Descomposicion de kalman
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Publicado: 31 de enero de 2012
MECH550P: Foundations in Control Engineering
Lecture 14 Kalman decomposition
Dr. Ryozo Nagamune Department of Mechanical Engineering University of British Columbia
Spring 2008
MECH550P :Foundations in Control Engineering
1
Review & Today’s topic
So far, we have learned controllability and observability:
Condition Decomposition Duality
Today, we will study the combination ofdecompositions for controllability and observability, called Kalman decomposition.
Spring 2008
MECH550P : Foundations in Control Engineering
2
Rudolf Emil Kalman (1930-)American-Hungarian Mathematical system theorist During 1950s & 60s, he developed state-space control theory
Controllability, observability Linear quadratic regulator Kalman filter etc.
Most of the theory in thiscourse have been established by Kalman!
Spring 2008 MECH550P : Foundations in Control Engineering 3
Two decompositions
SS model
System Decomposition for controllability Controllable partUncontrollable part
Spring 2008
Decomposition for observability Observable part Unobservable part
4
MECH550P : Foundations in Control Engineering
Kalman decomposition (idea)
SS modelSystem
Controllable & observable part Controllable & unobservable part Uncontrollable & observable part Uncontrollable & unobservable part
Spring 2008 MECH550P : Foundations in Control Engineering 5 Kalman decomposition (idea)
Conceptual figure (Not block diagram!) System
Spring 2008
MECH550P : Foundations in Control Engineering
6
Kalman decomposition
Every SS model can betransformed by z=Tx for some appropriate T into a canonical form:
Spring 2008
MECH550P : Foundations in Control Engineering
7
Remarks
(Aco,Bco): controllable & (Aco,Cco): observable Transferfunction is determined by ONLY controllable & observable parts. (next slide)
If uncontrollable and/or unobservable parts are unstable, we need to change the structure (actuators/sensors) of the...
Lecture 14 Kalman decomposition
Dr. Ryozo Nagamune Department of Mechanical Engineering University of British Columbia
Spring 2008
MECH550P :Foundations in Control Engineering
1
Review & Today’s topic
So far, we have learned controllability and observability:
Condition Decomposition Duality
Today, we will study the combination ofdecompositions for controllability and observability, called Kalman decomposition.
Spring 2008
MECH550P : Foundations in Control Engineering
2
Rudolf Emil Kalman (1930-)American-Hungarian Mathematical system theorist During 1950s & 60s, he developed state-space control theory
Controllability, observability Linear quadratic regulator Kalman filter etc.
Most of the theory in thiscourse have been established by Kalman!
Spring 2008 MECH550P : Foundations in Control Engineering 3
Two decompositions
SS model
System Decomposition for controllability Controllable partUncontrollable part
Spring 2008
Decomposition for observability Observable part Unobservable part
4
MECH550P : Foundations in Control Engineering
Kalman decomposition (idea)
SS modelSystem
Controllable & observable part Controllable & unobservable part Uncontrollable & observable part Uncontrollable & unobservable part
Spring 2008 MECH550P : Foundations in Control Engineering 5 Kalman decomposition (idea)
Conceptual figure (Not block diagram!) System
Spring 2008
MECH550P : Foundations in Control Engineering
6
Kalman decomposition
Every SS model can betransformed by z=Tx for some appropriate T into a canonical form:
Spring 2008
MECH550P : Foundations in Control Engineering
7
Remarks
(Aco,Bco): controllable & (Aco,Cco): observable Transferfunction is determined by ONLY controllable & observable parts. (next slide)
If uncontrollable and/or unobservable parts are unstable, we need to change the structure (actuators/sensors) of the...
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