Lecture 18

Lecture 18 - Lecture 18 State Space Analysis ECSE304...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 18: State Space Analysis Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 18 – State Space Analysis 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 – Lecture 12: The Sampling Theorem – Lecture 13: Discrete Time Processing of Continuous Time Signals – Lecture 14: Sampling of Discrete Time Signals • 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II • Review of Frequency Modulation – FM Demodulation • State Models of LTI Systems – State Variables and State Equations – Solutions of State Equations • Feed back LTI Systems – Models and applications of feedback systems – Stability of closed loop systems using root- locus techniques and Nyquist criterion – Relative stability, gain and phase margins Outline 4 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II Review of Frequency Modulation
Background image of page 2
5 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II Review of Frequency Modulation 6 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II • State Models of LTI Systems – The State Model, State Variables, and State Equations – Writing State Equation for Electrical Systems – Obtaining State Models from Integrator Realizations – Obtaining State Models for C-T LTI Systems – Canonical Forms Outline () it xt Axt But y tC x tD u t =+ ±
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
7 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II •G i v e n a causal C-T system with output y(t) and input u(t): • Suppose we want to determine y(t) for some time • We cannot do this from knowledge of for alone • We need to know the system state at time • Definition: The state , ,of a system at time : The portion of the past history of the system needed to determine the output for from knowledge of the input for State Model 0 tt 0 t 0 () x t 0 = 0 yt 0 ut 0 Causal C-T System 0 t t 0 8 Lecture 18 – State Space Analysis ECSE304 Signals and Systems II A non-zero state at time indicates the presence of energy in the system at time If a voltage is applied to an RL circuit at time , there will be current in the inductor at time that will affect the output for For finite dimensional state, the state of the system is an N dimensional column vector: The components are the state variables of the system State Model 0 t 0 x t 0 = 0 0 1 , , N x tx t RL Circuit: it 0 t
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/17/2011 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

Page1 / 14

Lecture 18 - Lecture 18 State Space Analysis ECSE304...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online