961ls08DesignSISO2 - Fall 2007 Linear Systems Chapter 08...

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Fall 2007 線性系統 Linear Systems Chapter 08 State Feedback & State Estimators (SISO) Feng-Li Lian NTU-EE Sep07 – Jan08 Materials used in these lecture notes are adopted from “Linear System Theory & Design,” 3rd. Ed., by C.-T. Chen (1999) NTUEE-LS8-DesignSISO-2 Feng-Li Lian © 2007 ± Introduction ± State Feedback (8.2) ± Regulation & Tracking (8.3) ± State Estimator (8.4) ± Feedback from Estimated States (8.5) ± State Feedback – Multivariable Case (8.6) ± State Estimators – Multivariable Case (8.7) ± Feedback from Estimated States – Multivariable Case (8.8) Outline
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NTUEE-LS8-DesignSISO-3 Feng-Li Lian © 2007 ± State Feedback (8.2) • State Feedback in Controllable Canonical Form Eigenvalue Assignment by Solving the Lyapunov Eqn ± Regulation & Tracking (8.3) Robust Tracking and Disturbance Rejection Stabilization ± State Estimator (8.4) • Full-Dimensional State Estimator Reduced-Dimensional State Estimator ± Feedback from Estimated States (8.5) Outline NTUEE-LS8-DesignSISO-4 Feng-Li Lian © 2007 Basic Concept of Feedback Control (8.1) r : reference signal u y Plant (system to be controlled) r
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NTUEE-LS8-DesignSISO-5 Feng-Li Lian © 2007 Basic Concept of Feedback Control – 2 u y output feedback control r : reference signal Plant (system to be controlled) u y state feedback control x Plant (system to be controlled) r + - r + - NTUEE-LS8-DesignSISO-6 Feng-Li Lian © 2007 State Feedback (SISO Systems) (8.2) Closed-loop system :
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NTUEE-LS8-DesignSISO-7 Feng-Li Lian © 2007 State Feedback (SISO Systems) – 2 u y + + NTUEE-LS8-DesignSISO-8 Feng-Li Lian © 2007 Theorem 8.1 (8.2) Proof :
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NTUEE-LS8-DesignSISO-9 Feng-Li Lian © 2007 Example 8.1 (8.2) controllable and observable State feedback: Controllability: Observability: Feedback system: NTUEE-LS8-DesignSISO-10 Feng-Li Lian © 2007 Example 8.1 – 2 Observability may change after state feedback Controllability: Observability:
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NTUEE-LS8-DesignSISO-11 Feng-Li Lian © 2007 Example 8.2 (8.2) State feedback: Feedback system: Characteristic Polynomial: NTUEE-LS8-DesignSISO-12 Feng-Li Lian © 2007 Example 8.2 – 2 Characteristic Polynomial:
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NTUEE-LS8-DesignSISO-13 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form (8.2) NTUEE-LS8-DesignSISO-14 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 2
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NTUEE-LS8-DesignSISO-15 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 3 NTUEE-LS8-DesignSISO-16 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 4
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NTUEE-LS8-DesignSISO-17 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 5 NTUEE-LS8-DesignSISO-18 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 6
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NTUEE-LS8-DesignSISO-19 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 7 NTUEE-LS8-DesignSISO-20 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 8
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NTUEE-LS8-DesignSISO-21 Feng-Li Lian © 2007 State Feedback in Controllable Canonical Form – 9 NTUEE-LS8-DesignSISO-22 Feng-Li Lian © 2007 In Summary – 1
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NTUEE-LS8-DesignSISO-23 Feng-Li Lian © 2007 In Summary – 2 NTUEE-LS8-DesignSISO-24 Feng-Li Lian © 2007 Theorem 8.2 (8.2) ( A , b , c ) ( A , b ) ( A , b , c )
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This note was uploaded on 07/21/2009 for the course EE 901-43400 taught by Professor Feng-lilian during the Fall '08 term at National Taiwan University.

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961ls08DesignSISO2 - Fall 2007 Linear Systems Chapter 08...

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