Adaptive Robust Adaptive Robust ControlControl F Foror Dual Stage Dual Stage

Hard DrivesHard Drives

راهنما : راهنما :استاد حمید استاد دکتر آقای حمید جناب دکتر آقای جنابراد راد تقی تقیاقراری حاجی هادی

برق مهندسی ارشد کارشناسی کنترل–دانشجویطوسی نصیرالدین خواجه دانشگاه

Dr. Hamid D. Taghirad

H.H.EghraryMS Student of Electrical EngineeringK.N.Toosi Univ.

2end Seminar Presentation 2end Seminar Presentation

Introduction to Adaptive Robust ControlIntroduction to Adaptive Robust Control

• Obstacles for Control Algorithm DesignObstacles for Control Algorithm Design

• Strategies for Performance Strategies for Performance ImprovementImprovement• Adaptive Robust Control (ARC) Adaptive Robust Control (ARC) For a For a HDDHDD Adaptive Control

Robust Control

• ARC via Discontinuous ProjectionARC via Discontinuous Projection

• ARC via Smooth ProjectionARC via Smooth Projection

• Desired Compensation Desired Compensation ARCARC

Sunday, August 12,2007

Obstacles for Control Algorithm Obstacles for Control Algorithm Design:Design:

•Inherent Nonlinearity

•Modeling Uncertainty

• Unknown But Reproducible

• for example: Unknown parameters

• Unreproducable

for example: model Disturbance

Strategies for Performance Strategies for Performance Improvement:Improvement:

•Nonlinear Analysis And SynthesisNonlinear Analysis And Synthesis

Deal With Nonlinearity Directly : Nonlinear Nonlinear ControlControl

•Fast Robust FeedbackFast Robust Feedback

Effective for both reproducible and none Reproducible Uncertainities

•Controled Learning For Uncertainity ReductionControled Learning For Uncertainity Reduction

Effective for Reproducible Uncertainities

Adaptive Robust ControlAdaptive Robust Control (ARC)(ARC)RobusRobustt

AdaptiveAdaptive

Drawbacks:•Transient Performance of the system is not Clear.•Unknown Nonlinear functions such as external disturbances are not considered.

Drawbacks:•Transient Performance of the system is not Clear.•Unknown Nonlinear functions such as external disturbances are not considered.

•Reduce the model uncertainty

•Zero Tracking Error (Without High gain Feedback)

•Attenuate the effect of model uncertainties throughrobust feedback.•InstantaneousReaction

Deterministic Robust ControlDeterministic Robust Control

•Use to Design Base Line Controller

Guarantee Guarantee Transient PerformanceTransient Performance Prescribed final tracking accuracyPrescribed final tracking accuracy

Adaptive ControlAdaptive Control

•Used to Design Supervisor

Improved Improved Asymptotic Input TrackingAsymptotic Input Tracking

Conventional Adaptation Law Estimated Parameters May not be Bounded

Deterministic Robust Control Requires Bounds On Uncertainties

Modify The Conventional Adaptation Law

Bounded Estimation ParametersBounded Estimation Parameters

Adaptive Robust ControlAdaptive Robust Control ForFor Hard Disk Drive Servo Hard Disk Drive Servo SystemSystem

x =x1 2

jx =u-Bx -A sign(x )-F +Fhys d2 2 f 2

y =x1

Tf fj B A d

d hys nd F F d d

min max:

:d dd d d

. . .1 2 3 4 d

x = x1 2

x =u- x - sign(x )-2 2 2

y =x1

Adaptive Control scheme: Robust Control scheme:

Adaptive Control scheme:

Stability Analysis:

Lyapanov Function:

1 12 22 2

V ea

ˆ : Parameter Estimation

ˆ Estimation Error

2

1

1

( )

1

1 ˆ ˆ

ˆ

ˆ ˆ 0

T

T

T

ke

e

diag

e e

V ee ea

ke

2aV ke

ResultsResults:: 0

0T

et

•Limitations Of Adaptive ControlLimitations Of Adaptive Control

•Transient Performance is Unknown

•Uncertain nonlinearity are not Considered

0

Robust Control scheme:

More In Detail:More In Detail:

• Error Dynamics

20

~s

T Ukee

2sU Choose The such that:

0.

)~

.(

2

2

s

Ts

Ue

Ue

Stability Analysis:

Lyapanov Function:

2

2

1eVs

eeVs .

keUe sT

20

~

20 )

~(

2keUeV s

Ts

)~

(20 s

T Ue

2keVsChoose small such that:Choose small such that:

0sV : Stable: Stable

•Tracking Error

•Steady State Steady State ErrorError

ke

2

)(

Decrease for decreasing Steady State ErrorDecrease for decreasing Steady State Errork

e

2)(

Parameter AdaptationParameter Adaptation

)~

.(2

TsUe

Adaptive Robust ControlAdaptive Robust Control

Conventional Adaptation Law Estimated Parameters May not be Bounded

Deterministic Robust Control Requires Bounds On Uncertainties

Modify The Conventional Adaptation Law

Bounded Estimation ParametersBounded Estimation Parameters

Adaptive Robust ControlAdaptive Robust Control

Via Discontinuous ProjectionVia Discontinuous Projection

max minˆ

ˆ ˆ0, ( , 0) ( , 0)Pr ( )

,

e or eoj e

e otherwise

ˆPr ( )oj e

minˆ ˆ ˆ4. 0, 0

maxˆ ˆ ˆ1. 0, 0

minˆ ˆ ˆ2. 0, 0

maxˆ ˆ ˆ3. 0, 0

Remains in

Remains in

Decreases

Increases

min

max min maxˆ

Parameter Uncertainty Parameter Uncertainty Bounded Bounded via Adaptation Progressvia Adaptation Progress

RobustRobust ControlControl Problem SolvedProblem Solved

0

1( ) ( ( , ) )

0

V v dv

Adaptive Robust ControlAdaptive Robust Control

Via Smooth ProjectionVia Smooth Projection

There is a Lyapanov Function :There is a Lyapanov Function :

Stability is GuaranteedStability is Guaranteed

Desired Compensation Desired Compensation ARCARC Remind ARC SchemeRemind ARC Scheme

Real Parameter MeasurementReal Parameter Measurement(Measurement Noise)

Static FeedbackStatic Feedback

Desired TrajectoryDesired Trajectory

DynamicDynamicStabilizingStabilizingFeedbackFeedback

Desired Compensation Desired Compensation ARCARC

Regressors Dose not Depend On Measurements Regressors Dose not Depend On Measurements

Eliminate Measurement Noise Effect on Parameter AdaptationEliminate Measurement Noise Effect on Parameter Adaptation Off-Line Regressors CalculationOff-Line Regressors Calculation

Fast Error Dynamic and Parameter AdaptationFast Error Dynamic and Parameter Adaptation

Facilitate Control Gain Tuning Process due to Facilitate Control Gain Tuning Process due to Separation of Robust Control And Parameter AdaptationSeparation of Robust Control And Parameter Adaptation