09-10Chapter 6_1 Basic concept of Root locus

# 09-10Chapter 6_1 Basic concept of Root locus - Basic...

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Basic Concepts of Root Locus Method Principle of Automatic Control CHAPTER 6 oot Locus(P200 Ch 7) By Hui Hui Wang Wang Root Locus(P.200, Ch.7) 浙江大学控制科学与工程学系

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Basic Concepts of Root Locus Method eview (Chapter 1- ) Review (Chapter 1 5) 9 Basic Concepts of Control System 9 Definitions, terms, block diagram, …… 9 System modeling and representation 9 ynamics of system---- odeling Dynamics of system modeling 9 Various models: differential equation; transfer function; state space model; signal flow graphs…… ;Relationship between various models 9 Linearization of nonlinear system 9 Control system characteristics 9 olution of linear differential equations: time response Solution of linear differential equations: time response 9 Solution of the state Equation 9 Routh’s stability criterion and steady-state error 9 ………… 2
Basic Concepts of Root Locus Method Outline of Chapter 6 troduction 9 Introduction 9 Basic Concepts of Root Locus Method 9 Geometrical Properties (Construction Rules) 9 Generalized Root Locus erformance characteristics 9 Performance characteristics 9 ……… 3

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Introduction 控制科学与工程学系
Basic Concepts of Root Locus Method ROOT LOCUS 1. Introduction For a system designer: two things are very important . 1) The stability -----determined by the roots obtained from the characteristic equation 1+G(s)H(s)=0 (Solving the equation or applying Routh’s criterion to this equation). 2) The degree of stability -----i.e.,the amount of overshoot, the settling time of the controlled variable( Specifications). The graphical methods in this text book the root-locus method ------in this chapter the frequency response approach ----- in the next chapter 5

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Basic Concepts of Root Locus Method ROOT LOCUS 1. Introduction The Root Locus Method: The Root Locus Concept hat is root loc s? Wh se it? What is root locus? Why use it? Root Locus Sketching ow to plot root locus? How to plot root locus? Performance characteristics here and how to use it? Where and how to use it? 6
Basic Concepts of Root Locus Method ROOT LOCUS 1. Introduction Definition: The root locus is a plot of the roots of the characteristic equation of the closed-loop system as a function of one system parameter varies , such as the gain of the open-loop transfer function. It is a method that determines how the poles move around the s-plane as we change one control parameter . This plot was introduced by Evans in 1948 and has been developed and used extensively in control engineering. 7

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Basic Concepts of Root Locus Method ROOT LOCUS 1. Introduction The difference between the root locus method and the Routh-Hurwitz method: The Root Locus Method ----- tells us the position of the poles in the s-plane for each value of a control parameter .
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09-10Chapter 6_1 Basic concept of Root locus - Basic...

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