Unpredictable change of the plant (disturbance) model in timeAdaptive Control – Landau, Lozano, M’Saad, Karimi

Outline Concepts Basic schemes Adaptive control versus Robust control Adaptive control configurations(open loop adaptation, direct and indirect adaptive control) Parameter adaptation algorithms RST digital controller Adaptive control: regimes of operation Identification in closed and controller redesign Adaptive regulation Use of a priori available information Adaptive control with multiple models Example of applicationsAdaptive Control – Landau, Lozano, M’Saad, Karimi

Conceptual antPrinciple of model basedcontrol n adaptive controlstructureRemark:An adaptive control system is nonlinear since controller parameters will depend upon u and yAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive control- Why ? High performance control systems may require precise tuningof the controller but plant (disturbance) model parameters maybe unknown or time-varying “Adaptive Control” techniques provide a systematic approach forautomatic on-line tuning of controller parameters “Adaptive Control” techniques can be viewed as approximationsof some nonlinear stochastic control problems (not solvable inpractice) Objective of “Adaptive Control” : to achieve and to maintainacceptable level of performance when plant (disturbance) modelparameters are unknown or varyAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control versus Conventional Feedback ControlDisturbancesActing uponcontrolled variablesActing upon the plantmodel parameters(modifying control system perf.)How to reduce theeffect of disturbances ?Conventionalfeedback controlAdaptivecontrolMeasurement:Controlled variablesMeasurement:Index of performance (I.P.)Adaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control – Basic ConfigurationAdjustable control rformanceMeasurementAdaptation schemeAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control versus Conventional Feedback ControlConventional FeedbackControl SystemAdaptive ControlSystemObj.: Monitoring of the “controlled”variables according to a certain IP forthe case of known parametersObj.: Monitoring of theperformance (IP) of the controlsystem for unknown and varyingparametersMeas.: Controlled variablesMeas.: Index of performance (IP)TransducerIP measurementReference inputDesired IPComparison blockComparison decision blockControllerAdaptation mechanismAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control versus Conventional Feedback ControlA conventional feedback control system is mainly dedicated tothe elimination of the effect of disturbances upon the controlledvariables.An adaptive control system is mainly dedicated to the eliminationof the effect of parameter disturbances (variations) upon theperformance of the control system.Adaptive control system hierarchical system: Level 1 : Conventional feedback system Level 2 : Adaptation loopAdaptive Control – Landau, Lozano, M’Saad, Karimi

Fundamental Hypothesis in Adaptive ControlFor any possible values of plant (disturbance) model parametersthere is a controller with a fixed structure and complexity suchthat the specified performances can be achieved with appropriatevalues of the controller parametersThe task of the adaptation loop is solely to search for the “good”values of the controller parametersAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control versus Robust ControlAdaptive control can further improve the performance of arobust control system by: expanding the range of uncertainty for which performancespecification can be achieved better tuning of the nominal controllerFor building an adaptive control systems robustness issues forthe underlying controller design can not be ignored.The objective is to add adaptation capabilities to a robust controllerand not to use adaptive approach for tuning a non robust controller.Adaptive Control – Landau, Lozano, M’Saad, Karimi

Conventional Control – Adaptive Control - Robust ControlConventional versus AdaptiveConventional versus RobustAdaptive Control – Landau, Lozano, M’Saad, Karimi

Conventional Control – Adaptive Control - Robust ControlRobust Adaptive Control and Adaptive Robust Controlare different.What we need : Robust Adaptation of a Robust ControllerAdaptive Control – Landau, Lozano, M’Saad, Karimi

Basic Adaptive Control ConfigurationsAdaptive Control – Landau, Lozano, M’Saad, Karimi

Open Loop Adaptive ControlENVIRONMENT ssumption: known and rigid relationship between somemeasurable variables (characterizing the environment) andthe plant model parametersCalled also: gain-scheduling systemsAdaptive Control – Landau, Lozano, M’Saad, Karimi

Indirect Adaptive IONPERFORMANCESPECIFICATIONSADJUSTABLECONTROLLER PLANTMODELESTIMATIONuPLANTy-Prediction (adaptation)erroru(t)y(t) Plant ModelBasic EstimationSchemePlantq-1AdjustablePredictoryˆ (t )εParametricAdaptationAlgorithmAdaptive Control – Landau, Lozano, M’Saad, Karimi

Direct Adaptive Control(model reference adaptive control)The reference model gives the desired time trajectory of the plant outputADAPTATION LOOPREFERENCEMODEL-εAdaptationerror PARAMETRICADAPTATIONALGORITHMADJUSTABLE -CONTROLLERuPLANTyResemblance with plant parameter estimation schemeReference modelAdjustable feedback syst.PlantAdjustable predictorAdaptive Control – Landau, Lozano, M’Saad, Karimi

Parametric adaptation algorithm (PAA)Parameter vector θ contains all the parameters of the model (or of the controller) New parameters Old parameters estimation estimation (vector) (vector) Adaptation Measurement Error prediction Gain function function (matrix) (vector) (scalar)Regressor vectorEstimatedParametervectorθˆ(t 1) θˆ(t ) FΦ (t )v(t 1)Adaptive Control – Landau, Lozano, M’Saad, Karimi(v f (ε ))

