Lecture 20- Controllability and Observability

Lecture 20- Controllability and Observability - Lecture 21...

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1 Lecture 21 ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 20: Controllability and Observability Reading: Boulet – Chapter 10 Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 21 ECSE304 Signals and Systems II Course Outline • Discrete-Time Fourier Series and DT Fourier Transform • The Z – Transform • Time and Frequency Analysis of DT Signals and Systems • Sampling Systems • Application to Communications Systems – Lecture 15: Amplitude Modulation – Lecture 16: Single Sideband and Pulse Amplitude Modulation – Lecture 17: Frequency and Time Division Multiplexing and Angle Modulation • State Models of Continuous Time LTI Systems – Lecture 18: State Space Analysis – Lecture 19: Solution of State Equations – Lecture 20: Observability and Controllability • Linear Feedback Systems – Lecture 22: Feedback Control Systems – Root Locus Stability – Lecture 23: Stability Analysis – Nyquist Criterion – Lecture 24: Stability Analysis – Gain and Phase Margins Quiz 3 Topics
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3 Lecture 21 ECSE304 Signals and Systems II • Equivalent State Representations: Linear transformation of state vector – Invariance of Eigenvalues • Obtaining a Diagonal Canonical Form Realization: Diagonalization of the A matrix • Controllability and Observability of State Space Systems • Introduction to Feedback Control Systems Outline wP x = 4 Lecture 21 ECSE304 Signals and Systems II • Let and be two sets of state variables specifying a system • Let these state variables be related by linear equations: … so in vector/matrix notation the transformed state variables are given by and Linear Transformation of State Vector N N 11 1 2 2 1 1 1 1 1 2 1 1 21 2 12 2 2 2 2 1 2 2 2 2 2 2 2 1 2 NN N N N N N N N N N N wp xp x p x w p p p x x p x p x w p p p x x p x p x w p p p x wx P =++ + ⎡⎤ ⎢⎥ =+ + + ⇒= + + ⎣⎦ "" ## # # # # # ±²²²²³²²²²´ x = , ,..., N xx x , ,..., N ww w 1 xP w =
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5 Lecture 21 ECSE304 Signals and Systems II Define state equations based on state vectors and : …where Answer two questions: 1.
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This note was uploaded on 02/08/2012 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

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Lecture 20- Controllability and Observability - Lecture 21...

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