iterative system identiﬁcation & control design: an...

Iterative System Identification & Control

Design:an approach to Adaptive

Control

Bob BitmeadMechanical & Aerospace Engineering

University of California, San Diego

MAE283B Approximate System Identification & ControlTuesday, April 3, 2012

Iterative System Identification & Control

Design:an approach to Adaptive

Control

Bob BitmeadMechanical & Aerospace Engineering

University of California, San Diego

MAE283B Approximate System Identification & Control

?

Tuesday, April 3, 2012

MAE 283B, Lecture 1, Slide Approximate System Identification & Control

The Big Picture

2Tuesday, April 3, 2012


The Big PictureThe interaction between modeling and model-based control design

when the objective is to achieve good feedback controland the model is derived from experimental data plus physics

premise: all models are necessarily approximatethe approximation properties are central






2

Aha!






2

Aha!The model fit and quality of fit affects the achieved controlThe presence of the feedback controller affects the model fit






2


This course is about formulating the connections






2


This course is about formulating the connectionsdo this so as to gain a synergism






2


This course is about formulating the connectionsdo this so as to gain a synergism

better models ⇒ better control ⇒ better models ⇒ ...



Messages about Modeling




Modeling involves approximation




Modeling involves approximationA general-relativistic, quantum-mechanical partial differential equation model for an ore crusher





Model approximation is a fungible but constrained quantity





Model approximation is a fungible but constrained quantityParsimony is needed






Modeling is an iterative process






Modeling is an iterative processModel development







Deductive Physics, Inductive System Identification







Deductive Physics, Inductive System IdentificationRinse and repeat








Modeling has a purpose








Modeling has a purposePrediction, simulation, control









Differing purposes make differing demands of model quality









Differing purposes make differing demands of model qualityModeling from data depends on the experiment conducted









Differing purposes make differing demands of model qualityModeling from data depends on the experiment conducted

including the presence of a feedback controller



Messages about Control



Messages about ControlFeedback control is used for a number of simultaneous purposes




Stabilization




StabilizationDisturbance rejection





Reference tracking





Reference trackingReduction in the effect of system variability






the feedback amplifier; Black, Nyquist, Bode






the feedback amplifier; Black, Nyquist, BodeAdvanced Control is Model-based







Model approximation is an in-built issue







Model approximation is an in-built issueThe nominal model — the specific model used for design







Model approximation is an in-built issueThe nominal model — the specific model used for designThe model error — the range of possible deviation from nominal








Performance — nominal model behavior








Performance — nominal model behaviorRobustness — variation due to model error



Messages about Adaptive Control




5

“Adaptive Control Theory has been a colossal waste of paper”




5

“Adaptive Control Theory has been a colossal waste of paper”Bob Bitmead




5

“Adaptive Control Theory has been a colossal waste of paper”Bob Bitmead, Adaptive Control Theorist




Adaptive Control seeks to combine on-line model adjustment and real-time controller design based on operational data taken during closed-loop plant operation

5

“Adaptive Control Theory has been a colossal waste of paper”Bob Bitmead, Adaptive Control Theorist





5


PlantController

IdentifierControlDesign

+

disturbance

output

input

model

+reference

, Adaptive Control Theorist





5


In spite of linear modeling and linear control design, this is a fiercely nonlinear problem

PlantController

IdentifierControlDesign

+

disturbance

output

input

model

+reference

, Adaptive Control Theorist



More Adaptive Control Messages



More Adaptive Control MessagesAdaptive Control involves simultaneous modeling and control design

Nonlinear nasties can appear — escapes, chaos, oscillationThis greatly upsets our linear thinking for models and controllers

Is there a way forward?






Adaptation is a learning approach to dealing with uncertaintyIt is well understood that learning is often antithetical to control

Control is designed to disguise system variationLearning is focused on exposing system variation






Adaptation is a learning approach to dealing with uncertaintyIt is well understood that learning is often antithetical to control

Control is designed to disguise system variationLearning is focused on exposing system variation

Dual Adaptive ControlStrike a balance between learning and controlling

Fel’dbaum 1960s



Modeling Approximation Formulalim

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Modeling Approximation Formula

It existsIt is a discrete frequency domain formula

Connected to time domain prediction errors

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Connected to time domain prediction errorsIt is useful

Model approximation is the subjectPlant, noise, plant model, noise model involved

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There are some free variables - design handlesInput spectrumData filter

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Closed-loop Modeling Formulalim

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But not much moreThe controller appears in the picture explicitly

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Robust Control Formulae!

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Robust Control Formulae

Formulae for robust stability and performance exist

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Formulae for robust stability and performance existThey are in the discrete frequency domain

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They involve designed properties

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They involve designed properties They involve model errors

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The controller is the design variable

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The controller is the design variable

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Course Outline



Course OutlineLecture 1 - Big picture, outline. You are here ➷



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophy



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopter



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief review



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loop



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structure



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loop



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust control



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust controlLecture 9 - Iterative approaches to modeling and control design



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust controlLecture 9 - Iterative approaches to modeling and control designLectures 10, 11 - Industrial example — Victoria Sugar Mill iterative design



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust controlLecture 9 - Iterative approaches to modeling and control designLectures 10, 11 - Industrial example — Victoria Sugar Mill iterative designLectures 12, 13 - Cautious controller tuning, Controller certification



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust controlLecture 9 - Iterative approaches to modeling and control designLectures 10, 11 - Industrial example — Victoria Sugar Mill iterative designLectures 12, 13 - Cautious controller tuning, Controller certificationLecture 14 - Iterative versus Adaptive Control



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust controlLecture 9 - Iterative approaches to modeling and control designLectures 10, 11 - Industrial example — Victoria Sugar Mill iterative designLectures 12, 13 - Cautious controller tuning, Controller certificationLecture 14 - Iterative versus Adaptive ControlLecture 15 - Observability in a stochastic context



Course OutlineLecture 1 - Big picture, outline. You are here ➷Lecture 2 - Modeling from data, some philosophyLecture 3 - Two examples of modeling for control; jet engine, helicopterLecture 4 - Prediction error modeling, a brief reviewLecture 5 - Approximation, bias formulæ in open and closed loopLecture 6 - Influencing model fit, experiment design, filtering, model structureLecture 7 - Influencing model fit in closed loopLecture 8 - Designing controllers with approximate models, robust controlLecture 9 - Iterative approaches to modeling and control designLectures 10, 11 - Industrial example — Victoria Sugar Mill iterative designLectures 12, 13 - Cautious controller tuning, Controller certificationLecture 14 - Iterative versus Adaptive ControlLecture 15 - Observability in a stochastic contextLecture 16 - Adaptive control in action — TCP network congestion control




10

Modeling

mostly




10

Modeling

mostly

Modeling

and control




10

Modeling

mostly

Modeling

and control

Adaptation



A quick note



A quick noteThe presentation in this course will be mostly focused on scalar systems; SISO or single-input/single-output

This is because the prediction-error approach to MIMO systems is not really well set out

There are central parameterization issuesTools such as subspace methods work well but the tying together of modeling and control design is still needed

The extension of the methods of iterative modeling and control design to the MIMO framework would be quite worthwhile

802.11g ⇒ 802.11n


iterative system identiﬁcation & control design: an...

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