Digital Control SystemThe control law is implemented on a digital computeru(k)e(k)r(k)DIGITALCOMPUTER u(t)y(t)PLANTDAC ActuatorProcessSensorZOH-y(k)CLOCKADC: analog to digital converterDAC: digital to analog converterZOH: zero order holdAdaptive Control – Landau, Lozano, M’Saad, KarimiADC

Digital Control SystemCLOCKe(k)r(k) u(k)COMPUTER-u(t)DAC ZOHy(t)PLANTy(k)ADCDISCRETIZED PLANT- Sampling time depends on thesystem bandwidth- Efficient use of computer resourcesAdaptive Control – Landau, Lozano, M’Saad, Karimi

The R-S-T Digital ControllerCLOCKr(t)Computer(controller)u(t)D/A ZOHy(t)PLANTA/DDiscretized Plantr(t)BmAmT -Controller1SRu(t)q d BAy(t)PlantModelq 1 y (t ) y (t 1)Adaptive Control – Landau, Lozano, M’Saad, Karimi

How to get a Direct Adaptive Control scheme ? Express the performance error in term of difference betweenthe parameters of an unknown optimal controller and thoseof the adjustable controller Re-parametrize indirect adaptive control scheme (if possible)such that the adaptive predictor will provide directly theestimated parameters of the controller.See : Adaptive Control (Landau, Lozano, M’Saad) pg 19The number of situation for which a direct adaptive controlscheme can be developed is limited.Adaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control Schemes. Regimes of operation Adaptive regime1. Controller parameters are updated at every sampling time2. Plant parameters are estimated at every sampling time butcontroller parameters are updated only every N samples (N small)3 Adaptation works only when there is enough excitation Self-tuning regime (parameters are supposed unknown but constant)1 Parameter adaptation algorithms with decreasing adaptation gain2 Controller parameters are either updated at every sampling timeor kept constant during parameter estimation3 An external excitation is applied during tuning or plant identificationRemarkIf controller parameters are kept constant during parameter estimation this is called“auto-tuning”. For the indirect approach this corresponds to “plant identificationin closed loop operation and controller redesign”Adaptive Control – Landau, Lozano, M’Saad, Karimi

Identification in Closed Loop and Adaptive Control Identification in closed loop operation using appropriatealgorithms provides better models for design An iterative approach combining identification in closed loopfollowed by a re-design of the controller is a very powerful(auto-)tuning schemeAdaptive Control – Landau, Lozano, M’Saad, Karimi

Iterative Identification in Closed Loopand Controller Re-DesignrT 1/Su-PlantR 1/S-Rq-d B/Auw y q-d B/A εCLy -ModelStep 1 : Identification in Closed Loop-Keep controller constant-Identify a new model such that εCLStep 2 : Controller Re – Design- Compute a new controller such that εCLRepeat 1, 2, 1, 2, 1, 2, Adaptive Control – Landau, Lozano, M’Saad, Karimi

Iterative Identification and Controller Redesign versus(Indirect) Adaptive ControlParameter Estimation Controller ComputationtN 1 : Adaptive Controlt 1Fixed (or time varying)Controller computed at( t) Parameter Estimationtt NtimeControllercomputedat (t N)timeN SmallAdaptive ControlN LargeIterative Identification in C.L.And Controller Re-designN Plant Identification in C.L. Controller Re-designThe iterative procedure introduces a time scaleseparation between identification / control designAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Control and Adaptive RegulationAdaptive ControlPlant model is unknown and time varyingThe disturbance model is known and constantAdaptive RegulationPlant model is known and constantThe disturbance model is unknown and time varyingAdaptive control and regulationVery difficult problem since is extremely hard to distinguish in theperformance (prediction) error what comes from plant modelerror and what comes from disturbance model errorRem:The “internal model principle” has to be used in all the casesAdaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Controlδ (t ) : Diracδ (t )(or e(t ))e(t ) : White noisedisturbance source (unmeasurable)inputPLANTDisturbancemodeloutputu (t )Plantmodel p(t )unmeasurabledisturbancey (t ) Objective : tracking/disturbance attenuation performance Focus on adaptation with respect to plant model parameters variations The model of the disturbance is assumed to be known and constant Only a level of attenuation in a frequency band is required* No effort is made to simultaneously estimate the model of the disturbance*) Except for known DC disturbances (use of integrators)Adaptive Control – Landau, Lozano, M’Saad, Karimi

Adaptive Regulationδ (t )(or e(t ))disturbance source (unmeasurable)inputPLANTDisturbancemodeloutputu (t )Plantmodel p(t )unmeasurabledisturbancey (t ) Objective : Suppressing the effect of the (unknown) disturbance* Focus on adaptation with respect to disturbance model parametersvariations Plant model is assumed to be known ( a priori system identification)and almost constant Small plant parameters variations handled by a robust control design No effort is made to simultaneously estimate the plant model*) Assumed to be characterized by a rational power spectrum if stationaryAdaptive Control – Landau, Lozano, M’Saad, Karimi