Chapter-8-Linear-Feedback-Systems-Student

# Chapter-8-Linear-Feedback-Systems-Student - Chapter 8...

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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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