Post on 19-Nov-2015
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ADAPTIVE CONTROL - DEFINITION
An adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters
Department for Automatic Control and Electronics Department for Automatic Control and Electronics
Faculty of Electrical EngineeringFaculty of Electrical Engineering
University of SarajevoUniversity of SarajevoSarajevo, December, 2013
Adnan Tahirovic
ADAPTIVE CONTROL - DEFINITION
ADAPTIVE CONTROL - HISTORY1960:
State Space
Stability Theory
Stochastic Control Theory
Dynamic Programming
Common Framework for lerning and adaptive control theory
System identification
1970: 1970:
Renaissance of adaptive control
(different estination schemes combined with various design methods)
1980:
Stability of adaptive systems with strong assumptions
Merging ideas of robust control and system identification
Robustness of adaptive control
Universal stability
1990:
Investigation of nonlinear systems
Adaptive control strong relations with ideas on learning
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
To design a robust controller, it is attempted to find acontroller such that the loop transfer function is large forthese frequencies at which there are large variations in theprocess transfer function.
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
To judge the conseqences of process variations fromopen-loop dynamics, it is better to use frequency responsesthan time responses.
It is necessary to have some information about thedesired crossover frequency of the closed-loop system.
AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
MRAS solves a problem in which the performancespecifications are given in terms of a reference model.
MRAS was originally introduced for flight control
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
MIT RULE:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
ALTERNATIVE:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
Adaptation of a feedforward gain:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
Adaptation of a feedforward gain:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
Adaptation of a feedforward gain:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
Adaptation of a feedforward gain:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
MRAS for a first order system:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
MRAS for a first order system:
Perfect model following:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)
MRAS for a first order system:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS for a first order system:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS for a first order system:
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
Barbalats lemma
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory
ADAPTIVE SCHEMES GAIN SCHEDULING
ADAPTIVE SCHEMES GAIN SCHEDULING
GS can be regarded as a mapping from processparameters to controller parameters.
GS can be implemented as a function or a table lookup.
ADAPTIVE SCHEMES GAIN SCHEDULING
It was originally used to accomodate changes in processgain only
It has a linear controller whose parameters are changedas a function of operating conditions in a programmed wayas a function of operating conditions in a programmed way
GS based on measurements of operating conditions ofthe process is often a good way to compansate for:
variations in process parameters or known nonlinearities of the process
ADAPTIVE SCHEMES GAIN SCHEDULING
The main problem is to find suitable scheduling variables
This is normaly done on the basis of knowledge of thephysics of a system
Ideally, there should be simple expressions for how thecontroller parameters relate to the scheduling variables
In process control the production rate can often bechosen as a scheduling variable, since time constants andtime delays are often inversely proportional to productionrate
ADAPTIVE SCHEMES GAIN SCHEDULING
When scheduling variables have been determined, thecontroller parameters are calculated at a number ofoperating conditions by using some suitable design method
The contoller is thus tuned or calibrated for each The contoller is thus tuned or calibrated for eachoperating condition
Stability and performance of the system are typicallyevaluated by simulation; particular attention is given to thetransition between different operating points
ADAPTIVE SCHEMES GAIN SCHEDULING
Some ideas:
Linearization of nonlinear actuators Gain scheduling based on measurements ofauxilary variablesauxilary variables Time scaling based on production rate
ADAPTIVE SCHEMES GAIN SCHEDULING
Linearization of nonlinear actuator
ADAPTIVE SCHEMES GAIN SCHEDULING
Linearization of nonlinear actuator
ADAPTIVE SCHEMES GAIN SCHEDULING
Linearization of nonlinear actuator
ADAPTIVE SCHEMES GAIN SCHEDULING
GS based on measurement of auxiliary variables
TANK IN WHICH THE CROSS SECTION A VARIESWITH HEIGHT h
ADAPTIVE SCHEMES GAIN SCHEDULING
GS based on measurement of auxiliary variables
TANK IN WHICH THE CROSS SECTION A VARIESWITH HEIGHT h
22 2
)()(
++=
sssT
ADAPTIVE SCHEMES GAIN SCHEDULING
Time scaling based on production rate
CONCENTRATION CONTROL
q(t) = const
ADAPTIVE SCHEMES GAIN SCHEDULING
Time scaling based on production rate
CONCENTRATION CONTROL
q(t) = const
ADAPTIVE SCHEMES GAIN SCHEDULING
Time scaling based on production rate
CONCENTRATION CONTROL
ADAPTIVE SCHEMES GAIN SCHEDULING
Time scaling based on production rate
CONCENTRATION CONTROL
q(t) = const