controllability and observabilityocw.snu.ac.kr/sites/default/files/note/ctrb-obsv.pdf · 2...
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Dongjun Lee
Controllability and Observability
Chen Ch. 6‐7
RughCh. 9‐11
Dongjun Lee (이동준)
Department of Mechanical & Aerospace EngineeringSeoul National University
Dongjun Lee
Some Linear Algebra
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Dongjun Lee
Controllability
x2:uncontrollablefromux1:unobservablefromy x:notCTRB,notOBSVduetosymmetry x1 x2:CTRB,yet,notx1‐x2
Dongjun Lee
Effect of State‐FB on CTRB
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Dongjun Lee
Reachability Map and CT‐LTV CTRB
Dongjun Lee
Reachability Map and DT‐LTV CTRB
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Dongjun Lee
Reachability Grammian
Dongjun Lee
Reachability Grammian and CTRB
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Dongjun Lee
CTRB of CT‐LTV System ‐ I
v in un‐CTRB subspace
Dongjun Lee
CTRB of CT‐LTV System ‐ II
effect of dB/dteffect thru A
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Dongjun Lee
CT‐LTV CTRB: Example 6.13
Dongjun Lee
Minimum Norm Control
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Dongjun Lee
Minimum Norm Control
Dongjun Lee
Controllability of CT‐LTI System
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Dongjun Lee
CT‐LTI System CTRB (cont’d)
Dongjun Lee
CT‐LTI System CTRB (cont’d)
q: left eigen‐vector
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Dongjun Lee
CTRB Invariance and Decomposition
Dongjun Lee
Canonical Decomposition ‐ I
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Dongjun Lee
Canonical Decomposition ‐ II
Dongjun Lee
CT‐LTI System CTRB (cont’d)
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Dongjun Lee
Example: Cart‐Pendulum
pendubot
Dongjun Lee
Example: CTRB Decomposition
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Dongjun Lee
Observability
known
known
known
Dongjun Lee
Observability Map and Grammian
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Dongjun Lee
Observability of CT‐LTV Systems
Dongjun Lee
Observability of CT‐LTI System
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Dongjun Lee
Geometry of CTRB and OBSV
Dongjun Lee
OBSV Decomposition ‐ I
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Dongjun Lee
OBSV Decomposition ‐ II
Dongjun Lee
Example: OBSV Decomposition
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Dongjun Lee
Kalman Decomposition
Dongjun Lee
Kalman Decomposition
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Dongjun Lee
Kalman Decomposition: Example
Dongjun Lee
Kalman Decomposition: Example
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Dongjun Lee
CTRB/OBSV Canonical Forms
Dongjun Lee
Coprime Fraction and Minimal Realization
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Dongjun Lee
Equivalence of Minimal Realizations
Dongjun Lee
Minimal and Characteristic Polynomials
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Dongjun Lee
MIMO Minimal Realization
Dongjun Lee
Minimal Realization: Example
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Dongjun Lee
Balanced Model Reduction
Dongjun Lee
Equivalence of WcWo
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Dongjun Lee
Balanced Realization
Dongjun Lee
Balanced Reduction
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Dongjun Lee
Balanced Reduction: Example