The 4th Multi-Symposium on Control Systems

A Compensation Principle for Controller Retrofit

Takayuki Ishizaki (Tokyo Institute of Technology)
Tomonori Sadamoto, Jun-ichi Imura (Tokyo Institute of Technology)
Retrofit = add new parts or substitute modernized equipment for preexisting ones

Motivation from Power Systems Control
IEEJ EAST30 Model (stable system composed of 30 generators)
parameters?
parameters?
parameters?

retrofit

localdisturbanceNorth east area

Area of interest  

parameters?
parameters?

Complete global modeling is unrealistic!!

Tokyo area Controller design by local model?
Stability? Better performance?
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Problem Formulation

possibly large scale

Subsystem of interest (model available)

Other subsystem(s) (model unavailable)

Assumption:(i)
are measurable(ii) the preexisting system without

Problem Find a retrofit controller(a) the whole system is kept stable and (b)is stable
such thatis made small for any

Hierarchical State-Space Expansion
Coupled state equation ofandastate-space expansion
to cascade realization

stable (assumption)

Hierarchical realization-dimstabilized bystable

Lemma Ifthendecoupled!

andandfor any
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Localized Controller Design
Hierarchical realization

Lemmamodel available!

Design a controller

such thatis stable andconstant

Then the closed-loop system is stable andGeneralization to dynamical controller design is straightforward

How to implement??
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Controller Implementation
How to implement??

withwithTheorem The closed-loop system with the retrofit controller
Compensatoris internally stable and it satisfies

by T. Sadamoto (Tokyo Inst. of Tech.)retrofit

Global performance

Application to Power Systems Control
low gain LQRhigh gain LQR

frequency deviation

HighLocal performance

unstable!

: with compensator: without compensator
time

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Retrofit Control without
Interconnection Signal Measurement?
Subsystem of interest (model available)

Other subsystem(s) (model unavailable)

Assumption:(i)is measurable(ii) the preexisting system without

Problem Find a retrofit controller(a) the whole system is kept stable and (b)is stable
such thatis made small for any

Parameterization via Projection
Coupled state equation ofandaIntroduction ofprojector

Hierarchical realization-dimLemma IfthenController

stabilized byandandsuch thatfor any
How to implement??
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Retrofit Controller ImplementationController & Compensator

withunavailable

thenLemma Ifthere exist

andsuch thatTheorem The closed-loop system with the retrofit controller
due touncontrollable

is internally stable and it satisfies

Generalization to Nonlinear Systems
Subsystem of interest (model available)possibly nonlinear& large scale

Other subsystem(s) (model unavailable)

Parameterized retrofit controller (state feedback)vanishes if

vanishes if

Controller design is based on local linear dynamics:
Designmakingsmall for11/13

by T. Sadamoto (Tokyo Inst. of Tech.)

Application toCollision Avoidance Control

driver property toavoid collision

Vehicle dynamics
Subsystem of interest
Other subsystems

Position deviation of vehicles(i) Sudden braking of(ii) Sudden braking of(iii) Larger braking ofnaïve linear state FBnaïve linear state FB max dim retrofit state FB

retrofit state FB

retrofit state FB low dim retrofit state FB

Low dim controller is practically reasonable as opposed to higher dim one

Concluding Remarks
Retrofit control
Localization of controller design and implementation
Stability guarantee and control performance improvement

Hierarchical state-space expansion
Redundant realization with cascade structure
Systematic analyses for stability and control performance

Systematic controller retrofit is enabled by a compensatorthat cancels out interference due to the dynamics
neglected in localized controller design

Thank you for your attention!

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