CH 1 CH 1 IntroductionIntroduction

Prof. Ming-Shaung JuProf. Ming-Shaung JuDept. of Mechanical EngineeriDept. of Mechanical Engineeri

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1. Introduction1. Introduction What is adaptive control?What is adaptive control?

An adaptive controller is a controller An adaptive controller is a controller with adjustable parameters and a with adjustable parameters and a mechanism for adjusting the mechanism for adjusting the parameters.parameters.

Adaptive control systems have two loopsAdaptive control systems have two loopsA normal feedback with process and A normal feedback with process and

controllercontrollerA parameter adjustment loop (slower A parameter adjustment loop (slower

dynamics)dynamics)

Structure of Adaptive Structure of Adaptive SystemsSystems

History of adaptive control History of adaptive control theorytheory

1950s design of autopilots for high 1950s design of autopilots for high performance aircraft (gain scheduling) speeds performance aircraft (gain scheduling) speeds & altitude& altitude

1960s control theories : state space & 1960s control theories : state space & stability, dynamic programming, system stability, dynamic programming, system identificationidentification

1970s different estimation schemes combined 1970s different estimation schemes combined with various design methodswith various design methods

Late 1970s-1980s proofs for stability of Late 1970s-1980s proofs for stability of adaptive systems, merge of robust control and adaptive systems, merge of robust control and system identificationsystem identification

USA X-15 experimental USA X-15 experimental aircraftaircraft

History of adaptive control History of adaptive control theory (cont’d)theory (cont’d)

1990s robustness of adaptive 1990s robustness of adaptive controllers, nonlinear system controllers, nonlinear system theory help understanding theory help understanding adaptive controladaptive control

2000s related to learning in 2000s related to learning in computer science, artificial computer science, artificial intelligenceintelligence

Why adaptive control Why adaptive control system?system?

Linear feedback has limited capability Linear feedback has limited capability to cope with parameter changes of to cope with parameter changes of the process and variations in the process and variations in disturbance characteristicsdisturbance characteristics

Process variations may due toProcess variations may due to Nonlinear actuatorsNonlinear actuators Large deviation of operating pointLarge deviation of operating point

Examples of variations in disturbanceExamples of variations in disturbance frequency contents of disturbancefrequency contents of disturbance

Adaptive SchemesAdaptive Schemes

Gain schedulingGain scheduling Model-reference adaptive Model-reference adaptive

controlcontrol Self-tuning regulatorSelf-tuning regulator Dual controlDual control

Gain SchedulingGain Scheduling

Speed (Mach no.)Altitude

Note: command & control signal are not utilized

Model-Reference Adaptive Model-Reference Adaptive ControlControl

Performance specification

e = ym-y

Self-Tuning RegulatorSelf-Tuning Regulator

System identification

DesiredIndirect adaptive

Certainty equivalent principle: estimates are used as if they are true parameters

Dual ControlDual Control Limitation of above schemes: parameter uncertaiLimitation of above schemes: parameter uncertai

nties not considerednties not considered When Certainty Equivalence Principle is not validWhen Certainty Equivalence Principle is not valid Augment process state and parameters into a neAugment process state and parameters into a ne

w state and formulate a nonlinear stochastic contw state and formulate a nonlinear stochastic control problem (stochastic optimal control )rol problem (stochastic optimal control )

Nonlinear estimator: conditional probability distrNonlinear estimator: conditional probability distribution of state p(zibution of state p(z｜｜ y, u) (hyper-state)y, u) (hyper-state)

Feedback controller maps hyperstate to controlFeedback controller maps hyperstate to control Maintain good control and small estimation errorMaintain good control and small estimation error

s (dual)s (dual)

Dual ControlDual Control

Adaptive Control Adaptive Control ProblemProblem

Process ModelProcess Model State space modelState space model Transfer function (matrix)Transfer function (matrix) Continuous-time or discrete-timeContinuous-time or discrete-time

Controller structureController structure A controller with adjustable parametersA controller with adjustable parameters Direct adaptive controlDirect adaptive control

Parameters tuned without characteristics of the process and its Parameters tuned without characteristics of the process and its disturbancedisturbance

Indirect adaptive controlIndirect adaptive control Process model and disturbance characteristics are estimated then Process model and disturbance characteristics are estimated then

use these information to design the controlleruse these information to design the controller

Design ProceduresDesign Procedures

1.1. Characterize desired behavior of Characterize desired behavior of closed-loop system (stability, closed-loop system (stability, performance)performance)

2.2. Determine a control law with Determine a control law with adjustable parametersadjustable parameters

3.3. Find a mechanism for adjusting the Find a mechanism for adjusting the parametersparameters

4.4. Implement the control lawImplement the control law