Chapter-8-Linear-Feedback-Systems-Student

Chapter-8-Linear-Fee - Chapter 8 Linear Feedback Systems Spring 2009/10 Lecture Tim Woo ELEC 215 Tim Woo Spring 2009/10 Chapter 8 1 Where we are

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ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 1 Chapter 8: Linear Feedback Systems Spring 2009/10 Lecture: Tim Woo

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ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 2 Laplace Transform Where we are Differential equations State-space model CTFT Hardware Implementation System Characteristics System Responses Closed-loop Systems Continuous-time z-Transform Difference equations State-space model DTFT Hardware Implementation System Characteristics System Responses Closed-loop Systems Discrete-time Mapping Done in 211 To be covered In progress Done Will be covered if available Open-loop Systems Open-loop Systems
ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 3 Expected Outcome • In this chapter, you will be able to – Understand the importance of linear feedback systems – Analogy the applications of linear feedback systems – Introduce and compare two methodologies on the evaluation of stability of feedback systems • the root-locus analysis • Nyquist stability criterion – Examine the conditions of stability of feedback systems by applying • the root-locus analysis • Nyquist stability criterion – Introduce and examine the concept of the margin of stability (gain and phase margins) in feedback system.

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ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 4 Outline • Section 11.0 Introduction • Section 11.1 Linear Feedback Systems • Section 11.2 Some applications and consequence of feedback • Section 11.3 Root-locus analysis of linear feedback systems • Section 11.4 The Nyquist stability criterion • Section 11.5 Gain and phase margins
ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 5 Section 11.0 Introduction So far, the systems we learnt are referred as open-loop systems. The output of a system is determined by the characteristics of the input signal. Example: 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (sec) Step response, θ (t) Step response with various input signal v(t) v(t) = u(t) v(t) = 2u(t) v(t) = 3u(t)

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ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 6 Section 11.0 Introduction Instead, we could suggest a different methods for pointing the telescope - the feedback system, by using the output of a system to control or modify the input. A feedback system is referred as Closed-loop system.
ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 7 Section 11.0 Introduction The closed-loop system have two important advantages: – Provide an error-correcting mechanism that can reduce sensitivity to the disturbances and to errors in the modeling of the system – Stabilize a system that is inherently unstable Typical applications – Chemical process control – Automotive fuel systems – Household heating systems – Aerospace systems – Stabilizing an inverted pendulum, etc

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ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 8 The basic feedback system is configured in H ( s ) (or H ( z ) ) is referred as the system function in the forward path G ( s ) (or G ( z ) ) is referred as the system function in the feedback path Section 11.1 Linear Feedback Systems
ELEC 215: Tim Woo Spring 2009/10 Chapter 8 - 9 Section 11.1 Linear Feedback Systems From the diagram, we obtain the relation ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( s Y s G s R s R s X s E s E

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This note was uploaded on 03/27/2011 for the course ELEC 215 taught by Professor Prof.kamtimwo during the Spring '11 term at HKUST.

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Chapter-8-Linear-Fee - Chapter 8 Linear Feedback Systems Spring 2009/10 Lecture Tim Woo ELEC 215 Tim Woo Spring 2009/10 Chapter 8 1 Where we are

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