DT Kalman filter - UBC Mechanical Engineering - University of ...

Remarks
• Separation principle holds! Thus, we can design LQR
controller and Kalman filter independently.
• The feedback structure is same as observer-based
based
control. Thus, in infinite horizon LQR plus steady state
KF cases, the eigenvalues of closed-loop loop A-matrix A
consists of the A-matrix A
of LQR feedback system with full
state feedback, and the A-matrix A
of Kalman filter.
• Recall that LQR has a good robust stability property
expressed by gain and phase margin (in SISO cases).
However, it is known that LQG may possibly lose such
good property (Doyle & Stein). This fact motivated
development of robust control theory.
Outline
• Review of discrete-time
time Kalman filter
• Duality between LQR and Kalman filter
• Steady-state
Kalman filter
• Linear Quadratic Gaussian
• Summary of the course
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Systematic controller design process
Reference
Controller
Actuator
Input
Disturbance
Plant
Output
Control and estimation of states
“State” has been the key concept in this course!
Control
Estimation
4. Implemenation
Controller
3. Design
Sensor
1. Modeling
Mathematical model
2. Analysis
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System
• Controllability & Observability
• State feedback & Observer
• Linear quadratic regulator & Kalman filter
Duality between control and estimation!
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